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Outline of basic music theory

From www.oscarvandillen.com

Introduction to music theory: an outline of basic music theory.

This outline offers a concise and complete overview of basic music theory.

Oscar van Dillen 2011

Contents

1 Introduction

2 Sound and hearing

2.1 Sound

2.2 Hearing

2.3 Physics of sound3 Musical notation

3.1 Notation of time and rhythm

3.1.1 Symbols for notes and rests

3.1.2 Meter

3.1.3 Time signature and bar

3.1.4 Binary time signatures

3.1.5 Dots

3.1.6 Ternary time signatures

3.1.7 Ties

3.1.8 Tuplets

3.1.9 Basic tempo indication

3.1.10 Correct rhythmical notation

3.1.11 Beaming

3.1.12 Odd time signatures

3.1.13 Complex time signatures

3.1.14 Notation of swing rhythm

3.2 Notation of pitch

3.2.1 Staff and clef

3.2.1.1 Staff lines and ledger lines

3.2.1.2 Commonly used clefs

3.2.1.3 Further study

3.2.2 Directions of notestems

3.2.3 Basic tones3.2.3.1 Definition of basic tones

3.2.3.2 Systems for basic tones

3.2.3.2.1 Alfabetic nomenclature

3.2.3.2.2 German nomenclature

3.2.3.2.3 Latin nomenclature

3.2.3.2.4 Relative Latin nomenclature

3.2.3.2.5 Indian nomenclature

3.2.3.2.6 Indian nomenclature transcribed


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3.2.4 Alteration

3.2.4.1 Definition of alteration

3.2.4.2 Symbols for alteration

3.2.4.3 Validity of alteration symbols

3.2.4.4 Microtone alteration


3.3 Notation of intervals, chords and harmony

3.4 Notation in scores3.5 Compact polyphonic notation

3.6 Other notation symbols

3.6.1 Tempo indications

3.6.1.1 Classical tempo notation

3.6.1.2 Metronome numbers

3.6.1.3 Counting value changes

3.6.1.4 Jazz tempo notation

3.6.2 Dynamic indications

3.6.3 Articulation

4 Basic building blocks of melody and harmony

4.1 Scales

4.1.1 Definition of scale4.1.2 Different scales

4.1.3 Basic major and minor scales

4.1.3.1 Major scale

4.1.3.2 Natural minor scale

4.1.3.3 Harmonic minor scale

4.1.3.4 Melodic minor scale

4.1.4 Definition of mode

4.1.5 Church modes

4.1.5.1 History and use

4.1.5.2 Basic notation

4.1.5.3 Notation on c4.1.6 Different modes

4.1.7 Further study

4.2 Intervals

4.2.1 Definition of interval

4.2.2 One sound

4.2.3 Basic intervals

4.2.4 Wide intervals

4.2.5 Perception of the interval

4.2.6 Basic intervals from c

4.2.7 Full names of the intervals

4.2.8 Intervals in order of chromatic size

4.2.9 Enharmonic equivalence4.2.10 Inversions of the intervals

4.2.11 Further study

4.3 Triads

4.3.1 Definition of triad

4.3.2 Basic notation

4.3.3 Types of triads

4.3.4 Symbols for triads

4.3.5 Inversions of triads

4.3.6 Other positions of triads

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7.2.5 Basic degrees as seventh chords

7.2.5.1 Seventh chord degrees in major

7.2.5.2 Seventh chord degrees in minor

7.3 Further study

8 Form

9 Footnotes

10 Questions

11 See also12 Book: "Outline of Music Theory" in preparation

13 External links

Introduction

Musicians have always studied music in two ways: both practically and theoretically, and both fields of study strongly

developed in the course of history, and are in fact still developing. Though the two are fundamentally different, both

share a common fate, in that each can only be fully learned from an accomplished master. Neither can be learned from

books alone, as they both involve practical skills.

The purpose of this text is to provide a concise outline and introduction to basic music theory. I sometimes also speak

of common theory as it comprises basic knowledge, tools, methods and models, shared in common by many

musical styles and traditions, which are commonly used in musicology as well. The study of musicology is very

different from that of music theory, as this more scientific approach to music leads to knowledge rather than to skills.

The masters one needs to study with musicology could as well be found in books, and such is never sufficient for

music and music theory.

The more one's musical skills grow, the more rewarding it is to develop one's musical theoretical skills as well.

Ideally, music theory connects four fields of study, as represented in the diagram below:

Music theory interconnects these four fields of study: hearing, singing, reading and writing, in the student's awareness

and brain, both as knowledge and as skill. It is not enough to know how something is or can be done (can be heard,

read, sung or written), the practical skills to actually do so oneself should be considered to be included in music

theoretical education and learning.

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With the emergence of ever more complicated models (which are generally presented in either visual or numerical

form) for analyzing or even constructing or composing music, it suddenly becomes important to remind oneself

always that music is made for the ears. When in doubt, the ears will convey the truth or falseness of any proposed

system of evaluation. Though this has so far been a more or less subjective criteria, basically shared by all knowing

ears, it probably won't be long before neurophysiology, with contemporary measurement instruments such as the

MRI scanner, will scientifically uncover the inner workings of the musical brain. With tools such as these, music

theory can develop into a phenomenological interdisciplinary field of study between art and science.

Sound and hearing

Sound

Sound is the perceived complex phenomenon of vibrations traveling as pressure waves through a medium. For all

living beings on earth this medium is either air or water. Such vibrations are called soundwhen they are perceived by

(our) hearing.

There are thus three components in sound: vibration, medium, hearing. Generally, silence is considered to be the

opposite of sound.

A musical sound can be recognized and defined by itspitch(or frequency), duration(or relative rhythmic value),

timbre(color or instrument), dynamics(loudness) andposition in space(relative to the listener).[1]

All music consists

of related sounds and silences, which can be symbolized by notation.

Hearing

Sound is perceived by our hearing, which is a result of our ears picking up vibrations in the air and translating these to

our brain, where the perception of hearing comes to awareness.

The ear translates vibrations in the ear into neural signals. Air-vibrations are received by the ear drum (tympanic

membrane) and transmitted by means of the three extremely small bones called ossicles (as the fossil record shows,

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these originally evolved from jaw bones), whose intricate lever-function is to reduce the amplitude of the vibration

while increasing the energy transmitted, to the inner ear (labyrinth). The middle ear thus translates pressure waves

(back) into mechanical vibrations. The inner ear serves two functions, those of hearing and of balance. The cochlea is

the coiled part of the inner ear which translates the mechanical vibrations into pressure waves in its internal fluid,

which are picked up by hair cells that convert their motion into electrical signals. These are in turn interpreted by

nerve cells that transform them into electrical impulses that travel through the auditory nerve to structures in the

brainstem for further processing. Hearing is a complicated mechanism!

Apart from having a vested interest in keeping one's ears in perfect condition, what most concerns musicians here, and

hence music theory, is basic knowledge about vibrations, especially those that we recognize as tones, as pitches.

Physics of sound

A tone is a complex combination of a series of regular vibrations, usually with one prominent frequency which is

experienced as the pitch. A regular vibration is scientifically named a frequency, expressed in Hz (Herz), cycles per

second.

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The amplitude of such a wave corresponds directly to the volume of a sound, the wavelength to its pitch, or frequency.

Standard tuning in music today is usually to A=440Hz which means there are 440 vibrations per second to produce

this tone. Although human hearing ranges between 25 to 20,000 Hz, the pitches actually used in music are roughly

between 25 and 5,000 Hz.

The basic regular vibration is a sine-wave, but all musical instruments actually produce a combination of various sine

waves for each tone. Differences in these combinations are perceived as various colors of sound. Some examples of

oscillograms are given below.

Most animals have a very different hearing (and correspondingly: sound producing) range from us humans. For

example, elephants and whales hear and communicate with subsonic frequencies (infrasound) over vast distances,

whereas bats and dolphins use a sonar system employing extremely high frequencies (ultrasound) to locate their prey

at short range, especially in conditions where sight will not avail them.

Various tones overlapping or sounding together will produce generations of audible combination tones from the

interference of their compound frequencies, producing complex harmonies and tensions between different tones,

described by the concepts consonance and dissonance.

