chapter five modality - tu dublin

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CHAPTER FIVE

MODALITY

Over the course of music history, the term, modality has been understood in a variety of

ways.1 In the context of Irish traditional music, its modern definition appears to be most

appropriate.

Taking the term in the modern, twofold sense, mode can be defined as either a ‘particularized scale’ or a ‘generalized tune’, or both, depending on the particular musical and cultural context. If one thinks of scale and tune as representing the poles of a continuum of melodic predetermination, then most of the area between can be designated one way or another as being in the domain of mode. To attribute mode to a musical item implies some hierarchy of pitch relationships, or some restriction on pitch successions; it is more than merely a scale. At the same time, what can be called the mode of a musical item is never so restricted as what is implied by referring to its ‘tune’; a mode is always at least a melody type or melody model, never just a fixed melody.2

From informal conversation with musicians from within the tradition, it is apparent that

the terms modality and tonality are sometimes confused. According to Harold Powers,

the term ‘tonality’ was first used:

by Choron in 1810 to describe the arrangement of the dominant and subdominant above and below the tonic and thus to differentiate the harmonic organization of modern music (tonalité moderne) from that of earlier music (tonalité antique).3

As can be seen, the term modality recalls an earlier system (tonalité antique), that was

displaced by tonal music, which in turn was followed by atonality in twentieth and

twenty-first-century music. Here, the term modality is used to encompass the various

‘particularized scales’ that are found in Irish traditional instrumental music and this

includes both the traditional pseudo-Greek modes and the gapped scales.

1 See: Powers, Harold S.: ‘Mode’, Grove Music Online. http://0-

www.oxfordmusiconline.com.ditlib.dit.ie/subscriber/article/grove/music/43718pg1 (Accessed 15 March 2013).

2 Ibid. 3 Ibid.

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5.1 Historiography

Some of the earliest discussions on modality are characterised by the idea that the age of

a tune can be determined from its mode. In Ireland, this may have begun with Edward

Bunting. Although he did not comment on the idea in his publications, a recent study by

Dr Colette Moloney has found that in a margin note in one of his manuscripts he

‘indicates various harp scales from different centuries […]. He does not, however, state

the source of these scales’.4 In the Ancient Music of Ireland (1840), under the title ‘Of

The Characteristics of Irish Melody’, Bunting considers two classes of Irish melody:

‘[…] those, namely, which are marked by the omission of the fourth and seventh tones

of the diatonic scale, or one of them, […]’.5 He insists that this absence of the fourth

and seventh degrees of the mode is a characteristically Irish trait,6 a statement that, as

will be discussed, has been the source of much debate until the mid-twentieth century.7

Petrie does not give much space to the discussion of modes in his published collections

but instead reserves commentary for the discussion of individual pieces. Perhaps his

most notable reference to the modes can be found in his discussion of ‘The Magic

Mist’, found in Volume Two of The Ancient Music of Ireland. Published posthumously

in 1882, here he notes that the presence of the tune’s ‘antique tonalities’ ‘[…] will, no

doubt, be somewhat startling and unpleasant to ears accustomed only to modern music;

though, to those familiarised to such tonalities, they will, I am persuaded, add to the

racy and impressive character of the air’.8 He continues:

I will not assert that the tonalities of this melody are exactly those found in either of the so-called Dorian or Eolian modes [sic], nor even of that Phrygian, to which Selden tells us "the Irish were wholly included"; but I may venture to say that their affinity with the tones of the Canto Fermo or old modes of the church – and particularly with those which have a minor character – must be at once apparent to, and arrest the attention of, all those who have made themselves acquainted with the peculiar characteristics of the old ecclesiastical or

4 These are from MS12/1, to be found as marginalia and do not appear in his published works.

Therefore, while they are relevant to the discussion, they are best viewed in: Moloney, Colette: The Irish Music Manuscripts of Edward Bunting (1773–1843): An Introduction and Catalogue, (Dublin: Irish Traditional Music Archive, 2000), 69,70.

5 Bunting, Edward: The Ancient Music of Ireland, (Dublin: Hodges and Smith, 1840), 13. 6 Ibid., 14. 7 While the debate on this matter ceases to be found from the mid-twentieth century onwards, in my

opinion, this argument was most convincingly overturned by James Travis, who provided numerous exceptions to the rule. See: Travis, James: ‘Irish National Music’, The Musical Quarterly, Vol. 24, (Oxford: The Oxford University Press, 1938), 465-473.

8 Petrie, George: The Ancient Music of Ireland, Vol. 2, (Dublin: Society for the Preservation and Publication of the Melodies of Ireland, 1882), 42.

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Gregorian mode. Interestingly, Bunting’s idea concerning the omission of the fourth and seventh degrees

of the mode is one of the few things that Petrie does not challenge.9 Perhaps one of the

first authors to critically consider Bunting’s statement is Frederick St. John Lacy who in

1890 wrote:

Well and good. Many airs can be produced in support of both of these assertions, but what of the multitude of those, unmistakably Irish, which have the fourth and seventh from the key-note, or which omit the submediant? How are we to explain away the fact of the exceptions to these rules outnumbering the examples that can be adduced in support of them?10

Lacy goes on to introduce a theory to demonstrate how modality has evolved in Irish

traditional music.11 Not unlike the opinion held by Bunting, Lacy’s thesis is that the

pentatonic modes are the oldest, and that heptatonic and diatonic modes later evolved.12

From the pentatonic mode – given as C, D, E, G, and A – and which might be thought

of as an Ionian pentatonic mode, Lacy derives a further four pentatonic modes by

beginning on each of the letters of the initial mode whilst retaining the interval

relationships. This can be thought of as correlating with the Dorian, Phrygian,

Mixolydian and Aeolian modes.13 Then, the process repeats with five hexatonic and a

further five heptatonic modal scales, yielding a total of fifteen examples in all.14 While

in earlier accounts authors had discussed the ‘omissions’ that they had observed in the

modes, and therefore they had at least implicitly discussed gapped modes, Lacy appears

to be the first writer to explicitly investigate the music’s pentatonic, hexatonic and

heptatonic modal characteristics.15

In 1903, the Rev. Dr Richard Henebry published Irish Music: being a matter of the 9 See: Ibid., 43 where it is apparent that indeed, Petrie has the evidence to challenge Bunting on this

aspect. To take one example, he draws attention to the omission of the second degree of the mode in the case of ‘The Magic Mist’.

10 Lacy, F. St. John: ‘Notes on Irish Music’ Proceedings of the Musical Association, 16th Session, (1889–1890), (Dublin: Taylor & Francis, and the Royal Musical Association), 184.

11 Ibid., 184-192. 12 The author himself uses the term ‘periods’ rather than modes to avoid confusion with the church

modes. 13 This gives 1. C, D, E, G, A, 2. D, E, G, A, C, 3. E, G, A, C, D, 4. G, A, C, D, E and 5. A, C, D, E, G. 14 Ibid., 185-186. 15 This type of commentary decreases significantly from here on in but resurfaces to great effect in the

work of Lacy’s pupil, Aloys Fleischmann, about a century later.

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examination of scales, modes, and keys, with practical instructions and examples for

players.16 This document is significant in that it is possibly the only one to attempt a

detailed discussion on temperament in Irish traditional music and his thoughts on this

appear to have been influential in his time.17 Henebry identifies two temperaments, a

first and a second ‘Irish scale’ and provides a fiddle fingerboard diagram so that the

positions of these modes can be located.18 However, since it is not possible to check

these examples against his sources, it is difficult to comment on their accuracy.

Nevertheless, the text does raise the point that while the tonal period has inclined

towards twelve tone equal temperament, it is almost without doubt that there was a

much more colourful spectrum at play within the modal system of Irish traditional

music.

For the time, James Travis’s 1938 paper Irish National Music is refreshing in its

objectivity.19 Even before Travis’s time, there was a claim that the inclusion of the

raised seventh in minor tunes was an affront to authenticity.20 Travis argues against the

absolutism of this stance noting that although the major seventh is rarely used in minor

tunes, it is by no means unknown.21 With the benefit of the array of recordings that exist

today, Travis would have had his point even further supported based on his basic thesis

that individual creativity will always provide an exception to the rule.22 Similar to Lacy,

Travis is critical of the ‘blind following’ of Bunting regarding the omission of the fourth

and seventh degrees.23 However, unlike Lacy, he refutes the idea of a Darwinian-type

16 Henebry, Richard: Irish Music: Being an Examination of the Matter of Scales, Modes, and Keys, with

Practical Instructions and Examples for Players, (Dublin: An Cló Cumann, Straid Mór na Trága, 1903).

17 As can be inferred through a reading of Cathaoir O’Braonain’s 1909 forward to The Roche Collection where Henebry’s work is referenced: See: Roche, Frank: The Frank Roche Collection, 2nd ed., (Cork: Ossian Publications, 1993).

18 Henebry: Irish Music: Being an Examination of the Matter of Scales, Modes, and Keys, with Practical Instructions and Examples for Players, 31.

19 Travis, James: ‘Irish National Music’, The Musical Quarterly, Vol. 24, (Oxford: The Oxford University Press, 1938), 451-480. While it is known that Travis was American, little else is known of him.

20 See: Joyce, Patrick Weston: Old Irish Folk Music and Songs, (London; New York: Longmans, Green, and Co.; [etc.], 1909), xvii. While Joyce does not specifically refer to Bunting, his message regarding the inappropriateness of the raised seventh, is abundantly clear.

21 Travis: ‘Irish National Music’, 466-467. 22 For instance, the raised seventh may be found in some versions of ‘The Colraine Jig’, and the ‘The

Blackbird Hornpipe’. While it is much more difficult to find examples of the harmonic minor scale, these inflections point to its usage as a colour.

23 Ibid., 472.

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evolution of modes,24 instead, rather convincingly arguing that they were selected for

their expressiveness whenever needed.25

Finally, Travis is possibly the first to demonstrate that modulation takes place ‘not only

between diatonic, hexatonic and pentatonic modes, but also between modes

representative of these different types’.26 By this statement, he is drawing attention to

the fact that there are many types of pentatonic and hexatonic modes, an area of

modality that as will be seen, is not fully explored until the late twentieth century. To

support this assertion, he gives examples from both tune parts and full tunes. In this

respect, his work differs from the largely restrictive writing of earlier authors and is

more musical as a result.

In more formal terms, in Our Musical Heritage Seán Ó Riada introduces the term ‘bi-

modality’.27 Despite the fact that Ó Riada used the term in describing a song, it is just as

applicable to instrumental music and describes a situation where a melody is found to

be in more than one mode. In Folk Music and Dances of Ireland Breandán Breathnach

understands modality in terms of ‘three systems’ and in doing so, echoes the earlier

work of Lacy. Breathnach’s first system relates to the heptatonic pseudo-Greek modes,

in relation to which he states that:

The Doh mode is the predominant one in Irish folk music. In fact over 60% of our music belongs to this mode. [...] Pieces ending on Soh account for approximately 15% of the total, [...] Airs in the Ray mode, accounting for somewhat over 10% of the music. [...] Airs in the La mode are the least numerous.28

The above estimate is notable for its omission of the hexatonic and pentatonic modes –

24 For example, Bunting and Lacy’s evolution of modes as described above. 25 Ibid., 471-473. His reference to Galilei’s 1581 Dialogo on p. 467 is particularly persuasive. Travis

states that ‘Galilei’s treatise is more illuminating. It establishes that Ireland possessed the double harp in the 16th century. The method of tuning the double harp described by Galilei reveals that the Irish were familiar with chromatics. It would be absurd to fancy them confined, with such an instrument, as regards scales or modes’. This is also not to say that in a genre so associated with the social element, a slip of the finger has not produced a tonal ‘mistake’ that was deemed to be nice and then commonly used.

26 Ibid., 476-477. 27 Ó Riada, Seán: Our Musical Heritage, eds. Tomás Ó Canainn; Thomas Kinsella, (Mountrath: Dolmen

Press, 1982), 37. 28 Breathnach, Breandán: Folk Music and Dances of Ireland, Revised Ed. 1977, (Dublin; Cork: Mercier

Press, 1993), 10-11.

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his second and third systems respectively, which Breathnach contends ‘constitute only a

relatively small proportion of the national repertory’.29 He also argues that there is only

one hexatonic mode, which is characterised by its omission of the seventh degree, and

similarly, that the only pentatonic mode is that which does not contain the fourth and

seventh degrees.30 As will be demonstrated when the work of Aloys Fleischmann is

discussed, these assertions are simply inaccurate. Rather, there is a variety of pentatonic

and hexatonic possibilities.31

Another of Breathnach’s ideas is the ‘underlying principle’, which states that a tune’s

mode can be identified by its key signature and its final note.32 While this approach

stretches back to the theoretical beginnings of modality,33 it is based on the idea of the

tune being heptatonic. Secondly, as acknowledged by Breathnach,34 some tunes are

‘circular’ meaning that they do not end on their home-note. Rather, these are designed

to propel into a repeat and must be ended on either the first note of the A-part or by

selecting an appropriate final note.

The concept of circularity is largely a tonal effect and can be found earlier in a number

of publications including Annie W. Patterson’s ‘The Characteristic Traits of Irish

Music’ (1897)35 and latterly, Ó Riada’s Our Musical Heritage (1963/1982).36 Most

notably, the circular tune is one in which its final note cannot in any circumstance be

29 Ibid., 12. 30 Ibid. 31 Although Fleischmann’s observations on tonality were exclusively based on material up to c.1850, his

statement that the fourth and fifth were the most usual absentees of a scale makes it difficult to consider that the pentatonic mode is less popular than the heptatonic variety.

32 Ibid., 10-11. This is worth remembering in relation to Breathnach’s statement as printed on the previous page.

33 See: Powers, Harold S.: ‘Mode’, Grove Music Online. http://0-www.oxfordmusiconline.com.ditlib.dit.ie/subscriber/article/grove/music/43718pg1 (Accessed 15 March 2013) where it is stated: ‘The nucleus of the concept of mode in its basic Western form may be illustrated in two early 11th-century Italian formulations: A tone or mode is a rule which distinguishes every chant in its final [scale degree]’ (Pseudo-Odo, Dialogus de Musica, Gerberts, 257); and ‘The first degree A and the fourth, D, are alike and are designated “of a single mode” because both have a tone beneath and [have] tone–semitone–tone–tone above’.

34 Breathnach: Folk Music and Dances of Ireland, 8-9. 35 Patterson, Annie W.: ‘The Characteristic Traits of Irish Music’, Proceedings of the Musical

Association, 23rd Sess., (1896–1897), (Taylor & Francis, 1897), 103. See also: Joyce, P.W.: Ancient Irish Music (Dublin: McGlashan and Gill, 1873), I7, 33, which is the source for Annie Patterson’s references to two examples of these ‘unending tunes’. It is worth noting that Joyce himself does not comment on this feature in respect of these two tunes.

36 Ó Riada: Our Musical Heritage, 21.

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used reliably to indicate its mode. Breathnach argues that circular tunes can be made ‘to

end on the appropriate final note and are so ended when a player concludes a bout of

music on playing one of them’.37 However, this cannot be taken as a rule of thumb

because some circular tunes, such as ‘The Connaughtman’s Rambles’,38 where its final

note, G would, in order to end the tune, most likely resolve onto either the F-sharp or A

because the home-note of the tune is D.39 As would become evident in accompanying

this tune, it is not correct to say that it is in a mode with a home-note of G, F-sharp or A.

While Breathnach’s writing is aimed at a more general audience, his advice is best taken

as a rule of thumb rather than a replacement for defining the modes by their

organisation of tones and semitones. The section ends with a nod at inflection and

range.40

In the opening lines of his chapter on ‘The Structure of Irish Traditional Music’, Tomás

Ó Canainn is critical of previous authors such as Bunting, Petrie, Joyce, and implicitly,

Breathnach, when he asserts that in only identifying the modes, authors are viewing the

topic too simplistically.41 One of Ó Canainn’s attempts at a more nuanced

understanding of the modes is through what he terms ‘note-frequency’.42 This is

essentially a quantitative system for calculating which notes are the most important

within a melody. It is based upon criteria such as the number of appearances of each

note in a tune and its appearance on strong beats of the bar.43 From this, it is then

possible to give each note a score so that those which are most ‘important’ can be

identified.44 While it serves a purpose as an analytical tool, Ó Canainn’s use of note

frequency to determine tonality is problematic.45 Taking the tune, ‘Cailleach an Airgid’,

which is reproduced at Ex. 5.1 below, he incorrectly states ‘this tune has […] a tonic A

and a dominant D’,46 this obviously due to the fact that the most commonly-found note

37 Breathnach: Folk Music and Dances of Ireland, 8-9. 38 For a transcription, see Chapter Ten, 484, Ex. 10.9. 39 If looking at the tune in terms of its individual parts, the A-part has a home-note of d’ and the B-part

has a home-note of b’. 40 Ibid., 14-15. 41 Ó Canainn, Tomás: Traditional Music in Ireland, 2nd ed., (Cork: Ossian, 1993), 27. 42 Ibid., 27-30. 43 Ibid. 44 Ibid., 29. 45 He did state that the deduction of tonality using note frequency would produce results that are

different from those arrived at when the key signature and/or final note are considered. 46 Ibid.

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was A, followed by D. He later notes that ‘the subdominant is either G or E’. In actual

fact, using the approach to defining modality that will be explained later in Section 5.2,

the A-part of the tune is in D Mixolydian hexatonic (minus the 3rd degree) while the B-

part is for the most part in D Ionian with c’’-naturals only being introduced in the final

two bars. Therefore, as can be seen, the note frequency idea is perhaps helpful in

understanding melodic design but it is misleading in determining modality.47

Ex. 5.1 Reproduction of Tomás Ó Canainn’s version of ‘Cailleach an Airgid’.48

The term ‘inflection’ is defined by Ó Canainn as ‘a note which appears in both [its]

sharpened and unsharpened forms’.49 Depending on the home-note, this could be

revised to include its flattened forms also.50 According to Ó Canainn: ‘The seventh is by

far the most commonly inflected note, but the third and occasionally the fourth degree

of the scale may be inflected’.51 However, in the playing of the Donegal fiddler Con

Cassidy, there are instances where the second and sixth degrees of the mode are also

inflected.52 Breathnach also discusses inflection using the term ‘accidental notes’53 and

while he notes the use of the C-sharp and F-natural, he does not state the keys to which

he is referring.54 Given that earlier he discusses the keys G, A, D and E, it can perhaps

47 However, it is very possible that this idea had influenced Mícheál Ó Súilleabháin’s set tone idea,

which will be explored in the following chapter. 48 Ó Canainn: Traditional Music in Ireland, 29. 49 Ibid., 30. 50 See Section 5.2, 188 for a definition. 51 Ibid., 33. 52 Cassidy, Con: Traditional Fiddle Music from Donegal, (Donegal: Cairdeas na bhFidiléirí, 2007), track

1. 53 See: Breathnach: Folk Music and Dances of Ireland, 13. Also a passing reference to inflection may be

found in: Travis: ‘Irish National Music’, 468. 54 Breathnach: Folk Music and Dances of Ireland, 13. Here I am using the term ‘key’ because it is used

by Breathnach.

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be assumed that his observations on inflection applies to modes that require these key-

signatures but this is unclear.55 To summarise, this means that all five degrees56 are

possibilities for inflection in a diatonic mode.

Both Breathnach and Travis have touched upon this topic but Ó Canainn goes the

furthest by giving a number of examples and uses these as the basis for a series of rules

to be postulated.57 Interestingly, Ó Canainn appears to see inflection as a better way of

conceptualising tunes than that of modal modulation. In contradicting the view of both

Travis and Ó Riada, Ó Canainn states that ‘Irish tunes rarely change mode and to base a

method of analysis on the assumption that they do seems foolish’.58 While it is

undeniable that some tunes make use of more than one mode, inflection is a helpful

solution to the problem of an eight-bar part potentially having to be thought of as being

in more than one mode in the same part. With the exception of one reel, the examples

upon which Ó Canainn bases his observations are song airs and so perhaps it requires a

leap of faith to apply the same rules to instrumental music. Notably however, no

mention is made of the importance of the inflection being placed on strong or weak

positions within the bar.

Ironically, the most valuable source for information on modality in Irish traditional

music is not a document relating to style but rather, is Aloys Fleischmann’s introduction

to his Sources of Irish Traditional Music.59 Published in 1998, the introduction includes

an overview of the different modes found in the material contained in the collection.

However, because the work is comprised of tunes that date from c.1600 until c.1855, it

may not bear witness to the idiosyncrasies of modality and the ways in which it may

have evolved since. However, it introduces a level of nuance that is considerably more

detailed than any of the studies that precede it, and in the context of this study it

establishes both a standard, and an approach that can be adapted and used here.

55 Breathnach: Folk Music and Dances of Ireland, 12. 56 See: Ó Canainn: ‘Traditional Music in Ireland’, 33. These are the 2nd, 3rd, 4th, 6th and 7th degrees of the

scale. Although the raised 4th and lowered 5th are enharmonic equivalents, known in other terms as the augmented fourth and diminished fifth. In his discussion of one of his examples, ‘Slow by the Shadows’, Ó Canainn actually talks about the need to ‘avoid the diminished fifth interval’ viewing it as a raised fourth instead.

57 For Ó Canainn’s rules, see: Ó Canainn: Traditional Music in Ireland, 33-34. 58 Ibid., 32. 59 See: Fleischmann, Aloys: Sources of Irish Traditional Music, (New York; London: Garland, 1998).

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In his analysis, Fleischmann covers six heptatonic modes over six pitches from C to A

and although he does not use the terms, by C he means Ionian, by D, Dorian, etc. until

he reaches the Aeolian mode. It is interesting that the Phrygian and Lydian modes are

found in the collection since they are not normally associated with Irish traditional

music. It is in relation to the hexatonic and pentatonic modes that the nuanced level of

Fleischmann’s work is apparent in that he indicates which notes are absent from each

mode whilst indicating enharmonic equivalents. This creates the largest number of

modes printed for its time.

Part of the reason for Fleischmann deciding on 1855 as a stopping-point, is due to a

proliferation of tune collections from this date onwards, and also the new influx of tune-

types, as discussed in the previous chapter.60 As styles, instrument specifications, and

virtuosity have evolved since, it can be assumed that an evolution in the modal language

has also occurred.

It is noticeable that in terms of each of the modes listed by Fleischmann, some

hexatonic and pentatonic options exist only in relation to particular pitch centres. Yet,

given the degree of transposition that occurs in music today, it is highly unlikely that a

particular mode would only be found in relation to one pitch centre. Rather, the same

mode can be found in relation to any of the pitch centres without sounding any less

traditional and indeed, this type of transposition is common. Therefore, while the list

includes a great deal of detail, it may be postulated that significantly more modes have

yet to be identified.

From the writings that have been investigated, the primary themes and hence, the

conceptual fields that will be explored here are: (1) home-notes, which are defined in

Section 5.2 and presented in Section 5.3, (2) modality: where the heptatonic modes are

focused on in Section 5.4.1, the hexatonic modes in Section 5.4.2 and the pentatonic

possibilities in Section 5.4.3, (3) inflection, which is explored in Section 5.5 and finally

(4), modulation, which follows in Section 5.6.

60 Ibid., xxviii.

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5.2 Method

As distinct from key-signature or key, within which a variety of modes can be found,

the term home-note is used to describe the ‘tonic’ note of the mode being used. This is

also distinct from the ‘final-note’, which in the case of circular tunes does not

correspond to the home-note. Moreover, as explained,61 the addition of an extra note to

a circular tune, which is used to bring the melody to a close, does not always correspond

to the home-note of a tune. This distinction will be observed throughout this thesis.

Following the approach laid down by Fleischmann, the heptatonic modes are taken as

the basis from which the hexatonic and pentatonic modes are determined. Technically

speaking, there are seven modes but in Irish traditional music as with most styles of

music, only six are used since the Locrian mode is omitted. As observed by Breathnach,

the modes have different frequencies of use within the genre, of which the Ionian,

Dorian, Mixolydian and Aeolian modes are significantly more popular than the

Phrygian and Lydian modes. Since all six have been observed in practice, they will be

explored here but since the Phrygian and Lydian modes are used so sparingly, these two

are not explored in terms of their hexatonic and pentatonic variations.

These six heptatonic modes are demonstrated below in Ex 5.2, following which, their

interval sequences are given in Table 5.1. The letter T signifies the interval of a tone and

the letter S denotes the interval of a semitone. I recommend that the individual modes

and their home-note be determined by the unique organisation of their intervals rather

than by the final note of a tune, which as was demonstrated above, is prone to error.62

61 See: Section 5.1, 178-179. 62 This is particularly true with ‘circular tunes’. Well-known examples of this include: ‘The

Connaughtman’s Rambles’ (see Chapter Ten, 484) and the March (to take one example) version of Welcome Home Gráinne’ (see Chapter Three, 103).

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Ex. 5.2 The six heptatonic modes used in Irish traditional music.

Table 5.1 The interval sequences of the six heptatonic modes used in Irish traditional

music.

Mode Interval Sequence

1. Ionian T-T-S-T-T-T-S

2. Dorian T-S-T-T-T-S-T

3. Phrygian S-T-T-T-S-T-T

4. Lydian T-T-T-S-T-T-S

5. Mixolydian T-T-S-T-T-S-T

6. Aeolian T-S-T-T-S-T-T

Since the hexatonic modes make use of six notes, within the context of a diatonic modal

framework, it is evident that one of the seven notes must be omitted. If the home-note is

kept, then any one of six different notes can be omitted each time. This results in six

hexatonic modes relative to each heptatonic mode but because of enharmonic

equivalents across the four more common modes, the total is twenty-one hexatonic

modes rather than the expected twenty-four modes.

In order to determine the possibilities, Table 5.2 below contains four boxes, within

which, the four hexatonic modes are written using letter names. For ease, the tonal

centre of d’ is taken because it is the most common modal centre in Irish traditional

instrumental music. From here, the options are worked out systematically. The pitch

that is omitted is noted by both its letter name and number. While the # symbol is used

for sharps, the ^ symbol is used to denote flats as the typical lower-case letter b could be

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confusing in combination with the note ‘b’. Through using this approach, it is easy to

see the enharmonic equivalents and omit them from the archive at Section 5.4.2.

Table 5.2 The hexatonic modes respective of the Ionian, Dorian, Mixolydian and

Aeolian modes.

Conceptual Field Hexatonic Modes

Conceptual Resolution Ionian, Dorian, Mixolydian & Aeolian.

