THE MELODIC USE OF THE

AUGMENTED SECOND IN

THE EIGHTEENTH CENTURY

THESIS

Presented to the Graduate Council of the

North Texas State College in Partial

Fulfillment of the Requirements

For the Degree of

MASTER OF MUSIC

by

197082Clifford Marion Shipp, B. M.

Orange, Texas

January, 1952

3 q

Iqo. oSo

197082

PREFACE

Any element of compositional resource in harmony should

merit a place of importance in accordance with the fre-

quency of usage of the particular element in the styles or

periods on which the study of harmony is based. The subject

of this problem was selected because the author felt that

the subject had been unnecessarily omitted by many of those

treatises and textbooks of theory and counterpoint which

were based on the stylistic elements, features, and devices

used in traditional harmony; that is, for the purpose of this

study, the music of the eighteenth century. This study does

not pretend to cover every possible aspect concerning the

problem in the Baroque and Classical styles of music compo-

sition. The underlying purpose of this research study is to

determine whether or not the subject of the problem should be

given a more important place in the study of music theory and

counterpoint based on the fundamental principles of the music

of the eighteenth century.

iii

TABLE 2OF CONTENTS

PagePREFACEiii

LIST OF TABLBvS . . . . . . . . . . . . . . . . y

LIST OF ILLUSTRATIONS. .. @.. .... vi

ChapterI. IITRODUCTION . . . . . . . . . . . . . . . . . 1

The ProblemMethod of Treatment: Objectives of the

Study

II. A DISCUSSION OF THE INTERVAL.............. 6

Opinions of Theory Textbook AuthorsOpinions of Counterpoint Textbook AuthorsEvolution of the Interval

III. H1W THE INTERVAL WAS USED IN THE MUSIC OF fHEEIGHThENTH CENMUY .. ............. 24

The IllustrationsClassification of the Uses of the Interval

IV. SUMARYPAD0CONCUSIO..-.........-..... . - 59

BIBLIOGRAPHY..*............ ........ ............. 62

iv

LIST OF TABLES

Table Page

1. Classificational Usages of the Interval . . . .60

2. Mediums of Form in which the Augmented SecondWas Used in the Eighteenth Century. . . . . . 61

V

LIST OF ILLU&TRATIONS

Figure Page

1. Robert G. Jones, Example of An AugmentedSecond . . . . . . . . . . . . . . . * . . . 12

2. Example of How the Augmented Second Qan BeUsed, According to Foote and Spalding. . . . 16

3. Intervallic Combination Causing An AugmentedSecond . . . . . . . . . . . . . . . . . . . 21

4. Vivaldi, Concerto inE minor for Bassoon,Orchestra, and Cembalo, Allegro, meas. 9-11. 28

5. Vivaldi, Concerto Grosso *in _Q ainor, Largo eCantabile, meas. 164-166 . . . . . . . . . . 28

6. Vivaldi, Concerto in .D minor for Bassoon andOrchestra, Allegro, meas. 52-55. . . . . . . 29

7. Vivaldi, Concerto in D minor for Violin andOrchestra, Andante Molto (2), meas. 9-11 . . 29

8. Bach, Praeludium und FuE in C-moll fUr Orgel,Fuge, meas. 30-33. . . . . . . . . . . . . . 30

9. Bach, Clavier-Concert in D-moll, Allegro,meas. 95-97. . . . . . . . . . . . . . . . . 31

10. Bach, Claxier-Concert LU1nD-mjl, Allegro,meas. 108-110. . . . . . . * . . . . . . . . 32

11. Bach, S jite Iin A-moll fur Clavier, Prelude,meas. 53-55. ....-. . . . . . . . . . . . 33

12. Bach, Sonate fur zwei Claviere und Pedal inC-moll, Largo, meas. 21-23 . . . . . . . . . 33

13. Bach, Sonate in H-moll fur Clavier und Fl5te,fourth movement, meas. 30-32 . . . . . . . . 33

14. Bach, Mass in B minor, Gloria, meas. 135-137 . 34

15. Bach, Cantate, Ach, Gott, vom Himmel sieh'darein, meas. 95-97. .-...... .. . . . . 35

vi

LIST OF ILLUSTRATIONS

figure Page

16. Haydn, yMphony No. 103 in Eb major, Andantepiu tosto allegretto, meas. 6o-62. . . . . . 36

17. Haydn, Symphony No. 103 in Eb major, Andantepiu tosto allegretto, meas. 71-73. . . . . . 37

18. Haydn, Symphony No. 99, Adagio, meas. 45-47. . 38

19. Stamitz, Divertimento in two parts for SoloViolin, Allegro, meas. 21-22 . . . . . . . . 39

20. vozart, StriQ uartet in F major, K. 590,Andante, meas. 12. .. ~....-... - - . . . . 39

21. Mozart, String quartet in A major, K. 464,Allegro, measC.T77-2V~.. . . . . . . . . . 40

22. Vivaldi, Concerto in Sol minore, Violin, Arohi,Cembalo, Allegro~meas. J -4. . . . . . . . 41

23. Bach, Cantate, Liebster Jesu, mein Verlangen,Aria, Adagio, meas. 2-4. . . . . . . . . . . 42

24. Bach, Cantate, Liebster Jesu, mein Verlangen,Aria, Adagio, meas. 30-32. . . . . . . - * 43

25. Bach, Sonata No. 1, Flauto Traverso e'Cembalo,Allegro, meas. 57-59 . . . . . . . . . . . . 44

26. Bach, Cantate, Es ist dir gesagt, Mensch, wasgut ist,)Arioso (Second part), meas. 54-56 . 44

27. Bach, Sonata IV, Violino e Cembalo, Largo,meas. 9-Il . . . - * - . . . . . - . . . . . 45

28. Bach, Partita I for Solo Violin, Bouree-Double,meas. 106-108--. . .........-.-.-.-.-. 45

29. Bach, Partita II in D minor for Solo Violin,Chaconne, meas.~T183. ... . . . . . . . . . 46

30. Bach, Sonata II in A minor for Solo Violin,Fugue, meas. 97-99 . . ...... . . . . . 46

vii

LIST OF ILLUSTRATIO1S

Figure Page

31. Bach, Suite II in D minor for Solo Violoncello,Prelude, meas. 13-15 . . . . . . . . . . . . 46

32. Bach, Sonata in E minor for Violin and Con-tinuo, Adagio, meas. 6-8 . . . . . . . . . . 46

33. Pergolesi, L'Addio, Cantata for Solo Sopranoand Orchestra, Recitative, meas. 11-13 . . . 47

34. Haydn, Mphony No. 99 in 1b major, VivaceAssai, meas. 104-106 . . . . . . . . . . . . 48

35. Haydn, Symphony No. 104 in D mjor, Finale:Spiritoso, meas. 137-139 . . . . . . . . . . 49

36. {aydn, Symphony No. 103 in Eb major, Allegrocon Spirito, meas. 193-195 . . . . . . . . . 50

37. Mozart, Stri:g quartet in D major, K. 499,Allegretto, meas. 211-213. - . . - - # . . . 51

38. Mozart, Str4ma quartet in b jgr, K. 428,Allegro non troppo, meas. 76-7S7 - . . - . . 52

39. Mozart, Serenade No. 7, K. 250, VIII, AllegroAssai, meas. 321-323 . . . . . . . . . . . . 52

40. Mozart, The ]agic Flute, K. 620, Aria, The1Queen of th-e ig-ht -.-- -----. 53

41. Hgndel, Concerto Grosso, Op. 6, No. 3,Andante, meas. 21-22 .-..-. . ... . . . . 54

42. _ozart, Strin Quartet in Eb major, K. 428,Allegro non troppo, meas. 53-55. . . . . . . 55

