Harmony - Wikipedia, The Free Encyclopedia

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10/17/13 1:10 PMHarmony - Wikipedia, the free encyclopedia

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Barbershop quartets, such as this US Navy group,sing 4-part pieces, made up of a melody line

(normally the lead) and 3 harmony parts.

HarmonyFrom Wikipedia, the free encyclopedia

In music, harmony is the use of simultaneous pitches

(tones, notes), or chords.[1] The study of harmony

involves chords and their construction and chord

progressions and the principles of connection that

govern them.[2] Harmony is often said to refer to the

"vertical" aspect of music, as distinguished from melodic

line, or the "horizontal" aspect.[3] Counterpoint, which

refers to the interweaving of melodic lines, and

polyphony, which refers to the relationship of separate

independent voices, are thus sometimes distinguished

from harmony.

In popular and jazz harmony, chords are named by theirroot plus various terms and characters indicating their

qualities. In many types of music, notably baroque,

romantic, modern and jazz, chords are often augmented

with "tensions". A tension is an additional chord member that creates a relatively dissonant interval in

relation to the bass. Typically, in the classical common practice period a dissonant chord (chord with

tension) "resolves" to a consonant chord. Harmonization usually sounds pleasant to the ear when there is a

balance between the consonant and dissonant sounds. In simple words, that occurs when there is a balance

between "tense" and "relaxed" moments.

Contents

1 Etymology and definitions

2 Historical rules3 Types4 Intervals

5 Chords and tension6 Perception of harmony

7 Consonance and dissonance in balance8 See also

9 References9.1 Footnotes9.2 Notations

10 External links

11 Further reading

Etymology and definitions

The term harmony derives from the Greek (harmona), meaning "joint, agreement, concord",[4]
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Rameau's 'Trait de l'harmonie'

(Treatise on Harmony) from 1722.

from the verb (harmozo), "to fit together, to join".[5] The term was often used for the whole field ofmusic, while "music" referred to the arts in general. In Ancient Greece, the term defined the combination of

contrasted elements: a higher and lower note.[6] Nevertheless, it is unclear whether the simultaneous

sounding of notes was part of ancient Greek musical practice; "harmona" may have merely provided a

system of classification of the relationships between different pitches. In the Middle Ages the term was used

to describe two pitches sounding in combination, and in the Renaissance the concept was expanded to

denote three pitches sounding together.[6]

It was not until the publication of Rameau's 'Trait de l'harmonie'

(Treatise on Harmony) in 1722 that any text discussing musical practice

made use of the term in the title, though that work is not the earliest

record of theoretical discussion of the topic. The underlying principle

behind these texts is that harmony sanctions harmoniousness (sounds

that 'please') by conforming to certain pre-established compositional

principles.[7]

Current dictionary definitions, while attempting to give concisedescriptions, often highlight the ambiguity of the term in modern use.

Ambiguities tend to arise from either aesthetic considerations (for

example the view that only "pleasing" concords may be harmonious) or

from the point of view of musical texture (distinguishing between

"harmonic" (simultaneously sounding pitches) and "contrapuntal"

(successively sounding tones).[7] In the words of Arnold Whittall:

While the entire history of music theory appears to depend on just

such a distinction between harmony and counterpoint, it is no less

evident that developments in the nature of musical composition

down the centuries have presumed the interdependenceat times amounting to integration, at

other times a source of sustained tensionbetween the vertical and horizontal dimensions of

musical space.

[7]

The view that modern tonal harmony in Western music began in about 1600 is commonplace in music

theory. This is usually accounted for by the 'replacement' of horizontal (of contrapuntal) writing, common in

the music of the Renaissance, with a new emphasis on the 'vertical' element of composed music. Modern

theorists, however, tend to see this as an unsatisfactory generalisation. As Carl Dahlhaus puts it:

It was not that counterpoint was supplanted by harmony (Bachs tonal counterpoint is surely no

less polyphonic than Palestrinas modal writing) but that an older type both of counterpoint and

of vertical technique was succeeded by a newer type. And harmony comprises not only the

(vertical) structure of chords but also their (horizontal) movement. Like music as a whole,

harmony is a process.

[8][9]

Descriptions and definitions of harmony and harmonic practice may show bias towards European (orWestern) musical traditions. For example, South Asian art music (Hindustani and Carnatic music) is
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frequently cited as placing little emphasis on what is perceived in western practice as conventional

'harmony'; the underlying 'harmonic' foundation for most South Asian music is the drone, a held open fifth

(or fourth) that does not alter in pitch throughout the course of a composition.[10] Pitch simultaneity in

particular is rarely a major consideration. Nevertheless many other considerations of pitch are relevant to the

music, its theory and its structure, such as the complex system of Rgas, which combines both melodic and

modal considerations and codifications within it.[11]

So, intricate pitches combinations that sound simultaneously do occur in Indian classical musicbut they

are rarely studied as teleological harmonic or contrapuntal progressionsas with notated Western music.