Musical notation

Music is a time-art; music consists of sound and silence, performed by musicians. In musical notation therefore,

symbols for both sound and silence are employed, set to a reading basis representing the flow of time. Although an

experienced musician is able to almost read music notation as one reads a book, the actual sound effect of a musical

score can only be fully appreciated by hearing. Notation is basically an instruction for performance, and less so an

actual representation of the sound produced.

Notation of time and rhythm

Symbols for notes and rests

To represent different durations of tones, different note symbols were developed. The normal ratio of durations is 1:2,

each smaller, faster note being twice as fast, or: half as long, which amounts to the same result, as the larger one. This

system begins with the whole note. The smaller values then are the half note, quarter note, eighth note, etc. Older

terms for some note symbols are still in use in some countries, such as quaver, semi-quaver and crotchet, but I

consider these to be outdated and prefer the numerical values and names.

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A similar system of symbols with relative durations is used for musical silences, called pauses or rests.

The whole restcan be used for two purposes:

A true whole rest, with the exact value of a whole note;1.

A full bar rest, not literally corresponding to and therefore independent of time signature.2.

Meter

Meter is a usually simple repeating cycle of rhythm originating from poetry. Rhythms are often linked to meters which

are also used in poetry. In Europe, these can be traced back to the ancient Greek meters, some of which have a binary

strucure:

iamb !-

trochee - !

spondee - -pyrrhic !!

others are ternary:

anapest !!-

dactyl - !!

amphibrach ! !

In Ottoman as well as in classical Arabic poetry[2]

, a related but more complex system of 16 different meters was

used, which explains why the rhythms in the music linked to these traditions are also more complex than those that are

common in the West.

Example of text and meter:[3]

There is a strong link to language and poetry in most musical traditions, and such naturally leads to the use of meter in

music. Meter in music is commonly represented by time signatures in notation. With the use of a time signature, it

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becomes mandatory to visually divide the notes into groups separated by vertical lines. Such groups are called bars.

Each bar within one time signature has the exact same duration, with no notes nor rests more nor less than its full

duration.

Time signature and bar

A time signature consists of two numbers, one above the other, without a horizontal line between them (it is not a

fraction). The upper number indicates the number of beats, the lower number represents the note value used for one

beat. Although time signatures using the quarter or eighth notes as basis are more common, theoretically many moreare possible, and indeed sometimes used. The most common time signatures are two-four, three-four, four-four and

six-eight. Eighth and smaller notes can now be grouped and visually linked together per beat. In grouping these

smaller note-values thick horizontal lines, called beams, are employed. These are double beams in the case of

sixteenth notes, triple beams with thirty-second notes, etc. It is also possible to thus beam together notes of different

values, as long as the beamed groups are a clear representation of the beat-structure. Further details on beaming will

be explained later in this outline.

With the use of time signatures, the notes become grouped in units called barsor measures, each group separated from

the next by a vertical line, called the barline.

Binary time signatures

Binary time signatures are time signatures that have two beats per beat, and can be recognized by the top number

being 2, 3, 4 etc. Usually the lower number is 4, pointing to the 1/4 note (sometimes the 1/2 note occurs in older

music). The following examples show how such time signatures can be used in their most simple form:

Dots

Note that the last bar of a piece always ends with a double barline. Note also that a dot is used here to make a

three-part note out of a two-part note: any dot adds 50% to its duration. A half note is the same as two quarter notes

which is two beats. The dotted half note however equals three quarter notes, which in these time signatures equals

three beats. Dots can be equally applied to notes and rests.

The following examples that also include rests show how these dots can be used for more complex rhythms:

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Ternary time signatures

Ternary time signatures are time signatures that have three beats per beat, and can be recognized by the top number

being 6, 9, 12 etc. Usually the lower number is 8, pointing to the 1/8 note; examples of these can be seen below:

Six-eight may be ternary per beat, it is in itself a binary time signature, as it has two beats per bar.

Note that with ternary beats, it is the dotted notes that represent a one-beat note!

Ties

So far we have seen note-values which fit neatly into a time signature, and durations which are also corresponding to

the basic structure. But not everything can be notated this way. Often it will be necessary to use more irregular

divisions and durations. The use of ties allows for more flexibility in connecting notes. Two notes tied together

become one value, and are performed as one tone.

Note how the second dot adds another 25%. The durations thus represented make sense only when notating sustained

tones, such as of singers or wind instruments. For percussive music, such ties are normally not used, and this very

same rhythm can be notated as below, with rests instead of ties:

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The tie is notated from one note head to the next note head, it cannot tie several notes together with one symbol only.

A tie cannot ever connect two different pitches, or tones, only two that are identical. The tie is therefore a rhythmical

symbol. Still, graphically the tie looks somewhat like a slur, but this is a sign to represent not the rhythmical, but theuninterrupted connection of various different tones being sung, played or bowed in one go. The difference is thus that

ties are always used between just two notes representing exactly the same pitches or tones. The slur will be shown

later, in the section on articulation.

As the relative silences of rests are identical, rests are never tied together!

Tuplets

Finally, to complete the rhythmic possibilities of musical notation, what are called tuplets allow for even more subtle

subdivisions, and even more variations per beat or beat-group become possible.

A tuplet is a temporary deviation from the theoretically normal division or subdivision within a time signature. Tupletscan be notated in various ways, with one number or a ratio (used especially for more unusual ratios). Depending on

whether the group is connected, square brackets can be used to indicate exactly which are the notes and durations

concerned. Tuplets always change from the time signature (sub)divisions to another regular (sub)division, which could

also be represented by time signature changes. Tuplets are used for temporary changes in rhythm or when time

signature changes would become too complicated for practical reading. The most common tuplet is the triplet,

allowing for three against two notes.

Other examples are the quadruplet (four against three), or quintuplet (five against four or three). It is also possible to

created nested tuplets: tuplets within tuplets. When writing such things, musicians often overlook simpler ways of

writing the exact same rhythm. As notation is intended for practical use by performers, overcomplicated notation tends

to create confusion and should be avoided. Besides, very complex ratios are hardly if ever performed mathematically

exact, except by percussionists. The following slightly complex example contains the same rhythm thrice, notated in

three different ways, ranging from simple to complex notation:

Of course, in these different examples, a slightly different counting and even tempo and feel are used. The indication

of tempo in notation is generally important, especially when the sheet music is to be studied in situations without

direct contact to the writer thereof.

Basic tempo indication

Basic tempo indications are done with the one-beat note-value, an =sign and the number of beats per minute (alsocalled bpm). The example above could then be notated in the following way, to produce three times the exact same

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rhythm, because of the tempo and counting adjustments notated:

Note that when changing the one-beat note, the equals sign =actually means becomes.

More on tempo indications can be found in the section on other notation symbols.

Correct rhythmical notation

But back to basics now. As stated above, it is mandatory that the structures of the time signatures remain explicitly

visible in notation. This means that connections through ties and vertical lines with shorter values must follow the

beats: it is a rule that rhythmic notation must always show the beats, the natural accents pertaining to the structure of

the time signature.

The first bar fails to show the third beat, which is the middle accent of the time signature. Such and similar notation is

rather unpractical and will easily lead to mistakes in performance. The second bar shows all the beats and is

technically correct. The third bar groups the beats evenly in two groups of two and is used very often in practice,

especially in faster tempos, as more of the 'feel' of the bars as a whole is represented in this notation. It is therefore

very important to write rhythm correctly, not only will incorrect notation lead to performance mistakes, but it also can

cost valuable rehearsal time.

Ritten stough spelt inca rectly maykes reeding tuff...

So similar to reading text, the easier it is to grasp the music notated at first sight, the less misunderstandings will occur.

The structures of the time signatures are therefore important to understand, so notation may follow them.