43. Mozart, String uartet in G major, K. 387,Minuetto (Trio, meas.li4MTt . . . . . .455

44. Mozart, Serenade No. 2, K. 250, VI, Andante,meas. 64-66. . ..-.-.-.-.......... . . . 56

45. Bach, Sonata IV f or Violin and Cembalo,Siciliano, meas. 4-6 . . . . . . . . . - . . 57

viii

LIST OF ILLUITRATION&

Figure Page

46. Pergolesi, Lontananza, Cantata for SopranoSolo and Cembalo, Recitative, No. 1,meas. 13-15. - - - - - - - . - - - . - - . . 57

47. Ha*hndel, Concerto Grosso Op. 6, No. 3, Andante,meas. 1 and 2. . . .# * . . - . . . . . . 58

ix

CHAPTER I

INTRODUCTION

The Problem

When a particular phase of music theory is omitted from

the contents of a treatise or textbook on that subject, the

omission can usually be ascribed to one of two causes.

Either the omitted phase is of little importance or it is

not used in the music of the period on which the treatise or

textbook is based. It is the purpose of this research study

to discuss a particular phase of music theory that has been

omitted or avoided by numerous counterpoint and theory text-

book authors. The material in the contents of this work is

based on a discussion of the melodic use of the augmented

second in the music of the eighteenth century.

Method of Treatment

An examination of sixty-three counterpoint and theory

textbooks and treatises based primarily on the styles and

techniques of music composed in the eighteenth and nine-

teenth centuries revealed that only eighteen of these books

even mentioned the augmented second. The remaining fifty-

two books omitted mention of the interval entirely.

Generally, a music theory or counterpoint textbook will

discuss in detail all the intervals that occur in the music

1

2

of the period or periods on which the text is based. The

major and minor thirds, the perfect fourth and perfect fifth,

the major and minor sixths, the major and minor seconds, and

the major and minor sevenths are all given careful explana-

tion as to their importance and frequency of appearance in

the music the author is using for the basic fundamental

foundation of his work. Generally speaking, the pedagogy of

traditional harmony is deep-rooted in the contrapuntal

harmonic styles of the eighteenth century.

For generations pedagogues of music theory have warned

their students of the incorrectness of a melodic interval of

an augmented second; meaning specifically, two adjacent scale

steps, normally in their unaltered function a whole step apart,

one of which has been altered by raising the upper note a

semi-tone or lowering the lower note a semi-tone; for example,

the interval between the sixth and seventh scale steps in the

harmonic form of the minor scale. Should a thorough explana-

tion be given as to exactly why this interval is incorrect in

the music of the eighteenth century, students could confi-

dently avoid the interval with no further thought. However,

twelve of the sixty-three books examined, stated specifically

that the interval was to be avoided because it was not only

difficult to sing but further, that it was not in the style

3

of the music composed in the eighteenth century.'

Since the interval is fairly common in both vocal and

instrumental music of the eighteenth century, a discussion has

been prepared from carefully selected illustrations from the

music of Johann Sebastian Bach (1685-1750), Georg Friedrich

H~ndel (1685-1759), Wolfgang Amadeus Mozart (1756-1791),

Giovanni Battista Pergolesi (1710-1736), and Antonio Vivaldi

(1675?-1743).

It is not the purpose of this study to enumerate the

appearances of the melodic usages of the augmented second in

the music of the composers represented herein by showing

lJohann Georg Albrechtsberger, Thorouh-Bass, Harmony,and Composition,

Joseph Humfrey Anger, A Treatise on Harmoy

Lawrence Abbott, The Listeners' Book on Harmoy

George C. Gow, h Structure of Music

Arthur Eaglefield Hull, Modern HaMpy

Robert Gomer Jones, Harmo and. Its ContrapuntalTreatment

Leo Rich Lewis, Do and. Don't in Harmon

William John Mitchell, Elementa Harmony

Thorvald Otterstrom, Manual ofHarmon

Nicholas Rimski-Korsakoff, Practical Manual of Harmoy

Arnold Schnberg, Theory of Harmoy

Arthur W. Foote and Walter R. Spalding, Modern Harmony

These books are discussed in Chapter II.

4

countless examples with no explanation, but to illustrate how

the interval was used. The illustrated examples are those of

a constant consistent usage. Infrequent usages will be dealt

with briefly to show that, as with any other phase of musie

theory, there are always exceptions to the general rule.

Due to the absence of reference material on the subject

the major part of the research is taken from the music itself.

Opinions and quotations of counterpoint and theory textbook

authors are used to illustrate what the several authors con-

sider to be the correct or incorrect use of the interval in

question. All the theory and counterpoint texts listed in

the bibliography are based on the traditional styles and

techniques of the seventeenth, eighteenth, and nineteenth

centuries.

No attempt has been made to set up a series of rigid

rules for the use of the interval in the styles dealt with

herein. There are, however, as in the case of any melodic

interval in music, several occurrences where the use of the

interval is most commonly employed. The use of the interval

in a melodic passage has been classified under five separate

headings. The frequency of usage will be determined by the

number of examples listed under each classification.2 Both

vocal and instrumental usages have been considered inasmuch

as several theory and counterpoint textbook authors state

2This information is discussed in Chapter III.

5

specifically that the interval must be avoided because of

vocal difficulties. 3

By bringing to light several aspects concerning the

melodic use of the augmented second in the music of the

eighteenth century, the student of music will have a solid

plan of reasoning at his disposal when he finds himself

confronted with a negative approach concerning the interval,

formulated not on fact but on traditional assumptions.

3For instance: Thorvald Otterstrom, Manual of Harmony,p. 11.

CHAPTER II

A Discussion of the Interval

In examining the various available theory and counter-

point books to find directions or rules for the melodic use

of the augmented second, the most significant discovery was

that most of the textbooks contained no reference to the

subject. There follows a list of theory textbooks and

treatises which contain no reference to the use of the

augmented second.1

Carrie Adelaide Alchin, Apad HarmoA. Olaf Anderson, First Forty Lessons in HarmoySir Edward Cuthbert Bairstow, CounterpjTnt and HarmonyRalph Lyman Baldwin, and Arthur F. H. Witte, Harmon

Simplified_Abramo Basevi, Introduzione ad Nuovo Sistema d'ArmoniaCarleton Bullis, Harmoie FormsLudwig Bussler, Elementary HarmonyGeorge Whitefield Chadwik, HarmoStanley Chapple, Language of HarmonyHugh Archibald Clarke, A y m of HarmonyGeorge Sherman Dickinson, The Growth and Use of HarmonyThusvelde Fetzer, Lehrgang zur Bildng des Klangbewusst-

seinsPercy Goetschius, The Theory and Practice of Tone-

relationsSir John Goss, An Introduction to Haimon and Thorough-

bassArthur Edward Heacox, Lessons in HarrnonyPaul Hindemith, A Concentrated Course in Traditional

HarmonySalomon Jadassohn, A Manual of HarmoyCharles Herbert Kitson, The Evolution of HarmonyGeorge Arthur Leighton, Harmony, Analytical and Applied

1A complete bibliographical entry for each one of thesebooks is listed in the Bibliography.