This contrasting emphasis (with regard to Indian music in particular) manifests itself in the different

methods of performance adopted: in Indian Music improvisation takes a major role in the structural

framework of a piece,[12] whereas in Western Music improvisation has been uncommon since the end of the

19th century.[13] Where it does occur in Western music (or has in the past), the improvisation either

embellishes pre-notated music or draws from musical models previously established in notated

compositions, and therefore use familiar harmonic schemes.[14]

Nevertheless, emphasis on the precomposed in European art music and the written theory surrounding itshows considerable cultural bias. The Grove Dictionary of Music and Musicians (Oxford University Press)

identifies this clearly:

In Western culture the musics that are most dependent on improvisation, such as jazz, have

traditionally been regarded as inferior to art music, in which pre-composition is considered

paramount. The conception of musics that live in oral traditions as something composed with

the use of improvisatory techniques separates them from the higher-standing works that use

notation.

[15]

Yet the evolution of harmonic practice and language itself, in Western art music, is and was facilitated by

this process of prior composition (which permitted the study and analysis by theorists and composers alike

of individual pre-constructed works in which pitches (and to some extent rhythms) remained unchanged

regardless of the nature of the performance).[16]

Historical rules

Some traditions of Western music performance, composition, and theory have specific rules of harmony.These rules are often described as based on natural properties such as Pythagorean tuning's law whole

number ratios ("harmoniousness" being inherent in the ratios either perceptually or in themselves) or

harmonics and resonances ("harmoniousness" being inherent in the quality of sound), with the allowable

pitches and harmonies gaining their beauty or simplicity from their closeness to those properties. This model

provides that the minor seventh and ninth are not dissonant (i.e., are consonant). While Pythagorean ratios

can provide a rough approximation of perceptual harmonicity, they cannot account for cultural

factors.[citation needed]

Early Western religious music often features parallel perfect intervals; these intervals would preserve the

clarity of the original plainsong. These works were created and performed in cathedrals, and made use of theresonant modes of their respective cathedrals to create harmonies. As polyphony developed, however, the
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Close position C major triad. Play

use of parallel intervals was slowly replaced by the English style of consonance that used thirds and sixths.

The English style was considered to have a sweeter sound, and was better suited to polyphony in that it

offered greater linear flexibility in part-writing. Early music also forbade usage of the tritone, as its

dissonance was associated with the devil, and composers often went to considerable lengths, via musica

ficta, to avoid using it. In the newer triadic harmonic system, however, the tritone became permissible, as the

standardization of functional dissonance made its use in dominant chords desirable.

Most harmony comes from two or more notes sounding simultaneouslybut a work can imply harmony

with only one melodic line by using arpeggios or hocket. Many pieces from the baroque period for solo

string instrumentssuch as Bach's Sonatas and partitas for solo violin and celloconvey subtle harmony

through inference rather than full chordal structures. These works create a sense of harmonies by using

arpeggiated chords and implied basslines. The implied basslines are created with low notes of short duration

that many listeners perceive as being the bass note of a chord. (See below):

Example of implied harmonies in J.S. Bach's Cello Suite no. 1 in G,

BWV 1007, bars 1-2. Play or Play harmony

Types

Carl Dahlhaus (1990) distinguishes between coordinate and

subordinate harmony. Subordinate harmony is the hierarchicaltonality or tonal harmony well known today. Coordinate harmony is

the older Medieval and Renaissance tonalit ancienne, "The term is

meant to signify that sonorities are linked one after the other without

giving rise to the impression of a goal-directed development. A first

chord forms a 'progression' with a second chord, and a second with a

third. But the former chord progression is independent of the later

one and vice versa." Coordinate harmony follows direct (adjacent)

relationships rather than indirect as in subordinate. Interval cycles

create symmetrical harmonies, which have been extensively used by

the composers Alban Berg, George Perle, Arnold Schoenberg, BlaBartk, and Edgard Varse'sDensity 21.5.

Close harmony and open harmony use close position and open position chords, respectively. See: voicing

(music) and close and open harmony.

Other types of harmony are based upon the intervals of the chords used in that harmony. Most chords used

in western music are based on "tertian" harmony, or chords built with the interval of thirds. In the chord C

Major7, C-E is a major third; E-G is a minor third; and G to B is a major third. Other types of harmony

consist of quartal harmony and quintal harmony.

Unison is considered a harmonic interval, just like a fifth or a third. What's unique about unison is that it is

two identical notes being played or sung together. Most people only consider thirds and fifths and sevenths
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Open position C major triad. Play

to be "harmony". But, unison does count as harmony, and is very

important in orchestration, especially. In Pop music, unison singing

is usually called "doubling" which is what The Beatles used to do a

lot in their early music. As a type of harmony, singing in unison or

playing the same notes, often using different musical instruments, at

the same time is commonly called monophonic harmonization.