Ionian 1. def#gab = no c# -7 2. def#gac# = no b -6 3. def#gbc# = no a -5 4. def#abc# = no g -4 5. degabc# = no f -3 6. df#gabc# = no e -2

Dorian 1. defgab = no c -7 2. defgac = no b -6 3. defgbc = no a -5 4. defabc = no g -4 5. degabc = no f -3 =MIX 5 6. dfgabc = no e -2

Mixolydian 1. def#gab = no c -7 = ION1 2. def#gac = no b -6 3. def#gbc = no a -5 4. def#abc = no g -4 5. degabc = no f# -3 6. df#gabc = no e -2

Aeolian 1. defgab^ = no c -7 2. defgac = no b^ -6=DOR 2 3. defgb^c = no a -5 4. defab^c = no g -4 5. degab^c = no f -3 6. dfgab^c = no e -2

Since pentatonic modes use five notes, there is an even greater number of possible

configurations. The same approach as described above is applied in Table 5.3 below.

Table 5.3 The pentatonic modes respective of the Ionian, Dorian, Mixolydian and

Aeolian modes.

Conceptual Field Pentatonic Modes

Conceptual Resolution Ionian, Dorian, Mixolydian & Aeolian.

Ionian 1. def#ga = no bc# -6.-7 2. def#gb = no ac# -5.-7 3. def#gc# = no ab -5.-6 4. def#ab = no gc# -4.-7 5. def#ac# = no gb -4.-6 6. def#bc# = no ga -4.-5

Dorian 1. defga = no bc -6.-7 2. defgb = no ac -5.-7 3. defgc = no ab -5.-6 4. defab = no gc -4.-7 5. defac = no gb -4.-6 6. defbc = no ga -4.-5

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7. degab = no f#c# -3.-7 8. degac# = no f#b -3.-6 9. degbc# = no f#a -3.-5 10. deabc# = no f#g -3.-4 11. df#gab = no ec# -2.-7 12. df#gac# = no eb -2.-6 13. df#gbc# = no ea -2.-5 14. df#abc# = no eg -2.-4 15. dgabc# = no ef# -2.-3

7. degab = no fc -3.-7 = Ion. 7, Mix.7 8. degac = no fb -3.-6 = Mix. 8 9. degbc = no fa -3.-5 = Mix. 9 10. deabc = no fg -3.-4 = Mix. 10 11. dfgab = no ec -2.-7 12. dfgac = no eb -2.-6 13. dfgbc = no ea -2.-5 14. dfabc = no eg -2.-4 15. dgabc = no ef -2.-3 = Mix. 15

Mixolydian 1. def#ga = no bc -6.-7 = Ion.1 2. def#gb = no ac -5.-7 = Ion.2 3. def#gc = no ab -5.-6 4. def#ab = no gc -4.-7 = Ion. 4 5. def#ac = no gb -4.-6 6. def#bc = no ga -4.-5 7. degab = no fc -3.-7 = Ion. 7 8. degac = no fb -3.-6 9. degbc = no fa -3.-5 10. deabc = no fg -3.-4 11. df#gab = no ec -2.-7 = Ion. 11 12. df#gac = no eb -2.-6 13. df#gbc = no ea -2.-5 14. df#abc = no eg -2.-4 15. dgabc = no ef -2.-3 = Dor.15

Aeolian 1. defga = no bc -6.-7 = Dor.1 2. defgb^ = no ac -5.-7 3. defgc = no ab -5.-6 = Dor. 3 4. degab^ = no fc -4.-7 = Dor. 4 5. defac = no gb -4.-6 = Dor 5 6. defb^c = no ga -4.-5 7. degab^ = no fc -3.-7 8. degac = no fb -3.-6 = Mix. 8 & Dor. 8 9. degb^c = no fa -3.-5 10. deab^c = no fg -3.-4 11. dfgab^ = no ec -2.-7 12. dfgac = no eb -2.-6 - = Dor. 12 13. dfgb^c = no ea -2.-5 14. dfab^c = no eg -2.-4 15. dgab^c = no ef -2.-3

The heptatonic, hexatonic and pentatonic modes can be found along a range of home-

notes. While key signatures up to three sharps are most common, bands like Dervish

sometimes use keys signatures of up to four flats.63 In addition to the more common d’

chanter, uilleann pipers often also have a b or b-flat chanter in their possession. It is not

uncommon also for fiddlers to tune their instrument up a semitone from d’ to e’-flat, or

down to by as much as b-flat. In effect, since tunes are composed within a variety of

modalities and the home-note itself is variable, each of the modal options will be

explored across all twelve home-notes.

When multiplied across twelve home-notes, the twenty-one hexatonic possibilities

result in a total of 252 options. Similarly, forty-four pentatonic options produce 528

possibilities and the six heptatonic modes: Ionian, Dorian, Phrygian, Lydian, 63 This will be evident upon listening to any of their albums, an example of which is: Dervish: Spirit,

(Nashville: Compass Records, 2003).

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Mixolydian and Aeolian, give rise to seventy-two options. In terms of modality, this

results in a total of 852 possibilities.

It is evident that authors such as Tomas Ó Canainn saw inflection and modal

modulation as being mutually exclusive ways of addressing chromatically altered notes

in a mode.64 However subjective, in the context of this study, inflection is considered to

be relevant in cases where the raising or lowering of a note is merely decorative and

does not induce any noticeable change to the modality of a tune or its part. In this sense

it applies to notes that are mostly on the weak parts of the beats as represented in Ex.

5.3 (also see Ex. 5.4 and 5.5).

It should be noted that there is a degree of subjectivity concerning the conceptualisation

of a metre. In this discussion, this is particularly true of 3/4, since it covers two tune-

types, the waltz and the mazurka, that are characterised by different organisations of

main beats within the bar.65 In terms of the waltz, the first beat is the strongest, the

second is less strong and the third is the weakest. Contrary to this however, the effect of

listening to a mazurka is that the second beat is the strongest. Given that in practice,

mazurkas are slightly more commonly-played than waltzes and that typically, Irish

traditional dance music moves in a quaver-based rhythm, the conceptualisation of three

strong crotchet beats appears to be more relevant to the type of music being studied

here.66

64 See: Ó Canainn: ‘Traditional Music in Ireland’, 32. As previously noted, Ó Canainn even went as far

as to say that ‘Irish tunes rarely change mode and to base a method of analysis on the assumption that they do seems foolish’.

65 The Narrative Air features a longer rhythmic value on the second beat of the bar and so might also be included in this list. However, this depends on how freely the tempo is interpreted.

66 This issue also applies to the area of melodic variation. See: Chapter Six, 240-241, 250 for further discussion.

191

Ex. 5.3 A demonstration of the weak parts of the beat in respect of the metres: 2/2, 3/4,

4/4, 2/4, 6/8, 9/8.

As identified in Section 5.2 above, the five degrees of the mode that can be inflected are

the 2nd, 3rd, 4th, 6th and 7th. For the purposes of this study, numbers are used to represent

the relevant degrees of the mode, each of which, except the fourth,67 may be in a raised

or lowered position. See Table 5.4 below.

Table 5.4 Number representing possible intervals.

Number and its associated scale degree

2 = Lowered or Raised 2nd

3 = Lowered or Raised 3rd

4 = Raised 4th

6 = Lowered or Raised 6th

7 = Lowered or Raised 7th

Whether or not the degree of the scale is lowered or raised depends on which of the four

most common modes is used. To demonstrate this, the Ionian, Dorian, Mixolydian and

Aeolian modes are listed in Table 5.5 below. In each section, the raised or lowered

nature of each degree of the mode is indicated. This is further illustrated in the context

of an improvised reel fragment in Ex. 5.4 below.

67 The fourth can only be raised.

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Table 5.5 The options for inflection respective of the Ionian, Dorian, Mixolydian and

Aeolian modes.

Conceptual Field Inflection

Conceptual Resolution Ionian, Dorian, Mixolydian & Aeolian

Ionian 1. Lowered Second 2. Lowered Third 3. Raised Fourth 4. Lowered Sixth 5. Lowered Seventh

Mixolydian 1. Lowered Second 2. Lowered Third 3. Raised Fourth 4. Lowered Sixth 5. Raised Seventh

Dorian 1. Lowered Second 2. Raised Third 3. Raised Fourth 4. Lowered Sixth 5. Raised Seventh

Aeolian 1. Lowered Second 2. Raised Third 3. Raised Fourth 4. Raised Sixth 5. Raised Seventh

Ex. 5.4 Illustration of inflection in respect of the Ionian, Dorian, Mixolydian and

Aeolian modes.

193

As there are five chromatic possibilities, it is possible for anything from one to all five

or any combination thereof (e.g. in the Dorian mode, the raised third and raised

seventh), to be used. When the number of combinations for the five options is

calculated in relation to any one of the four modes, a total of twenty-nine possibilities

exist.68

Generally speaking however, only one degree of the scale is inflected in any one

performance of a tune and even then, it is sparsely used. Inflection is a notable feature in

the music of the Donegal fiddle player Con Cassidy whose versions of traditional tunes

are still played today. The following is one of his slip jigs, which appears on an Altan

album entitled Another Sky and is simply called ‘Con’s Slip Jig’.69

Ex. 5.5 Use of inflection demonstrating the use of the raised fourth in ‘Con’s Slip Jig’.

In the context of this study, modulation is understood to result from the placement of

chromatically altered notes on the strong beats of a bar (see Ex. 5.6), see ‘Mooney’s

Reel’ at Ex. 5.8 below for one such example.70 This is generally accompanied by the

presence of a particular melodic contour that would not be associated with the main

mode in question. While it is most common for modulation to occur between parts of a

tune, when this type of modulation occurs within a tune part and is therefore brief, it can

68 See Section 5.6. 69 Altan: Another Sky, (Milwaukee: Narada Productions, 2000). 70 As will be explained below, two particular types of modulation are considered here.

194

be termed a ‘transitory modulation’. Both types will be discussed below.

Ex. 5.6 A demonstration of the main beats of the metres: 2/2, 3/4, 4/4, 2/4, 6/8, 9/8.

As stated earlier, modulation can be said to occur in a transitory sense when one or

more bars deviate from the main mode of a tune part, or in a structural sense when an

entire part is in a different mode from that of the other part or parts. From a general

analysis of audio recordings, I would venture that there are two types of modulation in

Irish traditional instrumental music: 1. where both the modes and their respective home-

notes are different, and 2. where the modes are different but the home-notes are the

same.

An example of a change of mode and change of home-note that features between two

different parts of the tune can be found in the well-known reel ‘The Glass of Beer’ (see

Ex. 5.7) in which the A-part is in B Aeolian Pentatonic (minus the second and sixth

degrees) while the B-part is in D Ionian Hexatonic (minus the seventh degree) or in

shortened form, B Aeol. Pent. -2,-6 and D Ion. Hex. -7.

195

Ex. 5.7 Modal modulation in the reel ‘The Glass of Beer’.

An example of a transitory modulation where the home-note stays the same but the

mode changes can be found in the A-part of ‘Mooney’s Reel’ as played by the Donegal

fiddler John Doherty in John Doherty: The Celebrated Recordings. In this example (see

Ex. 5.8), the A-part is in A Aeolian Hexatonic -6 while bars 3 and 7 allude to A

Mixolydian Pentatonic -4, -7.71 Despite an extra note being missing (-6), since modes

that only use four notes are not addressed here, the nearest pentatonic option is

referenced.

Ex. 5.8 Transitory modulation in the A-part of ‘Mooney’s Reel’.

While in respect of modulation, initially, the four most common modes, Ionian, Dorian,

Mixolydian and Aeolian were explored, as may be seen in relation to the practice-based

71 This could also be conceptualised as A Ionian Pent -4, -7. However, owing to the Am to G

progression that underpins an Aeolian mode, the Mixolydian option selected, which utilises an A to G progression, would fit better were the G and other notes to be used.

196

component discussed in Chapter Ten, musicians are frequently eager to explore more

unusual modulations using the Phrygian and Lydian modes and so these were later

included.72 Following an approach that is similar to the previous explorations of

inflection and modality, the options are determined in Table 5.6 below.

Table 5.6 Options for modal modulation respective of the Ionian, Dorian, Phrygian,

Lydian, Mixolydian and Aeolian modes.

Conceptual Field Modulation Conceptual Resolution Within the diatonic framework Ionian

1. Ion. to Ion. 2. Ion. to Dor. 3. Ion. to Phryg. 4. Ion. to Lyd. 5. Ion. to Mix. 6. Ion. to Aeol.

Lydian 1. Lyd. to Lyd. 2. Lyd. to Ion. = Ionian 4 3. Lyd. to Dor = Dorian 4 4. Lyd. to Phryg. = Lydian 4 5. Lyd. to Mix. 6. Lyd. to Aeol.

Dorian 1. Dor. to Dor. 2. Dor. to Ion. = Ionian 2 3. Dor. to Phryg. 4. Dor. to Lyd. 5. Dor. to Mix. 6. Dor. to Aeol.

Mixolydian 1. Mix. to Mix. 2. Mix. to Ion. = Ionian 5 3. Mix. to Dor = Dorian 5 4. Mix. to Phryg. = Phrygian 5 5. Mix. to Lyd. = Lydian 5 6. Mix. to Aeol.

Phrygian

1. Phryg. to Phryg 2. Phryg. to Ion. = Ionian 3 3. Phryg. to Dor = Dorian 3 4. Phryg. to Lyd. 5. Phryg. to Mix. 6. Phryg. to Aeol.

Aeolian 1. Aeol. to Aeol 2. Aeol. to Ion. = Ionian 6 3. Aeol. to Dor = Dorian 6 4. Aeol. to Phryg. = Phrygian 6 5. Aeol. to Lyd. = Lydian 6 6. Aeol. to Mix. = Mixolydian 6

When any repetitions and or enharmonic equivalents are extracted, there are six

possibilities for each of the two types of modal modulation that are listed in Section 5.6.

It should be noted that modulation where the home-note as opposed to the mode

72 See Chapter Ten, 541-542 for an example of the Phrygian mode. Chapter Ten, 600-601 includes

references to the Lydian mode.

197

changes (e.g. D Ionian to E Ionian) is also included in this study. Lastly, while

hexatonic and pentatonic modulations could occur, owing to the number of possibilities

to be seen in sections 5.4.1 to 5.4.3, this must be deferred for future study.

5.3 Home-note

The most commonly used home-notes are G, D and A with tunes in E now becoming

increasingly heard in sessions. In some of the older collections, F, B-flat and E-flat were

favoured and while tunes in F can sometimes be heard in sessions, these are less

common.73 However, since some uilleann pipe chanters can be found in B, Bb and C-

sharp amongst others, and occasionally, bands such as Dervish will tune to notes other

than concert pitch, (usually up a semitone from concert pitch), it is fathomable that

every home-note is viable for use.74

Table 5.7 The home-notes used in Irish traditional music, relevant to equal

temperament.

Conceptual Field The home-notes used in Irish traditional music

Conceptual Resolution Relevant to equal temperament

1. C

2. C#/ Db

3. D

4. D#/ Eb

5. E

6. F

7. F#/ Gb

8. G

9. G#/ Ab

10. A

11. A#/ Bb

12. B

73 See: Joyce, Patrick Weston: Old Irish Folk Music and Songs, (London; New York: Longmans, Green,

and Co.; [etc.], 1909). This collection contains numerous examples of up to three sharps and three flats.

74 See Dervish: Decade, (Nashville: Compass Records, 2001).

198

5.4.1 The Heptatonic Modes

In the following tables (5.8 -5.13) each of the heptatonic modes, from Ionian to Aeolian

is presented across twelve home-notes. This exercise was guided by the rule that the

simplest key-signature possible is used.75 Consequently, it will be noted that in all of the

tables presented from here until Section 5.5 a mixture of sharps and flats may be found.

Table 5.8 The Ionian mode in relation to twelve home-notes.

Conceptual Field Ionian Mode

Conceptual Resolution Based on twelve home-notes

75 For instance, rather than use C-sharp Lydian in Table 5.11 below, which would have required a key-

signature of G-sharp, it was more user-friendly in this case to use D-flat. It will be noted that in cases such as the Hexatonic and Pentatonic conceptual fields where there is a mixture of modes to be found, some complex key-signatures were unavoidable.

199

Table 5.9 The Dorian mode in relation to twelve home-notes.

Conceptual Field Dorian Mode

Conceptual Resolution Based on twelve home-

notes

200

Table 5.10 The Phrygian mode in relation to twelve home-notes.

Conceptual Field Phrygian Mode


201

Table 5.11 The Lydian mode in relation to twelve home-notes.

Conceptual Field Lydian Mode


202

Table 5.12 The Mixolydian mode in relation to twelve home-notes.

Conceptual Field Mixolydian Mode


203

Table 5.13 The Aeolian mode in relation to twelve home-notes.

Conceptual Field Aeolian Mode


5.4.2 The Hexatonic Modes

A hexatonic mode consists of six notes. Using the calculations made in Table 5.2 above,

the various hexatonic scales concerning the Ionian, Dorian, Mixolydian and Aeolian

modes have been identified. In each of the examples, the home-note is given, then the

mode from which it derives in its abbreviated form, followed by the degree of the

omitted note, which is preceded by a minus sign or dash. For example, C Ion. Hex.-7

implies that the B-natural is omitted whilst D Mix. Hex.-4 implies that the G is missing.

There are twenty-one hexatonic possibilities that can be used in Irish traditional music.

Furthermore, as these twenty-one modes can occur in relation to any of the twelve

home-notes, a total of 252 hexatonic modes are presented between Tables 5.14 to 5.25

204

below.

Table 5.14 The hexatonic possibilities across the Ionian, Dorian, Mixolydian and

Aeolian modes with c’ as the home-note.

Conceptual Field Hexatonic possibilities across the Ionian,

Dorian, Mixolydian and Aeolian modes

Conceptual Resolution Based on the home-note of c’

205


Aeolian modes with c’-sharp as the home-note.

Conceptual Field Hexatonic possibilities across the Ionian, Dorian,

Mixolydian and Aeolian modes

Conceptual Resolution Based on the home-note of c’-sharp

206


Aeolian modes with d’ as the home-note.



Conceptual Resolution Based on the home-note of d’

207


Aeolian modes with e’-flat as the home-note.



Conceptual Resolution Based on the home-note of e’-flat

208


Aeolian modes with e’ as the home-note.



Conceptual Resolution Based on the home-note of e’

209


Aeolian modes with f’ as the home-note.



Conceptual Resolution Based on the home-note of f’

210


Aeolian modes with f’-sharp as the home-note.



Conceptual Resolution Based on the home-note of f’-sharp

211


Aeolian modes with g’ as the home-note.



Conceptual Resolution Based on the home-note of g’

212


Aeolian modes with a’-flat as the home-note.



Conceptual Resolution Based on the home-note of a’-flat.

213


Aeolian modes with a’ as the home-note.



Conceptual Resolution Based on the home-note of a’

214


Aeolian modes with b’-flat as the home-note.



Conceptual Resolution Based on the home-note of b’-flat

215


Aeolian modes with b’ as the home-note.



Conceptual Resolution Based on the home-note of b’

5.4.3 The Pentatonic Modes

As is the case with the heptatonic and hexatonic examples, the possibilities presented

here relate to the four common modes: Ionian, Dorian, Mixolydian and Aeolian.

Because two notes are missing, there is an even greater number of possibilities than

with the hexatonic options and a greater number of enharmonic equivalents also exist.

As was discussed earlier, having discovered sixteen enharmonic equivalents between

the four modes, forty-four pentatonic options remain. When this figure is multiplied by

the twelve home-notes on which each can be played, 528 stylistic elements result. Each

is presented as an ascending scale from Table 5.26 to 5.37.

216

Table 5.26 The pentatonic possibilities across the Ionian, Dorian, Mixolydian and

Aeolian modes with c’ as the home-note.



Conceptual Resolution Based on the home-note of c’

217


Aeolian modes with c’-sharp as the home-note.

Conceptual Field Pentatonic possibilities across the Ionian,


Conceptual Resolution Based on the home-note of c’-sharp

218


Aeolian modes with d’ as the home-note.



Conceptual Resolution Based on the home-note of d’

219


Aeolian modes with e’-flat as the home-note.



Conceptual Resolution Based on the home-note of e’-flat

220


Aeolian modes with e’ as the home-note.



Conceptual Resolution Based on the home-note of e’

221


Aeolian modes with f’ as the home-note.



Conceptual Resolution Based on the home-note of f’

222


Aeolian modes with f’-sharp as the home-note.



Conceptual Resolution Based on the home-note of f’-sharp

223


Aeolian modes with g’ as the home-note.



Conceptual Resolution Based on the home-note of g’

224


Aeolian modes with a’-flat as the home-note.

Conceptual Field Pentatonic possibilities across the Ionian, Dorian,


Conceptual Resolution Based on the home-note of a’-flat

225


Aeolian modes with a’ as the home-note.



Conceptual Resolution Based on the home-note of a’

226


Aeolian modes with b’-flat as the home-note.



Conceptual Resolution Based on the home-note of b’-flat

227


Aeolian modes with b’ as the home-note.



Conceptual Resolution Based on the home-note of b’

228

5.5 Inflection

Table 5.38 demonstrates the twenty-nine possible combinations regarding inflection. As

described earlier, the note to be inflected and its relationship to the home-note is

denoted by the associated number.76 To take for example the eleventh stylistic element

in the conceptual field below, the code ‘3,6’ indicates that the third and sixth degrees of

the mode of the tune in question will be inflected. Whether each of the inflected notes is

raised or lowered will depend on the modality of the particular tune.77

Table 5.38 The possibilities for inflection within sets of one to five chromatic

possibilities in a diatonic framework.

Conceptual Field Inflection using degrees of the scale

Conceptual Resolution On one to five chromatic possibilities

1. = 2

2. = 3

3. = 4

4. = 6

5. = 7

6. = 2,3

7. = 2,4

8. = 2,6

9. = 2,7

10. = 3,4

11. = 3,6

12. = 3,7

13. = 4,6

14. = 4,7

15. = 6,7

16. = 2,3,4

17. = 2,3,6

18. = 2,3,7

19. = 2,4,6

20. = 2,4,7

21. = 2,6,7

22. = 3,4,6

23. = 3,4,7

24. = 3,6,7

25. = 4,6,7

26. = 2,3,4,6

27. = 2,3,6,7

28. = 2,4,6,7

29. =2,3,4,6,7

5.6 Modulation

In Table 5.39, twenty-one options are presented where both the mode and home-note

change upon switching tune-part. For instance, stylistic element number 4 below could

be realised in a two-part tune where the A-part is in D Ionian and the B-part is in A

Mixolydian. Of course the home-note aspect is variable but as there are numerous tunes 76 See Section 5.2, 188-189. 77 Ibid.

229

that follow this particular pattern, it is a likely outcome.78

As will be discussed in Chapter Ten, the button-accordionist Peter Browne employs

chromatic modulation in a transitory sense.79 I have only observed this once in practice

prior to noting it in Peter’s playing.80 Since the options on this level are multifarious and

not widely used, it is considered as an alternative to modal modulation and is included

here as a single option in a conceptual field of its own. All three conceptual fields are

now presented.

Table 5.39 The possibilities for modal modulation where the home-note does change.

Conceptual Field Modulation

Conceptual Resolution Mode = different or same. Home-note = different

1. Ionian to Ionian or vice versa

2. Ionian to Dorian or vice versa

3. Ionian to Phrygian or vice versa

4. Ionian to Mixolydian or vice versa

5. Ionian to Lydian or vice versa

6. Ionian to Aeolian or vice versa

7. Dorian to Dorian or vice versa

8. Dorian to Phrygian or vice versa

9. Dorian to Mixolydian or vice versa

10. Dorian to Lydian or vice versa

11. Dorian to Aeolian or vice versa

12. Phrygian to Phrygian or vice versa

13. Phrygian to Lydian or vice versa

14. Phrygian to Mixolydian or vice versa

15. Phrygian to Aeolian or vice versa

16. Lydian to Lydian or vice versa

78 Two such examples include the reels ‘The Wild Irishman’ and ‘The Dublin Reel’. 79 See Chapter Ten, 542-543 for further discussion. 80 This was noticed in a session in Donegal with the fiddle-player Stephen Campbell who used it in the

first three bars of the reel ‘Lord Ramsey’s’, which is also known as ‘Big John McNeill’. To my knowledge, he has not recorded this version.

230

17. Lydian to Mixolydian or vice versa

18. Lydian to Aeolian or vice versa

19. Mixolydian to Mixolydian or vice versa

20. Mixolydian to Aeolian or vice versa

21. Aeolian to Aeolian or vice versa

Table 5.40 The possibilities for modal modulation where the home-note does not

change.

Conceptual Field Modulation

Conceptual Resolution Mode = different. home-note = same

1. Ionian to Dorian or vice versa

2. Ionian to Phrygian or vice versa

3. Ionian to Mixolydian or vice versa

4. Ionian to Lydian or vice versa

5. Ionian to Aeolian or vice versa

6. Dorian to Phrygian or vice versa

7. Dorian to Mixolydian or vice versa

8. Dorian to Lydian or vice versa

9. Dorian to Aeolian or vice versa

10. Phrygian to Lydian or vice versa

11. Phrygian to Mixolydian or vice versa

12. Phrygian to Aeolian or vice versa

13. Lydian to Mixolydian or vice versa

14. Lydian to Aeolian or vice versa

15. Mixolydian to Aeolian or vice versa

231

Table 5.41 Transitory chromatic modulation.

Conceptual Field Transitory chromatic modulation

Conceptual Resolution One basic observation

1. Transitory chromatic modulation

Notwithstanding how commonly used particular examples might be, there are twelve

home-notes available in which to play Irish traditional music. Although the Ionian,

Dorian, Mixolydian and Aeolian modes are those most in use within the tradition, the

evidence suggests that the Phrygian and Lydian modes are also employed. Across

twelve home-notes, seventy-two heptatonic modal options were found. From twenty-

one hexatonic possibilities across twelve home-notes, there is a total of 252 options.

Similarly, forty-four pentatonic options across twelve home-notes give rise to 528

possibilities. In terms of modality, this results in a total of 864 stylistic elements across

thirty-one conceptual fields.

As found in Section 5.5, there are twenty-nine different configurations for inflection.

The study on modulation gave rise to a total of thirty-six options plus one extra option

in a conceptual field of its own regarding transitory chromatic modulation. In terms of

these extra stylistic devices associated with modality, sixty-one stylistic elements were

found across four conceptual fields. In total, this chapter contains 929 stylistic elements

across thirty-five conceptual fields.