In all time signatures, the first beat is considered to be an accent. Every beat is accented more than its subdivision, so

in 4/4 the first beat is stronger than the third, and both are stronger than beats two and four. In a longer series of

off-beat notes, usually called syncopations, the beat-structure behind these faster notes should always be visible in

notation, like the following example demonstrates:

A time signature adds a cycle, and hence a basic metric feel to a series of beats. Thus this series of twelve eighth-notes

can become musically very different, depending on the time signature:

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Beaming

Note values smaller than 1/4 can be beamedtogether with the help of horizontal lines connecting the notestems; thesereplace the value-flags and by connections allow for more visible structuring of the rhythms intended.

When writing or typesetting music notation, great care has to be taken to make the beams that touch each stem point

in the proper direction, which can be either left or right. The preferred direction follows from the rhythmical grouping,

where each group or subgroup is made into a visible unit by means of the value flags from the first note onwards all

pointing to the right (reading direction), whereas the last one to close the group points left, backwards, to indicated its

belonging to the prior notes. Any note following a beam pointing left should be on a beat or subbeat.

A further refinement in beaming is possible to be able to visually group the rhythm notated by breaking beams under a

common 1/8 beam, thus clearly showing the subdivision of each beat.

Odd time signatures

A time signature without regular division and subdivision is usually an odd time signature, consisting of a prime

number of beats, e.g. 5, 7 or 11. These are usually also complex time-signatures, and the intended irregular

subdivisions are also shown wherever possible in notation.

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Complex time signatures

Complex time signatures consist of a compound of irregular divisions, such as a 9/8 divided in 2+2+2+3, which is a

common Middle Eastern complex rhythm. In music where such are common, such are usually indicated with a simple

9/8 indication, as the irregular subdivisions are an integral part of the music style concerned.

When complex time signatures are not an integral part of the syle musicians perform (such as having the exampleabove performed by classically trained musicians), the subdivisions can better be notated more clearly with the

intended subdivision indicated in the time signature itself.

Notation of swing rhythm

"Swing" is a term used to denote Jazz interpretation of rhythmic notation, this means: in unequal eighth-notes. The

sixteenth notes are not affected by thisfeel.

Today swingis usually notated in another font type, and indicated by adding (SWING)at the top left of the sheet

music.

The 1/8 notes are approximately interpreted in triplets, with every upbeat accented.

Notation of pitch

Staff and clef

A staffin notation normally consists of 5 parallel horizontal lines. The position of a notehead on a staff determines its

pitch: a notehead can be notated either against or through lines.

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Special notation, such as for percussion, can also employ staves consisting of a different number of lines, even only of

1 line (e.g. for bass drum or tamtam).

At the beginning of most staves a clef is employed to determine its exact usage and to determine the pitches notated.

A clef(originally from French, meaning: key)determines which pitches are notated on a staff.

Staff lines and ledger lines

The staff lines are numbered upwards, starting with the lowest line:

This numbering is used when describing notation orally, in spoken language, but can also occur in descriptive writing.

Notes outside the staff are notated with the help of (one or multiple) ledger lines. Ledger lines are small horizontallines that act as a local extension of the staff at the position of the note, as can be seen in the next example, which

shows all the steps in basic tones in a four octave scale:

Commonly used clefs

The following four clefs for notating pitch are still in use today, but many more historical clefs can be encountered in

older sheet music[4]

.

The G clef(sometimes also called violin- or treble clef) is used for most woodwind instruments, violin and the

middle-high register in general. Middle C is notated on one ledger line below the staff.The F clef(also called bass clef) is used for low instruments, such as cello, double bass, bassoon and trombone,

and the low register in general. Middle C is notated on one ledger line above the staff.

The C clefcan occur on the third or fourth line:

On the third line it is called alto clefand used for viola and alto-trombone exclusively.

On the fourth line it is called tenor clefand used for the middle-high register of low instruments, such as

the cello, double bass and trombone.

In both cases, middle C is notated on the (middle) line where the clef is put.

Further study

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Special:Browse/Staff - browse to find more whiteboards treating staffs.

Special:Browse/Clef - browse to find more whiteboards treating clefs.

Directions of notestems

As seen in the basic forms of notes, those symbols with a notestem have two versions: one with the notestem upwards,

one with the notestem downwards. The proper direction of the notestem depends on severals circumtances:

The position of the single notehead (with 1/2 and 1/4 notes): only on the the third line of the staff one canchoose freely, but should still sometimes take some care at producing a logical sequence of notes, depending on

the grouping; noteheads below the third line have stems directing upwards, noteheads above the third line have

stems directing downwards (bars 1 and 2)

1.

When the average of the beamed group is neither above nor below the third line, one can freely choose in which

direction the stems should point. (bar 3)

2.

In more complex groups of notes connected with beams, the amount of "upwardness" of "downwardness" of all

the noteheads is calculated per group; when on average below the third line, stems go up, and when on average

above the third line, stems go down; (bars 4 and 5)

3.

Basic tones

Definition of basic tones

There are 7 basic tonesin most music, from which all other tones are derived by alteration. Together, these 7 basic

tones make up a diatonic scale, for example a church mode. These basic tones occur in different nomenclatures.

Note that a tone represents a pitch, and is technically not identical to a note.

Systems for basic tones

There are various and different systems and nomenclatures for basically the same 7 basic tones.

The examples in the following sections make use of 3 different clefs.

Alfabetic nomenclature

In the international Western system, the following basic tones are used:

c, d, e, f, g, a, b

This alfabetic nomenclature normally denotes the following tones in notation:

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German nomenclature

In the German nomenclature, the meaning of the letters is slightly deviant, as the b denotes an already altered tone in

notation:

c, d, e, f, g, a, h

Latin nomenclature

Latin nomenclature is another widely used and originally Western system, based upon Latin solmisation:

do, re, mi, fa, sol, la, si

Relative Latin nomenclature

The latin nomenclature can also be used relatively, and docan then mean any chromatic tone, for example:

Note that in these last transpositions, some basic tones are altered in the notation.

Alteration is treated in the next paragraph.

Indian nomenclature

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In Indian nomenclature the following basic tones or swaras are used:

SA, RE, GA, MA, PA, DHA, NI

These can be represented in notation as well, in Indian notation:

S R G M P D N

Indian nomenclature transcribed

Transcribed to Western notation, SA is usually rendered as c, even though on different instruments SA can vary, so

such transcriptions may need retranscription to a certain key if intended for pratical performance.

There are two systems representing the lower and higher octaves, one using a dot above or below the tone, such as !.The other system is more easy to use, typing on a computer keyboard, with apostrophes to the right when higher, such

as S' and to the left when in a lower octave, such as 'S. I will use the latter:

Further study

Special:Browse/Basic tone - browse to find whiteboards treating basic tones.

Alteration

Definition of alteration

Alterationin music is the changing of a basic tone, by raising or lowering it's pitch with one or two semitones or

other microtones; opening up possibilties of alteration is the first step in the direction of a chromatic system.

Symbols for alteration

In notation the following signs are used for this:

Sharp, to raise the pitch by one semitone;

Flat, to lower the pitch by one semitone;

Double sharp, to raise the pitch by two semitones;

Double flat, to lower the pitch by two semitones;

Natural, to correct any of the previous alterations.

In the example below, all these alterations are notated on a b, with the enharmonic equivalents added after each note,

but small:

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Validity of alteration symbols

Sharps and flats notated at the clef (notated beforethe time signature!) are indications of a key signature; see the

explanation on the circle of fifths. Sharps and flats as part of a key signature are valid for the whole staff and for all

octaves, until revoked or changed into a new key signature.

Incidental sharps and flats can occur anywhere within a bar, and are valid for that bar only and only in the octave

where they are placed. Often, so called cautionary accidentalsare added to the following bar, to prevent mistakes.

Cautionary accidentals can be

a sharp, to remind one that a former flat or natural of a previous bar is no longer valid;1.

a flat, to remind one that a former sharp or natural of a previous bar is no longer valid;2.

a natural, to remind one that a former sharp or flat of a previous bar is no longer valid.3.

All this is summarized in the slightly complex example below:

This melody is composed in C minor. When notating music, choosing the right key is indeed very important, as

"wrong notation" will confuse the reader, which is all too often also the future performer. The key is stated by the key

signature, and although the key here is somewhat ambiguous due to the abundant use of alterations, this key is still

confirmed by careful listening; and this impression could easily be reinforced by adding the proper harmonies to it.