6

7

Samuel A. Lieberson, Manual of Functional HarmoyAllen Irvine Mciose, The Contrapuntal Harmonic Technique

of the Ejhteenth CenturyCarl McKinley, Harmonic RelationsReginald Owen Morris, The Oxford HarmonyWalter Piston, Harmonytbenezer Proat, Harmoy: Its TIeory and PracticeErnst Friedrich Edward Richter, Manual of HarmonyMatthew Shirlaw, The Theory of HarmonyHermann Spielter, AManual o rjT onGeorge Sidney Thompson, A Course in fly9aS lirunDonald Nichols Tweedy, Manual of Harmonic TechniueJulius Vogler, A Modern Course in Harmo nGeorge Anson Wedge, Applied Harm

Opinions of Theory Textbook Authors

Further examination revealed that several theory text-

books and treatises did contain reference material concerning

the use of the augmented second. The following paragraphs

are devoted to a discussion of the various ideas and methods

of treatment concerning the interval in question, as stated

by several books which devoted material to the subject.

J. H. Anger2 states that the leap of an augmented second

presents vocal difficulties and should therefore be avoided.

He further states that although the use of the interval is

not altogether objectionable it should never appear in the

treble voice or be used in a melodic line.3 The following

rule is quoted for the use of a leap of an augmented second.

The skip of an augmented second is least objectionablewhen it occurs in a short scale passage in an innerpart, as at (n) and (o):4

2Joseph Humfrey Anger, A Treatise on Harmoy, Vol. I,p. 58.

3lbid., p. 58. 4lbid.. p. 83.

(N)f(a

Further evidence of the vocal problems involved, con-

cerning the interval, is discussed by Thorvald Otterstrom5

where he states: "In a melodic progression, augmented

seconds have been forbidden because of their vocal diffi-

culties." Otterstrom relegates his discussion of the in-

terval to the short preceding statement. No illustrative

material is presented to show exactly why the interval is

difficult when it is used in a vocal medium.

Johann Georg Albrechtsberger6 states that the aug-

mented second is defective in the music composition because

it is unmelodious. The following quotation is taken from

his book on thorough-bass and harmony.

Every skip to an augmented interval is unmelodious, andtherefore defective- for instance, to the augmentedsecond, from f to g#; to the augmented fourth, from cto f#; to the augmented fifth, from c to g#:

E~x. 169 AeMIrQ~ ~ '~

5Thorvald Otterstrom, Manual of Harmony, p. 11.

6Johann Georg Albrechtsberger, Thorough-Bass, Harmoy,and Composition, p. 26.

i

9

It is infinitely preferable to use the inversions ofthese intervals - that is, the same notes, but in adifferent position; for instance - the diminishedseventh instead of the augmented second; thediminished fifth instead of the augmented fourth;the diminished fourth instead of the augmented fifth:

Ex. 170

The French thereby. LKoechlin, refers to

the interval when he discuss Ice melodic writing.

According to Koechlin, it is permissible to use the augmented

second, ascending or descending, in a melodic line; however,

he warns the student to be able to avoid the interval. He

states:

dans une partie inter-et .**etmediare; mois il vaut

mieux savoir 16viter. 7

(et mme en descendant)

George C. Gow8 presents the following rules for the

avoidance of the interval:

4. while there are cases in which the augmented secondmay appear with good effect, it should usually beavoided as unmelodious.

6. Rule X. If a melody in seeking the nearest notewould be an augmented second let it move to the nearestnote in the opposite direction; and let the other fourparts likewise change their direction so far as isnecessary in order to avoid other faults and to pre-serve a good arrangement of the chord.

harles Koechlin, Traite de 'Harmonie, Vol. I, p. 11.

George Coleman Gow, The Structure of Music, p..83.

ON.", aw". I - ,, -, , - -- , I,- - -- it , " - .- 'Apm- - i,

10

These rules are adequate for the purpose of avoiding the

use of the augmented second but Gow presented no illustrative

material to exemplify just exactly how the first rule was to

be utilized, when and how the interval could be used, and why

it is considered to be unmelodious. The second rule is based

firmly on the principles of the first rule; however, the

first rule is bound, as in other instances, by a traditional

avoidance of the use of the interval, meaning specifically,

that there are vocal difficulties which supposedly occur when

the interval is employed in a melodic passage. Gows book9

is based on the principles of the Baroque, Classical, and

Romantic traditions of harmonic treatment. His examples

dealing with all other techniques and devices of traditional

harmony are numerous. Why, then, after setting such a prec-

edent, would he avoid an example of the augmented second

used melodically? Stating that the interval is unmelodious

is obviously based more on a personal opinion than on theo-

retical principles forbidding the use of the interval

(because it was unmelodious) in a melodic passage.

9 Ibid.

11

According to William J. MitchelllO the augmented second

appears only in mixed scalesll and in only one position

there. "It represents a complex, contrived situation rather

than an indiginous one."1 2

Mitchell continues, stating that the augmented second

will present a strong key defining value due to the leap

from the sub-mediant to the leading tone of the scale, thus

forming the interval. It is almost undoubtedly the outgrowth

of the combined elements of the major and minor scales. 1 3

Following the same line of reasoning Arnold Schonberg

states: "As a model for the skip of an augmented second I

suggest the so-called 'harmonic minor scale in which I

recognize the true melodic minor scale." 14

In a discussion of the interval, Robert G. Jones1 5

states the interval should appear between the sixth and

seventh scale steps of the harmonic form of the minor scale

when it is used; however, he further states that the interval

10William J. Mitchell, Elementary Harmony, p. 28.

11No explanation is made as to what the author means by"mixed scales."

12Ibid., p. 28. 13Ibid., p. 28.

"Arnold Schonberg, of Harmoy, p. 183.

15Robert Gomer Jones, Harmony and Its ContrapuntalTreatment, p. 21.

-.. . . - - -, 1. '13- t1imm" AL ",4fM-

12

should be avoided in vocal music. The following illustration

appears in Jones' discussion of the interval with reference

to its use in the minor scale.

OMANI

AO1rAugmented Second

Fig. l.--Rober G. Jones, example of an augmented second

According to Jones, the augmented second can be avoided in a

minor scale passage by using the melodic form of the scale. 1 6

He presents the following rule and illustration: "5. To

avoid the augmented second in the melodic progression of a

part, the sixth degree of the scale is raised chromatically.

In this, the observing student will recognize the melodic

form of the minor scale." 7

EX. V

i I

16Ibid., p. 21.

Ex, IV

---- -I F

.- OW-

r

.r

L-1,77 177t,

JEI/'B'HE-

:

.. ,,.,.

#11. A--

I

r

I' r

17Ibid p.2

. I P

13

Jones presents an excellent account of how the use of the

interval can be avoided but, as in previous instances, there

is no reason stating specifically why the interval should be

avoided in the first place, vocally or instrumentally.

During the Baroque and Classical periods composers were

in constant search of new melodic and harmonic devices to

add color and a distinctive flavor to their music. As early

as the time of J. $. Bach the exotic musical characteristics

of the East had seeped their way into Europe. According to

Lawrence Abbott18 this color could be achieved in many in-

stances by the use of augmented intervals. In his dis-

cussion of augmented and diminished intervals, Abbott warns

that the use of an augmented second should be strictly

avoided unless an exotic color or flavor is desired.19

Abbott continues his discussion of the augmented second

with reference to its place in the harmonic form of the

minor scale. He states:

...The truth is that the minor scale has several forms,each one being in the nature of a compromise. Thescale already illustrated 20 is the best one to use informing chords, but it has one serious defect: Anawkward interval of an augmented second between thesixth and seventh notes of the scale (between A-flatand B-natural in the scale of C minor). To avoid this

isLawrence Abbott, The Listener's Book on Harmony, p. 29.