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CHAPTER SIX

MELODIC VARIATION

The aim of this chapter is to find the possibilities for melodic variation through

manipulating a tune’s structural tones and its underlying harmonic structure

respectively. Structural tones may be understood as the notes that lie on the strong beats

of the bar while harmonic structure refers to the harmonies that could be considered to

underpin a tune’s melody.1

6.1 Historiography

Melodic variation is mentioned in the earliest descriptions of Irish music and while this

specifically refers to harpists, it is likely that it could also be applied to other

instruments that were extant.2 One such early example can be found in The Historical

Memoirs of the Irish Bards, where Walker quotes from Professor Patrick McDonald’s

1784 publication A Collection of Highland Vocal Airs. The context in which the

quotation is given seems to imply that McDonald’s description is relevant to the Irish

tradition also. It reads:

They endeavoured to outdo one another in playing the airs that were most esteemed with correctness, and with their proper expression. Such of them as were men of abilities, attempted to adorn them with graces and variations, or to produce what were called good sets [settings] of them. These were communicated to their successors, and by them transmitted with additions. By this means the pieces were preserved: and so long as they continued in the hands of native harpers, we may suppose that they were gradually improved, as whatever graces and variations they added to them, were consistent with, and tending to heighten and display the genuine spirit and expression of the music. The taste for that style of performance seems now, however, to be declining.3

1 See Chapter Five, Ex. 5.6, 194. 2 Cooper Walker, Joseph: Historical Memoirs of the Irish Bards, (Dublin: Luke White, 1786), 68-93.

Other instruments of the time include the pipes, fiddle and flute. 3 Ibid., 157.

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Although it is likely that Edward Bunting would have been familiar with Walker’s opus,

in his 1840 publication he stated that ‘a strain of music, once impressed on the popular

ear, never varies’.4 He is also noted for his claim that the defining aspect of Irish

melody is the ‘emphatic presence’ of the submediant. Both ideas are correctly refuted

by George Petrie a decade and a half later in his Ancient Music of Ireland.5 In fact, as

noted in Chapter One, Petrie very firmly establishes that multiple variations of the same

tune can be found6 and even claimed that finding the same version of an unpublished air

twice was a rarity.7 Indeed, other collectors of the time, most notably P.W. Joyce, were

aware of the idea of variation with the latter writing about it in the context of a piece of

music in his Ancient Irish Music in 1873. He states that:

In the same manner as languages are gradually changed by those who use them, so also it is with popular music. Great numbers of our airs have various “settings” as that one is occasionally in doubt whether they come from the same original, or are different airs altogether. We may imagine that such changes were often the result of incorrect transmissions from one player or singer to another; while in other cases, they were made deliberately as improvements, by fiddlers, pipers, or singers – each change slight in itself – but without any intention of altering the whole into what might be called a different melody. And it is easy to understand what indeed has not infrequently happened, that in this manner an air might in course of time, be altered gradually and almost insensibly, note by note as it were, so as ultimately to become nearly unrecognizable.8

Later in the Preface to his Old Irish Folk Music and Songs (1909) Joyce states that:

We know that most or all Irish airs, like the popular airs of other countries, have various settings or versions. In most cases these are the result of gradual and almost unintentional alterations made by singers and players; just as the words and phrases of a living colloquial language become gradually altered. But it is highly probable – indeed, I might say it is certain that some versions were directly and deliberately made by skilled musicians, who changed the time, or rate of movement, or both, with more or less change in the individual notes, often with the result of wholly altering the character of the air. In this manner – as I believe – one of each pair of the following tunes was formed from the other: but it is not easy to determine in each case which was the original […].9

4 Bunting, Edward: The Ancient Music of Ireland, (Dublin: Hodges and Smith, 1840), 1. 5 See: Petrie, George: The Ancient Music of Ireland, Vol. 1, (Dublin: M.H. Gill, 1855), 48 for his

commentary on Bunting’s statement regarding the submediant. 6 Ibid., 20. 7 Ibid., xv. 8 Joyce, Patrick Weston: Ancient Irish Music, (Dublin: McGlashan and Gill, 1873), 22. 9 Joyce, Patrick Weston: Old Irish Folk Music and Songs, (London; New York: Longmans, Green, and

Co.; [etc.], 1909), xiii.

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Joyce goes on to give several other examples and draws attention to a number of

variations of the same air. Despite both Petrie and Joyce’s clear acknowledgement that

many versions of the same melody exist, it appears that they may have seen it as an

inconvenience in that it made their work in establishing the original melody more

difficult.

Towards the end of the nineteenth century, Bunting’s idea that the submediant was of

particular importance was being further challenged. For instance, in 1890 Frederick St.

John Lacy queried: ‘How are we to explain away the fact of the exceptions to these

rules outnumbering the examples that can be adduced in support of them?’10 Rather,

Lacy goes on to suggest that various notes have varying weights of importance but that

it depends on the tune.

In the twentieth century, these ideas were explored in greater detail. Notably, Seán Ó

Riada’s idea of ‘regional styles’ might be seen to relate to Petrie’s observation that

tunes can be found in different versions in various parts of the country.11 Nevertheless,

while repertoire and melodic variation now play a defining role in the discussion of

regional styles, it is worth noting that Ó Riada did not specifically mention melodic

variation. His discussion of what he termed the ‘variation principle’ however did help to

give melodic variation a sense of importance.12 Although in this instance, this principle

applies to sean-nós singing, he later notes that it also pertains to instrumental music in

general. He states that:

It is not permissible for a sean-nós singer to sing any two verses of a song in the same way. There must be a variation of the actual notes in each verse, as well as a variation of rhythm. What makes one sean-nós singer better than another, more than anything else, is his ability to do this better. The variations must not interfere with the basic structure of the song. They must occur where they would give most point and effect.13

10 Lacy, F. St. John: ‘Notes on Irish Music’, Proceedings of the Musical Association, 16th Session,

(1889–1890), (Dublin: Taylor & Francis, and the Royal Musical Association), 184. Although this discussion can perhaps be seen to have inspired or informed Tomás Ó Canainn’s ‘Note Frequency’ and Mícheál Ó Súilleabháin’s ‘Set Tones’. Both of which are explored later in this chapter.

11 Although it is important to note that Ó Riada was specifically referring to the fiddle, flute and sean-nós traditions. Ó Riada, Seán: Our Musical Heritage, eds. Tomás Ó Canainn; Thomas Kinsella, (Mountrath: Dolmen Press, 1982), 51-60.

12 Ibid., 24. 13 Ibid.

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Again in relation to sean-nós singers, he discusses the idea of motivic variation in

relation to what he terms the ‘internal logic’ of Munster songs.14 In speaking of this, he

is referring to the fact that particular intervals – such as the fifth or fourth – tend to

appear in numerous guises within a tune. He also discusses motivic variation in the tune

‘An Raibh tú ag an gCarraig’ where he notes that ‘it begins with three notes in a certain

relationship, and this relationship is the hub of the whole song, the three notes being

inverted, permuted and combined right through’.15

In 1971, Breandán Breathnach gave a more concise and nuanced explanation stating

that melodic variation constitutes:

[…] a degree of instant composition. Here the group or bar is varied, perhaps only the skeleton of the phrase being retained. Each time the part is played some grouping is varied, no performance ever being the same.16

The ‘skeleton of the phrase’ is a reference to the melody in its most basic sense and

although it is not directly stated, this usually implies a greater fidelity to the melody’s

structural tones over its passing tones.17 It is known that Breathnach was at least

implicitly aware of this in that another one of his innovations was the creation of an

indexing system to aid the navigation of his collection of 5,000 tunes.18 He describes

this in his article from 1982 ‘Between the Jigs and Reels’ published in Ceol.19 He

found that these tunes could be given a numerical code generated from the intervals

created between the tune’s final note and the structural tones from its first two bars or

four bars in 3/4.20 This results in an eight-digit code comprised of two groups of four

for tunes in 4/4, a four-digit code for tunes in 6/8 and a six-digit code comprised of two

groups of three for tunes in 9/8, and a four-digit code for 3/4. 14 Ibid., 34-37. 15 Ibid., 35. 16 Breathnach, Breandán: Folk Music and Dances of Ireland, Revised Ed. 1977, (Dublin; Cork: Mercier

Press, 1993), 98. 17 It is difficult to know if this is what Petrie meant when he referred to a tune as ‘correct’. See Flynn for

an explanation of skeletal notation. Flynn, David: Traditional Irish Music: a path to new music, (PhD Diss., Dublin Institute of Technology, 2011), 48-51.

18 See: Breathnach, Breandán: ‘Between the Jigs and the Reels’, Ceol, ed., Breandán Breathnach, Vol. V, 2, (Dublin: Breandán Breathnach, March 1982), 48.

19 Ibid., 43-48. 20 In Breathnach’s writing, the final note is not necessarily the home-note of the key. Moreover, it

should be noted that Breathnach did not use the term ‘structural tones’.

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In all circular tunes, a final note must be postulated despite the fact that this is both

subjective and sometimes at odds with the identification of the tune’s home-note.21

While this was envisaged as a method for finding tunes that are contained in his index,

it also makes it possible to find the tune’s nearest version by looking at close variants

of its code.22

In 1972, Tomás Ó Canainn follows suit by again formalising pre-existing ideas. Such is

the case with what he terms ‘note frequency’ which can be understood as an attempt to

account for the perceived importance or concentration of particular notes within a

tune.23 His analytical method for understanding this much-discussed phenomenon is

summarised in the following statement:

All this leads to a method for assessing the relative importance of notes in a tune, based on the following criteria: (1) a note frequency count giving a point for each appearance of the note (2) the addition of a further point (a) to a note which occurs on the strong beat. (b) to the highest note on its first appearance. (c) to the lowest note on its first appearance. (d) to a note proceeded by a leap greater than a fifth. (e) to the first stressed note. (f) to a long note (e.g. a dotted crotchet in a jig).24

While this underpins the significance of particular intervals in a more nuanced way than

had previously been attempted, it is more of an analytical tool than something that can

be used as a catalyst for improvised melodic variation. On a more practical level, he

discusses ‘motivic aspects of Irish music’ in which he demonstrates how a three-note

motif is developed through rhythmic variation, transposition and inversion in the slow

air ‘An Raibh tú ar an gCarraig’.25 In speaking of this form of motivic development, Ó

Canainn states that ‘such development results in a type of linear music which is

essentially distinct from the more diverse and freer forms which make up the vast

majority of Irish tunes’.26

21 See Chapter Five, 186. 22 Other information such as the tune’s source and any alternative titles is also noted on the cards. 23 Ó Canainn, Tomás: Traditional Music in Ireland, 2nd ed., (Cork: Ossian, 1993), 27-30. 24 Ibid., 28. 25 Ibid., 34-35. Incidentally, this is also the example that Ó Riada used to demonstrate his ‘internal logic’

of the Munster songs. See: Ó Riada: Our Musical Heritage, 35. 26 See: Ibid., 36. His final example ‘De Bharr na gCnoc’, demonstrates the motivic build up within the

larger structures as had been demonstrated by Travis.

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Influenced by Ó Canainn, the new importance given to melodic variation is set in

context six years later in Lawrence E. McCullough’s ‘Style in Traditional Irish Music’

(1977). Here, the author classes melodic (and rhythmic) variation as one of the four

main variables of which their ‘occurrence or non-occurrence characterizes every

performance and serves as the basic evaluative standards by which an individual’s

performance is judged by other musicians’.27

A decade later, Mícheál Ó Súilleabháin presents the idea of ‘set accented tones’ in an

attempt to understand melodic variation in the music of his subject, the fiddler Tommie

Potts.28 This idea can be seen to have parallels with aspects of Ó Canainn’s ‘note

frequency’, Breathnach’s indexing system and the twentieth-century practice of

structural tone analysis.29 Ó Súilleabháin’s thesis is that:

Within a performance, the musician would appear to be holding on to certain individual tones which occur at important accentuated points. It is the occurrence, or deliberate non-occurrence, of these tones which appears to provide the necessary point of reference for the performer.30

While this is most likely an implicit process on the part of the performer, it is probably

the most refined way of conceptualising a system that could potentially be used in

practice. Another aspect of melodic variation, which is described in Ó Súilleabháin’s

work, is the use of what might be termed stock variations. 31 These are quite commonly

used and imply that a musician has a repertoire of motifs that can be either specific to a

27 McCullough, Lawrence E.: ‘Style in Traditional Irish Music’, Ethnomusicology, Vol. 21, No.1,

(University of Illinois Press, 1977), 85. 28 Ó Súilleabháin, Mícheál: Innovation and Tradition in the Music of Tommie Potts, (PhD Diss.,

Queen’s University Belfast, 1987), 42. 29 Ó Canainn: Traditional Music in Ireland, 28. Breathnach: ‘Between the Jigs and the Reels’, 43-48. An

overview on the use of structural tones in twentieth-century styles of analysis may be found at: Bent, Ian D.; Pople, Anthony: ‘Analysis’, Grove Music Online, Oxford University Press. http://0-www.oxfordmusiconline.com.ditlib.dit.ie/subscriber/article/grove/music/41862pg2 (Accessed 1 Sept 2013).

30 Ó Súilleabháin: Innovation and Tradition in the Music of Tommie Potts, (PhD Diss., Queen’s University Belfast, 1987), 42.

31 While this is described in Ó Súilleabháin’s doctoral thesis, he gives it particular focus in: Ó Súilleabháin, Mícheál: ‘The Litany of the Saints: musical quotations and influences in the music of Tommie Potts’, Inbhear, Volume 1, Issue 1, (2010), 1-46 www.inbhear.ie (Accessed 21 March 2012). Also see: Ó Súilleabháin, Mícheál: “Traditional Ears’: Perception and Analysis in Irish Traditional Music’, Dear Far-Voiced Veteran: Essays in Honour of Tom Munnelly, ed. Anne Clune, (Co Clare: The Old Kilfarboy Society, 2007), 249-276.

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particular tune or which can be used in a series of tunes, almost possessing a

metaphorical life of their own. Outside of Ó Súilleabháin’s work, it is rare to find

descriptions of this type of stylistic practice, perhaps since musicians’ stock variations

are often so personalised as to make them difficult to detect and catalogue without

dedicated study.32

The Melodic Tradition of Ireland appeared in 1990 and is the first book to focus solely

on melody in Irish traditional music.33 Written by James R. Cowdery, this publication is

an attempt to address melodic variation through understanding melodic contour. While

it is interesting from an academic point of view, the graphs used to demonstrate melodic

difference lack defined points of reference such as exact pitches or intervals. In the

context of this study, its content is therefore unsuitable to be used as a catalyst.

In much the same vein as Ó Canainn’s discussion of the motivic aspects of Irish

traditional music, Robert Harvey’s dissertation on The Music of John Brady and its

Integration and Influence on the Irish Traditional Repertoire (2010) contains an

analysis of motivic development in the compositions of his subject. Like Ó Canainn,

Harvey discusses inversion and the retrograde development of motifs but unlike Ó

Canainn, he also discusses ‘fragmentation’ where a part of the original motif is

developed through inversion and retrograde treatment.34 He also discusses both

arpeggiated and scalic motifs and introduces the idea of a ‘signature motif’ which, in

John Brady’s case, is defined as ‘a two-note idea which rises by step and is immediately

followed in sequence a pitch lower’.35 Indeed, it is probable that there are more

signature motifs than those employed by John Brady but further study would be needed

to uncover to what extent this might be true.

32 However, one such dedicated study, Robert Harvey’s analysis of the compositions of John Brady, will

be discussed below. 33 See: Cowdery, James R.: The Melodic Tradition of Ireland, (Kent, Ohio: The Kent State University

Press, 1990). 34 Harvey, Robert: The Music of John Brady and its Integration and Influences on the Irish Traditional

Repertoire, (MMus. Diss., Dublin Institute of Technology), 33. 35 Ibid., 36. This could also be thought of as a descending scale in the structural tones of a piece. It might

also be more simply referred to as ‘interchangeable segments’ which is described in Ó Súilleabháin: Innovation and Tradition in the Music of Tommie Potts, 49.

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In addition to the conceptualisation of melody through stock variation and structural

tones, it can also be understood through the underlying harmonic structure that is

implied by the melody. While various styles of harmony have been documented from

the earliest sources, it seems that the role of harmonic structure in both the construction

and variation of a tune’s melody has not yet been explored.36

On the other hand, the earliest references to accompaniment relate to the harp music and

can be found as far back as Cambrensis’s account where he mentions the use of

‘intricate polyphony’.37 This has been substantiated by scholars such as Joan Rimmer

who notes that the Latin word for polyphony ‘organum’ denotes a ‘two-part music with

a complex and brilliant upper part’ above a slower moving lower part.38 She suggests

that ‘it was precisely these qualities that Edward Bunting praised six hundred years later

in Denis Hempson […]’.39 In as much as this earliest source of information on harp

accompaniment is interesting, Colette Moloney notes that ‘there are only ten tunes in

the manuscripts or printed volumes for which Bunting provides even a fragmented harp

bass’.40 The main style it would seem is a ‘tonic-drone effect [that] may have

similarities in the drone accompaniment [of] uilleann piping or warpiping’.41 In his

1938 paper, ‘Irish National Music’, James Travis offers a clearer perspective on the

bardic style of harmony and adds a number of other possibilities to the discussion.

No more than echoes persist of the harmony of antique Celtic harp music. The mentality which supported its dissonances and its chords of the sixth has regressed if not vanished, and in its place has risen another, upon the origins of which it had perhaps long ago looked with scorn as rustic or popular. It is true that the melodic formations of many tunes – for example, “Wink and She’ll Follow You” (p.461) – are reminiscent of the dissonant chords of ancient harpers; but these progressions reflect also a mentality capable of mingling such dissonances, in a consistent style, possibly never actualized as a theoretical system with harmony quartal and quintal as well as tertian, formations pentatonic as well as diatonic and hexatonic.42

36 That is despite this being a well-known approach to composition and improvisation in Jazz music. 37 See: Rimmer, Joan: The Irish Harp, (Cork: The Mercier Press for the Cultural Relations Committee of

Ireland, 1969), 30. 38 Ibid. 39 Ibid. 40 Moloney, Colette: The Irish Music Manuscripts of Edward Bunting (1773–1843): An Introduction

and Catalogue, (Dublin: Irish Traditional Music Archive, 2000), 75. 41 Ibid. 42 Travis, James: ‘Irish National Music’, The Musical Quarterly, Vol. 24, (Oxford: The Oxford

University Press, 1938), 479.

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In mentioning triadic and dyadic harmony, which comprises tertian, quartal and quintal

styles, Travis’s work is possibly the first to describe different types of harmony. In

recent times, extended harmony has been applied to traditional music with bands such

as Flook aiming to bring a more jazz-inspired feel to the music.43 This type of harmony

can also be heard to influence the compositions of present day composers such as Dave

Flynn whose melodies frequently outline major seven chords.44 The question then is to

establish how ideas as outlined by scholars can be used to inform musical practice by

helping to determine the stylistic choices that are available, and to develop a language

that can be used to easily and explicitly employ this knowledge.

From this overview, three points for conceptualising melody in Irish traditional music

have been found. These are: 1. The structural tones of a tune, 2. The tune’s implied

harmonic structure and 3. Stock variation. While stock variation is a very common

approach to improvisation, its highly personalised and nuanced nature would require a

specific study for it to be properly explored, notwithstanding the fact that its scope is

infinite. Therefore, this study will focus on structural tones and melodic construction

that results from implied harmonic structures.

6.2 Methodology

As previously stated, structural tones can be found on the strong beats of the bar.45

Following Breathnach’s approach, and as explained above, this implies eight tones in

two bars in 4/4, four tones in two bars of jigs in 6/8 and polkas in 2/4. While Breathnach

used six tones in two bars in 9/8, he only used the first beat of the first four bars of tunes

in 3/4. Since Breathnach’s objectives obviously differ from the purposes of this chapter,

in this study, the three structural tones that are found in one bar of 3/4 are instead used.

The rationale behind this is that three structural tones in one bar evidently gives more

options for melodic variation than would one structural tone per bar. Moreover, in every

other metre, Breathnach’s structural tones occur on each crotchet in simple metres or on

each dotted crotchet in compound metres. Using three structural tones for a bar of 3/4 is

43 Flook: Flatfish, (England: Flatfish Records, 1999). 44 See: Flynn, David: Draíocht, (Frisbee Records, 2006), track 6. 45 See Chapter Five, Ex. 5.6, 191.

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therefore also more consistent. Finally, it should be noted that since three structural

tones are used in one bar of 9/8, these codes are interchangeable with those of 3/4 and

only need to be printed once.

In conformation to the degrees of the diatonic scale, only numbers between one and

seven are used in this coding system. In a departure from Breathnach’s approach46 and

as explained in the previous chapter, the home-note is determined by calculating the

tune’s mode through its organisation of tones and semitones.47 Similarly to Breathnach

however, the lowered or raised nature of the degree of the scale that is referenced will

depend on the modality of the tune in question.48

It should also be noted that Breathnach uses a small line above or below a number to

indicate when a pitch exceeds or falls below the middle range of a mode, respectively.

This is demonstrated in Fig. 6.1 below:49

Fig. 6.1 Breathnach’s demonstration of how various pitches are written. Example taken

from ‘Between the Jigs and Reels’.

This approach is not adopted here because as opposed to the seven degrees of the

diatonic scale, the number of permutations generated by the sixteen notes in

Breathnach’s example gives rise to a list of permutations that is much beyond the remit

of this study. Moreover, the use of permutations drawing from a pool of sixteen options

would create melodic contours that are not idiomatic of the genre.50 Rather, in this

46 See Chapter Five, 178-179 for a discussion as to why Breathnach’s approach is problematic in this

context. Breathnach identified the home-note of a tune based on its final note. 47 See Chapter Five, 183-184. Therefore, the first degree of the mode will naturally be the home-note of

the tune. 48 See Chapter Five, 188-189 where this was discussed and the precise nature of the intervals relative to

the Ionian, Dorian, Mixolydian and Aeolian mode were given. 49 See: Breathnach: ‘Between the Jigs and the Reels’, 44. 50 For instance, it would create options where structural tones could be separated by an interval of as

much as a major sixteenth and follow with leaps of a similar range.

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context it is more fruitful to use a maximum of seven pitches because it allows the full

number of options to be determined, and in practice, it is concise enough to allow for a

musical and authentic-sounding realisation of the ensuing melodic contour.

To illustrate how the code relates to a particular musical example, the first two bars of

the well-known reel ‘The Sally Gardens’ is selected and presented in Ex. 6.1 below. For

notes that are beyond the range of one octave, for instance the d’ on the second beat of

bar one, the number five is employed irrespective of its placement relative to the middle

or main octave (g’-g’’).51 Hence the code for the two bars below is 1.5.3.1 | 5.6.5.2,

with full stops used to separate the structural tones and a vertical line used to indicate

the bar line.

Ex. 6.1 An illustration of where the structural tones fall using the first two bars of the

reel ‘The Sally Gardens’.

It follows that every possible combination of the numbers one to seven must be worked

out for sets of four figures and also for sets of three figures. In order to do this, the

permutations formula nr is used where n signifies the number of digits to choose from

(7) and the superscript r signifies the particular choice of them (3 or 4). Since the

possible combinations are many, the most precise way to find the answers is to use an

online permutation calculator.52 The screenshot at Fig. 6.2 below shows the calculator

page where the figures are inputted and the results page can be seen at Fig. 6.3.

51 However, the range of the pitches will be indicated in Chapter Ten, Section 10.4.2, 505-532 where

they are used for the purposes of analysis rather than catalysts. 52 See: http://www.mathsisfun.com/combinatorics/combinations-permutations-calculator.html

(Accessed 12 March 2013).

243

Fig. 6.2 Screenshot from the Combinations and Permutations Calculator used in

generating the data for sets of three.

244

Fig. 6.3 How the results are presented using this programme.

As can be seen above, as there are seven degrees of the scale from which to choose the

number seven was inputted as n, then the number four was entered for r, signifying the

total number of structural tones that can be in a set relevant to 4/4. When these were

calculated, 2,401 possibilities were found. To find sets of three structural tones, the

formula n=7 and r=3 was used to find 343 possibilities. The results were then copied

and pasted to a word document where the brackets were removed and the commas

replaced with full stops. From this, they were ordered into the tables that can be found

in Section 6.3 below.

245

While this is mainly envisaged with regard to structural tones, and hence a crotchet or

dotted crotchet movement, the focus could also be shifted to sets of three and four

quavers, which may be used to determine the smaller building blocks of melody.53

Thus, the codes listed in Section 6.3 can be considered a hybrid catalyst in that they can

be used in respect of both structural tones and also, what could be termed ‘motoric

tones’ or the groups of three or four quaver patterns. As is the nature of the musical

catalyst process, it is through being able to identify what stylistic elements are in use in

any one example that those that that are not present can be considered as options.

The two examples below demonstrate how the codes might be used in practice where

the melody of the first two bars of ‘The Maid Behind the Bar’ is varied through

conceptualising its structural tones (Ex. 6.2) and its motoric tones (Ex. 6.3). In Ex. 6.2,

its original code: 3.5.5.2 / 3.5.5.8 is changed to 3.5.4.2 / 4.5.1.7. In Ex 6.3 the same

process is undertaken in respect of the motoric tones where one note is changed in the

first bar and six notes are varied in the second bar.

Ex. 6.2 Demonstration of melodic variation using codes to modify structural tones.

Ex. 6.3 Demonstration of melodic variation using codes to modify motoric tones.

53 This is not unlike what is referred to by Robert Harvey in his thesis as a ‘signature motif’. Effectively,

if the same three or four-digit number were to turn up a number of times, it could be considered to be a ‘signature’ motif. Also see: Flynn: Traditional Irish Music: a path to new music, 275. Flynn has suggested that there are a number of ‘common motifs found in Irish tunes. It could be argued that almost every traditional Irish tune is based on a combination of some of these common motifs. Knowledge of these is essential in order to compose material that bears any resemblance to the melodic character of traditional Irish music’.

246

In addition to structural tones, variation can also be understood in terms of the implied

harmonic structure of tunes, which is itself highly stylised. Unlike the study of

structural tones, here there are two aspects to consider, first, the implied harmonies of a

melody and secondly, where the changes of harmony occur within a one-bar, two-bar,

or four-bar segment.