The key however is therefore not as apparent as it may seem from merely glancing at the key signature: for example

there are five c's and just two e!'s, furthermore quite some extra alterations occur, plus it seems to first end in major,

before reverting back to minor at last.[5]

When in doubt, the hearing takes priority over reading in determining "what

key is it". Now this example was composed to demonstrate how to read accidentals in practice, and so it contains a

number of details which need special attention:

The bars in detail:

Immediately the 6th and 7th notes of the scale of c minor (natural minor being always taken as a key signature)

are altered, to create a temporary minor melodic scale, the c#is notated correctly as such, and not to be

confused with the d!, which appears later: here it is a leading tonefrom ctowards d;

1.

The second tone, c, has a cautionary accidentaladded to it: a natural, reminding the reader that the validity of

the sharp just before is cancelled by the new bar. Whithout the natural, this tone would still be cnatural, but this

fact could easily be overlooked during performance. The cautionary accidental placed before the a!is put in

parentheses (this is a matter of taste for the engraver[6]

), eliminating the likelihood of another abeing

erroneously performed here. Parenthesizing cautionary accidentals is merely another possible style, and

normally the use of the two different styles of cautionary accidentals is avoided in one and the same bar (or even

2.

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in one and the same piece of sheet music altogether); however, in this example this is done for obvious

instructional reasons.

Two more incidental accidentals: d!and bnatural; although not a single b!appears in the melody, it still

belongs at the clef, as it is part of the correct key signature.

3.

A most uncommon sight: the second, higher, dhas no sign to make clear whether here also a d!was intended; a

possible cautionary accidental has been omitted. Confusing passages like this will often lead to varying

performances of the same sheet music. According to the strict rule however, the second dis natural, and should

be performed as such. Hearing should confirm its logic (or not, as much modern music can be ambiguous in

such matters).

4.

This bar contains no cautionary accidentals, and the student should try to read it properly him- or herself,

applying the rules which have been set out and explained before.

5.

In some modern notation, flats and sharps are never valid beyond the note before which they are placed. In such

notation often also bars and a time signature are missing (even though such music is not necessarily without rhythm),

and sheet music like this should normally mention this out of the ordinary use of accidentals in a footnote or preface.

Microtone alteration

There is is no general standardization as to how to notate the finer-than-semitone intonations sometimes prescribed by

composers or played by performers. In different books and scores, various alternatives have been used. In any case,notation does allow for precise quarter tone alteration and finer microtones such as shrutis and commas, as well as

completely different tuning systems such as the Huygens-Fokker 31 tone system[7]

.

Further study

Special:Browse/Alteration - browse to find whiteboards treating alteration.

Notation of intervals, chords and harmony

When notating simultaneous pitches, these are placed in exact vertical correspondance (one above the other), except

with neighbouring notes or smaller, as these will partially obliterate each other: these are placed diagonally or next toeach other when identical. The placement of the notes is independent of the presence or absence of notestems, in the

examples below the notestems are present for easier reference.

Notation in scores

Multiple staves can be combined into a staff-system, normal use of a staff-system will assign one staff to each

instrument. Square brackets are used to group a staff-system (or a part of it) together, curly brackets assign more than

one staff to one instrumental part, as is e.g. customary in piano notation.

In a staff-system multiple staves are vertically synchronized like layers of simultaneous notation, the staves are

connected at least at the beginning, but usually also at the end. Normally the bar lines are drawn through all the staves

of a staff-system, but in case of a large score barlines between groups are not vertically connected.

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As a rule, the staves of higher pitched instruments are put above thos of the lower instruments. If this is done per

group for all instruments of the classical orchestra, we call this the score-orderof the staves.

The following orchestrated example is based upon the same music as the above, yet by its very orchestral sound

implies a slower tempo. It also has a larger staff-system in which the instrument groups are visually linked by the use

of square brackets on the left. The groups are also kept visually apart by the interrupted barlines between the groups:

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In the above example there is still a lot missing: there are still no signs added to indicate tempo, dynamics, articulation

or other special performance indications such as trills, mutes for the brass, stick type for timpani and so on.

In a score like this it is possible to notate several musical instruments on one staff, to save space. Note however, that in

these cases the notestems of the parts point in different directions (one-staff polyphonic notation).

This score, set in normal score-order for the classical orchestra (top to bottom) is:

Woodwind instruments (pic, 2fl, 2ob, 2cl, bcl, 2bsn, cbn)Brass Instruments (4 hn, 3tp, 3tbn, tb)

Percussion (timp)

Strings (vi1, vi2, vla, vc, cb)

Any additional solo-instrument would have to be added just above the first violin staff of the string section.

Compact polyphonic notation

Notation of chords is a simple way of notating more than one simultaneous tone on a staff. Using this notation of

connecting several noteheads to one notestem, has one limitation however: all tones must have the same timing and

rhythm. In various cases it may be desirable to notate more than one melody on one and the same staff, with different

timing and rhythm for each changing part. The example below was composed to demonstrate what a simple two-voice

notation could look like: all tones belonging to a melody share the same direction of notestems.

More complex notation can be encountered using this compact polyphonic notation, especially in certain editions of

the keyboard fugues of Johann Sebastian Bach, where often also rests are included in this type of notation[8]

.

Other notation symbols

Tempo indications

An essential part of music, and therefore of notation, is the tempo. The very same music, performed in different tempi,

can have vastly different effects and atmospheres. A proper choice of tempo is one of the main things any musician

should be keenly aware of, and this choice is often dependent on the acoustic properties of the venue where a certain

performance takes place as well.

There are many ways of notating tempo, all basic ways are indicated in the example below:

Classical tempo notation

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Classical tempo notation is done inItalianterms, a short list of which is given here:

Largo- Literally: broad, wide: very slow, one of the slowest tempo indications, only surpassed by the

superlative term Larghissimo; another variation is the diminutive Larghetto, slightly less slow

Lento- Literally: slow: generally slow, not further specified

Grave- Literally: heavy: for serious music, with a procession-like tempo but much slower than Andante

Adagio- Literally: gentle, quietly, carefully: medium slow

Andante- Literally: going: slightly slow, like strolling rather than walkin; the diminutive Andantinois slightly

less slow, and generally lighterModerato- Literally: moderate: moderate tempo, neither slow nor fast

Allegro- Literally: merry, cheerful: generally fast, but not too fast; the diminutive Allegrettois lighter and less

fast

Vivace- Literally: lively: fast and lively

Presto- Literally:prompt, immediate: very fast, the fastest tempo indication, only surpassed by the superlative

term Prestissimo

Other Italian tempo-related terms which are relative to prior parts can also be encountered:

Meno mosso- Literally: less motion: less fast than the passage before

Istesso tempo- Literally: same tempo: same tempo as before, even though this may seem to not be the case

Tempo primo- Literally:first tempo: revert to the tempo of the first section of the piece

Metronome numbers

Beethoven was one of the first composers to use a metronome. Metronomes until

recently had a limited numer of standard positions, a selection still often

encountered in scores, ranging from 40-208 in steps of 3, 4, 6 or 8:

40 - 44 - 48 - 52 - 56 - 60 (indicated "Largo")

60 - 63 - 66 (indicated "Larghetto")

66 - 69 - 72 - 76 (indicated "Adagio")

76 - 80 - 84 - 88 - 92 - 96 - 100 - 104 - 108 (indicated "Andante")108 - 112 - 116 - 120 (indicated "Moderato")

120 - 126 - 132 - 138 - 144 - 152 - 160 - 168 (indicated "Allegro")

168 - 176 - 184 - 192 - 200 (indicated "Presto")

200 - 208 (indicated "Prestissimo")

Today digital metronomes are in widespread use and allow for a stepwise choice of

tempi in beats per minute, ranging from 40 - 208 in steps of 1.[9]

An interesting fact is that the tempo numbers correspond by and large by the number of beats per minute a living

human heart can support: at lower and at higher rates a person dies.

Counting value changes

Counting value changes can be exactly notated by comparing note values, one should take care in reading and writing

this, as the equalssign =should be read as becomes: meaning in the example above, that the counting value of thequarter note is henceforward replaced by the dotted quarter note as counting value, while not changing counting

tempo.