1 9Ibid., p. 81.

20Abbott refers to the harmonic minor scale.

14

uncouth interval musicians have devised another scale touse in forming minor melodies....This revised scale iscalled the MELODIC MINOR SCALE to distinguish it fromthe minor scale already quoted, which is called theHARMONIC MINOR SCALE..... 21

With reference to the augmented second and its place in

Oriental music Abbott says:

...One striking characteristic of Oriental melodies,however, is worth knowing about: their frequent use ofthe augmented second. In ordinary music this uncouthinterval is shunned as being awkward and queer. Soinsistent have European musicians been on avoiding itthat they have gone to great lengths of using two extrascales in the minor mode - the ascending and descendingmelodic scales - just to avoid the skip of an augmentedsecond which occurs between the sixth and seventh tonesof the harmonic minor scale (see page 39). Consequentlythis interval has become a trademark of Oriental music,at least in the eyes of European and American musicians.Let us suppose that a Hollywood composer wishes tocreate the exotic atmosphere of Bagdad. He need notgo to the trouble of searching out an authentic melodyof that section of Asia; all he has to do is write hisown tune, plentifully sprinkled with augmented seconds.This is what he might turn out.

Here is an original melody which does not pretend to beof musical importance. But it proves its point, thatthe augmented seconds provide an unmistakable- Easternflavor. The X's are placed between each pair of noteswhich forms the interval of an augmented second.22

21 Lawrence Abbott, _p. Cit., p. 39.

2 Ibid., pp. 226-227.

15

Arthur Foote and Walter R. Spalding23 regard the aug-

mented second as a marked feature of the harmonic minor

scale. They explain that although the interval can be used

melodically with great effect, it is better to avoid it in

the inner voices of chord progressions.

...Much more latitude is allowed on this point ininstrumental music than would be advisable in unaccom-panied music for voices, for the augmented second issomewhat difficult to sing in tune.

60. In writing exercises in the minor mode the chiefnew points to be observed are these: First, theintroduction and the resolution of the three dissonanttriads (110, 111+, VITO); Second, that no voice maymove over the interval of an augmented second or fourth.The diminished triad (110) may be connected with thetriads VI and IV, and almost always resolves to thedominant.

...Observe the unvocal progression below the augmentedsecond, and the good and vocal interval of the dimin-ished fifth. 4

An interesting point is that Foote and Spalding state

that the use of the augmented second melodically or in an

23 Athur Foote and Walter R. Spalding, Modern Harmony,p. 39.

24Ibid., p. 39.

16

inner voice is permissible if the leap of the interval is by

step from the sub-mediant to the leading tone or vice versa,

(this leap forming the augmented second), thereby making the

interval more natural to sing.25

Fig. 2.--Example of how the augmented second can beused, according to Foote and Spalding.

In the remaining texts which mention the interval, the

authors relegate their discussion of the problem to a mere

sentence or two.

According to Arthur Eaglefield Hull26 the augmented

second appeared in melodic form long before the minor ninth

and the augmented sixth chords came into harmony.

Leo Rich Lewis27 states that in Medieval music all aug-

mented intervals were so objectionable that they were regarded

as unmusical. He further states that even in modern vocal

music augmented skips are questionable.

25Ibid., p. 121.

26Arthur Eaglefield Hull, Modern Harmon, p. 163.

27Leo Rich Lewis, Do and Don't in Harmn_, p. 208.

17

Nicholas Rimski-Korsakoff28 refers to the augmented

second and all other augmented intervals as being strictly

forbidden in the study of harmony. Consequently, the aug-

mented second cannot be used in either major or minor

harmonic modes.

Opinions of Counterpoint Textbook Authors

An examination of several counterpoint texts revealed

that the majority of textbooks and treatises on this subject

also omitted mention of the augmented second. There follows

a list of counterpoint books which contain no reference to

the interval.29

Theodore Dubois, Traite'de Countrepoint et de FIsIueJohann Joseph Fux, Gradu-sad ParnassumCharles Herbert Kitson, The Art of CounterpointWalter Piston, CounterpontAlfred Madeley Richardson, Fundamental CounterpointErnst Friedrich Eduard Richter, Manual of iIe and

Double CounterpointBernhard Ziehn, Canoniache Studien

Further examination revealed that several counterpoint

books do make reference to the augmented second. The

following paragraphs are devoted to a discussion of various

opinions and ideas, concerning the interval, of several

counterpoint treatise and textbook authors.

28Nicholas Rimski-Korsakoff, Practical Manual of Harmny,p. 13.

A complete bibliographical entry for each of thesebooks is listed in the Bibliography.

Is

According to G. G. Bernardi30 the augmented second was

not rare in the music of the seventeenth and eighteenth

centuries. He states:

Further, as an immediate result of melodrama (XVIICentury) composers, even in polyphony, began to conformtheir music to the text; so that, a few intervals re-pudiated by theorists, were used in actual practicebecause they expressed musically the idea conveyed bythe works.(l)

(1) 1 need only cite the name of Benedetto Marcello, inwhose Psalms examples abound. The following instance, amongnumerous others, will suffice:

The interval of an augmented second at the words 11ilgrande eccesso"1 (lit., "the great transgression".)

IL egmN k4CR

...And be it noted that Benedetto Marcello was broughtup in the school of Palestrina. In fact, he studied withFrancesco Gasparini da Luca, who had been a pupil of Arcan-gelo Corelli who, in his turn, had studied with that MatteoSimonelli, a disciple of Gregario Allegri, who was known asthe Palestrina of the XVII Century.

...Finally, the fixing of the new tonalities (major andminor) and the development of a rational theory ofharmony by virtue of which every melody must rest uponan harmonic basis, rendered regularly acceptable certainintervals which had been heretofore proscribed. (1)

(1) Such are the leap of a diminished 5th, that of anaugmented second, of a diminished 7th or of a diminished 4th,fruits of the harmonic minor scale; ,..31

3 0 G. G. Bernardi, Counterpoint, pp. 21-22.

3lIbid._,p. 22.

19

In opposition to Bernardi, Charles W. Pearce32 makes

the following deductions concerning the interval:

69. For melodic purposes, this gap of an augmentedsecond has to be smoothed over by chromatically raisingthe sixth degree; so that the minor scale, both ascend-ing and descending takes this "melodic" form;

i.e., its upper tetrachord is to all intents and pur-poses chromatic (see Fig. 20).

...The following intervals, all of which liebetween various degrees of the minor scale formulaare strictly forbidden in the composition of anycontrapuntal melody.33

tanAT SA TN& AL( MflNTED A oMEN TEDS rCQND CO1)

32Charles W. Pearce, Modern Academic Counterpoint,p. 18.

Ip. 1$.

20

According to Gustave Soderlund34 augmented and dimin-

ished intervals are forbidden in the contrapuntal styles of.

the sixteenth, seventeenth and eighteenth centuries except

when the interval is used as a "dead interval"; that is, an

interval relationship between the end of one phrase and the

beginning of the next.

Percy Goetschius35 discusses the possibilities of using

the augmented second in the following manner.

C. The mildly dissonant intervals, permitted todominate occasional Essential tones, are:

the diminished 5th; in Vthe augmented 4th;

the diminished 7th; in V9 incomplete (Dim. 7ththe augmented 2nd; Chord)

And those minor 7ths and major 2nds which represent goodchords of the seventh.