Harmonically then, since the music is modal and with pentatonic and hexatonic

modalities simply requiring the omission of notes, in order to work out the harmonic

possibilities, the chords I, ii, iii, IV, V, vi are used. It should be noted that augmented,

diminished (and hence chord vii) and other chromatic harmonies are so rarely outlined

in tunes that their inclusion here is not explored. While in the context of this study

Roman Numerals are the most effective way of indicating the possible harmonic

combinations, they are not widely used by traditional musicians. By way of an

explanation, the example below indicates the particular harmony associated with each

numeral.54

Ex. 6.4 Illustration of the harmony denoted by the Roman numerals I – vi.

In contrast to the study on structural tones, here, chord I follows the key-signature

as opposed to the home-note. Hence, a key-signature of two sharps will mean that

chord I is D major and a key-signature of four flats will signify that chord I is A-

flat major etc. If the key-signature is D major and the mode being used in E

Dorian, its most-used chord is likely to be ii. Similarly, in the same key-signature,

54 It should also be noted that it is conventional that major chords are denoted by upper-case script and

minor chords are written in lower case.

247

if the mode that is used is A Mixolydian, then the most used chord is V (also see

Ex. 6.6).55

The reason for this approach is that were chord one corresponding to the home-

note in the case of the Dorian mode for instance, many more variables, such as i,

ii, III, vi°, VIII would have to be considered with regard to permutations. Were

this to happen, it would create a list of options that would be both unwieldy and

prone to unidiomatic content. For instance, a progression such as i, I, III, iii would

occur, which does not fit within any mode and hence is not associable with the

style of the genre.

To employ this ‘language’ in the diatonic sense in which it is used here, it is possible to

understand the melodic construction of any traditional tune through the harmony that is

implied by its melody. The example below demonstrates how the first two bars of two

traditional tunes may be conceptualised in terms of their harmonic structure. There is

always a degree of subjectivity concerning what might be regarded as the correct

harmonic structure. As demonstrated in Ex. 6.5, the fourth chord of the reel ‘The

Moving Cloud’, here assigned as chord ii, could also be considered to be chord vi if the

notes g’e’g’ are thought to be more persuasive than the a’ and e’ on the third and fourth

beats respectively. A similar type of subjectivity could be considered to apply to the

second bar of the reel ‘The Sally Gardens’, which could be conceptualised as chord iii

rather than chord I depending on how important the note e’’ is considered to be.

Therefore, as will be noted, a degree of interpretation is a characteristic of this

approach.

55 This is actually in line with how the modes are understood using tonic sol-fa where the Ionian mode is

conceptualised as do-do’, the Dorian mode as re-re’ and so on.

248

Ex. 6.5 An interpretation of the harmonic structure of (a) ‘The Moving Cloud’ and (b)

‘The Sally Gardens’.

One of the more striking features of the implied harmonic structure of the melodies, and

which is evident in ‘The Sally Gardens’ above, is that they seem to be characterised by

their lack of deviation from the tonic harmony, except at cadence points. This itself may

help to explain why drone-accompaniment has long been used and works quite well.

Indeed, it is particularly at cadence points that the more complex harmonic changes

occur. In these cases, it is not unusual for the harmony to change at the pace of a

crotchet or dotted crotchet.

Codes are needed to reflect this information and consequently, the three and four-digit

codes for harmonic structure could be applied at:

1. a one-bar conceptual resolution, allowing for a maximum of two or four harmonic

changes respectively depending on whether the beats move in dotted crotchets or

crotchets

2. a two-bar conceptual resolution which would imply a maximum of four possible

harmonic changes at the rate of a minim or dotted crotchet, and finally,

3. a four-bar conceptual resolution which would imply a maximum harmonic movement

at a bar-per-bar rate.

Since the examples given in Ex. 6.5 demonstrate harmonic change at a conceptual

resolution of two-bars, the following transcription at Ex. 6.6 illustrates how a four-digit

249

code (V, V, V, IV) could be used at a conceptual resolution of four bars respectively. In

Ex. 6.7 below, the four-digit code (I, V, vi, vi) is demonstrated at a one-bar conceptual

resolution and hence, it moves in crotchets.

Ex. 6.6 An illustration of implied harmonic patterns (sets of four) at a four-bar

conceptual resolution.

Ex. 6.7 An illustration of implied harmonic patterns (sets of four) at a one-bar

conceptual resolution.

The same formula (nr) as was used to find the structural tone options is again used to

find the various harmonic structures that are possible. As before, repetitions are allowed

within the sets of three and four chords/harmonies and in doing so, it is possible to find

every option. This includes examples where the harmony either does not change at all,

such as I.I.I.I, changes to varying degrees, or changes a maximum number of times such

as I.IV.V.I

In order to demonstrate how this information can be realised creatively in practice, the

following variations at Ex. 6.8 show how the harmonic structure underpinning the first

two bars of the well-known reel ‘Rolling in the Rye Grass’ can be altered to influence

the construction of its melody. These are all explored at a two-bar conceptual resolution,

meaning that the melodic realisation of the implied harmony is calculated at a minim

per minim rate.

250

Ex. 6.8 Melodic variations derived from alterations in the harmonic structure of the first

two bars of the reel ‘Rolling in the Rye Grass’, (D Ionian).

6.3 Structural Tones

In this section, the possibilities are presented in both three and four-digit sets. As stated,

this stylistic data can be used to conceptualise melodic variation at a number of

conceptual resolutions. Sets of four serve the vast majority of tune-types e.g. those in

2/2, 4/4, 2/4 and 6/8 while sets of three serve the less popular slip jig, mazurka and

waltz tune-types.

251

Table 6.1 Every structural tone combination within a three-note set, relevant to one bar

of diatonic tunes in both 3/4 and 9/8.

Conceptual Field Structural Tones

Conceptual Resolution Three note possibilities

1. 1.1.1

2. 1.1.2

3. 1.1.3

4. 1.1.4

5. 1.1.5

6. 1.1.6

7. 1.1.7

8. 1.2.1

9. 1.2.2

10. 1.2.3

11. 1.2.4

12. 1.2.5

13. 1.2.6

14. 1.2.7

15. 1.3.1

16. 1.3.2

17. 1.3.3

18. 1.3.4

19. 1.3.5

20. 1.3.6

21. 1.3.7

22. 1.4.1

23. 1.4.2

24. 1.4.3

25. 1.4.4

26. 1.4.5

27. 1.4.6

70. 2.3.7

71. 2.4.1

72. 2.4.2

73. 2.4.3

74. 2.4.4

75. 2.4.5

76. 2.4.6

77. 2.4.7

78. 2.5.1

79. 2.5.2

80. 2.5.3

81. 2.5.4

82. 2.5.5

83. 2.5.6

84. 2.5.7

85. 2.6.1

86. 2.6.2

87. 2.6.3

88. 2.6.4

89. 2.6.5

90. 2.6.6

91. 2.6.7

92. 2.7.1

93. 2.7.2

94. 2.7.3

95. 2.7.4

96. 2.7.5

139. 3.6.6

140. 3.6.7

141. 3.7.1

142. 3.7.2

143. 3.7.3

144. 3.7.4

145. 3.7.5

146. 3.7.6

147. 3.7.7

148. 4.1.1

149. 4.1.2

150. 4.1.3

151. 4.1.4

152. 4.1.5

153. 4.1.6

154. 4.1.7

155. 4.2.1

156. 4.2.2

157. 4.2.3

158. 4.2.4

159. 4.2.5

160. 4.2.6

161. 4.2.7

162. 4.3.1

163. 4.3.2

164. 4.3.3

165. 4.3.4

208. 5.2.5

209. 5.2.6

210. 5.2.7

211. 5.3.1

212. 5.3.2

213. 5.3.3

214. 5.3.4

215. 5.3.5

216. 5.3.6

217. 5.3.7

218. 5.4.1

219. 5.4.2

220. 5.4.3

221. 5.4.4

222. 5.4.5

223. 5.4.6

224. 5.4.7

225. 5.5.1

226. 5.5.2

227. 5.5.3

228. 5.5.4

229. 5.5.5

230. 5.5.6

231. 5.5.7

232. 5.6.1

233. 5.6.2

234. 5.6.3

277. 6.5.4

278. 6.5.5

279. 6.5.6

280. 6.5.7

281. 6.6.1

282. 6.6.2

283. 6.6.3

284. 6.6.4

285. 6.6.5

286. 6.6.6

287. 6.6.7

288. 6.7.1

289. 6.7.2

290. 6.7.3

291. 6.7.4

292. 6.7.5

293. 6.7.6

294. 6.7.7

295. 7.1.1

296. 7.1.2

297. 7.1.3

298. 7.1.4

299. 7.1.5

300. 7.1.6

301. 7.1.7

302. 7.2.1

303. 7.2.2

252

28. 1.4.7

29. 1.5.1

30. 1.5.2

31. 1.5.3

32. 1.5.4

33. 1.5.5

34. 1.5.6

35. 1.5.7

36. 1.6.1

37. 1.6.2

38. 1.6.3

39. 1.6.4

40. 1.6.5

41. 1.6.6

42. 1.6.7

43. 1.7.1

44. 1.7.2

45. 1.7.3

46. 1.7.4

47. 1.7.5

48. 1.7.6

49. 1.7.7

50. 2.1.1

51. 2.1.2

52. 2.1.3

53. 2.1.4

54. 2.1.5

55. 2.1.6

56. 2.1.7

57. 2.2.1

58. 2.2.2

59. 2.2.3

97. 2.7.6

98. 2.7.7

99. 3.1.1

100. 3.1.2

101. 3.1.3

102. 3.1.4

103. 3.1.5

104. 3.1.6

105. 3.1.7

106. 3.2.1

107. 3.2.2

108. 3.2.3

109. 3.2.4

110. 3.2.5

111. 3.2.6

112. 3.2.7

113. 3.3.1

114. 3.3.2

115. 3.3.3

116. 3.3.4

117. 3.3.5

118. 3.3.6

119. 3.3.7

120. 3.4.1

121. 3.4.2

122. 3.4.3

123. 3.4.4

124. 3.4.5

125. 3.4.6

126. 3.4.7

127. 3.5.1

128. 3.5.2

166. 4.3.5

167. 4.3.6

168. 4.3.7

169. 4.4.1

170. 4.4.2

171. 4.4.3

172. 4.4.4

173. 4.4.5

174. 4.4.6

175. 4.4.7

176. 4.5.1

177. 4.5.2

178. 4.5.3

179. 4.5.4

180. 4.5.5

181. 4.5.6

182. 4.5.7

183. 4.6.1

184. 4.6.2

185. 4.6.3

186. 4.6.4

187. 4.6.5

188. 4.6.6

189. 4.6.7

190. 4.7.1

191. 4.7.2

192. 4.7.3

193. 4.7.4

194. 4.7.5

195. 4.7.6

196. 4.7.7

197. 5.1.1

235. 5.6.4

236. 5.6.5

237. 5.6.6

238. 5.6.7

239. 5.7.1

240. 5.7.2

241. 5.7.3

242. 5.7.4

243. 5.7.5

244. 5.7.6

245. 5.7.7

246. 6.1.1

247. 6.1.2

248. 6.1.3

249. 6.1.4

250. 6.1.5

251. 6.1.6

252. 6.1.7

253. 6.2.1

254. 6.2.2

255. 6.2.3

256. 6.2.4

257. 6.2.5

258. 6.2.6

259. 6.2.7

260. 6.3.1

261. 6.3.2

262. 6.3.3

263. 6.3.4

264. 6.3.5

265. 6.3.6

266. 6.3.7

304. 7.2.3

305. 7.2.4

306. 7.2.5

307. 7.2.6

308. 7.2.7

309. 7.3.1

310. 7.3.2

311. 7.3.3

312. 7.3.4

313. 7.3.5

314. 7.3.6

315. 7.3.7

316. 7.4.1

317. 7.4.2

318. 7.4.3

319. 7.4.4

320. 7.4.5

321. 7.4.6

322. 7.4.7

323. 7.5.1

324. 7.5.2

325. 7.5.3

326. 7.5.4

327. 7.5.5

328. 7.5.6

329. 7.5.7

330. 7.6.1

331. 7.6.2

332. 7.6.3

333. 7.6.4

334. 7.6.5

335. 7.6.6

253

60. 2.2.4

61. 2.2.5

62. 2.2.6

63. 2.2.7

64. 2.3.1

65. 2.3.2

66. 2.3.3

67. 2.3.4

68. 2.3.5

69. 2.3.6

129. 3.5.3

130. 3.5.4

131. 3.5.5

132. 3.5.6

133. 3.5.7

134. 3.6.1

135. 3.6.2

136. 3.6.3

137. 3.6.4

138. 3.6.5

198. 5.1.2

199. 5.1.3

200. 5.1.4

201. 5.1.5

202. 5.1.6

203. 5.1.7

204. 5.2.1

205. 5.2.2

206. 5.2.3

207. 5.2.4

267. 6.4.1

268. 6.4.2

269. 6.4.3

270. 6.4.4

271. 6.4.5

272. 6.4.6

273. 6.4.7

274. 6.5.1

275. 6.5.2

276. 6.5.3

336. 7.6.7

337. 7.7.1

338. 7.7.2

339. 7.7.3

340. 7.7.4

341. 7.7.5

342. 7.7.6

343. 7.7.7

Table 6.2 Structural tone combinations within a four-note set beginning with 1,

relevant to one bar of diatonic tunes in 4/4 and two bars of such in 2/4 or 6/8.