Jazz tempo notation

In jazz, tempi are generally loosely notated, and may greatly vary per performance; even one and the same piece can

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be recorded or performed at a wide variety of tempi. For reading notated Jazz, the following short list of commonly

used terms is given here:

(BALLAD)- "Jazz ballad": slow, to very slow, generally with swing notation

(MED BALLAD)- "Medium ballad": medium slow, with swing notation

(MED)- "Medium tempo": with swing notation

(MED WALTZ)- "Medium waltz": medium tempo waltz, in 3/4, usually with swing notation

(BOSSA)- "Bossa Nova": medium tempo with non-swing notation

(MED UP LATIN)- "Medium up tempo, Latin": with non swing notation(FAST 3)- "Fast in three": fast 3/4 tempo

(UP)- "Up tempo": fast or very fast, with swing notation

Dynamic indications

Dynamic indications are indications of the loudness, or sound volume, of the music to be performed.

The basic dynamic indications are usually printed in bold italics, and are given in the example below:

TheseItalianterms are explained here:

pp,pianissimo: very soft

p,piano: soft

mp, mezzo piano: medium soft

mf, mezzo forte: medium loud

f,forte: loud

ff,fortissimo: very loud

In contemporary composed music, the fourfould indicationsppppandffffare quite common, and even up to a sixfold

pppppcan be found with a composer like Morton Feldman. Nevertheless all these indications are quite relative and

one should not be mistaken about the apparent precision they seem to imply. In practice, many more shades and

differences than e.g. MIDI allows for (128 steps) are possible, but it makes no sense trying to notate such fine nuances.

When for example a whole passage is indicated mfit will be only a computer to play all these notes at the same

volume; all performers subtly vary the loudness of individual notes, this practice is a normal organic element of

human music in all styles and from all ages.

Other terms are:

fp,fortepiano: a loud beginning, then an immediately soft sustained tone; variations such asfpporffmpand thelike are also possbible

sfz, sforzatoor rf, rinforzato: reinforced tone, especially at the beginning, which is generally less an accent but

more a quick though gradual temporal loudness growing into and leaving the beginning of a tone

Gradual and sudden transitions of dynamics are also possible, both can be seen in the example below:

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crescendo, or cresc.: getting louder gradually, it is also possible to indicate this by widening lines

diminuendo, or dim.is the same as decrescendoor decresc.: getting gradually softer, it is also possible toindicate this by narrowing lines

subito, or sub.: "suddenly" inItalian, indicating a sudden transistion to another, often unexpected, sound

volume; typically, in the example aboveffcomes unexpectedly after a diminuendoand an unexpectedppafter a

crescendo; the word subitonot only clarifies this beyond doubt but more importantly a performer is more likely

to not oversee this intended sudden dynamic transistion

As a final remark to these indications being relative, let it be noted that for orchestral or bigband use a mffor a

trumpet more or less equals afof a section of violins, (tenor or alto) saxophone or a french horn, and even affof a

flute or solo violin, if measured in dB[10]

. But all these dynamics depend not only on the timbre[11]

but also on the

register of the note played; for example a single piccolo playingfin its highest register can always be heard, even with

10 trumpets playingffat the same time.

Articulation

There is a wide variety of possible articulations, many of which can be notated. But as articulation depends not only

on style but also on the musical instrument used, these articulations can greatly vary in practice. Even such basic

articulations as staccatoare very different in performance between for example a violin and a flute player, both

classically trained. One should always check how certain players or types of players respond to certain articulation

signs before prescribing these in a musical score.

Some examples of articulations are provided in the example below:

In different styles, there are different attitudes as well towards notated articulation. Jazz performers are used to

choosing most if not all articulations themselves, often on the spot, as improvised, even when they are written out

exactly in the sheet music; leading to a lively performance for sure, though perhaps not as a composer originally

intended. In Jazz big bands one can expect more discipline as to the exact performance of notated articulation,

especially with regard to slurs and short or accented notes. When working with classically trained musicians on the

other hand, one needs to alwaysprovide at least a minimum of notated articulation, or none at all will be performed: in

this tradition, players don't usually add their own articulations and are not used to improvising even these, unless they

are soloists and performing as such. Especially string players that perform in sections need to coordinate their bowing,

and will always change bowing direction when notes are not slurred. For this reason, at least the slurring of groups of

notes into phrases can be recommended for string orchestras, because in this case (and only in this particular case:

with string groups) it is true that adding slurs is almost mandatory, as writing them will always lead to a better and

more coordinated performance, almost even independent of how the slurs are placed.

When providing articulation however, one should take care not to overburden the sheet music with too many signs and

symbols, as this may lead performers' attention away from the more essential structural elements of the music, such as

phrasing and breath, and so as not to provoke unnecessary mistakes.

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Basic building blocks of melody and harmony

Scales

Definition of scale

A scaleis a collection of tones arranged in a stepwise ascending or descending order, usually spanning one octave,sometimes two.

The above example in notation is of a theoretical nature, because notation without a clef on the staff does not define

the pitches.

Different scales

Different scales can start and end on different tones or tonics, and alteration of tones can be used to achieve an even

greater variety of scales. There are numerous scales used throughout the world, sometimes with different ascending

and descending scales.

A larger set of scales can be derived from basic major, minor and diminished scales.

Basic major and minor scales

Major scale

The major scale consists of two identical tetrachords(4 note groups), each 1 - 1 - "separated by a whole tone,together: 1 1 "1 1 1 "

From the major scale the church modes are derived. As a church mode, this scale is called ionian.

Natural minor scale

From the major scale the natural minor scale can be derived.

The natural minor scale is derived from the major scale, which runs from its 6th step: 1 "1 1 "1 1, and it is calledaeolian as part of the church modes.

Harmonic minor scale

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The harmonic minor scale is derived from natural minor by not lowering the seventh step: 1 "1 1 "1"".

This scale is not a diatonic scale, as there is an augmented second appearing between the 6th and 7th steps.

From the harmonic minor, the harmonic minor modes can be derived.

Melodic minor scale

The melodic minor scale is derived from both major and minor by combining the lower and upper tetrachords of each,

1 "1and 1 1 "thus running: 1 "1 1 1 1 ".

From the melodic minor, the melodic minor modes can be derived.

Definition of mode

A mode, like a scale, is a collection of tones arranged in a stepwise ascending or descending order, generally spanning

one octave.

More than a scale, in musical practice, a mode can have specific melodic requirements for performance, such as a

specific order of playing the pitches involved in a makam or raga. Music based on the use of modes is generally called

modalmusic, and though not excluding the use of harmony, this term is generally used in opposition to music

"powered" by functional harmony, which is called tonalmusic.

Church modes

The church modesare modes which are derived from degrees of the major scale.

"Church modes" is the conventional name for the seven basic theoretical medieval diatonic scales and their related

derivatives, which were at the time used in European church music. This modal system was used in medieval music,

yet their names are older and derived from ancient Greek music theory.

In their basic form the church modes can be notated with only basic tones.

History and use

The church mode system is the predecessor to the Western major-minor diatonic system. The name "church modes"

still refers to their usage in christian Gregorian chantand early polyphony, but since they are a result of a

standardization process, they cannot be but a theoretically simplified (and thus highly censored) representation of what

was actually sung in early Christendom, which must have had music and scales taken from a much older music, and

larger collection of scales, used outside of, not exclusively before the existence of, the christian church. The 7

surviving modes incorporated into this collection are purely diatonical[12]

, and derived from 1 basic scale, they each

just start and end on a different tone.

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Since the development of Jazz

theory, the church modes, or shorter:

"the modes", have become an

integral part of teaching

improvisation to jazz musicians. An

extraordinary example of a very

elaborate system for modal

improvisation in jazz is George

Russel'sLydian chromatic concept

of tonal organization[13]

. Although

the practical value of church modes

for modal jazz (mostly with

alterations) is undisputed, in fast

music ("up tempo") with fast

changes of harmony ("changes"),

their actual use remains highly

questionable from a theoretical point

of view, and is of little practical use.