The diminished and augmented intervals are by no meansinfrequent;...

In his discussion, Goetschius does not make reference

to any rules or actual illustrations which govern the use of

the augmented second in a melodic passage.

Victor Vaughn Lytle3 6 states that, where melody is con-

cerned, all augmented leaps are forbidden. The following

information is presented under the heading of "Preliminary

Statements" in Lytle's book on counterpoint.

34Gustave Fredric Soderlund, Direct Approach to Counter-pn p. 9.

35Percy Goetschius, ounter Applied, p. 21.

36Victor Vaughn Lytle, The Theory and Practice of StrictCounterpoint, p. 3.

21

PROHIBITED All augmented leaps at any time.LIEAPS 6th, major. Some theorists permit its use

but older authorities condemn it.7ths, all kinds.One, or two, leaps exceeding an octave.Any two leaps forming a major 7th.Two major thirds forming an augmented 5th.

A similar but more definite restriction of the use of

the interval is made by R. 0. Morris.37

4. Leaps of an augmented interval are to be avoided,except possibly between the 6th and 7th degrees of theharmonic minor scale. And in such a situation it ispreferable (and usually feasible) to use the melodicminor form instead.

Evolution of the Interval

Although there are no available illustrations to uphold

the fact, there is a great possibility that augmented and

diminished intervals used melodically had their origin in

the various permutations of the medieval modes:38 the melod-

ic leap of the interval evolving from harmonic intervallic

combinations of voices as illustrated in the following

example.

Fig. 3.--In, an augmentedsecond.

37R. 0. Morris, Introduction to Counter nt, p. 11.

38A. 1,. Richardson, he Medieval Modes, p. 14.

22

It was the custom in medieval music3 9 not to write in the

accidentals, thereby leaving the permutation to the per-

sonal discretion of the performer. The various permuta-

tions of the modes were so strongly recognized and under-

stood that the insertion of accidentals was a matter of

choice. However, although it has already been assumed that

the sources of augmented and diminished intervals possibly

stem from modal sources, there were certain rules regarding

those intervals that were realized as stylistic of the

music: the melodic leaps of diminished and augmented

intervals were forbidden.4 0 The question then arises as

to how these intervals have their source in a school of

musical thought where they were forbidden. There follows a

possible explanation.

The harmonic form of the minor scale is one of the

major resources of examples of the leap of an augmented

second in the music of the eighteenth century. The authen-

tic form of the Aeolean mode very nearly approaches the

harmonic minor scale, the specific difference being the

seventh scale step and whether or not it is altered by

raising it one semitone. There is a possibility that, while

the seventh tone of the Aeolean mode was raised a semitone,

39 This term concerns itself with those periods of musicwhich flourished from approximately the ninth to the begin-ning of the fifteenth century.

40 Ibid., p. 14.

23

the sixth tone could also have been raised in the same

manner, thus forming the melodic form of the minor scale.41

There is no certainty as to the exact date of the first

appearance of the augmented second in a melodic passage.

The information divulged in the preceding paragraphs cannot

be considered final, authentic, or absolute inasmuch as the

assumptions are based on possibilities of the evolution of

the interval and not on actual illustrative material showing

the presence of the interval in an authentic music example.

The minor scale and its forms did not find their way

into music as a compositional resource until after the be-

ginning of the seventeenth century. At this time the modes

fell into disuse.42 The minor scale and its forms presented

themselves for composers' disposal in the seventeenth cen-

tury, consequently bringing about the first principal re-

source of the augmented second; i.e., the leap between the

sixth and seventh scale steps of the harmonic minor scale.

Exact dates and references to a composition in which the

first form of the harmonic minor scale appears are unknown.

4lIbid., P. 14.

42Willi Apel, "Major and Minor" Harvard Dictionary ofMusic, pp. 421-422.

CHAPTER III

HOW THE INTERVAL WAS USED IN TH

MUSIC OF THE EIGHTEENTH CENTURY

The Illustrations

The illustrations in this chapter serve a dual purpose.

First, and most important, the illustrations serve as an

authentic source for a comparative study of the various

melodic usages of the augmented second in the music of the

eighteenth century; and second, the illustrations have been

selected from actual musical works of outstanding composers

of the eighteenth century, thus revealing authentic proof

that the augmented second was an element of compositional

resource in the late Baroque and Classical periods. Since

there is a very similar, almost identical, correlation be-

tween the vocal treatment and instrumental treatment of the

interval, vocal and instrumental examples are listed under

the same classification. In many instances, fragments are

taken from the same musical work. This method of treatment

was formulated to exemplify how a melodic motive (which has

an augmented second) that is introduced early in the compo-

sition, is developed and the changes, if any, that take

place in the course of its development.

24

25

The number of illustrations cited under each classifi-

ca tionl is governed largely by how common the interval is,

(in that particular classification), in the composer's

works. For example, the bulk of illustrative fragments

are taken from the music of J. S. Bach. This is done for

two reasons:: (1) Bach used the interval more often and in

more of his works than did his contemporaries; and (2) the

great majority of the theory and counterpoint texts examined

in the research study of this problem used Bach's music as

a source for their illustrative materials.

In many instances there are only one or two mediums of

composition represented for several composers. These frag-

ments, in such instances, have been selected from the type

of work or medium in which the augmented second most fre-

quently occurred in that particular composer's music.

Naturally, it would be an almost impossible and futile

attempt to make a catalog of every instance in every work

of the composers represented herein. Each example was chosen

to be illustrated in this chapter after a careful comparative

examination had been made of scores of examples duplicating

the particular case in which the interval was used.

The composers represented in this chapter were selected

because their music is generally considered to be the ultimate

representative of the styles of late Baroque and Classical

IEach classification is discussed in detail.

*MONO~

26

composition. Those examples taken from the music of J. S.

Bach were selected from more than one thousand examples tabu-

lated from the complete works of the composer. This accounts

for the abundance of Bach illustrations listed in this

chapter. An examination of the music of G. F. Handel re-

vealed that the augmented second rarely appeared in his

music. A study of all the available music of Handel reveal-

ed that he did not use the interval vocally. Naturally,

there are possibilities of existing vocal music, which has

been lost, in which HAndel did employ the interval.

The fundamental purpose of the illustrations shown in

the following pages is to prove: (1) the augmented second

was used melodically in the music of the eighteenth century;

and (2) it was used in both vocal and instrumental forms of

composition.

Classification of the Usagesof the Interval

The classification of the different ways the interval

was used was derived from the following method of treatment.

Every available work of the composers represented herein was

closely examined to see whether or not the interval was used.

When an example was found, the following information was

noted: (a) medium of composition, (b) what precedes the

interval, (c) the interval, (d) what follows the interval,

and (e) the texture of the work in which the interval

27

appears. This process was applied to hundreds of instances

and in every case the results were tabulated under a specific

classification.

From a comparative analytic study of the tabulated

examples, it was found that the interval was used largely in

the same manner by every composer whose works were examined.

Further examination revealed that the interval was employed

in three specific instances. They are as follows:

1. in an ascending or descending harmonic minor scalepassage;

2. in an ascending or descending pattern which out-lines a diminished triad;

3. as an appoggiatura; and,

4. examples were also found which contain combinationsof the preceding usages.2

The following pages are devoted to illustrations of these

four classifications in which the interval was employed.

Classification One: the augmented second used melodically

in an ascending or descending harmonic minor scale passage.

In Figure 4 the interval is used in the melodic line

which outlines a short sequential pattern between the first

and second violins.