Conceptual Resolution Four note possibilities beginning with 1

1. 1.1.1.1

2. 1.1.1.2

3. 1.1.1.3

4. 1.1.1.4

5. 1.1.1.5

6. 1.1.1.6

7. 1.1.1.7

8. 1.1.2.1

9. 1.1.2.2

10. 1.1.2.3

11. 1.1.2.4

12. 1.1.2.5

13. 1.1.2.6

14. 1.1.2.7

15. 1.1.3.1

70. 1.2.3.7

71. 1.2.4.1

72. 1.2.4.2

73. 1.2.4.3

74. 1.2.4.4

75. 1.2.4.5

76. 1.2.4.6

77. 1.2.4.7

78. 1.2.5.1

79. 1.2.5.2

80. 1.2.5.3

81. 1.2.5.4

82. 1.2.5.5

83. 1.2.5.6

84. 1.2.5.7

139. 1.3.6.6

140. 1.3.6.7

141. 1.3.7.1

142. 1.3.7.2

143. 1.3.7.3

144. 1.3.7.4

145. 1.3.7.5

146. 1.3.7.6

147. 1.3.7.7

148. 1.4.1.1

149. 1.4.1.2

150. 1.4.1.3

151. 1.4.1.4

152. 1.4.1.5

153. 1.4.1.6

208. 1.5.2.5

209. 1.5.2.6

210. 1.5.2.7

211. 1.5.3.1

212. 1.5.3.2

213. 1.5.3.3

214. 1.5.3.4

215. 1.5.3.5

216. 1.5.3.6

217. 1.5.3.7

218. 1.5.4.1

219. 1.5.4.2

220. 1.5.4.3

221. 1.5.4.4

222. 1.5.4.5

277. 1.6.5.4

278. 1.6.5.5

279. 1.6.5.6

280. 1.6.5.7

281. 1.6.6.1

282. 1.6.6.2

283. 1.6.6.3

284. 1.6.6.4

285. 1.6.6.5

286. 1.6.6.6

287. 1.6.6.7

288. 1.6.7.1

289. 1.6.7.2

290. 1.6.7.3

291. 1.6.7.4

254

16. 1.1.3.2

17. 1.1.3.3

18. 1.1.3.4

19. 1.1.3.5

20. 1.1.3.6

21. 1.1.3.7

22. 1.1.4.1

23. 1.1.4.2

24. 1.1.4.3

25. 1.1.4.4

26. 1.1.4.5

27. 1.1.4.6

28. 1.1.4.7

29. 1.1.5.1

30. 1.1.5.2

31. 1.1.5.3

32. 1.1.5.4

33. 1.1.5.5

34. 1.1.5.6

35. 1.1.5.7

36. 1.1.6.1

37. 1.1.6.2

38. 1.1.6.3

39. 1.1.6.4

40. 1.1.6.5

41. 1.1.6.6

42. 1.1.6.7

43. 1.1.7.1

44. 1.1.7.2

45. 1.1.7.3

46. 1.1.7.4

47. 1.1.7.5

85. 1.2.6.1

86. 1.2.6.2

87. 1.2.6.3

88. 1.2.6.4

89. 1.2.6.5

90. 1.2.6.6

91. 1.2.6.7

92. 1.2.7.1

93. 1.2.7.2

94. 1.2.7.3

95. 1.2.7.4

96. 1.2.7.5

97. 1.2.7.6

98. 1.2.7.7

99. 1.3.1.1

100. 1.3.1.2

101. 1.3.1.3

102. 1.3.1.4

103. 1.3.1.5

104. 1.3.1.6

105. 1.3.1.7

106. 1.3.2.1

107. 1.3.2.2

108. 1.3.2.3

109. 1.3.2.4

110. 1.3.2.5

111. 1.3.2.6

112. 1.3.2.7

113. 1.3.3.1

114. 1.3.3.2

115. 1.3.3.3

116. 1.3.3.4

154. 1.4.1.7

155. 1.4.2.1

156. 1.4.2.2

157. 1.4.2.3

158. 1.4.2.4

159. 1.4.2.5

160. 1.4.2.6

161. 1.4.2.7

162. 1.4.3.1

163. 1.4.3.2

164. 1.4.3.3

165. 1.4.3.4

166. 1.4.3.5

167. 1.4.3.6

168. 1.4.3.7

169. 1.4.4.1

170. 1.4.4.2

171. 1.4.4.3

172. 1.4.4.4

173. 1.4.4.5

174. 1.4.4.6

175. 1.4.4.7

176. 1.4.5.1

177. 1.4.5.2

178. 1.4.5.3

179. 1.4.5.4

180. 1.4.5.5

181. 1.4.5.6

182. 1.4.5.7

183. 1.4.6.1

184. 1.4.6.2

185. 1.4.6.3

223. 1.5.4.6

224. 1.5.4.7

225. 1.5.5.1

226. 1.5.5.2

227. 1.5.5.3

228. 1.5.5.4

229. 1.5.5.5

230. 1.5.5.6

231. 1.5.5.7

232. 1.5.6.1

233. 1.5.6.2

234. 1.5.6.3

235. 1.5.6.4

236. 1.5.6.5

237. 1.5.6.6

238. 1.5.6.7

239. 1.5.7.1

240. 1.5.7.2

241. 1.5.7.3

242. 1.5.7.4

243. 1.5.7.5

244. 1.5.7.6

245. 1.5.7.7

246. 1.6.1.1

247. 1.6.1.2

248. 1.6.1.3

249. 1.6.1.4

250. 1.6.1.5

251. 1.6.1.6

252. 1.6.1.7

253. 1.6.2.1

254. 1.6.2.2

292. 1.6.7.5

293. 1.6.7.6

294. 1.6.7.7

295. 1.7.1.1

296. 1.7.1.2

297. 1.7.1.3

298. 1.7.1.4

299. 1.7.1.5

300. 1.7.1.6

301. 1.7.1.7

302. 1.7.2.1

303. 1.7.2.2

304. 1.7.2.3

305. 1.7.2.4

306. 1.7.2.5

307. 1.7.2.6

308. 1.7.2.7

309. 1.7.3.1

310. 1.7.3.2

311. 1.7.3.3

312. 1.7.3.4

313. 1.7.3.5

314. 1.7.3.6

315. 1.7.3.7

316. 1.7.4.1

317. 1.7.4.2

318. 1.7.4.3

319. 1.7.4.4

320. 1.7.4.5

321. 1.7.4.6

322. 1.7.4.7

323. 1.7.5.1

255

48. 1.1.7.6

49. 1.1.7.7

50. 1.2.1.1

51. 1.2.1.2

52. 1.2.1.3

53. 1.2.1.4

54. 1.2.1.5

55. 1.2.1.6

56. 1.2.1.7

57. 1.2.2.1

58. 1.2.2.2

59. 1.2.2.3

60. 1.2.2.4

61. 1.2.2.5

62. 1.2.2.6

63. 1.2.2.7

64. 1.2.3.1

65. 1.2.3.2

66. 1.2.3.3

67. 1.2.3.4

68. 1.2.3.5

69. 1.2.3.6

117. 1.3.3.5

118. 1.3.3.6

119. 1.3.3.7

120. 1.3.4.1

121. 1.3.4.2

122. 1.3.4.3

123. 1.3.4.4

124. 1.3.4.5

125. 1.3.4.6

126. 1.3.4.7

127. 1.3.5.1

128. 1.3.5.2

129. 1.3.5.3

130. 1.3.5.4

131. 1.3.5.5

132. 1.3.5.6

133. 1.3.5.7

134. 1.3.6.1

135. 1.3.6.2

136. 1.3.6.3

137. 1.3.6.4

138. 1.3.6.5

186. 1.4.6.4

187. 1.4.6.5

188. 1.4.6.6

189. 1.4.6.7

190. 1.4.7.1

191. 1.4.7.2

192. 1.4.7.3

193. 1.4.7.4

194. 1.4.7.5

195. 1.4.7.6

196. 1.4.7.7

197. 1.5.1.1

198. 1.5.1.2

199. 1.5.1.3

200. 1.5.1.4

201. 1.5.1.5

202. 1.5.1.6

203. 1.5.1.7

204. 1.5.2.1

205. 1.5.2.2

206. 1.5.2.3

207. 1.5.2.4

255. 1.6.2.3

256. 1.6.2.4

257. 1.6.2.5

258. 1.6.2.6

259. 1.6.2.7

260. 1.6.3.1

261. 1.6.3.2

262. 1.6.3.3

263. 1.6.3.4

264. 1.6.3.5

265. 1.6.3.6

266. 1.6.3.7

267. 1.6.4.1

268. 1.6.4.2

269. 1.6.4.3

270. 1.6.4.4

271. 1.6.4.5

272. 1.6.4.6

273. 1.6.4.7

274. 1.6.5.1

275. 1.6.5.2

276. 1.6.5.3

324. 1.7.5.2

325. 1.7.5.3

326. 1.7.5.4

327. 1.7.5.5

328. 1.7.5.6

329. 1.7.5.7

330. 1.7.6.1

331. 1.7.6.2

332. 1.7.6.3

333. 1.7.6.4

334. 1.7.6.5

335. 1.7.6.6

336. 1.7.6.7

337. 1.7.7.1

338. 1.7.7.2

339. 1.7.7.3

340. 1.7.7.4

341. 1.7.7.5

342. 1.7.7.6

343. 1.7.7.7

256





1. 2.1.1.1

2. 2.1.1.2

3. 2.1.1.3

4. 2.1.1.4

5. 2.1.1.5

6. 2.1.1.6

7. 2.1.1.7

8. 2.1.2.1

9. 2.1.2.2

10. 2.1.2.3

11. 2.1.2.4

12. 2.1.2.5

13. 2.1.2.6

14. 2.1.2.7

15. 2.1.3.1

16. 2.1.3.2

17. 2.1.3.3

18. 2.1.3.4

19. 2.1.3.5

20. 2.1.3.6

21. 2.1.3.7

22. 2.1.4.1

23. 2.1.4.2

24. 2.1.4.3

25. 2.1.4.4

26. 2.1.4.5

27. 2.1.4.6

70. 2.2.3.7

71. 2.2.4.1

72. 2.2.4.2

73. 2.2.4.3

74. 2.2.4.4

75. 2.2.4.5

76. 2.2.4.6

77. 2.2.4.7

78. 2.2.5.1

79. 2.2.5.2

80. 2.2.5.3

81. 2.2.5.4

82. 2.2.5.5

83. 2.2.5.6

84. 2.2.5.7

85. 2.2.6.1

86. 2.2.6.2

87. 2.2.6.3

88. 2.2.6.4

89. 2.2.6.5

90. 2.2.6.6

91. 2.2.6.7

92. 2.2.7.1

93. 2.2.7.2

94. 2.2.7.3

95. 2.2.7.4

96. 2.2.7.5

139. 2.3.6.6

140. 2.3.6.7

141. 2.3.7.1

142. 2.3.7.2

143. 2.3.7.3

144. 2.3.7.4

145. 2.3.7.5

146. 2.3.7.6

147. 2.3.7.7

148. 2.4.1.1

149. 2.4.1.2

150. 2.4.1.3

151. 2.4.1.4

152. 2.4.1.5

153. 2.4.1.6

154. 2.4.1.7

155. 2.4.2.1

156. 2.4.2.2

157. 2.4.2.3

158. 2.4.2.4

159. 2.4.2.5

160. 2.4.2.6

161. 2.4.2.7

162. 2.4.3.1

163. 2.4.3.2

164. 2.4.3.3

165. 2.4.3.4

208. 2.5.2.5

209. 2.5.2.6

210. 2.5.2.7

211. 2.5.3.1

212. 2.5.3.2

213. 2.5.3.3

214. 2.5.3.4

215. 2.5.3.5

216. 2.5.3.6

217. 2.5.3.7

218. 2.5.4.1

219. 2.5.4.2

220. 2.5.4.3

221. 2.5.4.4

222. 2.5.4.5

223. 2.5.4.6

224. 2.5.4.7

225. 2.5.5.1

226. 2.5.5.2

227. 2.5.5.3

228. 2.5.5.4

229. 2.5.5.5

230. 2.5.5.6

231. 2.5.5.7

232. 2.5.6.1

233. 2.5.6.2

234. 2.5.6.3

277. 2.6.5.4

278. 2.6.5.5

279. 2.6.5.6

280. 2.6.5.7

281. 2.6.6.1

282. 2.6.6.2

283. 2.6.6.3

284. 2.6.6.4

285. 2.6.6.5

286. 2.6.6.6

287. 2.6.6.7

288. 2.6.7.1

289. 2.6.7.2

290. 2.6.7.3

291. 2.6.7.4

292. 2.6.7.5

293. 2.6.7.6

294. 2.6.7.7

295. 2.7.1.1

296. 2.7.1.2

297. 2.7.1.3

298. 2.7.1.4

299. 2.7.1.5

300. 2.7.1.6

301. 2.7.1.7

302. 2.7.2.1

303. 2.7.2.2

257

28. 2.1.4.7

29. 2.1.5.1

30. 2.1.5.2

31. 2.1.5.3

32. 2.1.5.4

33. 2.1.5.5

34. 2.1.5.6

35. 2.1.5.7

36. 2.1.6.1

37. 2.1.6.2

38. 2.1.6.3

39. 2.1.6.4

40. 2.1.6.5

41. 2.1.6.6

42. 2.1.6.7

43. 2.1.7.1

44. 2.1.7.2

45. 2.1.7.3

46. 2.1.7.4

47. 2.1.7.5

48. 2.1.7.6

49. 2.1.7.7

50. 2.2.1.1

51. 2.2.1.2

52. 2.2.1.3

53. 2.2.1.4

54. 2.2.1.5

55. 2.2.1.6

56. 2.2.1.7

57. 2.2.2.1

58. 2.2.2.2

59. 2.2.2.3

97. 2.2.7.6

98. 2.2.7.7

99. 2.3.1.1

100. 2.3.1.2

101. 2.3.1.3

102. 2.3.1.4

103. 2.3.1.5

104. 2.3.1.6

105. 2.3.1.7

106. 2.3.2.1

107. 2.3.2.2

108. 2.3.2.3

109. 2.3.2.4

110. 2.3.2.5

111. 2.3.2.6

112. 2.3.2.7

113. 2.3.3.1

114. 2.3.3.2

115. 2.3.3.3

116. 2.3.3.4

117. 2.3.3.5

118. 2.3.3.6

119. 2.3.3.7

120. 2.3.4.1

121. 2.3.4.2

122. 2.3.4.3

123. 2.3.4.4

124. 2.3.4.5

125. 2.3.4.6

126. 2.3.4.7

127. 2.3.5.1

128. 2.3.5.2

166. 2.4.3.5

167. 2.4.3.6

168. 2.4.3.7

169. 2.4.4.1

170. 2.4.4.2

171. 2.4.4.3

172. 2.4.4.4

173. 2.4.4.5

174. 2.4.4.6

175. 2.4.4.7

176. 2.4.5.1

177. 2.4.5.2

178. 2.4.5.3

179. 2.4.5.4

180. 2.4.5.5

181. 2.4.5.6

182. 2.4.5.7

183. 2.4.6.1

184. 2.4.6.2

185. 2.4.6.3

186. 2.4.6.4

187. 2.4.6.5

188. 2.4.6.6

189. 2.4.6.7

190. 2.4.7.1

191. 2.4.7.2

192. 2.4.7.3

193. 2.4.7.4

194. 2.4.7.5

195. 2.4.7.6

196. 2.4.7.7

197. 2.5.1.1

235. 2.5.6.4

236. 2.5.6.5

237. 2.5.6.6

238. 2.5.6.7

239. 2.5.7.1

240. 2.5.7.2

241. 2.5.7.3

242. 2.5.7.4

243. 2.5.7.5

244. 2.5.7.6

245. 2.5.7.7

246. 2.6.1.1

247. 2.6.1.2

248. 2.6.1.3

249. 2.6.1.4

250. 2.6.1.5

251. 2.6.1.6

252. 2.6.1.7

253. 2.6.2.1

254. 2.6.2.2

255. 2.6.2.3

256. 2.6.2.4

257. 2.6.2.5

258. 2.6.2.6

259. 2.6.2.7

260. 2.6.3.1

261. 2.6.3.2

262. 2.6.3.3

263. 2.6.3.4

264. 2.6.3.5

265. 2.6.3.6

266. 2.6.3.7

304. 2.7.2.3

305. 2.7.2.4

306. 2.7.2.5

307. 2.7.2.6

308. 2.7.2.7

309. 2.7.3.1

310. 2.7.3.2

311. 2.7.3.3

312. 2.7.3.4

313. 2.7.3.5

314. 2.7.3.6

315. 2.7.3.7

316. 2.7.4.1

317. 2.7.4.2

318. 2.7.4.3

319. 2.7.4.4

320. 2.7.4.5

321. 2.7.4.6

322. 2.7.4.7

323. 2.7.5.1

324. 2.7.5.2

325. 2.7.5.3

326. 2.7.5.4

327. 2.7.5.5

328. 2.7.5.6

329. 2.7.5.7

330. 2.7.6.1

331. 2.7.6.2

332. 2.7.6.3

333. 2.7.6.4

334. 2.7.6.5

335. 2.7.6.6

258

60. 2.2.2.4

61. 2.2.2.5

62. 2.2.2.6

63. 2.2.2.7

64. 2.2.3.1

65. 2.2.3.2

66. 2.2.3.3

67. 2.2.3.4

68. 2.2.3.5

69. 2.2.3.6

129. 2.3.5.3

130. 2.3.5.4

131. 2.3.5.5

132. 2.3.5.6

133. 2.3.5.7

134. 2.3.6.1

135. 2.3.6.2

136. 2.3.6.3

137. 2.3.6.4

138. 2.3.6.5

198. 2.5.1.2

199. 2.5.1.3

200. 2.5.1.4

201. 2.5.1.5

202. 2.5.1.6

203. 2.5.1.7

204. 2.5.2.1

205. 2.5.2.2

206. 2.5.2.3

207. 2.5.2.4

267. 2.6.4.1

268. 2.6.4.2

269. 2.6.4.3

270. 2.6.4.4

271. 2.6.4.5

272. 2.6.4.6

273. 2.6.4.7

274. 2.6.5.1

275. 2.6.5.2

276. 2.6.5.3

336. 2.7.6.7

337. 2.7.7.1

338. 2.7.7.2

339. 2.7.7.3

340. 2.7.7.4

341. 2.7.7.5

342. 2.7.7.6

343. 2.7.7.7





1. 3.1.1.1

2. 3.1.1.2

3. 3.1.1.3

4. 3.1.1.4

5. 3.1.1.5

6. 3.1.1.6

7. 3.1.1.7

8. 3.1.2.1

9. 3.1.2.2

10. 3.1.2.3

11. 3.1.2.4

12. 3.1.2.5

13. 3.1.2.6

14. 3.1.2.7

15. 3.1.3.1

70. 3.2.3.7

71. 3.2.4.1

72. 3.2.4.2

73. 3.2.4.3

74. 3.2.4.4

75. 3.2.4.5

76. 3.2.4.6

77. 3.2.4.7

78. 3.2.5.1

79. 3.2.5.2

80. 3.2.5.3

81. 3.2.5.4

82. 3.2.5.5

83. 3.2.5.6

84. 3.2.5.7

139. 3.3.6.6

140. 3.3.6.7

141. 3.3.7.1

142. 3.3.7.2

143. 3.3.7.3

144. 3.3.7.4

145. 3.3.7.5

146. 3.3.7.6

147. 3.3.7.7

148. 3.4.1.1

149. 3.4.1.2

150. 3.4.1.3

151. 3.4.1.4

152. 3.4.1.5

153. 3.4.1.6

208. 3.5.2.5

209. 3.5.2.6

210. 3.5.2.7

211. 3.5.3.1

212. 3.5.3.2

213. 3.5.3.3

214. 3.5.3.4

215. 3.5.3.5

216. 3.5.3.6

217. 3.5.3.7

218. 3.5.4.1

219. 3.5.4.2

220. 3.5.4.3

221. 3.5.4.4

222. 3.5.4.5

277. 3.6.5.4

278. 3.6.5.5

279. 3.6.5.6

280. 3.6.5.7

281. 3.6.6.1

282. 3.6.6.2

283. 3.6.6.3

284. 3.6.6.4

285. 3.6.6.5

286. 3.6.6.6

287. 3.6.6.7

288. 3.6.7.1

289. 3.6.7.2

290. 3.6.7.3

291. 3.6.7.4

259

16. 3.1.3.2

17. 3.1.3.3

18. 3.1.3.4

19. 3.1.3.5

20. 3.1.3.6

21. 3.1.3.7

22. 3.1.4.1

23. 3.1.4.2

24. 3.1.4.3

25. 3.1.4.4

26. 3.1.4.5

27. 3.1.4.6

28. 3.1.4.7

29. 3.1.5.1

30. 3.1.5.2

31. 3.1.5.3

32. 3.1.5.4

33. 3.1.5.5

34. 3.1.5.6

35. 3.1.5.7

36. 3.1.6.1

37. 3.1.6.2

38. 3.1.6.3

39. 3.1.6.4

40. 3.1.6.5

41. 3.1.6.6

42. 3.1.6.7

43. 3.1.7.1

44. 3.1.7.2

45. 3.1.7.3

46. 3.1.7.4

47. 3.1.7.5

85. 3.2.6.1

86. 3.2.6.2

87. 3.2.6.3

88. 3.2.6.4

89. 3.2.6.5

90. 3.2.6.6

91. 3.2.6.7

92. 3.2.7.1

93. 3.2.7.2

94. 3.2.7.3

95. 3.2.7.4

96. 3.2.7.5

97. 3.2.7.6

98. 3.2.7.7

99. 3.3.1.1

100. 3.3.1.2

101. 3.3.1.3

102. 3.3.1.4

103. 3.3.1.5

104. 3.3.1.6

105. 3.3.1.7

106. 3.3.2.1

107. 3.3.2.2

108. 3.3.2.3

109. 3.3.2.4

110. 3.3.2.5

111. 3.3.2.6

112. 3.3.2.7

113. 3.3.3.1

114. 3.3.3.2

115. 3.3.3.3

116. 3.3.3.4

154. 3.4.1.7

155. 3.4.2.1

156. 3.4.2.2

157. 3.4.2.3

158. 3.4.2.4

159. 3.4.2.5

160. 3.4.2.6

161. 3.4.2.7

162. 3.4.3.1

163. 3.4.3.2

164. 3.4.3.3

165. 3.4.3.4

166. 3.4.3.5

167. 3.4.3.6

168. 3.4.3.7

169. 3.4.4.1

170. 3.4.4.2

171. 3.4.4.3

172. 3.4.4.4

173. 3.4.4.5

174. 3.4.4.6

175. 3.4.4.7

176. 3.4.5.1

177. 3.4.5.2

178. 3.4.5.3

179. 3.4.5.4

180. 3.4.5.5

181. 3.4.5.6

182. 3.4.5.7

183. 3.4.6.1

184. 3.4.6.2

185. 3.4.6.3

223. 3.5.4.6

224. 3.5.4.7

225. 3.5.5.1

226. 3.5.5.2

227. 3.5.5.3

228. 3.5.5.4

229. 3.5.5.5

230. 3.5.5.6

231. 3.5.5.7

232. 3.5.6.1

233. 3.5.6.2

234. 3.5.6.3

235. 3.5.6.4

236. 3.5.6.5

237. 3.5.6.6

238. 3.5.6.7

239. 3.5.7.1

240. 3.5.7.2

241. 3.5.7.3

242. 3.5.7.4

243. 3.5.7.5

244. 3.5.7.6

245. 3.5.7.7

246. 3.6.1.1

247. 3.6.1.2

248. 3.6.1.3

249. 3.6.1.4

250. 3.6.1.5

251. 3.6.1.6

252. 3.6.1.7

253. 3.6.2.1

254. 3.6.2.2

292. 3.6.7.5

293. 3.6.7.6

294. 3.6.7.7

295. 3.7.1.1

296. 3.7.1.2

297. 3.7.1.3

298. 3.7.1.4

299. 3.7.1.5

300. 3.7.1.6

301. 3.7.1.7

302. 3.7.2.1

303. 3.7.2.2

304. 3.7.2.3

305. 3.7.2.4

306. 3.7.2.5

307. 3.7.2.6

308. 3.7.2.7

309. 3.7.3.1

310. 3.7.3.2

311. 3.7.3.3

312. 3.7.3.4

313. 3.7.3.5

314. 3.7.3.6

315. 3.7.3.7

316. 3.7.4.1

317. 3.7.4.2

318. 3.7.4.3

319. 3.7.4.4

320. 3.7.4.5

321. 3.7.4.6

322. 3.7.4.7

323. 3.7.5.1

260

48. 3.1.7.6

49. 3.1.7.7

50. 3.2.1.1

51. 3.2.1.2

52. 3.2.1.3

53. 3.2.1.4

54. 3.2.1.5

55. 3.2.1.6

56. 3.2.1.7

57. 3.2.2.1

58. 3.2.2.2

59. 3.2.2.3

60. 3.2.2.4

61. 3.2.2.5

62. 3.2.2.6

63. 3.2.2.7

64. 3.2.3.1

65. 3.2.3.2

66. 3.2.3.3

67. 3.2.3.4

68. 3.2.3.5

69. 3.2.3.6

117. 3.3.3.5

118. 3.3.3.6

119. 3.3.3.7

120. 3.3.4.1

121. 3.3.4.2

122. 3.3.4.3

123. 3.3.4.4

124. 3.3.4.5

125. 3.3.4.6

126. 3.3.4.7

127. 3.3.5.1

128. 3.3.5.2

129. 3.3.5.3

130. 3.3.5.4

131. 3.3.5.5

132. 3.3.5.6

133. 3.3.5.7

134. 3.3.6.1

135. 3.3.6.2

136. 3.3.6.3

137. 3.3.6.4

138. 3.3.6.5

186. 3.4.6.4

187. 3.4.6.5

188. 3.4.6.6

189. 3.4.6.7

190. 3.4.7.1

191. 3.4.7.2

192. 3.4.7.3

193. 3.4.7.4

194. 3.4.7.5

195. 3.4.7.6

196. 3.4.7.7

197. 3.5.1.1

198. 3.5.1.2

199. 3.5.1.3

200. 3.5.1.4

201. 3.5.1.5

202. 3.5.1.6

203. 3.5.1.7

204. 3.5.2.1

205. 3.5.2.2

206. 3.5.2.3

207. 3.5.2.4

255. 3.6.2.3

256. 3.6.2.4

257. 3.6.2.5

258. 3.6.2.6

259. 3.6.2.7

260. 3.6.3.1

261. 3.6.3.2

262. 3.6.3.3

263. 3.6.3.4

264. 3.6.3.5

265. 3.6.3.6

266. 3.6.3.7

267. 3.6.4.1

268. 3.6.4.2

269. 3.6.4.3

270. 3.6.4.4

271. 3.6.4.5

272. 3.6.4.6

273. 3.6.4.7

274. 3.6.5.1

275. 3.6.5.2

276. 3.6.5.3

324. 3.7.5.2

325. 3.7.5.3

326. 3.7.5.4

327. 3.7.5.5

328. 3.7.5.6

329. 3.7.5.7

330. 3.7.6.1

331. 3.7.6.2

332. 3.7.6.3

333. 3.7.6.4

334. 3.7.6.5

335. 3.7.6.6

336. 3.7.6.7

337. 3.7.7.1

338. 3.7.7.2

339. 3.7.7.3

340. 3.7.7.4

341. 3.7.7.5

342. 3.7.7.6

343. 3.7.7.7





1. 4.1.1.1

2. 4.1.1.2

3. 4.1.1.3

70. 4.2.3.7

71. 4.2.4.1

72. 4.2.4.2

139. 4.3.6.6

140. 4.3.6.7

141. 4.3.7.1

208. 4.5.2.5

209. 4.5.2.6

210. 4.5.2.7

277. 4.6.5.4

278. 4.6.5.5

279. 4.6.5.6

261

4. 4.1.1.4

5. 4.1.1.5

6. 4.1.1.6

7. 4.1.1.7

8. 4.1.2.1

9. 4.1.2.2

10. 4.1.2.3

11. 4.1.2.4

12. 4.1.2.5

13. 4.1.2.6

14. 4.1.2.7

15. 4.1.3.1

16. 4.1.3.2

17. 4.1.3.3

18. 4.1.3.4

19. 4.1.3.5

20. 4.1.3.6

21. 4.1.3.7

22. 4.1.4.1

23. 4.1.4.2

24. 4.1.4.3

25. 4.1.4.4

26. 4.1.4.5

27. 4.1.4.6

28. 4.1.4.7

29. 4.1.5.1

30. 4.1.5.2

31. 4.1.5.3

32. 4.1.5.4

33. 4.1.5.5

34. 4.1.5.6

35. 4.1.5.7

73. 4.2.4.3

74. 4.2.4.4

75. 4.2.4.5

76. 4.2.4.6

77. 4.2.4.7

78. 4.2.5.1

79. 4.2.5.2

80. 4.2.5.3

81. 4.2.5.4

82. 4.2.5.5

83. 4.2.5.6

84. 4.2.5.7

85. 4.2.6.1

86. 4.2.6.2

87. 4.2.6.3

88. 4.2.6.4

89. 4.2.6.5

90. 4.2.6.6

91. 4.2.6.7

92. 4.2.7.1

93. 4.2.7.2

94. 4.2.7.3

95. 4.2.7.4

96. 4.2.7.5

97. 4.2.7.6

98. 4.2.7.7

99. 4.3.1.1

100. 4.3.1.2

101. 4.3.1.3

102. 4.3.1.4

103. 4.3.1.5

104. 4.3.1.6

142. 4.3.7.2

143. 4.3.7.3

144. 4.3.7.4

145. 4.3.7.5

146. 4.3.7.6

147. 4.3.7.7

148. 4.4.1.1

149. 4.4.1.2

150. 4.4.1.3

151. 4.4.1.4

152. 4.4.1.5

153. 4.4.1.6

154. 4.4.1.7

155. 4.4.2.1

156. 4.4.2.2

157. 4.4.2.3

158. 4.4.2.4

159. 4.4.2.5

160. 4.4.2.6

161. 4.4.2.7

162. 4.4.3.1

163. 4.4.3.2

164. 4.4.3.3

165. 4.4.3.4

166. 4.4.3.5

167. 4.4.3.6

168. 4.4.3.7

169. 4.4.4.1

170. 4.4.4.2

171. 4.4.4.3

172. 4.4.4.4

173. 4.4.4.5

211. 4.5.3.1

212. 4.5.3.2

213. 4.5.3.3

214. 4.5.3.4

215. 4.5.3.5

216. 4.5.3.6

217. 4.5.3.7

218. 4.5.4.1

219. 4.5.4.2

220. 4.5.4.3

221. 4.5.4.4

222. 4.5.4.5

223. 4.5.4.6

224. 4.5.4.7

225. 4.5.5.1

226. 4.5.5.2

227. 4.5.5.3

228. 4.5.5.4

229. 4.5.5.5

230. 4.5.5.6

231. 4.5.5.7

232. 4.5.6.1

233. 4.5.6.2

234. 4.5.6.3

235. 4.5.6.4

236. 4.5.6.5

237. 4.5.6.6

238. 4.5.6.7

239. 4.5.7.1

240. 4.5.7.2

241. 4.5.7.3

242. 4.5.7.4

280. 4.6.5.7

281. 4.6.6.1

282. 4.6.6.2

283. 4.6.6.3

284. 4.6.6.4

285. 4.6.6.5

286. 4.6.6.6

287. 4.6.6.7

288. 4.6.7.1

289. 4.6.7.2

290. 4.6.7.3

291. 4.6.7.4

292. 4.6.7.5

293. 4.6.7.6

294. 4.6.7.7

295. 4.7.1.1

296. 4.7.1.2

297. 4.7.1.3

298. 4.7.1.4

299. 4.7.1.5

300. 4.7.1.6

301. 4.7.1.7

302. 4.7.2.1

303. 4.7.2.2

304. 4.7.2.3

305. 4.7.2.4

306. 4.7.2.5

307. 4.7.2.6

308. 4.7.2.7

309. 4.7.3.1

310. 4.7.3.2

311. 4.7.3.3

262

36. 4.1.6.1

37. 4.1.6.2

38. 4.1.6.3

39. 4.1.6.4

40. 4.1.6.5

41. 4.1.6.6

42. 4.1.6.7

43. 4.1.7.1

44. 4.1.7.2

45. 4.1.7.3

46. 4.1.7.4

47. 4.1.7.5