For pedagogical use these modes arestill a wonderful beginners-tool to

enhance auditive awareness and

develop a sense of melody, interval

and harmony, and for developing

instrumental improvisation,

independent of style; however, they

have little practical value for

improvising over fast changes.

Different modal systems exist in

other traditions, such as the Arabic

moqqaam-, the Turkish makam-, theNorth Indian (often somewhat

ethnocentrically called "Hindustani")

thaat-, and South Indian (also called

"Carnatic") melakarta- systems.

Basic notation

The 7 basic modes are:

Ionian - from c to c - c d e f g

a b c

Dorian - from d to d - d e f g a b c d

Phrygian - from e to e - e f g a b c d e

Lydian - from f to f - f g a b c d e f

Mixolydian - from g to g - g a b c d e f g

Aeolian - from a to a - a b c d e f g a

Locrian - from b to b - b c d e f g a b

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The basic notation of these modes consists of basic tones and can be done without any alterations (click these music

examples for playback):

Notation on c

When notating all these modes on c, there appears a different logical order, by the number of alterations needed.

Thus a partial circle of fifths is found with the help of the original tonics: F - C - G - D - A - E - B.

Different modes

Different modes can start and end on different fundamental tones or tonics, and alteration of tones can be used to

achieve an even greater variety of modes. There are numerous modes used throughout the world, sometimes with

different ascending and descending scales.

Further study

Special:Browse/Scale - browse to find more whiteboards treating scales.

Special:Browse/Mode - browse to find more whiteboards treating modes.

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IntervalsDefinition of interval

An intervalin music is the sound of exactly two tones sounding together, or one after the other.

All intervals can be measured by the number of diatonic steps and by their semitone distances. More technically, an

interval can also be described as a frequency ratio relationship between two stable vibrations. All intervals can also

occur on (above or below) all tones.

Many different tunings and hence intervals have been developed and used in various traditions[14]

, this Outline of

basic music theory treats the internationally customary tuning in Equal Temperament[15]

.

One sound

The sounding together of two tones creates a blending of the two into a new, specific sound, is called the interval.

Within the sound of each interval, partial tones can be perceived, emerging from the interaction of frequencies as sum-

and difference tones. Each interval thus consists of far more than just the two tones played or performed, it is a

complex sound which is at first perceived as a whole.

Basic intervals

Due to notation, intervals are named by the distance between the two basic tones they consist of.

When the lowest tone is counted as 1, the name of the interval follows from counting in diatonic steps upwards

(although reversing this direction gives the same result):

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Wide intervals

Wider than the octave, music theory describes larger intervals. Though similar, the sound of these is also quite

different from that of their related narrower intervals.

The similarity with the narrower basic intervals lies in the fact, that both contain the same harmonic content: the same

pitches of tones. Yet the actual sound of these wide intervals, e.g. with regard to consonance and dissonance, is at the

same time so different, that they can be considered as independent musical entities as well: these are intervals in their

own right, and not mere octave transpositions.

Perception of the interval

The unique sound of each interval can be immediately recognized by hearing, making it in fact a truly fundamental

element of all music.

When listening to two simultaneous tones, their pitches and frequencies mix and react, creating even more tones

sounding together: interference tones. This complex of tones becomes one comprehensive sound, and the individual

pitches become acoustically more or less absorbed into the human perception of the single interval: the interval itself

is in fact perceived as louder than the individual tones it consists of. It is human perception which "summarizes" the

tones into the single interval, but it has good acoustic reasons to do so. Thus the interval is equally the basic

prerequisite for all melody as it is for harmony.

Basic intervals from c

The basic intervals using only basic tones from care shown below (click to play the examples).

The second series consists in fact of inversions of the first, in reverse order.

Full names of the intervals

A full name of an interval consists of the qualityplus the distance, such as minor second(m2),perfect fifth(P5), or

augmented sixth(A6) etc.

Each interval thus has a "first" and a "last name".

For the purpose of shorter and easier writing the names of the intervals are abbreviated in the following way: the

intervals are represented by numbers, their qualities by preceding letters.

Summary of the abbreviations:

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d m P M A

unisons d1 P1 A1

seconds d2 m2 M2 A2

thirds d3 m3 M3 A3

fourths d4 P4 A4

fifths d5 P5 A5

sixths d6 m6 M6 A6

sevenths d7 m7 M7 A7

octaves d8 P8 A8

Qualities:

M= Major

m= minor

P= Perfect

A= Augmented

d= diminished

Distances:

1= unison

2= second

3= third

4= fourth

5= fifth

6= sixth

7= seventh

8= octave

The whiteboard image shows the semitone relationships between the qualities of intervals:

perfectare the unison, fourth, fifth and octave plus wider versions of these;[16]

majoris larger than minor;augmentedis larger than major or perfect;

diminishedis smaller than minor or perfect.

Finally, double diminished and double augmented intervals are theoretically possible, but extremely rare.

The table below thus lists all possible basic intervals. Below the table, these are also presented in notation, with cas

reference tone (remember, all intervals can occur on -above or below- all tones!).

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semitones -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13

interval d1P1,

d2

A1,

m2

M2,

d3

A2,

m3

M3,

d4

A3,

P4

A4,

d5

P5,

d6

A5,

m6

M6,

d7

A6,

m7

M7,

d8

A7,

P8 A8

Intervals in order of chromatic size

The table below lists all possible basic intervals in order of number of semitones, these are also presented in notation

with their enharmonic equivalents, with cas reference tone (remember, all intervals can occur on -above or below- all

tones!).

Enharmonic equivalence

The possibility of writing one and the same sound with two different diatonic spellings is called enharmonic

equivalence; such two intervals are enharmonically the same. When listened to separately, the number of semitones

will determine the sound, and in ear-training usually the simpler spelling is heard, interpreted and given. Within a

certain musical context however, more complex phenomena may occur, requiring specific writing, spelling and

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nature type

P"P 2"7

M"m 3"6

A"d 4"5

nomenclature, giving prevalence to one of the two possibilities for contextual reasons.

In one case, a special name was assigned to such a pair of enharmically equivalent intervals: the name tritonecan be

used to designate both the augmented fourth and the diminished fifth; this unique interval acoustically equals its own

inversion. The name was derived from the fact that this interval equals exactly three whole tone distances (six

semitones).

Inversions of the intervals

The inversions describe close relationships between intervals in pairs: an interval and its inversion use the same notes,

but in different order or position. The two inversions together span a perfect octave, 12 semitones, thus the inversion

of aMajor thirdis the minor sixth, calculated as M3 (4 semitones) and m6 (8 semitones), together 4 + 8 = 12

semitones (P8).

The close relationship between inversions can be clearly heard, as well as the fundamental difference in sound. No

interval should be mixed up with its inversion, they are not identical, nor is one derived from the other[17]

.

The inversions are below presented in notation, with cas reference tone (remember, all intervals can occur on -above

or below- all tones!).

The inversion of a perfect interval is always a perfect interval, the inversion of a major interval always a minor

interval, the inversion of a diminished interval always an augmented interval, and all vice versa as well. The inversion

of a second is a seventh, of a third a sixth, of a fourth a fifth, and vice versa. The tritoneis the only interval which is

enharmonically the sameas its inversion, such as can be heard by clicking and playing the above example.

A table to help quickly find the names of the inversions is given here:

Further study

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Special:Browse/Interval - browse to find whiteboards treating intervals.

Triads

Definition of triad

A triadis a special type of chord which consists of 3 different tones, in consecutive thirds.

The triad thus consists of a minimum of three intervals: 2 thirds and 1 fifth, or their respective inversions.

Basic notation

The basic notation of a triad, is by virtually taking tones 1, 3 and 5 of a scale and writing them together.

The examples below use the basic tones only and can be clicked for playback.

Basic scale and triad of c:

Basic scale and triad of d:

Basic scale and triad of e:

Basic scale and triad of f:

Basic scale and triad of g:

Basic scale and triad of a:

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Triad Symbols

Major Maj M !