2The various combinations of usages will be discussedlater in this chapter.

ILIi

X Q a va 1 d, i Concerto in-E.C> 4* for Bassoon,Orchestra, and Cembalo, Allegro, me-.as, 9-110

t -U,kilo

w w W,

NNW.TIF WT EEft PF IQ AV pt A& I I I IW ImPTIV'jq7' 00

Fig. 5.--Vivaldi, Concerto GrossoCantabile, meas. 164-106.

W7 -3p---- _

in C majiQ,

- IiI~ ' wr-

Largo e

Figures 5, 6 and 7 are all examples which illustrate the

consistency with which Vivaldi used the interval in this

classification. In each instance the formation of the har-

monic minor scale outline is dependent on the placement of the

augmented second.

EiE

- I _''i1-'

Combdo

V -F

_

-

1.1

29

IA

Fig. 6.--Vivaldi, Concerto in D minor for Bassoon andOrchestra, Allegro, meas. 52-55

As M

L,' rFig. 7.--Vivaldi, Concerto in D minor for Violin and

Orchestra, Andante Molto (2), meas.~9-11.

~vv~.J

LIL-LJ

" -1- - _fA

U6

ro

OEir,

L

--lot AM,

AW-A

--7 a

II As ._.a:..r .r .r I- el"N -

i

4L -106 &Ask

Ads,

rw AM

ION":

f

j.

30

lIip. ~ _____________ _ _ _ _ _ _ _ _ _A_ _ _ _ _ _ _ _ __7I

w ' ~ p

I'-di1l

lo IIIPOI O" IAIf-tfl '1 2 .AP

I It7K 17FI -~ I 1

Fig. 8.--.Bach, Praeludium und ugein C-moll fur OrgelFuge, meas. 30-33.

In Fig. 9, Bach uses the interval twice in the samemeasure, repeating it in a melodic sequence, thereby making

the interval more emphatic. The passage in which the in-

terval occurs is taken by the solo instrument. The texture,

as in Fig. 8, is thin. Attention is directed to the melodic

line where Bach incorporates the interval in repeated

motives.

A melodic figure similar to the one illustrated in Fig.9 is used in Fig. 10 in the bass line of the solo instrument

as a contrapuntal counterpart to the melodic line which is

..1

Of

I

.6m : I o

dpsop-MM.-domomw WAMWWA I

. ..

_

.

k ,_

_ - .-.

T-

31

played in unison by the first and second violins. It is

feasible to assume that the passage which contains the

augmented second merits a considerable degree of importance

kI~

&v, l0

1~~ja - 1 WEIt1)~.L ttzzzzIV 1 r1

t I

-a-

NVWt

Apr -dAL,~ i

A 06V%_ _ _ _ _ _ _ _ _ _

7?

Fig. 9.--Bach, Clavier-Concert in D-moll, Allegro,meas. 95-97.

owing to the fact that it is a descending line in counter-

point to the ascending melody.

Vr1v~~

) J'-- - -

I I

Ilk

qw

F

WZI

__

17 LV

's'ow

77

Eff AV

L-" Pr

LA

..........

I

pP -a- -

V

i ii

V

I

Cemao

32

j,0007

Fig. 10.--Bach, Clavier-Concprt in. DL-Qi, Allegro,meas. 108-110.

Figures 11 and 12 are in contrast to this method of

treatment, whereas Fig. 13 is an example of the interval

treated similarly to Fig. 10 in a smaller medium.

a

Ir Ar, I 'U, I- A "AV, NOW violsrl

11 w A 'lid 1,

I s

'I' yAi pop"----. Nod MAP,a POT71 I 1,4w

'AV 1w AFAIL I A -111 t

U a

AO*M do -rIM-4 31 iff Am

lk

OW

ol oq oq

AS

MR,

AVh-A I awl

Am AmId PW

9F_: L

hi, I

(

33

aII I -

A A AV t 1,I I ME

I- ap - Wo 7, IAC-M JE"IE X-N11 II Uw

I f2 2] II

A -

w ~ ~ air..

~ tfL tjL

Fig. ll.--Bach, Suite II in A-moll fur Clavier,Prelude, meas. 53-55.

ff"u.

1#6tv MIN -- F

APAPI t

-1 AFF

AMI

4F---------------A 41

Fig. 12.--Bach, SorC-moll, Largo, meas. 21.

VIIF--

iate ffir zwei Claviere und Pedal inM23.

F1g. 13.--Bach, Sonate in H-moll fur Clavier und Fl5te,fourth movement, meas. 30-32

ROF

Jim.

;(:(

f

v

P s

-- w16,

W- #.

r------ --... sr

i.

34

The illustration shown in Fig. 14 was selected not only

ri

2

=d

- 14

a_._ 0

_____ L.............z

~~iiwi4440 - NA~V-4 /

mA v o tiTba no~- 'N ts3 iSO -

G - -Wb f' - -

ri44b

ig.

TA- - -- -

676

Fig. 14.--4Bach, Mass in B minor, Gloria, meas. 135-137

G

-Y-

Mi -

f

warmas e

I..

r

A

F

41

L 7 1

77-

N' TA

16A 1-

ppt Ho - m N/S-qs

PAY HOI

,

-7-

VO

I ir-Ito"

35

because it is an excellent example of Bach's use of the in-

terval in a vocal medium, but also because the illustration

is taken from one of the composer's greatest choral works.

In this instance the augmented second is used in the, vocal

bass line which is coupled with the basso continuo. As in

preceding illustrations the interval appears in a moving

contrapuntal passage.

In contrast to Fig. 14, Fig. 15 is an example of Bach's

placement of the interval in the vocal soprano line which,

in this case, is a slow descending passage. The high

0

0

LA, S,'

_ _AN _ _ __

t 4J $N '1 W ~ AR

GIOWIA A

Fig. 15.--Bach, Cantate, Ach, Got t , vom Himmel sieh'darein, meas. 95-97.

tessitura of the soprano line at this point will add to the

36

intensity of the interval. In this instance the pitch and

the tempo determine the degree of importance Bach attached

to the interval.

Haydn's method of treating the interval is comparable

to that of Bach in that the interval is placed in an outer

voice in a moving part.

Figures 16 and 17 illustrate how ifaydn introduces the

interval in an ascending scale passage. In the course of

__C

f IT I __-__ ____ _ _

Ae1

Fig. 16.--Haydn, ympony No. 103 in Eb major Andantepiu tosto allegretto, means. 60-2~

ft:

f~A0

I 1

i

Y

h

VtnA .

-or Wo

37

the thematic development, the scale passage is inverted.

1 ' _;w4

f 1 1. -

Fig. 17.--Haydn, Symphony No. Q3 in ma r, Andantepiu tosto allegretto, meas. 71-73.

In Fig. 18 a rhythmic, melodic, and semi-sequential motive

is taken by the first violins. It is this motive which

contains the augmented second.

VtA!

IFLO

PFe

41,

- - - - --w --W-N1 '-w -- I- -"Ro-"-woe

low#

67 I.

02Vo

ka

___ __- -_ z zzzzm " c-I1___41 1 1 L ~ 1 it~ l

II

Fig. 18.--Haydn, SyMphony No. 9_, Adagio, meas. 45-47

oa

L

_____

-

-- t

r b (0.

IM "'

.,"MPO.bb6.--

39

Johann Stamitz uses the interval twice in the same

measure: first in the accompanying voice and again in the

melodic line. His use of the interval is consistent with

and conforms strictly to the preceding illustrations of his

contemporaries. Fig. 19 is also an interesting illustration

from the standpoint of the solo medium.