48. 4.1.7.6

49. 4.1.7.7

50. 4.2.1.1

51. 4.2.1.2

52. 4.2.1.3

53. 4.2.1.4

54. 4.2.1.5

55. 4.2.1.6

56. 4.2.1.7

57. 4.2.2.1

58. 4.2.2.2

59. 4.2.2.3

60. 4.2.2.4

61. 4.2.2.5

62. 4.2.2.6

63. 4.2.2.7

64. 4.2.3.1

65. 4.2.3.2

66. 4.2.3.3

67. 4.2.3.4

105. 4.3.1.7

106. 4.3.2.1

107. 4.3.2.2

108. 4.3.2.3

109. 4.3.2.4

110. 4.3.2.5

111. 4.3.2.6

112. 4.3.2.7

113. 4.3.3.1

114. 4.3.3.2

115. 4.3.3.3

116. 4.3.3.4

117. 4.3.3.5

118. 4.3.3.6

119. 4.3.3.7

120. 4.3.4.1

121. 4.3.4.2

122. 4.3.4.3

123. 4.3.4.4

124. 4.3.4.5

125. 4.3.4.6

126. 4.3.4.7

127. 4.3.5.1

128. 4.3.5.2

129. 4.3.5.3

130. 4.3.5.4

131. 4.3.5.5

132. 4.3.5.6

133. 4.3.5.7

134. 4.3.6.1

135. 4.3.6.2

136. 4.3.6.3

174. 4.4.4.6

175. 4.4.4.7

176. 4.4.5.1

177. 4.4.5.2

178. 4.4.5.3

179. 4.4.5.4

180. 4.4.5.5

181. 4.4.5.6

182. 4.4.5.7

183. 4.4.6.1

184. 4.4.6.2

185. 4.4.6.3

186. 4.4.6.4

187. 4.4.6.5

188. 4.4.6.6

189. 4.4.6.7

190. 4.4.7.1

191. 4.4.7.2

192. 4.4.7.3

193. 4.4.7.4

194. 4.4.7.5

195. 4.4.7.6

196. 4.4.7.7

197. 4.5.1.1

198. 4.5.1.2

199. 4.5.1.3

200. 4.5.1.4

201. 4.5.1.5

202. 4.5.1.6

203. 4.5.1.7

204. 4.5.2.1

205. 4.5.2.2

243. 4.5.7.5

244. 4.5.7.6

245. 4.5.7.7

246. 4.6.1.1

247. 4.6.1.2

248. 4.6.1.3

249. 4.6.1.4

250. 4.6.1.5

251. 4.6.1.6

252. 4.6.1.7

253. 4.6.2.1

254. 4.6.2.2

255. 4.6.2.3

256. 4.6.2.4

257. 4.6.2.5

258. 4.6.2.6

259. 4.6.2.7

260. 4.6.3.1

261. 4.6.3.2

262. 4.6.3.3

263. 4.6.3.4

264. 4.6.3.5

265. 4.6.3.6

266. 4.6.3.7

267. 4.6.4.1

268. 4.6.4.2

269. 4.6.4.3

270. 4.6.4.4

271. 4.6.4.5

272. 4.6.4.6

273. 4.6.4.7

274. 4.6.5.1

312. 4.7.3.4

313. 4.7.3.5

314. 4.7.3.6

315. 4.7.3.7

316. 4.7.4.1

317. 4.7.4.2

318. 4.7.4.3

319. 4.7.4.4

320. 4.7.4.5

321. 4.7.4.6

322. 4.7.4.7

323. 4.7.5.1

324. 4.7.5.2

325. 4.7.5.3

326. 4.7.5.4

327. 4.7.5.5

328. 4.7.5.6

329. 4.7.5.7

330. 4.7.6.1

331. 4.7.6.2

332. 4.7.6.3

333. 4.7.6.4

334. 4.7.6.5

335. 4.7.6.6

336. 4.7.6.7

337. 4.7.7.1

338. 4.7.7.2

339. 4.7.7.3

340. 4.7.7.4

341. 4.7.7.5

342. 4.7.7.6

343. 4.7.7.7

263

68. 4.2.3.5

69. 4.2.3.6

137. 4.3.6.4

138. 4.3.6.5

206. 4.5.2.3

207. 4.5.2.4

275. 4.6.5.2

276. 4.6.5.3





1. 5.1.1.1

2. 5.1.1.2

3. 5.1.1.3

4. 5.1.1.4

5. 5.1.1.5

6. 5.1.1.6

7. 5.1.1.7

8. 5.1.2.1

9. 5.1.2.2

10. 5.1.2.3

11. 5.1.2.4

12. 5.1.2.5

13. 5.1.2.6

14. 5.1.2.7

15. 5.1.3.1

16. 5.1.3.2

17. 5.1.3.3

18. 5.1.3.4

19. 5.1.3.5

20. 5.1.3.6

21. 5.1.3.7

22. 5.1.4.1

23. 5.1.4.2

70. 5.2.3.7

71. 5.2.4.1

72. 5.2.4.2

73. 5.2.4.3

74. 5.2.4.4

75. 5.2.4.5

76. 5.2.4.6

77. 5.2.4.7

78. 5.2.5.1

79. 5.2.5.2

80. 5.2.5.3

81. 5.2.5.4

82. 5.2.5.5

83. 5.2.5.6

84. 5.2.5.7

85. 5.2.6.1

86. 5.2.6.2

87. 5.2.6.3

88. 5.2.6.4

89. 5.2.6.5

90. 5.2.6.6

91. 5.2.6.7

92. 5.2.7.1

139. 5.3.6.6

140. 5.3.6.7

141. 5.3.7.1

142. 5.3.7.2

143. 5.3.7.3

144. 5.3.7.4

145. 5.3.7.5

146. 5.3.7.6

147. 5.3.7.7

148. 5.4.1.1

149. 5.4.1.2

150. 5.4.1.3

151. 5.4.1.4

152. 5.4.1.5

153. 5.4.1.6

154. 5.4.1.7

155. 5.4.2.1

156. 5.4.2.2

157. 5.4.2.3

158. 5.4.2.4

159. 5.4.2.5

160. 5.4.2.6

161. 5.4.2.7

208. 5.5.2.5

209. 5.5.2.6

210. 5.5.2.7

211. 5.5.3.1

212. 5.5.3.2

213. 5.5.3.3

214. 5.5.3.4

215. 5.5.3.5

216. 5.5.3.6

217. 5.5.3.7

218. 5.5.4.1

219. 5.5.4.2

220. 5.5.4.3

221. 5.5.4.4

222. 5.5.4.5

223. 5.5.4.6

224. 5.5.4.7

225. 5.5.5.1

226. 5.5.5.2

227. 5.5.5.3

228. 5.5.5.4

229. 5.5.5.5

230. 5.5.5.6

277. 5.6.5.4

278. 5.6.5.5

279. 5.6.5.6

280. 5.6.5.7

281. 5.6.6.1

282. 5.6.6.2

283. 5.6.6.3

284. 5.6.6.4

285. 5.6.6.5

286. 5.6.6.6

287. 5.6.6.7

288. 5.6.7.1

289. 5.6.7.2

290. 5.6.7.3

291. 5.6.7.4

292. 5.6.7.5

293. 5.6.7.6

294. 5.6.7.7

295. 5.7.1.1

296. 5.7.1.2

297. 5.7.1.3

298. 5.7.1.4

299. 5.7.1.5

264

24. 5.1.4.3

25. 5.1.4.4

26. 5.1.4.5

27. 5.1.4.6

28. 5.1.4.7

29. 5.1.5.1

30. 5.1.5.2

31. 5.1.5.3

32. 5.1.5.4

33. 5.1.5.5

34. 5.1.5.6

35. 5.1.5.7

36. 5.1.6.1

37. 5.1.6.2

38. 5.1.6.3

39. 5.1.6.4

40. 5.1.6.5

41. 5.1.6.6

42. 5.1.6.7

43. 5.1.7.1

44. 5.1.7.2

45. 5.1.7.3

46. 5.1.7.4

47. 5.1.7.5

48. 5.1.7.6

49. 5.1.7.7

50. 5.2.1.1

51. 5.2.1.2

52. 5.2.1.3

53. 5.2.1.4

54. 5.2.1.5

55. 5.2.1.6

93. 5.2.7.2

94. 5.2.7.3

95. 5.2.7.4

96. 5.2.7.5

97. 5.2.7.6

98. 5.2.7.7

99. 5.3.1.1

100. 5.3.1.2

101. 5.3.1.3

102. 5.3.1.4

103. 5.3.1.5

104. 5.3.1.6

105. 5.3.1.7

106. 5.3.2.1

107. 5.3.2.2

108. 5.3.2.3

109. 5.3.2.4

110. 5.3.2.5

111. 5.3.2.6

112. 5.3.2.7

113. 5.3.3.1

114. 5.3.3.2

115. 5.3.3.3

116. 5.3.3.4

117. 5.3.3.5

118. 5.3.3.6

119. 5.3.3.7

120. 5.3.4.1

121. 5.3.4.2

122. 5.3.4.3

123. 5.3.4.4

124. 5.3.4.5

162. 5.4.3.1

163. 5.4.3.2

164. 5.4.3.3

165. 5.4.3.4

166. 5.4.3.5

167. 5.4.3.6

168. 5.4.3.7

169. 5.4.4.1

170. 5.4.4.2

171. 5.4.4.3

172. 5.4.4.4

173. 5.4.4.5

174. 5.4.4.6

175. 5.4.4.7

176. 5.4.5.1

177. 5.4.5.2

178. 5.4.5.3

179. 5.4.5.4

180. 5.4.5.5

181. 5.4.5.6

182. 5.4.5.7

183. 5.4.6.1

184. 5.4.6.2

185. 5.4.6.3

186. 5.4.6.4

187. 5.4.6.5

188. 5.4.6.6

189. 5.4.6.7

190. 5.4.7.1

191. 5.4.7.2

192. 5.4.7.3

193. 5.4.7.4

231. 5.5.5.7

232. 5.5.6.1

233. 5.5.6.2

234. 5.5.6.3

235. 5.5.6.4

236. 5.5.6.5

237. 5.5.6.6

238. 5.5.6.7

239. 5.5.7.1

240. 5.5.7.2

241. 5.5.7.3

242. 5.5.7.4

243. 5.5.7.5

244. 5.5.7.6

245. 5.5.7.7

246. 5.6.1.1

247. 5.6.1.2

248. 5.6.1.3

249. 5.6.1.4

250. 5.6.1.5

251. 5.6.1.6

252. 5.6.1.7

253. 5.6.2.1

254. 5.6.2.2

255. 5.6.2.3

256. 5.6.2.4

257. 5.6.2.5

258. 5.6.2.6

259. 5.6.2.7

260. 5.6.3.1

261. 5.6.3.2

262. 5.6.3.3

300. 5.7.1.6

301. 5.7.1.7

302. 5.7.2.1

303. 5.7.2.2

304. 5.7.2.3

305. 5.7.2.4

306. 5.7.2.5

307. 5.7.2.6

308. 5.7.2.7

309. 5.7.3.1

310. 5.7.3.2

311. 5.7.3.3

312. 5.7.3.4

313. 5.7.3.5

314. 5.7.3.6

315. 5.7.3.7

316. 5.7.4.1

317. 5.7.4.2

318. 5.7.4.3

319. 5.7.4.4

320. 5.7.4.5

321. 5.7.4.6

322. 5.7.4.7

323. 5.7.5.1

324. 5.7.5.2

325. 5.7.5.3

326. 5.7.5.4

327. 5.7.5.5

328. 5.7.5.6

329. 5.7.5.7

330. 5.7.6.1

331. 5.7.6.2

265

56. 5.2.1.7

57. 5.2.2.1

58. 5.2.2.2

59. 5.2.2.3

60. 5.2.2.4

61. 5.2.2.5

62. 5.2.2.6

63. 5.2.2.7

64. 5.2.3.1

65. 5.2.3.2

66. 5.2.3.3

67. 5.2.3.4

68. 5.2.3.5

69. 5.2.3.6

125. 5.3.4.6

126. 5.3.4.7

127. 5.3.5.1

128. 5.3.5.2

129. 5.3.5.3

130. 5.3.5.4

131. 5.3.5.5

132. 5.3.5.6

133. 5.3.5.7

134. 5.3.6.1

135. 5.3.6.2

136. 5.3.6.3

137. 5.3.6.4

138. 5.3.6.5

194. 5.4.7.5

195. 5.4.7.6

196. 5.4.7.7

197. 5.5.1.1

198. 5.5.1.2

199. 5.5.1.3

200. 5.5.1.4

201. 5.5.1.5

202. 5.5.1.6

203. 5.5.1.7

204. 5.5.2.1

205. 5.5.2.2

206. 5.5.2.3

207. 5.5.2.4

263. 5.6.3.4

264. 5.6.3.5

265. 5.6.3.6

266. 5.6.3.7

267. 5.6.4.1

268. 5.6.4.2

269. 5.6.4.3

270. 5.6.4.4

271. 5.6.4.5

272. 5.6.4.6

273. 5.6.4.7

274. 5.6.5.1

275. 5.6.5.2

276. 5.6.5.3

332. 5.7.6.3

333. 5.7.6.4

334. 5.7.6.5

335. 5.7.6.6

336. 5.7.6.7

337. 5.7.7.1

338. 5.7.7.2

339. 5.7.7.3

340. 5.7.7.4

341. 5.7.7.5

342. 5.7.7.6

343. 5.7.7.7





1. 6.1.1.1

2. 6.1.1.2

3. 6.1.1.3

4. 6.1.1.4

5. 6.1.1.5

6. 6.1.1.6

7. 6.1.1.7

8. 6.1.2.1

9. 6.1.2.2

10. 6.1.2.3

11. 6.1.2.4

70. 6.2.3.7

71. 6.2.4.1

72. 6.2.4.2

73. 6.2.4.3

74. 6.2.4.4

75. 6.2.4.5

76. 6.2.4.6

77. 6.2.4.7

78. 6.2.5.1

79. 6.2.5.2

80. 6.2.5.3

139. 6.3.6.6

140. 6.3.6.7

141. 6.3.7.1

142. 6.3.7.2

143. 6.3.7.3

144. 6.3.7.4

145. 6.3.7.5

146. 6.3.7.6

147. 6.3.7.7

148. 6.4.1.1

149. 6.4.1.2

208. 6.5.2.5

209. 6.5.2.6

210. 6.5.2.7

211. 6.5.3.1

212. 6.5.3.2

213. 6.5.3.3

214. 6.5.3.4

215. 6.5.3.5

216. 6.5.3.6

217. 6.5.3.7

218. 6.5.4.1

277. 6.6.5.4

278. 6.6.5.5

279. 6.6.5.6

280. 6.6.5.7

281. 6.6.6.1

282. 6.6.6.2

283. 6.6.6.3

284. 6.6.6.4

285. 6.6.6.5

286. 6.6.6.6

287. 6.6.6.7

266

12. 6.1.2.5

13. 6.1.2.6

14. 6.1.2.7

15. 6.1.3.1

16. 6.1.3.2

17. 6.1.3.3

18. 6.1.3.4

19. 6.1.3.5

20. 6.1.3.6

21. 6.1.3.7

22. 6.1.4.1

23. 6.1.4.2

24. 6.1.4.3

25. 6.1.4.4

26. 6.1.4.5

27. 6.1.4.6

28. 6.1.4.7

29. 6.1.5.1

30. 6.1.5.2

31. 6.1.5.3

32. 6.1.5.4

33. 6.1.5.5

34. 6.1.5.6

35. 6.1.5.7

36. 6.1.6.1

37. 6.1.6.2

38. 6.1.6.3

39. 6.1.6.4

40. 6.1.6.5

41. 6.1.6.6

42. 6.1.6.7

43. 6.1.7.1

81. 6.2.5.4

82. 6.2.5.5

83. 6.2.5.6

84. 6.2.5.7

85. 6.2.6.1

86. 6.2.6.2

87. 6.2.6.3

88. 6.2.6.4

89. 6.2.6.5

90. 6.2.6.6

91. 6.2.6.7

92. 6.2.7.1

93. 6.2.7.2

94. 6.2.7.3

95. 6.2.7.4

96. 6.2.7.5

97. 6.2.7.6

98. 6.2.7.7

99. 6.3.1.1

100. 6.3.1.2

101. 6.3.1.3

102. 6.3.1.4

103. 6.3.1.5

104. 6.3.1.6

105. 6.3.1.7

106. 6.3.2.1

107. 6.3.2.2

108. 6.3.2.3

109. 6.3.2.4

110. 6.3.2.5

111. 6.3.2.6

112. 6.3.2.7

150. 6.4.1.3

151. 6.4.1.4

152. 6.4.1.5

153. 6.4.1.6

154. 6.4.1.7

155. 6.4.2.1

156. 6.4.2.2

157. 6.4.2.3

158. 6.4.2.4

159. 6.4.2.5

160. 6.4.2.6

161. 6.4.2.7

162. 6.4.3.1

163. 6.4.3.2

164. 6.4.3.3

165. 6.4.3.4

166. 6.4.3.5

167. 6.4.3.6

168. 6.4.3.7

169. 6.4.4.1

170. 6.4.4.2

171. 6.4.4.3

172. 6.4.4.4

173. 6.4.4.5

174. 6.4.4.6

175. 6.4.4.7

176. 6.4.5.1

177. 6.4.5.2

178. 6.4.5.3

179. 6.4.5.4

180. 6.4.5.5

181. 6.4.5.6

219. 6.5.4.2

220. 6.5.4.3

221. 6.5.4.4

222. 6.5.4.5

223. 6.5.4.6

224. 6.5.4.7

225. 6.5.5.1

226. 6.5.5.2

227. 6.5.5.3

228. 6.5.5.4

229. 6.5.5.5

230. 6.5.5.6

231. 6.5.5.7

232. 6.5.6.1

233. 6.5.6.2

234. 6.5.6.3

235. 6.5.6.4

236. 6.5.6.5

237. 6.5.6.6

238. 6.5.6.7

239. 6.5.7.1

240. 6.5.7.2

241. 6.5.7.3

242. 6.5.7.4

243. 6.5.7.5

244. 6.5.7.6

245. 6.5.7.7

246. 6.6.1.1

247. 6.6.1.2

248. 6.6.1.3

249. 6.6.1.4

250. 6.6.1.5

288. 6.6.7.1

289. 6.6.7.2

290. 6.6.7.3

291. 6.6.7.4

292. 6.6.7.5

293. 6.6.7.6

294. 6.6.7.7

295. 6.7.1.1

296. 6.7.1.2

297. 6.7.1.3

298. 6.7.1.4

299. 6.7.1.5

300. 6.7.1.6

301. 6.7.1.7

302. 6.7.2.1

303. 6.7.2.2

304. 6.7.2.3

305. 6.7.2.4

306. 6.7.2.5

307. 6.7.2.6

308. 6.7.2.7

309. 6.7.3.1

310. 6.7.3.2

311. 6.7.3.3

312. 6.7.3.4

313. 6.7.3.5

314. 6.7.3.6

315. 6.7.3.7

316. 6.7.4.1

317. 6.7.4.2

318. 6.7.4.3

319. 6.7.4.4

267

44. 6.1.7.2

45. 6.1.7.3

46. 6.1.7.4

47. 6.1.7.5

48. 6.1.7.6

49. 6.1.7.7

50. 6.2.1.1

51. 6.2.1.2

52. 6.2.1.3

53. 6.2.1.4

54. 6.2.1.5

55. 6.2.1.6

56. 6.2.1.7

57. 6.2.2.1

58. 6.2.2.2

59. 6.2.2.3

60. 6.2.2.4

61. 6.2.2.5

62. 6.2.2.6

63. 6.2.2.7

64. 6.2.3.1

65. 6.2.3.2

66. 6.2.3.3

67. 6.2.3.4

68. 6.2.3.5

69. 6.2.3.6

113. 6.3.3.1

114. 6.3.3.2

115. 6.3.3.3

116. 6.3.3.4

117. 6.3.3.5

118. 6.3.3.6

119. 6.3.3.7

120. 6.3.4.1

121. 6.3.4.2

122. 6.3.4.3

123. 6.3.4.4

124. 6.3.4.5

125. 6.3.4.6

126. 6.3.4.7

127. 6.3.5.1

128. 6.3.5.2

129. 6.3.5.3

130. 6.3.5.4

131. 6.3.5.5

132. 6.3.5.6

133. 6.3.5.7

134. 6.3.6.1

135. 6.3.6.2

136. 6.3.6.3

137. 6.3.6.4

138. 6.3.6.5

182. 6.4.5.7

183. 6.4.6.1

184. 6.4.6.2

185. 6.4.6.3

186. 6.4.6.4

187. 6.4.6.5

188. 6.4.6.6

189. 6.4.6.7

190. 6.4.7.1

191. 6.4.7.2

192. 6.4.7.3

193. 6.4.7.4

194. 6.4.7.5

195. 6.4.7.6

196. 6.4.7.7

197. 6.5.1.1

198. 6.5.1.2

199. 6.5.1.3

200. 6.5.1.4

201. 6.5.1.5

202. 6.5.1.6

203. 6.5.1.7

204. 6.5.2.1

205. 6.5.2.2

206. 6.5.2.3

207. 6.5.2.4

251. 6.6.1.6

252. 6.6.1.7

253. 6.6.2.1

254. 6.6.2.2

255. 6.6.2.3

256. 6.6.2.4

257. 6.6.2.5

258. 6.6.2.6

259. 6.6.2.7

260. 6.6.3.1

261. 6.6.3.2

262. 6.6.3.3

263. 6.6.3.4

264. 6.6.3.5

265. 6.6.3.6

266. 6.6.3.7

267. 6.6.4.1

268. 6.6.4.2

269. 6.6.4.3

270. 6.6.4.4

271. 6.6.4.5

272. 6.6.4.6

273. 6.6.4.7

274. 6.6.5.1

275. 6.6.5.2

276. 6.6.5.3

320. 6.7.4.5

321. 6.7.4.6

322. 6.7.4.7

323. 6.7.5.1

324. 6.7.5.2

325. 6.7.5.3

326. 6.7.5.4

327. 6.7.5.5

328. 6.7.5.6

329. 6.7.5.7

330. 6.7.6.1

331. 6.7.6.2

332. 6.7.6.3

333. 6.7.6.4

334. 6.7.6.5

335. 6.7.6.6

336. 6.7.6.7

337. 6.7.7.1

338. 6.7.7.2

339. 6.7.7.3

340. 6.7.7.4

341. 6.7.7.5

342. 6.7.7.6

343. 6.7.7.7

268





1. 7.1.1.1

2. 7.1.1.2

3. 7.1.1.3

4. 7.1.1.4

5. 7.1.1.5

6. 7.1.1.6

7. 7.1.1.7

8. 7.1.2.1

9. 7.1.2.2

10. 7.1.2.3

11. 7.1.2.4

12. 7.1.2.5

13. 7.1.2.6

14. 7.1.2.7

15. 7.1.3.1

16. 7.1.3.2

17. 7.1.3.3

18. 7.1.3.4

19. 7.1.3.5

20. 7.1.3.6

21. 7.1.3.7

22. 7.1.4.1

23. 7.1.4.2

24. 7.1.4.3

25. 7.1.4.4

26. 7.1.4.5

27. 7.1.4.6

70. 7.2.3.7

71. 7.2.4.1

72. 7.2.4.2

73. 7.2.4.3

74. 7.2.4.4

75. 7.2.4.5

76. 7.2.4.6

77. 7.2.4.7

78. 7.2.5.1

79. 7.2.5.2

80. 7.2.5.3

81. 7.2.5.4

82. 7.2.5.5

83. 7.2.5.6

84. 7.2.5.7

85. 7.2.6.1

86. 7.2.6.2

87. 7.2.6.3

88. 7.2.6.4

89. 7.2.6.5

90. 7.2.6.6

91. 7.2.6.7

92. 7.2.7.1

93. 7.2.7.2

94. 7.2.7.3

95. 7.2.7.4

96. 7.2.7.5

139. 7.3.6.6

140. 7.3.6.7

141. 7.3.7.1

142. 7.3.7.2

143. 7.3.7.3

144. 7.3.7.4

145. 7.3.7.5

146. 7.3.7.6

147. 7.3.7.7

148. 7.4.1.1

149. 7.4.1.2

150. 7.4.1.3

151. 7.4.1.4

152. 7.4.1.5

153. 7.4.1.6

154. 7.4.1.7

155. 7.4.2.1

156. 7.4.2.2

157. 7.4.2.3

158. 7.4.2.4

159. 7.4.2.5

160. 7.4.2.6

161. 7.4.2.7

162. 7.4.3.1

163. 7.4.3.2

164. 7.4.3.3

165. 7.4.3.4

208. 7.5.2.5

209. 7.5.2.6

210. 7.5.2.7

211. 7.5.3.1

212. 7.5.3.2

213. 7.5.3.3

214. 7.5.3.4

215. 7.5.3.5

216. 7.5.3.6

217. 7.5.3.7

218. 7.5.4.1

219. 7.5.4.2

220. 7.5.4.3

221. 7.5.4.4

222. 7.5.4.5

223. 7.5.4.6

224. 7.5.4.7

225. 7.5.5.1

226. 7.5.5.2

227. 7.5.5.3

228. 7.5.5.4

229. 7.5.5.5

230. 7.5.5.6

231. 7.5.5.7

232. 7.5.6.1

233. 7.5.6.2

234. 7.5.6.3

277. 7.6.5.4

278. 7.6.5.5

279. 7.6.5.6

280. 7.6.5.7

281. 7.6.6.1

282. 7.6.6.2

283. 7.6.6.3

284. 7.6.6.4

285. 7.6.6.5

286. 7.6.6.6

287. 7.6.6.7

288. 7.6.7.1

289. 7.6.7.2

290. 7.6.7.3

291. 7.6.7.4

292. 7.6.7.5

293. 7.6.7.6

294. 7.6.7.7

295. 7.7.1.1

296. 7.7.1.2

297. 7.7.1.3

298. 7.7.1.4

299. 7.7.1.5

300. 7.7.1.6

301. 7.7.1.7

302. 7.7.2.1

303. 7.7.2.2

269

28. 7.1.4.7

29. 7.1.5.1

30. 7.1.5.2

31. 7.1.5.3

32. 7.1.5.4

33. 7.1.5.5

34. 7.1.5.6

35. 7.1.5.7

36. 7.1.6.1

37. 7.1.6.2

38. 7.1.6.3

39. 7.1.6.4

40. 7.1.6.5

41. 7.1.6.6

42. 7.1.6.7

43. 7.1.7.1

44. 7.1.7.2

45. 7.1.7.3

46. 7.1.7.4

47. 7.1.7.5

48. 7.1.7.6

49. 7.1.7.7

50. 7.2.1.1

51. 7.2.1.2

52. 7.2.1.3

53. 7.2.1.4

54. 7.2.1.5

55. 7.2.1.6

56. 7.2.1.7

57. 7.2.2.1

58. 7.2.2.2

59. 7.2.2.3

97. 7.2.7.6

98. 7.2.7.7

99. 7.3.1.1

100. 7.3.1.2

101. 7.3.1.3

102. 7.3.1.4

103. 7.3.1.5

104. 7.3.1.6

105. 7.3.1.7

106. 7.3.2.1

107. 7.3.2.2

108. 7.3.2.3

109. 7.3.2.4

110. 7.3.2.5

111. 7.3.2.6

112. 7.3.2.7

113. 7.3.3.1

114. 7.3.3.2

115. 7.3.3.3

116. 7.3.3.4

117. 7.3.3.5

118. 7.3.3.6

119. 7.3.3.7

120. 7.3.4.1

121. 7.3.4.2

122. 7.3.4.3

123. 7.3.4.4

124. 7.3.4.5

125. 7.3.4.6

126. 7.3.4.7

127. 7.3.5.1

128. 7.3.5.2

166. 7.4.3.5

167. 7.4.3.6

168. 7.4.3.7

169. 7.4.4.1

170. 7.4.4.2

171. 7.4.4.3

172. 7.4.4.4

173. 7.4.4.5

174. 7.4.4.6

175. 7.4.4.7

176. 7.4.5.1

177. 7.4.5.2

178. 7.4.5.3

179. 7.4.5.4

180. 7.4.5.5

181. 7.4.5.6

182. 7.4.5.7

183. 7.4.6.1

184. 7.4.6.2

185. 7.4.6.3

186. 7.4.6.4

187. 7.4.6.5

188. 7.4.6.6

189. 7.4.6.7

190. 7.4.7.1

191. 7.4.7.2

192. 7.4.7.3

193. 7.4.7.4

194. 7.4.7.5

195. 7.4.7.6

196. 7.4.7.7

197. 7.5.1.1

235. 7.5.6.4

236. 7.5.6.5

237. 7.5.6.6

238. 7.5.6.7

239. 7.5.7.1

240. 7.5.7.2

241. 7.5.7.3

242. 7.5.7.4

243. 7.5.7.5

244. 7.5.7.6

245. 7.5.7.7

246. 7.6.1.1

247. 7.6.1.2

248. 7.6.1.3

249. 7.6.1.4

250. 7.6.1.5

251. 7.6.1.6

252. 7.6.1.7

253. 7.6.2.1

254. 7.6.2.2

255. 7.6.2.3

256. 7.6.2.4

257. 7.6.2.5

258. 7.6.2.6

259. 7.6.2.7

260. 7.6.3.1

261. 7.6.3.2

262. 7.6.3.3

263. 7.6.3.4

264. 7.6.3.5

265. 7.6.3.6

266. 7.6.3.7

304. 7.7.2.3

305. 7.7.2.4

306. 7.7.2.5

307. 7.7.2.6

308. 7.7.2.7

309. 7.7.3.1

310. 7.7.3.2

311. 7.7.3.3

312. 7.7.3.4

313. 7.7.3.5

314. 7.7.3.6

315. 7.7.3.7

316. 7.7.4.1

317. 7.7.4.2

318. 7.7.4.3

319. 7.7.4.4

320. 7.7.4.5

321. 7.7.4.6

322. 7.7.4.7

323. 7.7.5.1

324. 7.7.5.2

325. 7.7.5.3

326. 7.7.5.4

327. 7.7.5.5

328. 7.7.5.6

329. 7.7.5.7

330. 7.7.6.1

331. 7.7.6.2

332. 7.7.6.3

333. 7.7.6.4

334. 7.7.6.5

335. 7.7.6.6

270

60. 7.2.2.4

61. 7.2.2.5

62. 7.2.2.6

63. 7.2.2.7

64. 7.2.3.1

65. 7.2.3.2

66. 7.2.3.3

67. 7.2.3.4

68. 7.2.3.5

69. 7.2.3.6

129. 7.3.5.3

130. 7.3.5.4

131. 7.3.5.5

132. 7.3.5.6

133. 7.3.5.7

134. 7.3.6.1

135. 7.3.6.2

136. 7.3.6.3

137. 7.3.6.4

138. 7.3.6.5

198. 7.5.1.2

199. 7.5.1.3

200. 7.5.1.4

201. 7.5.1.5

202. 7.5.1.6

203. 7.5.1.7

204. 7.5.2.1

205. 7.5.2.2

206. 7.5.2.3

207. 7.5.2.4

267. 7.6.4.1

268. 7.6.4.2

269. 7.6.4.3

270. 7.6.4.4

271. 7.6.4.5

272. 7.6.4.6

273. 7.6.4.7

274. 7.6.5.1

275. 7.6.5.2

276. 7.6.5.3

336. 7.7.6.7

337. 7.7.7.1

338. 7.7.7.2

339. 7.7.7.3

340. 7.7.7.4

341. 7.7.7.5

342. 7.7.7.6

343. 7.7.7.7

6.4 Harmonic Structures

The following conceptual fields from Tables 6.9 to 6.15 contain 1,296 stylistic

elements. The first table features examples that begin with the chord of I, the second

table featuring examples that begin with the chord of ii and so on until chord vi is

reached.

Table 6.9 Potential harmonic structures in sets of three, relevant to one, two, four

or eight-bar segments of diatonic tunes in 2/2, 4/4, 2/4, 6/8.