Minor min m -

Diminished dim d

Augmented Aug A +

Flat 5 !5 -5

Double

diminished(no symbol)

Basic scale and triad of b:

Types of triads

Consisting of 2 thirds and one fifth, the thirds can be major or minor, and the fifth can be perfect, diminished or

augmented, there are 6 types of triads.

Major triad: consisting of a major third, a minor third and a perfect fifth;

Minor triad: consisting of a minor third, a major third and a perfect fifth;

Augmented triad: consisting of a major third, a major third and an augmented fifth;

Diminished triad: consisting of a minor third, a minor third and a diminished fifth;

Flat 5 triad: consisting of a major third, a diminished third and a diminished fifth;

Double Diminished triad: consisting of a diminished third, a major third and a diminished fifth.

These triads can occur on any tone, the examples below are the 6 triads of c(alterations are needed to obtain the

tones):

Symbols for triads

For most music in which improvising plays an important role, symbols are used for triads and chords.

There is no unity in the systems used for these symbols, as different symbols occur in different books.

Below is a table summarizing the most commonly used chord-symbols for triads:

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Inversions of triads

A triad is still considered to be the same triad when the 3 tones it consists of are presented in another position than the

basic 1-3-5 described so far. There are three basic positions for a triad:

The 1 is the lowest tone, this is called root position, short: root1.

The 3 is the lowest tone, this is called first inversion or sixth position, short: 62.

The 5 is the lowest tone, this is called second inversion or six-four position, short: 6-43.

The acoustic properties are different, yet these positions can be perceived as derived from one basic structure: the

triad. This perception evolved by the end of the 15th century in Europe, and the triads (and their inversions) quickly

entered Western classical music to dominate it for centuries to come, at the cost of the polyphony which prevailed

before. Harmony thus replaced melody as the structuring principle of musical logic.

The examples below are the positions of the triads of c:

The names of the inversions are derived from the intervallic structure: the inversions of the thirds become sixths

(major, minor or augmented), and the inversions of the fifths become fourths (perfect, augmented or diminished).

Other positions of triads

Any chord with more than just three tones, but consisting of just three tones making up a triad, is also perceived as,

and considered to be, a triad. In this way, triads can be performed with more pitches, yet three basic tones only, as is

the case in many compositions for piano, band, choir, ensemble or orchestra.

Other designations for positions of triads are:

closed position- short CP, when no triad-tones fit between the tones played, the position of the lowest tone, the

bass, is disregarded in this respect

open position- short OP, when exactly one triad tone would fit between the tones played, the position of the

lowest tone, the bass, is disregarded in this respect

mixed position- short MP, when the position has a mix of "open" and "closed" intervals, the position of the

lowest tone, the bass, is disregarded in this respect

octave position- short 8P, when the highest tone played is the 1

third position- short 3P, when the highest tone played is the 3

fifth position- short 5P, when the highest tone played is the 5

Some examples, demonstrating these positions of the triad of c-major, for piano:

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Use of triads

Any scale or mode can be harmonizedby forming triads on its steps, these triads (or, when expanded: seventh chords)

are called degrees.

The harmony thus obtained is proper to that particular scale itself and can be modal or tonal, depending on its use.

Further study

Special:Browse/Triad - browse to find more whiteboards treating triads.

Seventh chords

Definition of seventh chord

A seventh chordis a special type of

chord which consists of 4 different

tones, in consecutive thirds.

The seventh chord thus consists of a

minimum of six intervals: 3 thirds, 2

fifths and 1 seventh, or their

respective inversions.

A seventh chord can be regarded as

en expanded triad; each seventh

chord itself consists of 2 triads.

The relationships of all types of

seventh chords with their constituent

triads and intervals are shown in the

whiteboard picture.

Basic notation

The basic notation of a seventh chord, is by virtually taking tones 1, 3, 5 and 7 of a scale and writing them together,

sounding as one.

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The example below uses the basic tones only and can be clicked for playback.

Types of seventh chords

Consisting of 3 thirds, 2 fifths and 1 seventh, the thirds can be major, minor or diminished, fifths can be perfect,

diminished or augmented, the sevenths can be major, minor or diminished. There are no seventh chords which contain

an augmented third, as the enharmonic equivalence of this interval, the perfect fourth, is such a strong consonant that

its top note would acoustically assume the position of the root of the whole chord, thus leading to the perception of an

extended triad. Thus the number of possible seventh chords is limited to just 11:

Major seventh: consisting of a major third, a minor third, a major third, two perfect fifths and a major seventh1.

Dominant seventh: consisting of a major third, a minor third, a minor third; one perfect fifth, one diminished

fifth and a minor seventh

2.

Minor seventh: consisting of a minor third, a major third, a minor third; two perfect fifths and a minor seventh

(enharmonically equivalent to a Major triad with added 6 in third inversion)

3.

Minor major seventh: consisting of a minor third, a major third, a major third; one perfect fifth, one augmented

fifth and a major seventh

4.

Half diminished: consisting of two minor thirds, a major third; one diminished fifth, a perfect fifth and a minor

seventh (enharmonically equivalent to a Minor triad with added 6 in third inversion)

5.

Diminished seventh: consisting of three minor thirds; two diminished fifth and a diminished seventh

(enharmonically equivalent to itself in all inversions)

6.

Augmented seventh: consisting of two major thirds, a minor third; an augmented fifth, a perfect fifth and a

major seventh

7.

Augmented dominant: consisting of two major thirds, a diminished third; an augmented fifth, a diminished

fifth and a minor seventh

8.

Flat 5 dominant: consisting of a major third, a diminished third, a major third; two diminished fifths and a

minor seventh (enharmonically equivalent to itself in second inversion)

9.

Double diminished minor seventh: consisting of a diminished third, a major third, a major third, a diminished

fifth, an augmented fifth and a minor seventh (enharmonically equivalent to an Augmented dominant in third

inversion)

10.

Double diminished seventh: consisting of a diminished third, a major third, a minor third, a diminished fifth, a

perfect fifth and a diminished seventh (enharmonically equivalent to a Dominant seventh in third inversion)

11.

The whiteboard image shows the relative mutual proximity and similarity of the 9 basic seventh chords. The arrows

indicate how an alteration of one chord tone will change the chord into a neighbouring, different, but closely related,related seventh chord.

All seventh chords can occur on any tone, the notated example below shows all 11 theoretically possible seventh

chords of c(alterations are needed to obtain the correct tones). In practice however, only 9 seventh chords have actual

chord-symbols: the last two seventh chords have no chord-symbol of themselves. These two would rather be notated

as third inversions, slash chords of d(D7#5/C and D7/C, as notated in small black notes), of which they are

enharmonic equivalents:

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Seventh chord Symbols

Major seventh maj7 M7 !7

Dominant seventh Dom7 7

Minor major seventh minmaj7 mM7 -!7

Minor seventh min7 m7 -7

Half diminished min7!5 m7!5

Diminished seventh dim7 d7 7

Augmented seventh maj7#5 M7#5 !7+5

Augmented dominant 7#5 7+5 +7

Flat 5 dominant 7!5 7-5

Symbols for seventh chords

For most music in which improvisation plays an important role, symbols are used for seventh chords.

There is no unity in the systems used for these symbols, as different symbols occur in different books.

Below is a table summarizing the most commonly used chord-symbols for seventh chords:

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Double diminished types

(notated as

third

inversions on

another root)

Inversions of seventh chords

A seventh chord is still considered to be the same seventh chord when the 4 tones it consists of are presented in

another position than the basic 1-3-5-7 described so far. There are four basic positions for a seventh chord:

The 1 is the lowest tone, this is called root position, short: root1.

The 3 is the lowest tone, this is called first inversion or six-five position, short: 6-52.

The 5 is the lowest tone, this is called second inversion or four-three position, short: 4-33.

The 7 is the lowest tone. this is called third inversion or second position, short: 24.

The acoustic properties are different, yet these positions can be perceived as derived from one basic structure: the

seventh chord.

The examples below are basic positions of seventh chords of cand on c:

The names of the inversions are

derived from the intervallic

structure: the inversions of the thirds

become sixths (major, minor or

augmented), the inversions of the

fifths become fourths (perfect,

augmented or diminished) and the

inversions of the sevenths become

seconds (major, minor or

augmented).