Fig. 19.--St amit z, Dv er-tmenu-:Violin, Allegro, meas. 21-22.

In the following example, which is taken from a string

quartet, Mozart uses the interval in a scale passage which

is taken by the first violins. The interval is in an outer

voice which, in this instance, is the only moving part.

Fig. 20.--Mozart, trinQuartet in F major K. 590,Andante, meas. 12.

40

I jp W'Idj-A777

*1

I C 7 F-

Fig. 2 1.--Mozart, Strin Quartet i A major, K. 464Allegro, meas. 124-126.

Classification Two: The augmented second used as a part of

an ascending or descending melodic passage which outlines adiminished triad.

In Fig. 22 Vivaldi uses the augmented second in the solo

violin part. The diminished triad is outlined in measure

nineteen with the ascending progression of eighth notes be-

ginning on the third beat of the measure; i.e., G, Bb, C#.The interval is used in a melodic, moving part.

YLe'

1, W

L t UF ja AIF

OC, -1

ramp

II L'g

-,-,I

I

tTm

-Jamb^' '" ! 1 1 r w

fU " i

; r u rI-

1..

AlikAj 1,war -z- iLOF# LI' AL

%,

L

001ow-

I

400000000"Aw- Ao

A A - L 1, 1-, V 17-

41

AN I" AMI i;

400"%F V - 116

Fig. 22.--Vivaldi, Concerto in Sol minore Violin,Archi, Cembalo, Allegro, meas. 18-20.

In the following examples, which were taken from a Bach

Cantata, the interval is used early in the course of the

composition and then in the course of development the inter-

val is used again in a similar figure, this time in a

sequential pattern. In Fig. 23 the diminished triad isoutlined in the first violin part with an ascending pro-

gression of eighth notes, A, C, D#. Fig. 24 illustrates the

same pattern in sequential form, the diminished triad being

outlined by a similar ascending progression of eighth notes,G, Bb, C#, and A, C , D#.

FEW 'Tiff'' - Iv "I- I I -1t

4-

qbj Ar, - I F-11, J04A

A',- J-7M"V

L-T77-1- avAm

42

II_ __ _ __ _ _W-7-WWA NW WINr AidNNWd

rJIA A~ lii 'tmtS'r~rF Irr'u rr r~~~~~mf I L... Li IW L= 7 f ~

LU .In- I ~ .

1 0 '1J0 17-1

fit-

Fig. 23.--Bach, Cantate, Liebster Jesu, mein Verlangen,Aria, Adagio, meas. 2-4.

A

vtj

Pei -

AM

Abe

TP IF" 30wo

wl- 0 , - -- I , I -. ddppp-- A, , t

Aimd Afth-

- s

,,' I - 11,

T

43

00 LAIL-Air UAn "a A&, am

pol-m-

MWIM'-.w

1001

I'M AI~ j1, a -

SDLI 1S44 6 vet, s A.~unQ M r

Fig. 24.--Bach, Canta, Liebster Jesu, mein Verlangen,Aria, Adagio, meas. 30-32.

The method of treatment in Figures 25 and 27 is similar

to that of the two preceding illustrations, the specific

difference being the medium of composition.

~f4

%Nor,

,-AltFlw- ALA I %V 29--A Ai i'l IFFWW 0 IHI -AA &0 q

wig I Lo tw''.17

"t-

IDV

a

tIAi fl ia e C

44

1~iun FT1 4.F v i TA S -, ,

;4T~~'2.1 ~ 'ULW. LLmom IF: -ior, I' og!: r rSol"

Ad

I J' 1-,' mow

1004I

Aw, %&-is IF ter ZE Ejull -A , , I ,PF At'UP at -, __jL ''

Fig. 25.--Bach, Sonata No. Flauto Traverso ece-balo, Allegro, meas. 57-59.

-Af,

F a T -V t

I V 1117 -I-=

CL

JK & ------------

arWIF PW ar AL

............

Ot-F-M, I I W -U .10

AL -4: vog MIR

I T-4

wr

Fig. 26.--Bach, Cantate, Es ist dir gesagt, Mensch, wasgut ist, Arioso (Second part), meas. 54-56.

A.p 0

,r v 0 V - OF If' ,

01'

I#-

45

11 F- t t ~ wrI")rz~Tr~i

I 14 1,71 1 -17~z LIL~ M RS - -r

Of -OP,F- AP -4---~ -

y

Fi.Lg. 2 7.--Bach, Sonata IV, Violino e Cembalo, Largo,meas. 9-1l.

In Fig. 28 Bach uses the interval in a solo medium andin two instances, consistently developing two sequentialmotives.

rI _ --

. or Solo Violin, Bouree-Double

Figures 29, 30, 31 and 32 add to an account of Bacht smethod of treating the interval in the solo medium.

, -- w VZ5 e

kA j

-P

T-W-F-'r

__ a

L,

Am

o 00 Soft

I I-A-1 Aa M--Aws, AP

;MAN*

LtL6AVL..L'Jl--JLft w-E

I:ii-

46

Fig. 29.--Bach, Partita II in D minor for Solo Violin,Chaconne, meas. 81-853.

Fig. 30.--Bach, Sonata II i n minor for Solo violin,Fugue, meas. 97-99.

Fig. 31.--Bach, Suite II in D minor for Solo Violon-cello, Prelude, meas. 13-15.

Fig. 32.--B~ach, Sonata in E minor Lor Violin andContinue, Adagio, mea.6-.

47

The augmented second appears frequently in the vocal

recitative. In Fig. 33 the interval is used in the vocal

line which is the only moving part. The diminished triad

is outlined by the descending progression, B, G#, F, and D.

The prominence of the interval, in this particular case, will

depend largely on the performance.

Fig. 33.--Pergolesi, L'Addio, Cantata for Solo Sopranoand Orchestra, Recitative, meas. 11-13.

In Fig. 34 Haydn uses the interval in six instances

within two measures. Figures 35 and 36 give an account of

Haydn's usage of the interval in a melodic line. These

methods of treatment compare consistently with those of Bach

and Vivaldi.

NMIlw IW,

WW

ANN%& AM As

06,

mWff

NOWOMEN

oleo-,

ME=

IA 0.

40

I -A V

I dr -- F-"

.4 Ab

AF

vil

106

L .44

AO- a N. I I

jw k L 1 6 TW ------------

Fig. 34.--Haydn, ymphon No. 9_ in Eb major, VivaceAssai, meas. 104-106.

j

I1

49

w

a - --- __ _ _ __ __ .. __

F -,

n - -

- U

-OF

I-d--- - --- -- -- - -_.. - - - , -- -.I --

Fig. 35.--Haydn, Symphony No. 104 in D major-Fn -&piritoso, meas. 137-139

FLj

Nov%

a

e S

94

50

L2K7-11E-1

FL

I

C

Fig. 36.--Haydn, Symphony No. 103 Eb jaor, Allegro conSpirito, meas, 193-195.

-l

- g

.,L2 --Z

(%)

Ye-

'Opt& 4

-FM

mA

1

i 3

- -(

..... .

51

Mozart generally places the interval in an outer voice

of a melodic passage. However, the composer did not limit

his use of the interval in other methods of treatment. In

Fig. 37 the interval is incorporated with a contrapuntalmotive which is taken by the second violin. Fig. 38 is an

64 LAk, id IMF

ok-71

I 'A

I Jo

11 L low"*""own" 77 f ,

mk _, Akv

dL-V

EEO-4, if i

p Ir Wftw Fla

Fig. 37.--Mozart, Strin quartet in D m. K. 499Allegretto, meas. 211-213.~~~ ~~

example of Mozart's more frequent usage of the interval in

an outer voice of a melodic line.