Conceptual Field Harmonic Structures

Conceptual Resolution Three note possibilities

1. I.I.I

2. I.I.ii

3. I.I.iii

4. I.I.IV

5. I.I.V

6. I.I.vi

7. I.ii.I

8. I.ii.ii

44. ii.ii.ii 45. ii.ii.iii 46. ii.ii.IV

47. ii.ii.V

48. ii.ii.vi

49. ii.iii.I 50. ii.iii.ii 51. ii.iii.iii

87. iii.iii.iii

88. iii.iii.IV

89. iii.iii.V

90. iii.iii.vi

91. iii.IV.I

92. iii.IV.ii

93. iii.IV.iii

94. iii.IV.IV

130. IV.IV.IV

131. IV.IV.V

132. IV.IV.vi

133. IV.V.I

134. IV.V.ii

135. IV.V.iii

136. IV.V.IV

137. IV.V.V

173. V.V.V

174. V.V.vi

175. V.vi.I

176. V.vi.ii

177. V.vi.iii

178. V.vi.IV

179. V.vi.V

180. V.vi.vi

271

9. I.ii.iii

10. I.ii.IV

11. I.ii.V

12. I.ii.vi

13. I.iii.I 14. I.iii.ii 15. I.iii.iii 16. I.iii.IV

17. I.iii.V

18. I.iii.vi

19. I.IV.I

20. I.IV.ii

21. I.IV.iii

22. I.IV.IV

23. I.IV.V

24. I.IV.vi

25. I.V.I

26. I.V.ii

27. I.V.iii

28. I.V.IV

29. I.V.V

30. I.V.vi

31. I.vi.I

32. I.vi.ii

33. I.vi.iii

34. I.vi.IV

35. I.vi.V

36. I.vi.vi

37. ii.I.I 38. ii.I.ii 39. ii.I.iii 40. ii.I.IV

52. ii.iii.IV

53. ii.iii.V

54. ii.iii.vi

55. ii.IV.I

56. ii.IV.ii

57. ii.IV.iii

58. ii.IV.IV

59. ii.IV.V

60. ii.IV.vi

61. ii.V.I

62. ii.V.ii

63. ii.V.iii

64. ii.V.IV

65. ii.V.V

66. ii.V.vi

67. ii.vi.I

68. ii.vi.ii

69. ii.vi.iii

70. ii.vi.IV

71. ii.vi.V

72. ii.vi.vi

73. iii.I.I 74. iii.I.ii 75. iii.I.iii 76. iii.I.IV

77. iii.I.V

78. iii.I.vi

79. iii.ii.I 80. iii.ii.ii 81. iii.ii.iii 82. iii.ii.IV

83. iii.ii.V

95. iii.IV.V

96. iii.IV.vi

97. iii.V.I

98. iii.V.ii

99. iii.V.iii

100. iii.V.IV

101. iii.V.V

102. iii.V.vi

103. iii.vi.I

104. iii.vi.ii

105. iii.vi.iii

106. iii.vi.IV

107. iii.vi.V

108. iii.vi.vi

109. IV.I.I

110. IV.I.ii

111. IV.I.iii

112. IV.I.IV

113. IV.I.V

114. IV.I.vi

115. IV.ii.I

116. IV.ii.ii

117. IV.ii.iii

118. IV.ii.IV

119. IV.ii.V

120. IV.ii.vi

121. IV.iii.I

122. IV.iii.ii

123. IV.iii.iii

124. IV.iii.IV

125. IV.iii.V

126. IV.iii.vi

138. IV.V.vi

139. IV.vi.I

140. IV.vi.ii

141. IV.vi.iii

142. IV.vi.IV

143. IV.vi.V

144. IV.vi.vi

145. V.I.I

146. V.I.ii

147. V.I.iii

148. V.I.IV

149. V.I.V

150. V.I.vi

151. V.ii.I

152. V.ii.ii

153. V.ii.iii

154. V.ii.IV

155. V.ii.V

156. V.ii.vi

157. V.iii.I

158. V.iii.ii

159. V.iii.iii

160. V.iii.IV

161. V.iii.V

162. V.iii.vi

163. V.IV.I

164. V.IV.ii

165. V.IV.iii

166. V.IV.IV

167. V.IV.V

168. V.IV.vi

169. V.V.I

181. vi.I.I

182. vi.I.ii

183. vi.I.iii

184. vi.I.IV

185. vi.I.V

186. vi.I.vi

187. vi.ii.I

188. vi.ii.ii

189. vi.ii.iii

190. vi.ii.IV

191. vi.ii.V

192. vi.ii.vi

193. vi.iii.I

194. vi.iii.ii

195. vi.iii.iii

196. vi.iii.IV

197. vi.iii.V

198. vi.iii.vi

199. vi.IV.I

200. vi.IV.ii

201. vi.IV.iii

202. vi.IV.IV

203. vi.IV.V

204. vi.IV.vi

205. vi.V.I

206. vi.V.ii

207. vi.V.iii

208. vi.V.IV

209. vi.V.V

210. vi.V.vi

211. vi.vi.I

212. vi.vi.ii

272

41. ii.I.V

42. ii.I.vi

43. ii.ii.I

84. iii.ii.vi

85. iii.iii.I 86. iii.iii.ii

127. IV.IV.I

128. IV.IV.ii

129. IV.IV.iii

170. V.V.ii

171. V.V.iii

172. V.V.IV

213. vi.vi.iii

214. vi.vi.IV

215. vi.vi.V

216. vi.vi.vi

Table 6.10 Potential harmonic structures in sets of four beginning with chord I,

relevant to one, two, four or eight-bar segments of diatonic tunes in 2/2, 4/4, 2/4,

6/8.


Conceptual Resolution Sets of Four beginning with I

1. I.I.I.I

2. I.I.I.ii

3. I.I.I.iii

4. I.I.I.IV

5. I.I.I.V

6. I.I.I.vi

7. I.I.ii.I

8. I.I.ii.ii

9. I.I.ii.iii

10. I.I.ii.IV

11. I.I.ii.V

12. I.I.ii.vi

13. I.I.iii.I

14. I.I.iii.ii

15. I.I.iii.iii

16. I.I.iii.IV

17. I.I.iii.V

18. I.I.iii.vi

19. I.I.IV.I

20. I.I.IV.ii

44. I.ii.ii.ii 45. I.ii.ii.iii 46. I.ii.ii.IV

47. I.ii.ii.V

48. I.ii.ii.vi

49. I.ii.iii.I 50. I.ii.iii.ii 51. I.ii.iii.iii 52. I.ii.iii.IV

53. I.ii.iii.V

54. I.ii.iii.vi

55. I.ii.IV.I

56. I.ii.IV.ii

57. I.ii.IV.iii

58. I.ii.IV.IV

59. I.ii.IV.V

60. I.ii.IV.vi

61. I.ii.V.I

62. I.ii.V.ii

63. I.ii.V.iii

87. I.iii.iii.iii

88. I.iii.iii.IV

89. I.iii.iii.V

90. I.iii.iii.vi

91. I.iii.IV.I

92. I.iii.IV.ii

93. I.iii.IV.iii

94. I.iii.IV.IV

95. I.iii.IV.V

96. I.iii.IV.vi

97. I.iii.V.I

98. I.iii.V.ii

99. I.iii.V.iii

100. I.iii.V.IV

101. I.iii.V.V

102. I.iii.V.vi

103. I.iii.vi.I

104. I.iii.vi.ii

105. I.iii.vi.iii

106. I.iii.vi.IV

130. I.IV.IV.IV

131. I.IV.IV.V

132. I.IV.IV.vi

133. I.IV.V.I

134. I.IV.V.ii

135. I.IV.V.iii

136. I.IV.V.IV

137. I.IV.V.V

138. I.IV.V.vi

139. I.IV.vi.I

140. I.IV.vi.ii

141. I.IV.vi.iii

142. I.IV.vi.IV

143. I.IV.vi.V

144. I.IV.vi.vi

145. I.V.I.I

146. I.V.I.ii

147. I.V.I.iii

148. I.V.I.IV

149. I.V.I.V

173. I.V.V.V

174. I.V.V.vi

175. I.V.vi.I

176. I.V.vi.ii

177. I.V.vi.iii

178. I.V.vi.IV

179. I.V.vi.V

180. I.V.vi.vi

181. I.vi.I.I

182. I.vi.I.ii

183. I.vi.I.iii

184. I.vi.I.IV

185. I.vi.I.V

186. I.vi.I.vi

187. I.vi.ii.I

188. I.vi.ii.ii

189. I.vi.ii.iii

190. I.vi.ii.IV

191. I.vi.ii.V

192. I.vi.ii.vi

273

21. I.I.IV.iii

22. I.I.IV.IV

23. I.I.IV.V

24. I.I.IV.vi

25. I.I.V.I

26. I.I.V.ii

27. I.I.V.iii

28. I.I.V.IV

29. I.I.V.V

30. I.I.V.vi

31. I.I.vi.I

32. I.I.vi.ii

33. I.I.vi.iii

34. I.I.vi.IV

35. I.I.vi.V

36. I.I.vi.vi

37. I.ii.I.I

38. I.ii.I.ii

39. I.ii.I.iii

40. I.ii.I.IV

41. I.ii.I.V

42. I.ii.I.vi

43. I.ii.ii.I

64. I.ii.V.IV

65. I.ii.V.V

66. I.ii.V.vi

67. I.ii.vi.I

68. I.ii.vi.ii

69. I.ii.vi.iii

70. I.ii.vi.IV

71. I.ii.vi.V

72. I.ii.vi.vi

73. I.iii.I.I 74. I.iii.I.ii 75. I.iii.I.iii 76. I.iii.I.IV

77. I.iii.I.V

78. I.iii.I.vi

79. I.iii.ii.I 80. I.iii.ii.ii 81. I.iii.ii.iii 82. I.iii.ii.IV

83. I.iii.ii.V

84. I.iii.ii.vi

85. I.iii.iii.I 86. I.iii.iii.ii

107. I.iii.vi.V

108. I.iii.vi.vi

109. I.IV.I.I

110. I.IV.I.ii

111. I.IV.I.iii

112. I.IV.I.IV

113. I.IV.I.V

114. I.IV.I.vi

115. I.IV.ii.I

116. I.IV.ii.ii

117. I.IV.ii.iii

118. I.IV.ii.IV

119. I.IV.ii.V

120. I.IV.ii.vi

121. I.IV.iii.I

122. I.IV.iii.ii

123. I.IV.iii.iii

124. I.IV.iii.IV

125. I.IV.iii.V

126. I.IV.iii.vi

127. I.IV.IV.I

128. I.IV.IV.ii

129. I.IV.IV.iii

150. I.V.I.vi

151. I.V.ii.I

152. I.V.ii.ii

153. I.V.ii.iii

154. I.V.ii.IV

155. I.V.ii.V

156. I.V.ii.vi

157. I.V.iii.I

158. I.V.iii.ii

159. I.V.iii.iii

160. I.V.iii.IV

161. I.V.iii.V

162. I.V.iii.vi

163. I.V.IV.I

164. I.V.IV.ii

165. I.V.IV.iii

166. I.V.IV.IV

167. I.V.IV.V

168. I.V.IV.vi

169. I.V.V.I

170. I.V.V.ii

171. I.V.V.iii

172. I.V.V.IV

193. I.vi.iii.I

194. I.vi.iii.ii

195. I.vi.iii.iii

196. I.vi.iii.IV

197. I.vi.iii.V

198. I.vi.iii.vi

199. I.vi.IV.I

200. I.vi.IV.ii

201. I.vi.IV.iii

202. I.vi.IV.IV

203. I.vi.IV.V

204. I.vi.IV.vi

205. I.vi.V.I

206. I.vi.V.ii

207. I.vi.V.iii

208. I.vi.V.IV

209. I.vi.V.V

210. I.vi.V.vi

211. I.vi.vi.I

212. I.vi.vi.ii

213. I.vi.vi.iii

214. I.vi.vi.IV

215. I.vi.vi.V

216. I.vi.vi.vi

274

Table 6.11 Potential harmonic structures in sets of four beginning with chord ii, relevant

to one, two, four or eight-bar segments of diatonic tunes in 2/2, 4/4, 2/4, 6/8.


Conceptual Resolution Sets of Four beginning with ii

1. ii.I.I.I

2. ii.I.I.ii

3. ii.I.I.iii

4. ii.I.I.IV

5. ii.I.I.V

6. ii.I.I.vi

7. ii.I.ii.I

8. ii.I.ii.ii

9. ii.I.ii.iii

10. ii.I.ii.IV

11. ii.I.ii.V

12. ii.I.ii.vi

13. ii.I.iii.I

14. ii.I.iii.ii

15. ii.I.iii.iii

16. ii.I.iii.IV

17. ii.I.iii.V

18. ii.I.iii.vi

19. ii.I.IV.I

20. ii.I.IV.ii

21. ii.I.IV.iii

22. ii.I.IV.IV

23. ii.I.IV.V

24. ii.I.IV.vi

25. ii.I.V.I

26. ii.I.V.ii

27. ii.I.V.iii

44. ii.ii.ii.ii 45. ii.ii.ii.iii 46. ii.ii.ii.IV

47. ii.ii.ii.V

48. ii.ii.ii.vi

49. ii.ii.iii.I 50. ii.ii.iii.ii 51. ii.ii.iii.iii 52. ii.ii.iii.IV

53. ii.ii.iii.V

54. ii.ii.iii.vi

55. ii.ii.IV.I

56. ii.ii.IV.ii

57. ii.ii.IV.iii

58. ii.ii.IV.IV

59. ii.ii.IV.V

60. ii.ii.IV.vi

61. ii.ii.V.I

62. ii.ii.V.ii

63. ii.ii.V.iii

64. ii.ii.V.IV

65. ii.ii.V.V

66. ii.ii.V.vi

67. ii.ii.vi.I

68. ii.ii.vi.ii

69. ii.ii.vi.iii

70. ii.ii.vi.IV

87. ii.iii.iii.iii

88. ii.iii.iii.IV

89. ii.iii.iii.V

90. ii.iii.iii.vi

91. ii.iii.IV.I

92. ii.iii.IV.ii

93. ii.iii.IV.iii

94. ii.iii.IV.IV

95. ii.iii.IV.V

96. ii.iii.IV.vi

97. ii.iii.V.I

98. ii.iii.V.ii

99. ii.iii.V.iii

100. ii.iii.V.IV

101. ii.iii.V.V

102. ii.iii.V.vi

103. ii.iii.vi.I

104. ii.iii.vi.ii

105. ii.iii.vi.iii

106. ii.iii.vi.IV

107. ii.iii.vi.V

108. ii.iii.vi.vi

109. ii.IV.I.I

110. ii.IV.I.ii

111. ii.IV.I.iii

112. ii.IV.I.IV

113. ii.IV.I.V

130. ii.IV.IV.IV

131. ii.IV.IV.V

132. ii.IV.IV.vi

133. ii.IV.V.I

134. ii.IV.V.ii

135. ii.IV.V.iii

136. ii.IV.V.IV

137. ii.IV.V.V

138. ii.IV.V.vi

139. ii.IV.vi.I

140. ii.IV.vi.ii

141. ii.IV.vi.iii

142. ii.IV.vi.IV

143. ii.IV.vi.V

144. ii.IV.vi.vi

145. ii.V.I.I

146. ii.V.I.ii

147. ii.V.I.iii

148. ii.V.I.IV

149. ii.V.I.V

150. ii.V.I.vi

151. ii.V.ii.I

152. ii.V.ii.ii

153. ii.V.ii.iii

154. ii.V.ii.IV

155. ii.V.ii.V

156. ii.V.ii.vi

173. ii.V.V.V

174. ii.V.V.vi

175. ii.V.vi.I

176. ii.V.vi.ii

177. ii.V.vi.iii

178. ii.V.vi.IV

179. ii.V.vi.V

180. ii.V.vi.vi

181. ii.vi.I.I

182. ii.vi.I.ii

183. ii.vi.I.iii

184. ii.vi.I.IV

185. ii.vi.I.V

186. ii.vi.I.vi

187. ii.vi.ii.I

188. ii.vi.ii.ii

189. ii.vi.ii.iii

190. ii.vi.ii.IV

191. ii.vi.ii.V

192. ii.vi.ii.vi

193. ii.vi.iii.I

194. ii.vi.iii.ii

195. ii.vi.iii.iii

196. ii.vi.iii.IV

197. ii.vi.iii.V

198. ii.vi.iii.vi

199. ii.vi.IV.I

275

28. ii.I.V.IV

29. ii.I.V.V

30. ii.I.V.vi

31. ii.I.vi.I

32. ii.I.vi.ii

33. ii.I.vi.iii

34. ii.I.vi.IV

35. ii.I.vi.V

36. ii.I.vi.vi

37. ii.ii.I.I

38. ii.ii.I.ii

39. ii.ii.I.iii

40. ii.ii.I.IV

41. ii.ii.I.V

42. ii.ii.I.vi

43. ii.ii.ii.I

71. ii.ii.vi.V

72. ii.ii.vi.vi

73. ii.iii.I.I 74. ii.iii.I.ii 75. ii.iii.I.iii 76. ii.iii.I.IV

77. ii.iii.I.V

78. ii.iii.I.vi

79. ii.iii.ii.I 80. ii.iii.ii.ii 81. ii.iii.ii.iii 82. ii.iii.ii.IV

83. ii.iii.ii.V

84. ii.iii.ii.vi

85. ii.iii.iii.I 86. ii.iii.iii.ii

114. ii.IV.I.vi

115. ii.IV.ii.I

116. ii.IV.ii.ii

117. ii.IV.ii.iii

118. ii.IV.ii.IV

119. ii.IV.ii.V

120. ii.IV.ii.vi

121. ii.IV.iii.I

122. ii.IV.iii.ii

123. ii.IV.iii.iii

124. ii.IV.iii.IV

125. ii.IV.iii.V

126. ii.IV.iii.vi

127. ii.IV.IV.I

128. ii.IV.IV.ii

129. ii.IV.IV.iii

157. ii.V.iii.I

158. ii.V.iii.ii

159. ii.V.iii.iii

160. ii.V.iii.IV

161. ii.V.iii.V

162. ii.V.iii.vi

163. ii.V.IV.I

164. ii.V.IV.ii

165. ii.V.IV.iii

166. ii.V.IV.IV

167. ii.V.IV.V

168. ii.V.IV.vi

169. ii.V.V.I

170. ii.V.V.ii

171. ii.V.V.iii

172. ii.V.V.IV

200. ii.vi.IV.ii

201. ii.vi.IV.iii

202. ii.vi.IV.IV

203. ii.vi.IV.V

204. ii.vi.IV.vi

205. ii.vi.V.I

206. ii.vi.V.ii

207. ii.vi.V.iii

208. ii.vi.V.IV

209. ii.vi.V.V

210. ii.vi.V.vi

211. ii.vi.vi.I

212. ii.vi.vi.ii

213. ii.vi.vi.iii

214. ii.vi.vi.IV

215. ii.vi.vi.V

216. ii.vi.vi.vi

Table 6.12 Potential harmonic structures in sets of four beginning with chord iii,

relevant to one, two, four or eight-bar segments of diatonic tunes in 2/2, 4/4, 2/4, 6/8.


Conceptual Resolution Sets of Four beginning with iii

1. iii.I.I.I

2. iii.I.I.ii

3. iii.I.I.iii

4. iii.I.I.IV

5. iii.I.I.V

6. iii.I.I.vi

7. iii.I.ii.I

8. iii.I.ii.ii

44. iii.ii.ii.ii 45. iii.ii.ii.iii 46. iii.ii.ii.IV

47. iii.ii.ii.V

48. iii.ii.ii.vi

49. iii.ii.iii.I 50. iii.ii.iii.ii 51. iii.ii.iii.iii

87. iii.iii.iii.iii

88. iii.iii.iii.IV

89. iii.iii.iii.V

90. iii.iii.iii.vi

91. iii.iii.IV.I

92. iii.iii.IV.ii

93. iii.iii.IV.iii

94. iii.iii.IV.IV

130. iii.IV.IV.IV

131. iii.IV.IV.V

132. iii.IV.IV.vi

133. iii.IV.V.I

134. iii.IV.V.ii

135. iii.IV.V.iii

136. iii.IV.V.IV

137. iii.IV.V.V

173. iii.V.V.V

174. iii.V.V.vi

175. iii.V.vi.I

176. iii.V.vi.ii

177. iii.V.vi.iii

178. iii.V.vi.IV

179. iii.V.vi.V

180. iii.V.vi.vi

276

9. iii.I.ii.iii

10. iii.I.ii.IV

11. iii.I.ii.V

12. iii.I.ii.vi

13. iii.I.iii.I 14. iii.I.iii.ii 15. iii.I.iii.iii 16. iii.I.iii.IV

17. iii.I.iii.V

18. iii.I.iii.vi

19. iii.I.IV.I

20. iii.I.IV.ii

21. iii.I.IV.iii

22. iii.I.IV.IV

23. iii.I.IV.V

24. iii.I.IV.vi

25. iii.I.V.I

26. iii.I.V.ii

27. iii.I.V.iii

28. iii.I.V.IV

29. iii.I.V.V

30. iii.I.V.vi

31. iii.I.vi.I

32. iii.I.vi.ii

33. iii.I.vi.iii

34. iii.I.vi.IV

35. iii.I.vi.V

36. iii.I.vi.vi

37. iii.ii.I.I 38. iii.ii.I.ii 39. iii.ii.I.iii 40. iii.ii.I.IV

52. iii.ii.iii.IV

53. iii.ii.iii.V

54. iii.ii.iii.vi

55. iii.ii.IV.I

56. iii.ii.IV.ii

57. iii.ii.IV.iii

58. iii.ii.IV.IV

59. iii.ii.IV.V

60. iii.ii.IV.vi

61. iii.ii.V.I

62. iii.ii.V.ii

63. iii.ii.V.iii

64. iii.ii.V.IV

65. iii.ii.V.V

66. iii.ii.V.vi

67. iii.ii.vi.I

68. iii.ii.vi.ii

69. iii.ii.vi.iii

70. iii.ii.vi.IV

71. iii.ii.vi.V

72. iii.ii.vi.vi

73. iii.iii.I.I 74. iii.iii.I.ii 75. iii.iii.I.iii 76. iii.iii.I.IV

77. iii.iii.I.V

78. iii.iii.I.vi

79. iii.iii.ii.I 80. iii.iii.ii.ii 81. iii.iii.ii.iii 82. iii.iii.ii.IV

83. iii.iii.ii.V

95. iii.iii.IV.V

96. iii.iii.IV.vi

97. iii.iii.V.I

98. iii.iii.V.ii

99. iii.iii.V.iii

100. iii.iii.V.IV

101. iii.iii.V.V

102. iii.iii.V.vi

103. iii.iii.vi.I

104. iii.iii.vi.ii

105. iii.iii.vi.iii

106. iii.iii.vi.IV

107. iii.iii.vi.V

108. iii.iii.vi.vi

109. iii.IV.I.I

110. iii.IV.I.ii

111. iii.IV.I.iii

112. iii.IV.I.IV

113. iii.IV.I.V

114. iii.IV.I.vi

115. iii.IV.ii.I

116. iii.IV.ii.ii

117. iii.IV.ii.iii

118. iii.IV.ii.IV

119. iii.IV.ii.V

120. iii.IV.ii.vi

121. iii.IV.iii.I

122. iii.IV.iii.ii

123. iii.IV.iii.iii

124. iii.IV.iii.IV

125. iii.IV.iii.V

126. iii.IV.iii.vi

138. iii.IV.V.vi

139. iii.IV.vi.I

140. iii.IV.vi.ii

141. iii.IV.vi.iii

142. iii.IV.vi.IV

143. iii.IV.vi.V

144. iii.IV.vi.vi

145. iii.V.I.I

146. iii.V.I.ii

147. iii.V.I.iii

148. iii.V.I.IV

149. iii.V.I.V

150. iii.V.I.vi

151. iii.V.ii.I

152. iii.V.ii.ii

153. iii.V.ii.iii

154. iii.V.ii.IV

155. iii.V.ii.V

156. iii.V.ii.vi

157. iii.V.iii.I

158. iii.V.iii.ii

159. iii.V.iii.iii

160. iii.V.iii.IV

161. iii.V.iii.V

162. iii.V.iii.vi

163. iii.V.IV.I

164. iii.V.IV.ii

165. iii.V.IV.iii

166. iii.V.IV.IV

167. iii.V.IV.V

168. iii.V.IV.vi

169. iii.V.V.I

181. iii.vi.I.I

182. iii.vi.I.ii

183. iii.vi.I.iii

184. iii.vi.I.IV

185. iii.vi.I.V

186. iii.vi.I.vi

187. iii.vi.ii.I

188. iii.vi.ii.ii

189. iii.vi.ii.iii

190. iii.vi.ii.IV

191. iii.vi.ii.V

192. iii.vi.ii.vi

193. iii.vi.iii.I

194. iii.vi.iii.ii

195. iii.vi.iii.iii

196. iii.vi.iii.IV

197. iii.vi.iii.V

198. iii.vi.iii.vi

199. iii.vi.IV.I

200. iii.vi.IV.ii

201. iii.vi.IV.iii

202. iii.vi.IV.IV

203. iii.vi.IV.V

204. iii.vi.IV.vi

205. iii.vi.V.I

206. iii.vi.V.ii

207. iii.vi.V.iii

208. iii.vi.V.IV

209. iii.vi.V.V

210. iii.vi.V.vi

211. iii.vi.vi.I

212. iii.vi.vi.ii

277

41. iii.ii.I.V

42. iii.ii.I.vi

43. iii.ii.ii.I

84. iii.iii.ii.vi

85. iii.iii.iii.I 86. iii.iii.iii.ii

127. iii.IV.IV.I

128. iii.IV.IV.ii

129. iii.IV.IV.iii

170. iii.V.V.ii

171. iii.V.V.iii

172. iii.V.V.IV

213. iii.vi.vi.iii

214. iii.vi.vi.IV

215. iii.vi.vi.V

216. iii.vi.vi.vi

Table 6.13 Potential harmonic structures in sets of four beginning with chord IV,