The whiteboard image shows a full

table of the nine seventh chords thathave chord symbols, in all

inversions on c(not "of" c, as only

the root positions are C chords!).

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perfect consonants imperfect consonants dissonants

P1, P8, P5, P4 M3, m3, M6, m6

M2, m2, M7, m7, tritoneplus all augmented and diminished intervals

(no matter if they are enharmonically

consonant)

Use of seventh chords

Any scale or mode can be harmonizedby forming seventh chords on its steps. These seventh chords are then called

degrees.

The harmony thus obtained is proper to that particular scale itself and can be modal or tonal, depending on its use.

Further study

Special:Browse/Seventh chord - browse to find more whiteboards treating seventh chords.

Consonance and dissonance

Definitions of consonance and dissonance

Consonantliterally means: sounding together

Dissonantliterally means: sounding apart

Let us stop a moment and consider these concepts more closely. Especially the concept dissonantmay seem strange inthe context of music, which after all consists of sounds combined together into one piece. When playing simultaneous

sounds, these will "sound together" by the very definition of their simultaneousness. The whole purpose of introducing

the concepts of consonance and dissonance however, is to make distinctions in the nature and quality of the

innummerable possibilities of combining sounds. But then, why just make this distinction seemingly oversimple and

merely dual, almost resembling the opposites "good" vs "bad"?[18]

The quality of the "sound together" is in fact strongly depending on the musically formal and harmonical contexts in

which it occurs. Correspondingly, according to Louis & Thuilles "Harmonielehre" one should distinguish between the

phenomena of acoustic dissonanceand interpretational dissonance(German:Auffassungsdissonant)[19]

. I consider

this phenomenon as an integral part of the concept of harmonyin a wider sense, and distinguish further between

formally and harmonically contextual dissonances.

Before going into finer detail, we shall consider the traditional classical theoretical view on consonance versus

dissonance first.

Traditional classification of intervals in consonant and dissonant

Traditionally, only the basic the intervals are classified, based on their use in the type of harmony used in classical

music.

This classification, though all too often still taught as factual, is actually rather outdated and of little practical value for

most contemporary music, such as Jazz, Pop and World music, as well as contemporary composition; hence we will

take a closer look at their actual acoustic properties next.

Acoustic order of consonance and dissonance in intervals

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An attempt has been made here to establish an acoustic order of the basic and wide intervals, starting with the most

consonant, gradually evolving to the more dissonant, somewhat like Hindemith'sReihe 2[20]

. In this order it can be

observed how the wide intervals are in fact found in perhaps unexpected places for the traditionally educated music

theoreticians, but as "the proof of the pudding is in the eating", in sound "the proof of the theory is in the hearing", as

one can observe oneself.

This order may be true for these intervals exactly as notated, on cone octave below central c, and yet it may differ

somewhat when gradually transposed to other tones, more so even in different registers. Also, this order can basically

be regarded to be true for the instrument on which it is perceived, here: the piano. But consonance and dissonance

depend on the harmonics-structure of the instrument used, as well as on the medium for the sound waves: the air itself,

so far taken for granted. Dolphins, porpoises and whales, living and using an enormous variety of sounds under water,in many more octaves than we humans can perceive, should have a quite different perception of these intervals. Good

examples of completely different sets of intervals in world music are offered by Indonesian gamelan: the bells used

produce totally different overtones than the piano.

When composing, arranging or improvising, great care has to be taken to judge the sounds intended not on mere

theoretical grounds, but on the actual perception intended, clearly and precisely defined, taking exact register positions

into account, or else one may end up with music that looks good, but sounds bad, as is all too often the case when

relying too much on general theoretical knowledge, superficially studied, only partly digested and not fully

understood.[21]

Consonance and dissonance in scales

Consonance and dissonance in scales is generated from the presence and position of contextual harmonically

dissonant intervalsembedded within a particular scale. Thus all diatonic scales contain at least one tritone, and most

pentatonic scales have no dissonant intervals at all.

Dissonance in a scale adds a harmonic element of tension to its melodic structure, certain tones always stand out in a

particular scale, exactly because of this.

Let us consider this in the church modes.

The most remarkable tones by which we recognize the church modes are:

the sharp 4 in lydian1.

the flat 7 in mixolydian2.

the natural 6 in dorian3.

the flat 2 in phrygian4.

the flat 5 in locrian5.

Which does make one wonder about the two remaining modes: by what special characteristics do we recognize ionian

and aeolian, also known as the basic major and minor scales, or do they stand out in a negative sense, by having no

special characteristics at all?

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chord type: consonants dissonants

triads maj and min all others:, #5 , !5 and double dim

seventh chords maj7 and min7all others:7, minmaj7, , 7, maj7#5, 7#5 and

7!5

Now, as the image presented here

attempts to show:

all remarkable tones are part

of an embedded tritone;

1.

in all 5 remarkable cases this

tritone is connected to the

basic triad 1-3-5 supporting

the scale, the remarkable tonebeing outside the triad on 2, 4,

6 or 7 (except in locrian which

has the tritone on 1-5);

2.

only in ionian (4-7) and

aeolian (2-6) the complete

embedded tritone is

disconnected from this basic

triad.

3.

So we can conclude that the major

and natural minor scales are well

suited for tonal music, which

depends on the use of triads 1-3-5

throughout, as the tritones embedded

in these scales do not burden its

basic sound with dissonance,

reserving its embedded tension to be

used on degrees other than its proper

tonic I.

The accuracy of this phenomenological observation and line of reasoning are strongly confirmed by the fact that for

tonal use, the minor harmonic scale is customary, which does not flatten the 7th tone, and which like natural minor has

a tritone between 2 and 6. In this scale a second tritone is introduced by the natural 7, adding more tension to thisscale. The position of this additional tritone now is remarkably enough between 4 and 7: exactly the same as in ionian

(major). Therefore we can conclude that by embedding both tritones the minor harmonic scale combines the tension

roperties of major and minor into one scale, which sheds quite a new light on the concepts of molldurand durmoll,

which are customary in functional harmony.[22]

Finally, this procedure gives some clues as to how one can go about harmonizing makams and ragas, and in fact to the

different phenomenology of harmony itself in music based on modes such as these, many of which are not

harmonically connected to 3 and 5 by their performance traditions.

Traditional classification of chords in consonant and dissonant

Traditionally, only chords with perfect fifths between 1 and 5, and in the case of seventh chords also between 3 and 7,are considered consonant.

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Noteworthy is that the second inversion of the consonant chords is considered to be a typical contextual dissonant.

Use of consonance and dissonance

Consonance is a term that describes the phenomenon of several sounds or pitches blending together, almost as if

becoming one, a unity of sound. Dissonance on the other hand, is a term that describes tensionin sound, as if sounds

or pitches do not blend together, and remain separate auditive entities. The apperception of whether sounds do or do

not blend is highly subjective however, and strongly dependent on musical context, whereas tensionis a moreobjectively measurable property in sound itself.

Infunctional harmony, that is: harmony employing degrees and thus harmonic functions, the usual order is that of an

increase of tension followed by a moment relaxation, so using more and increasing dissonance, to be followed and the

tension released by consonance. The consonance is always chosen in relation to the musical context, the dissonants

employed are style- and context-related as well. As a general rule however, it is the dissonants which represent the

strongest expressional means in harmony.

Circle of fifths

Major scales in order of accidentals

It is possible to construct a major scale on every tone, and different accidentals are needed to induce the proper order

of steps: whole, whole, halfin both tetrachords (4 tone scale part). Only the scale of c majoryields this without use of

accidentals. Both c d e fand g a b cshare this structure: 1 1 ". These tetrachords are both connected to thefundamental c, the first has it as lowest, the second as highest note. The remaining interval f gis a consequence of this

tetrachordal construction, and in itself a whole step (major second). The total scale thus shows 1 1 "1 1 1 ".

When constructing this on different tones, we can set the scales we find into the following order by number of

accidentals, those we find having sharps:

And those we find having flats:

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If we allow for the

outline of basic music theory - www.oscarvandillen.com

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