A A'

52

Fig. 38.--Mozart, Strig Qartet in Eb ma or K. 428Allegro non troppo, meas. 76-7& ~ ~

)

a

"dou

1- Am

L "'~'~

4

4I__

Fig. 39.--Mozart,Assai, meas. 321-323.

Serenade No. 7, K. 250, VIII, Allegro

feI

'5

--- 777

I . 11 _

I

" Th I

I

'

-

i

k V .9

5000,

53

Mozart uses the augmented second frequently in his

arias. The interval appears often in the solo voice as

illustrated in Fig. 40.

V 7Ve~ -~*~~L~ve ,~,p~ U~N FAM -

Fig. 40.--Mozart, The Magic Flute, K. 620, Aria Thequeen of the Night.

Classification Three: The augmented second used as anappoggi atura.

Due to various contradicting conceptions of theoreticalterminology, an appoggiatura, for the purpose of this study,will mean specifically a non-harmonic tone which leaves thechord tone by leap and resolves by leap. In this case, thefirst note of the augmented second is the chord tone and thesecond note of the interval is the non-harmonic tone. Al-though the augmented second is theoretically classified byadjacent scalewise terxainology (and therefore considered ascale step), the interval can be considered a leap for thepurpose of this study.

$~v

54

In Fig. 41 the appoggiatura is formed by the descending

progression, G# to fP, on the second and third beats of the

measure.

I

Notv Lw I Id h k

Now A-A

**mow

fie

A :AWF

W. Aim t,

PF AD-A&A

Fig. 41.--Handel, Concerto Grosso, Op. 6, No. 3,Andante, meas. 21-22.

The descending progression, E-Db- C, in Fig. 42 would at

first appear to be an outline of a diminished triad. How-

ever, careful examination will disclose that the leap from

Db to C is actually an appoggiatura figure. The rhythmic

construction of the figure completely destroys any audible

conception of a diminished triad. The Db is closely allied

with the following c which is more conclusive evidence of

this example being an appoggiatura.

lCtor~

Vt4i

55

II i~~___

____ __

AMI

Fig. 42.--Mozart, Strin Quartet in Eb majorAllegro non troppo, meas. 53-55.

K. 428,

In Fig. 43 the appoggiatura evolves from the leap of the

augmented second; i.e., from f1 to G#. In this instance the

h I __

I., -e

LIit A I

Fig. 43.0--Mozart, quart in majorKMinuetto (Trio), meas. 114-116. ~~.3

'I'

r_ i

56

G# also completes the formation of an augmented sixth chord.

In Fig. 44 the appoggiatura is made by the ascending

progression of eighth notes, e-natural, f-double-sharp, g-

sharp.

1J~I P~ 0t~ I .1 2- - I i 111 -a -,-

3~

~T j~J7I~I~ZAM

viil

. ~- - ~ 7 F

r

~~-bomb.-

IF 71

4p

Aoor

L la#w

N*ow

Fig. 44.--Mozart, Serenade No. 7 , K. 250, VI, Andante,meas. 64-66.

Classification Four: the augmented second used in

It

:g

AS

r77F W 1.0 1 1 " - ,- -, 1 1- .I

Af

IJ

8O

------ At

"06

dift tooit-

(

1

WL

Am

lo #' AA1 0 A

,ON

=77I , TT-qw- -0. 9- 1 -

I-4

Li

VAep

w

I -

"____ir.mL

---ow,

I .zi-. .. -- - - ,. " , " - - , ,- -

57

combination of the preceding usages.

In Fig. 45 the diminished triad is formed in the

ascending pattern F, D, Bq, and Ab while simultaneously the

augmented second from B to Ab serves as an appoggiatura to

the g-major triad.

V n _ __ _ __ _ __ _ __ _

Fi_ _ _ _

U____

AV

UI~

Fig. 45.--Bach, Sonata IV for Violin and GembaloSiciliano, meas. 4-6.

Fig. 46 is also a combination of Classifications Two and

-. .LS1EV "~A>LiIF

t AJTv

L .2

jr-Tw IF#asTIttt go-

Fig. 46 .-- Pergolesi, Lontananza, Cantata for Soprano$olo and Cembalo, Recitative No. 1, meas. 13-15.

Three.

I

...........

RA, AjMW Di,

Li IEI

v

III -L

-Moe.

The following illustration is an example of one of

several miscellaneous usages of the interval. These usages

conform to none of the preceding classifications and are

rare in the music of the eighteenth century.

4f,~

rV

Fig. 47.--HUndel, Concerto Grosso Op. 6, No. 3Andante, meas. I and 2.

An examination of Handel's music revealed that he usedthe augmented second rarely. Further examination revealed

that in no instance did Handel use the interval in a vocal

medium of composition.

CHAPTEiR IV

SUMAIRY AND CONCLUSION

The purpose of this study was to determine from authen-

tic sources whether or not the augmented second was used

melodically in music composed in the eighteenth century. Themethod of treating the problem was to examine the music of

the composers represented in the preceding chapters to see

whether or not these particular composers used the interval.

When a melodic example of the interval was discovered, the

following information was noted: how the interval was

employed, the conditions which occurred when the interval wasused, and the medium of performance in which the interval

appeared.

The information presented in the preceding chapters

should be conclusive evidence that the augmented second wasa melodic element of compositional resource in the music ofthe Baroque and Classical periods. The use of the intervalwas not restricted to an instrumental medium of performanceby all the composers of these periods. From a study of thevocal works of J. S. Bach, W. A. Mozart, and G. B. Pergolesiit was discovered that these composers put no restrictions onthe use of the interval in a vocal medium.

Although there are possibilities of other existing

59

60

methods of use, it was discovered that the interval was

employed in four instances:

(1) in an ascending or descending harmonic minorscale passage;

(2) in an ascending or descending pattern whichoutlines a diminished triad;

(3) as an appoggiatura; and,

(4) combinations of the preceding usages.

The following table illustrates the classifications of

the interval as used by the composers dealt with in this

study.

Table 1

CLASSIFICATIQNAL USAGES OF THE INTERVAL

Composer

BachH0andelHaydnMozartPergolesiSt amit zVivaldi

IiiiiIYesNoYesYesNoYesYes

Classification

IV

Yes No YesNo Yes NoYes No NoYes Yes NoYes No YesNo No NoYes No No

An analytic study of the music of the composers repre-

sented herein revealed that some composers used the interval

frequently in all forms, whereas other composers restricted

the use of the interval to an instrumental form and in some

cases even examples of this type were found to be rare.

61

Table 2

EvLDIUJMS OF FOR M IN WHICH THE AUG-MPED SECONDWAS USED IN THE EIGHTEENTH CETURY

liedium of Form

Voc al

Bach YesHandel NoHaydn NoMozart YesPergolesi YesStamitz Vocal works of

this composer arenot available

Vivaldi No

Instrument al

YesYesYesYesYes

YesYes

It is the desire of the author that the information

divulged in this study will prove to be an asset to the

student of music theory and counterpoint when he is con-

fronted with the interval in connection with the stylistic

trends of traditional harmony. However, when such- a problem

arises, in any course of musical study, the student is

strongly recommended to examine the music itself, using this

as the final authentic source of information.

Composer

MI IN

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70

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A*Aq

71

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72

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