Conceptual Resolution Sets of Four beginning with IV

1. IV.I.I.I

2. IV.I.I.ii

3. IV.I.I.iii

4. IV.I.I.IV

5. IV.I.I.V

6. IV.I.I.vi

7. IV.I.ii.I

8. IV.I.ii.ii

9. IV.I.ii.iii

10. IV.I.ii.IV

11. IV.I.ii.V

12. IV.I.ii.vi

13. IV.I.iii.I

14. IV.I.iii.ii

15. IV.I.iii.iii

16. IV.I.iii.IV

17. IV.I.iii.V

18. IV.I.iii.vi

19. IV.I.IV.I

20. IV.I.IV.ii

44. IV.ii.ii.ii

45. IV.ii.ii.iii

46. IV.ii.ii.IV

47. IV.ii.ii.V

48. IV.ii.ii.vi

49. IV.ii.iii.I

50. IV.ii.iii.ii

51. IV.ii.iii.iii

52. IV.ii.iii.IV

53. IV.ii.iii.V

54. IV.ii.iii.vi

55. IV.ii.IV.I

56. IV.ii.IV.ii

57. IV.ii.IV.iii

58. IV.ii.IV.IV

59. IV.ii.IV.V

60. IV.ii.IV.vi

61. IV.ii.V.I

62. IV.ii.V.ii

63. IV.ii.V.iii

87. IV.iii.iii.iii

88. IV.iii.iii.IV

89. IV.iii.iii.V

90. IV.iii.iii.vi

91. IV.iii.IV.I

92. IV.iii.IV.ii

93. IV.iii.IV.iii

94. IV.iii.IV.IV

95. IV.iii.IV.V

96. IV.iii.IV.vi

97. IV.iii.V.I

98. IV.iii.V.ii

99. IV.iii.V.iii

100. IV.iii.V.IV

101. IV.iii.V.V

102. IV.iii.V.vi

103. IV.iii.vi.I

104. IV.iii.vi.ii

105. IV.iii.vi.iii

106. IV.iii.vi.IV

130. IV.IV.IV.IV

131. IV.IV.IV.V

132. IV.IV.IV.vi

133. IV.IV.V.I

134. IV.IV.V.ii

135. IV.IV.V.iii

136. IV.IV.V.IV

137. IV.IV.V.V

138. IV.IV.V.vi

139. IV.IV.vi.I

140. IV.IV.vi.ii

141. IV.IV.vi.iii

142. IV.IV.vi.IV

143. IV.IV.vi.V

144. IV.IV.vi.vi

145. IV.V.I.I

146. IV.V.I.ii

147. IV.V.I.iii

148. IV.V.I.IV

149. IV.V.I.V

173. IV.V.V.V

174. IV.V.V.vi

175. IV.V.vi.I

176. IV.V.vi.ii

177. IV.V.vi.iii

178. IV.V.vi.IV

179. IV.V.vi.V

180. IV.V.vi.vi

181. IV.vi.I.I

182. IV.vi.I.ii

183. IV.vi.I.iii

184. IV.vi.I.IV

185. IV.vi.I.V

186. IV.vi.I.vi

187. IV.vi.ii.I

188. IV.vi.ii.ii

189. IV.vi.ii.iii

190. IV.vi.ii.IV

191. IV.vi.ii.V

192. IV.vi.ii.vi

278

21. IV.I.IV.iii

22. IV.I.IV.IV

23. IV.I.IV.V

24. IV.I.IV.vi

25. IV.I.V.I

26. IV.I.V.ii

27. IV.I.V.iii

28. IV.I.V.IV

29. IV.I.V.V

30. IV.I.V.vi

31. IV.I.vi.I

32. IV.I.vi.ii

33. IV.I.vi.iii

34. IV.I.vi.IV

35. IV.I.vi.V

36. IV.I.vi.vi

37. IV.ii.I.I

38. IV.ii.I.ii

39. IV.ii.I.iii

40. IV.ii.I.IV

41. IV.ii.I.V

42. IV.ii.I.vi

43. IV.ii.ii.I

64. IV.ii.V.IV

65. IV.ii.V.V

66. IV.ii.V.vi

67. IV.ii.vi.I

68. IV.ii.vi.ii

69. IV.ii.vi.iii

70. IV.ii.vi.IV

71. IV.ii.vi.V

72. IV.ii.vi.vi

73. IV.iii.I.I

74. IV.iii.I.ii

75. IV.iii.I.iii

76. IV.iii.I.IV

77. IV.iii.I.V

78. IV.iii.I.vi

79. IV.iii.ii.I

80. IV.iii.ii.ii

81. IV.iii.ii.iii

82. IV.iii.ii.IV

83. IV.iii.ii.V

84. IV.iii.ii.vi

85. IV.iii.iii.I

86. IV.iii.iii.ii

107. IV.iii.vi.V

108. IV.iii.vi.vi

109. IV.IV.I.I

110. IV.IV.I.ii

111. IV.IV.I.iii

112. IV.IV.I.IV

113. IV.IV.I.V

114. IV.IV.I.vi

115. IV.IV.ii.I

116. IV.IV.ii.ii

117. IV.IV.ii.iii

118. IV.IV.ii.IV

119. IV.IV.ii.V

120. IV.IV.ii.vi

121. IV.IV.iii.I

122. IV.IV.iii.ii

123. IV.IV.iii.iii

124. IV.IV.iii.IV

125. IV.IV.iii.V

126. IV.IV.iii.vi

127. IV.IV.IV.I

128. IV.IV.IV.ii

129. IV.IV.IV.iii

150. IV.V.I.vi

151. IV.V.ii.I

152. IV.V.ii.ii

153. IV.V.ii.iii

154. IV.V.ii.IV

155. IV.V.ii.V

156. IV.V.ii.vi

157. IV.V.iii.I

158. IV.V.iii.ii

159. IV.V.iii.iii

160. IV.V.iii.IV

161. IV.V.iii.V

162. IV.V.iii.vi

163. IV.V.IV.I

164. IV.V.IV.ii

165. IV.V.IV.iii

166. IV.V.IV.IV

167. IV.V.IV.V

168. IV.V.IV.vi

169. IV.V.V.I

170. IV.V.V.ii

171. IV.V.V.iii

172. IV.V.V.IV

193. IV.vi.iii.I

194. IV.vi.iii.ii

195. IV.vi.iii.iii

196. IV.vi.iii.IV

197. IV.vi.iii.V

198. IV.vi.iii.vi

199. IV.vi.IV.I

200. IV.vi.IV.ii

201. IV.vi.IV.iii

202. IV.vi.IV.IV

203. IV.vi.IV.V

204. IV.vi.IV.vi

205. IV.vi.V.I

206. IV.vi.V.ii

207. IV.vi.V.iii

208. IV.vi.V.IV

209. IV.vi.V.V

210. IV.vi.V.vi

211. IV.vi.vi.I

212. IV.vi.vi.ii

213. IV.vi.vi.iii

214. IV.vi.vi.IV

215. IV.vi.vi.V

216. IV.vi.vi.vi

279

Table 6.14 Potential harmonic structures in sets of four beginning with chord V,



Conceptual Resolution Sets of Four beginning with V

1. V.I.I.I

2. V.I.I.ii

3. V.I.I.iii

4. V.I.I.IV

5. V.I.I.V

6. V.I.I.vi

7. V.I.ii.I

8. V.I.ii.ii

9. V.I.ii.iii

10. V.I.ii.IV

11. V.I.ii.V

12. V.I.ii.vi

13. V.I.iii.I

14. V.I.iii.ii

15. V.I.iii.iii

16. V.I.iii.IV

17. V.I.iii.V

18. V.I.iii.vi

19. V.I.IV.I

20. V.I.IV.ii

21. V.I.IV.iii

22. V.I.IV.IV

23. V.I.IV.V

24. V.I.IV.vi

25. V.I.V.I

26. V.I.V.ii

44. V.ii.ii.ii

45. V.ii.ii.iii

46. V.ii.ii.IV

47. V.ii.ii.V

48. V.ii.ii.vi

49. V.ii.iii.I

50. V.ii.iii.ii

51. V.ii.iii.iii

52. V.ii.iii.IV

53. V.ii.iii.V

54. V.ii.iii.vi

55. V.ii.IV.I

56. V.ii.IV.ii

57. V.ii.IV.iii

58. V.ii.IV.IV

59. V.ii.IV.V

60. V.ii.IV.vi

61. V.ii.V.I

62. V.ii.V.ii

63. V.ii.V.iii

64. V.ii.V.IV

65. V.ii.V.V

66. V.ii.V.vi

67. V.ii.vi.I

68. V.ii.vi.ii

69. V.ii.vi.iii

87. V.iii.iii.iii

88. V.iii.iii.IV

89. V.iii.iii.V

90. V.iii.iii.vi

91. V.iii.IV.I

92. V.iii.IV.ii

93. V.iii.IV.iii

94. V.iii.IV.IV

95. V.iii.IV.V

96. V.iii.IV.vi

97. V.iii.V.I

98. V.iii.V.ii

99. V.iii.V.iii

100. V.iii.V.IV

101. V.iii.V.V

102. V.iii.V.vi

103. V.iii.vi.I

104. V.iii.vi.ii

105. V.iii.vi.iii

106. V.iii.vi.IV

107. V.iii.vi.V

108. V.iii.vi.vi

109. V.IV.I.I

110. V.IV.I.ii

111. V.IV.I.iii

112. V.IV.I.IV

130. V.IV.IV.IV

131. V.IV.IV.V

132. V.IV.IV.vi

133. V.IV.V.I

134. V.IV.V.ii

135. V.IV.V.iii

136. V.IV.V.IV

137. V.IV.V.V

138. V.IV.V.vi

139. V.IV.vi.I

140. V.IV.vi.ii

141. V.IV.vi.iii

142. V.IV.vi.IV

143. V.IV.vi.V

144. V.IV.vi.vi

145. V.V.I.I

146. V.V.I.ii

147. V.V.I.iii

148. V.V.I.IV

149. V.V.I.V

150. V.V.I.vi

151. V.V.ii.I

152. V.V.ii.ii

153. V.V.ii.iii

154. V.V.ii.IV

155. V.V.ii.V

173. V.V.V.V

174. V.V.V.vi

175. V.V.vi.I

176. V.V.vi.ii

177. V.V.vi.iii

178. V.V.vi.IV

179. V.V.vi.V

180. V.V.vi.vi

181. V.vi.I.I

182. V.vi.I.ii

183. V.vi.I.iii

184. V.vi.I.IV

185. V.vi.I.V

186. V.vi.I.vi

187. V.vi.ii.I

188. V.vi.ii.ii

189. V.vi.ii.iii

190. V.vi.ii.IV

191. V.vi.ii.V

192. V.vi.ii.vi

193. V.vi.iii.I

194. V.vi.iii.ii

195. V.vi.iii.iii

196. V.vi.iii.IV

197. V.vi.iii.V

198. V.vi.iii.vi

280

27. V.I.V.iii

28. V.I.V.IV

29. V.I.V.V

30. V.I.V.vi

31. V.I.vi.I

32. V.I.vi.ii

33. V.I.vi.iii

34. V.I.vi.IV

35. V.I.vi.V

36. V.I.vi.vi

37. V.ii.I.I

38. V.ii.I.ii

39. V.ii.I.iii

40. V.ii.I.IV

41. V.ii.I.V

42. V.ii.I.vi

43. V.ii.ii.I

70. V.ii.vi.IV

71. V.ii.vi.V

72. V.ii.vi.vi

73. V.iii.I.I

74. V.iii.I.ii

75. V.iii.I.iii

76. V.iii.I.IV

77. V.iii.I.V

78. V.iii.I.vi

79. V.iii.ii.I

80. V.iii.ii.ii

81. V.iii.ii.iii

82. V.iii.ii.IV

83. V.iii.ii.V

84. V.iii.ii.vi

85. V.iii.iii.I

86. V.iii.iii.ii

113. V.IV.I.V

114. V.IV.I.vi

115. V.IV.ii.I

116. V.IV.ii.ii

117. V.IV.ii.iii

118. V.IV.ii.IV

119. V.IV.ii.V

120. V.IV.ii.vi

121. V.IV.iii.I

122. V.IV.iii.ii

123. V.IV.iii.iii

124. V.IV.iii.IV

125. V.IV.iii.V

126. V.IV.iii.vi

127. V.IV.IV.I

128. V.IV.IV.ii

129. V.IV.IV.iii

156. V.V.ii.vi

157. V.V.iii.I

158. V.V.iii.ii

159. V.V.iii.iii

160. V.V.iii.IV

161. V.V.iii.V

162. V.V.iii.vi

163. V.V.IV.I

164. V.V.IV.ii

165. V.V.IV.iii

166. V.V.IV.IV

167. V.V.IV.V

168. V.V.IV.vi

169. V.V.V.I

170. V.V.V.ii

171. V.V.V.iii

172. V.V.V.IV

199. V.vi.IV.I

200. V.vi.IV.ii

201. V.vi.IV.iii

202. V.vi.IV.IV

203. V.vi.IV.V

204. V.vi.IV.vi

205. V.vi.V.I

206. V.vi.V.ii

207. V.vi.V.iii

208. V.vi.V.IV

209. V.vi.V.V

210. V.vi.V.vi

211. V.vi.vi.I

212. V.vi.vi.ii

213. V.vi.vi.iii

214. V.vi.vi.IV

215. V.vi.vi.V

216. V.vi.vi.vi

Table 6.15 Potential harmonic structures in sets of four beginning with chord vi,



Conceptual Resolution Sets of Four beginning with vi

1. vi.I.I.I

2. vi.I.I.ii

3. vi.I.I.iii

4. vi.I.I.IV

5. vi.I.I.V

6. vi.I.I.vi

7. vi.I.ii.I

44. vi.ii.ii.ii

45. vi.ii.ii.iii

46. vi.ii.ii.IV

47. vi.ii.ii.V

48. vi.ii.ii.vi

49. vi.ii.iii.I

50. vi.ii.iii.ii

87. vi.iii.iii.iii

88. vi.iii.iii.IV

89. vi.iii.iii.V

90. vi.iii.iii.vi

91. vi.iii.IV.I

92. vi.iii.IV.ii

93. vi.iii.IV.iii

130. vi.IV.IV.IV

131. vi.IV.IV.V

132. vi.IV.IV.vi

133. vi.IV.V.I

134. vi.IV.V.ii

135. vi.IV.V.iii

136. vi.IV.V.IV

173. vi.V.V.V

174. vi.V.V.vi

175. vi.V.vi.I

176. vi.V.vi.ii

177. vi.V.vi.iii

178. vi.V.vi.IV

179. vi.V.vi.V

281

8. vi.I.ii.ii

9. vi.I.ii.iii

10. vi.I.ii.IV

11. vi.I.ii.V

12. vi.I.ii.vi

13. vi.I.iii.I

14. vi.I.iii.ii

15. vi.I.iii.iii

16. vi.I.iii.IV

17. vi.I.iii.V

18. vi.I.iii.vi

19. vi.I.IV.I

20. vi.I.IV.ii

21. vi.I.IV.iii

22. vi.I.IV.IV

23. vi.I.IV.V

24. vi.I.IV.vi

25. vi.I.V.I

26. vi.I.V.ii

27. vi.I.V.iii

28. vi.I.V.IV

29. vi.I.V.V

30. vi.I.V.vi

31. vi.I.vi.I

32. vi.I.vi.ii

33. vi.I.vi.iii

34. vi.I.vi.IV

35. vi.I.vi.V

36. vi.I.vi.vi

37. vi.ii.I.I

38. vi.ii.I.ii

39. vi.ii.I.iii

51. vi.ii.iii.iii

52. vi.ii.iii.IV

53. vi.ii.iii.V

54. vi.ii.iii.vi

55. vi.ii.IV.I

56. vi.ii.IV.ii

57. vi.ii.IV.iii

58. vi.ii.IV.IV

59. vi.ii.IV.V

60. vi.ii.IV.vi

61. vi.ii.V.I

62. vi.ii.V.ii

63. vi.ii.V.iii

64. vi.ii.V.IV

65. vi.ii.V.V

66. vi.ii.V.vi

67. vi.ii.vi.I

68. vi.ii.vi.ii

69. vi.ii.vi.iii

70. vi.ii.vi.IV

71. vi.ii.vi.V

72. vi.ii.vi.vi

73. vi.iii.I.I

74. vi.iii.I.ii

75. vi.iii.I.iii

76. vi.iii.I.IV

77. vi.iii.I.V

78. vi.iii.I.vi

79. vi.iii.ii.I

80. vi.iii.ii.ii

81. vi.iii.ii.iii

82. vi.iii.ii.IV

94. vi.iii.IV.IV

95. vi.iii.IV.V

96. vi.iii.IV.vi

97. vi.iii.V.I

98. vi.iii.V.ii

99. vi.iii.V.iii

100. vi.iii.V.IV

101. vi.iii.V.V

102. vi.iii.V.vi

103. vi.iii.vi.I

104. vi.iii.vi.ii

105. vi.iii.vi.iii

106. vi.iii.vi.IV

107. vi.iii.vi.V

108. vi.iii.vi.vi

109. vi.IV.I.I

110. vi.IV.I.ii

111. vi.IV.I.iii

112. vi.IV.I.IV

113. vi.IV.I.V

114. vi.IV.I.vi

115. vi.IV.ii.I

116. vi.IV.ii.ii

117. vi.IV.ii.iii

118. vi.IV.ii.IV

119. vi.IV.ii.V

120. vi.IV.ii.vi

121. vi.IV.iii.I

122. vi.IV.iii.ii

123. vi.IV.iii.iii

124. vi.IV.iii.IV

125. vi.IV.iii.V

137. vi.IV.V.V

138. vi.IV.V.vi

139. vi.IV.vi.I

140. vi.IV.vi.ii

141. vi.IV.vi.iii

142. vi.IV.vi.IV

143. vi.IV.vi.V

144. vi.IV.vi.vi

145. vi.V.I.I

146. vi.V.I.ii

147. vi.V.I.iii

148. vi.V.I.IV

149. vi.V.I.V

150. vi.V.I.vi

151. vi.V.ii.I

152. vi.V.ii.ii

153. vi.V.ii.iii

154. vi.V.ii.IV

155. vi.V.ii.V

156. vi.V.ii.vi

157. vi.V.iii.I

158. vi.V.iii.ii

159. vi.V.iii.iii

160. vi.V.iii.IV

161. vi.V.iii.V

162. vi.V.iii.vi

163. vi.V.IV.I

164. vi.V.IV.ii

165. vi.V.IV.iii

166. vi.V.IV.IV

167. vi.V.IV.V

168. vi.V.IV.vi

180. vi.V.vi.vi

181. vi.vi.I.I

182. vi.vi.I.ii

183. vi.vi.I.iii

184. vi.vi.I.IV

185. vi.vi.I.V

186. vi.vi.I.vi

187. vi.vi.ii.I

188. vi.vi.ii.ii

189. vi.vi.ii.iii

190. vi.vi.ii.IV

191. vi.vi.ii.V

192. vi.vi.ii.vi

193. vi.vi.iii.I

194. vi.vi.iii.ii

195. vi.vi.iii.iii

196. vi.vi.iii.IV

197. vi.vi.iii.V

198. vi.vi.iii.vi

199. vi.vi.IV.I

200. vi.vi.IV.ii

201. vi.vi.IV.iii

202. vi.vi.IV.IV

203. vi.vi.IV.V

204. vi.vi.IV.vi

205. vi.vi.V.I

206. vi.vi.V.ii

207. vi.vi.V.iii

208. vi.vi.V.IV

209. vi.vi.V.V

210. vi.vi.V.vi

211. vi.vi.vi.I

282

40. vi.ii.I.IV

41. vi.ii.I.V

42. vi.ii.I.vi

43. vi.ii.ii.I

83. vi.iii.ii.V

84. vi.iii.ii.vi

85. vi.iii.iii.I

86. vi.iii.iii.ii

126. vi.IV.iii.vi

127. vi.IV.IV.I

128. vi.IV.IV.ii

129. vi.IV.IV.iii

169. vi.V.V.I

170. vi.V.V.ii

171. vi.V.V.iii

172. vi.V.V.IV

212. vi.vi.vi.ii

213. vi.vi.vi.iii

214. vi.vi.vi.IV

215. vi.vi.vi.V

216. vi.vi.vi.vi

6.5 Styles of Harmony

While it was found that melodic construction or variation based on harmonic structures

is not documented in the literature, styles of harmonising a tune are described. Of these,

drones have been in use for quite some time as a feature of piping.56 The use of dyads is

probably a more recent style and describes chords that use only two pitches, most often

the root and fifth. These are often called ‘power chords’ and are associated with

‘supergroups’ such as Altan and the Bothy Band who may be credited with their

introduction. Triads are perhaps the most common type of homophonic accompaniment

and use three notes: the root, third and fifth, in any inversion. Accordion bass buttons

contain triads, which can be sounded on the depression of a single button. Triads are

also used in the type of piano accompaniment that is associated with the céilí band style.

Extended diatonic harmony describes the use of sevenths (major and minor), ninths,

(usually major) and more unusually, elevenths and thirteenths. This type of harmony is

much rarer and recent and is found in the playing of contemporary musicians such as

Mícheál Ó Súilleabháin and David Flynn, both of whom have studied classical and jazz

music. As stated earlier, chromatic harmony is a relatively rare feature in Irish

traditional music but since it is occasionally found in some compositions, it is included

as an option below. At the same time however, it is not worth the level of exploration

that comes with permutations because such a large number of options would yield

examples that would likely never occur in practice. Furthermore, extended chromatic

56 Although it is worth noting that drone-use in piping is often employed indiscriminately with regard to

the home-note of a tune and so volume and texture rather than harmonisation may be the more salient conceptual fields in this regard.

283

harmony is much rarer and involves the extension of chromatic chords in the same

manner as the extension of diatonic harmony as explained above.

Tertian harmony moves either at a third above or a sixth below the melody. It is

relatively common in ‘chamber’ arrangements of Irish traditional music but is used

sparingly. It can be heard as a subtle feature in the final tune, ‘Fintan McManus’s’ on

Altan’s Island Angel album.57 Quartal and quintal harmony involves moving in parallel

fourths or fifths respectively. It is much rarer again but one such example of its use can

be found in the opening section of Mícheál Ó Súilleabháin’s arrangement of ‘Christmas

Eve’.58 Parallel octaves are a staple feature of the fiddle music associated with

Southwest Donegal and Co. Kerry but are also used, albeit sparingly, in concertina

playing. Finally, counterpoint was popularised by members of the band Planxty and is

associated with the bouzouki and mandolin in this case. Other musicians, notably the

fiddler Ciaran Tourish (1967– ) use it occasionally in arrangements with the band Altan.

Table 6.16 Harmonic styles observed in the tradition.

Conceptual Field Harmonic Styles

Conceptual Resolution From observation

1. Drones/ single bass notes (Homophonic)

2. Dyads (Homophonic)

3. Triads (Homophonic)

4. Extended diatonic harmony (Homophonic)

5. Chromatic Harmony (Homophonic)

6. Extended Chromatic Harmony (Homophonic)

7. Tertian (Polyphonic)

8. Quartal/ Quintal (Polyphonic)

9. Parallel Octaves (Polyphonic)

10. Counterpoint

57 Altan: Island Angel, (Danbury, CT: Green Linnet, 1993), track 1. 58 Mícheál Ó Súilleabháin: Between Worlds, (London: Virgin Records, 1995), track 1.

284

6.6 Motivic Development and Variation

As noted in Section 6.1, motifs can be developed in a variety of ways. When these are

analysed, the following, as illustrated in Table 6.17, are possible.

1. Retrograde Pitch using the same rhythm

2. Retrograde Rhythm using the same pitches

3. Retrograde Pitch and Rhythm

4. Pitch Variation – on the strong or weak beats or both

5. Rhythmic Variation

6. Pitch and Rhythmic Variation

7. Retrograde Pitch and Rhythmic Variation

8. Retrograde Rhythmic and Pitch Variation

9. Transposition, usually within the same mode – as is evident in the fourth part of

the reel ‘Farewell to Ireland’, a detailed explanation of which may be found in

Ex. 7.4 of Chapter Seven.59

In some cases, passing notes can be added to the motif as diminutions of existing notes

but this is really a form of ornamentation and so further discussion on this aspect is left

to Chapter Nine. Although the observations of both Ó Canainn and Ó Riada amongst

others are based upon the slow air tune-type and the development of the three-note

motif at the beginning of a tune, as evidenced by Robert Harvey, this can equally apply

to other small motifs elsewhere in the tune and in the dance music genre.

59 See Chapter Seven, 294-295.

285

Table 6.17 Nine approaches to motivic development.

Conceptual Field Motivic Development

Conceptual Resolution One Bar Examples

6.7 Compass/ Range

Compass or range describes the interval created between the lowest and highest notes

that are either possible on an instrument or found in a piece.60 In this case, it is

understood to be the range utilised within a tune. Breathnach states that ‘the vast

majority of airs have a range varying from nine to eleven notes. Scarcely any exceed a

range of thirteen notes, and few have less than an octave’.61 Although it is unclear as to

whether he is referring to song airs or instrumental airs, from my own experience of the

tradition, it would seem that his comment applies to both types. He goes on to point out

‘one freak’ that contains only two notes.62

60 Rushton. Julian: ‘Range [Compass]’, Grove Music Online. http://0-

www.oxfordmusiconline.com.ditlib.dit.ie:80/subscriber/article/grove/music/22879 (Accessed 21 March 2012).

61 Breathnach: Folk Music and Dances of Ireland, 14. 62 Ibid. This is a reference to the tune or rather, or ‘school boy chant’ entitled ‘Harry Duff’.

286

The upper ranges suggested by Breathnach are a conservative guess. As subjective as it

is to decide the widest and narrowest range, the interval of a perfect fifth is given as the

narrowest example because through experimenting with playing tunes with greater

ranges, the identity of these tunes could still be maintained, even in this more confined

space. On the other hand, the well-known reel ‘The Mason’s Apron’ – in the version

popularised by the revered Belfast fiddler Seán Maguire – may very well have the

widest range. This tune can span from a (touched generally as the final note of a

descending run to end the tune), to (at the other extreme in one of the many parts

modified by Maguire) a g’’’-sharp or high a’’’.63 Similarly, the hornpipe ‘The

Mathematician’ can reach a g’’’ or a’’’ depending on the version. These examples are

very much the exception but do demonstrate the often-dazzling results when a musician

or composer plays with compass/range as a conceptual field. Consequently, for the

purposes of this study, a compass from the fifth to the three-octave mark is selected, and

this gives rise to eighteen possibilities as demonstrated in Table 6.18 below.

Table 6.18 Various ranges likely to be found in traditional tunes or arrangements

thereof.

Conceptual Field Compass / Range

Conceptual Resolution From 5th to 3 octaves

1. 5th

2. 6th

3. 7th

4. One 8ve

5. One 8ve + 2nd

6. One 8ve + 3rd

7. One 8ve + 4th

8. One 8ve + 5th

9. One 8ve + 6th

10. One 8ve + 7th

11. Two 8ve

12. Two 8ve + 2nd

13. Two 8ve + 3rd

14. Two 8ve + 4th

15. Two 8ve + 5th

16. Two 8ve + 6th

17. Two 8ve + 7th

18. Three Octaves

63 For a recording of Maguire playing this tune, see: Various Artists: Milestone at the Garden: Irish

Fiddle Masters from the 78RPM Era, (Rounder CD, 1996), track 19.

287

The study of structural tones yielded 343 stylistic elements when sets of three structural

tones were considered. In terms of sets of four structural tones, a total of 2,401

possibilities were found. This gives a total of 2,744 possibilities across eight conceptual

fields that can be realised as either structural tones or motoric tones.

The study of potential harmonic structures resulted in a series of stylistic data that may

be used to affect the construction of a melody through imposed harmonic progressions.

Using sets of four, which cover the majority of tune-types, 1,296 possibilities have been

found. Added to the 216 possibilities using sets of three, which is suited to tune-types

such as the slip jig, mazurka and waltz, a total of 1,512 stylistic elements have been

identified across seven conceptual fields.

In the study of the various styles of harmony that are used in the genre, a total of ten

types have been established. In terms of variation on a motivic level, nine basic

approaches have been found to exist. Finally, eighteen ranges within which a tune can

be played have been found. In total, this chapter contains 4,293 stylistic elements across

eighteen conceptual fields.

chapter five modality - tu dublin

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