Intervals

An interval is the relationship between two separate musical pitches.

For example, in the melody Twinkle Twinkle Little Star, the first two

notes (the first "twinkle") and the second two notes (the second

"twinkle") are at the interval of one fifth. What this means is that if

the first two notes were the pitch C, the second two notes would be the pitch "G"four scale notes, or seven

chromatic notes (a perfect fifth), above it.

The following are common intervals:

Root Major third Minor third Fifth

C E E G

D F F A

D F F A

E G G B

E G

G BF A A C

F A A C

G B B D

A C C E

A C C E

B D D F

B D D F

Therefore, the combination of notes with their specific intervals a chord creates harmony. For example,

in a C chord, there are three notes: C, E, and G. The note C is the root. The notes E and G provide harmony,

and in a G7 (G dominant 7th) chord, the root G with each subsequent note (in this case B, D and F) provide

the harmony.

In the musical scale, there are twelve pitches. Each pitch is referred to as a "degree" of the scale. The names

A, B, C, D, E, F, and G are insignificant. The intervals, however, are not. Here is an example:
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1 2 3 4 5 6 7 8

C D E F G A B C

D E F G A B C D

As can be seen, no note always corresponds to a certain degree of the scale. The tonic, or 1st-degree note,

can be any of the 12 notes (pitch classes) of the chromatic scale. All the other notes fall into place. For

example, when C is the tonic, the fourth degree or subdominant is F. When D is the tonic, the fourth degree

is G. While the note names remain constant, they may refer to different scale degrees, implying different

intervals with respect to the tonic. The great power of this fact is that any musical work can be played or

sung in any key. It is the same piece of music, as long as the intervals are the samethus transposing the

melody into the corresponding key. When the intervals surpass the perfect Octave (12 semitones), these

intervals are called compound intervals, which include particularly the 9th, 11th, and 13th Intervalswidely

used in jazz and blues Music.

Compound Intervals are formed and named as follows:

2nd + Octave = 9th3rd + octave = 10th

4th + Octave = 11th5th + octave = 12th6th + Octave = 13th7th + octave = 14th

The reason the two numbers don't "add" correctly is that one note is counted twice. Apart from this

categorization, intervals can also be divided into consonant and dissonant. As explained in the following

paragraphs, consonant intervals produce a sensation of relaxation and dissonant intervals a sensation of

tension. In tonal music, the term consonant also means "brings resolution" (to some degree at least, whereasdissonance "requires resolution").

The consonant intervals are considered the perfect unison, octave, fifth, fourth and major and minor third

and sixth, and their compound forms. An interval is referred to as "perfect" when the harmonic relationship

is found in the natural overtone series (namely, the unison 1:1, octave 2:1, fifth 3:2, and fourth 4:3). The

other basic intervals (second, third, sixth, and seventh) are called "imperfect" because the harmonic

relationships are not found mathematically exact in the overtone series. In classical music the perfect fourth

above the bass may be considered dissonant when its function is contrapuntal. Other intervals, the second

and the seventh (and their compound forms) are considered Dissonant and require resolution (of the

produced tension) and usually preparation (depending on the music style used). It should be noted that the

effect of dissonance is perceived relatively within musical context: for example, a major seventh interval

alone (i.e. C up to B) may be perceived as dissonant, but the same interval as part of a major seventh chord

may sound relatively consonant. A tritone (the interval of the fourth step to the seventh step of the major

scale, i.e. F to B) sounds very dissonant alone, but less so within the context of a dominant seventh chord

(G7 or D7 in that example).

Chords and tension

Main article: Chord (music)

Main article: Consonance and dissonance
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In the Western tradition, in music after the seventeenth century, harmony is manipulated using chords,

which are combinations of pitch classes. In tertian harmony, so named after the interval of a third, the

members of chords are found and named by stacking intervals of the third, starting with the "root", then the

"third" above the root, and the "fifth" above the root (which is a third above the third), etc. (Note that chord

members are named after their interval above the root.) Dyads, the simplest chords, contain only two

members (see power chords).

A chord with three members is called a triad because it has three members, not because it is necessarily built

in thirds (see Quartal and quintal harmony for chords built with other intervals). Depending on the size of

the intervals being stacked, different qualities of chords are formed. In popular and jazz harmony, chords are

named by their root plus various terms and characters indicating their qualities. To keep the nomenclature as

simple as possible, some defaults are accepted (not tabulated here). For example, the chord members C, E,

and G, form a C Major triad, called by default simply a C chord. In an A chord (pronounced A-flat), the

members are A, C, and E.

In many types of music, notably baroque, romantic, modern and jazz, chords are often augmented with

"tensions". A tension is an additional chord member that creates a relatively dissonant interval in relation tothe bass. Following the tertian practice of building chords by stacking thirds, the simplest first tension is

added to a triad by stacking on top of the existing root, third, and fifth, another third above the fifth, giving a

new, potentially dissonant member the interval of a seventh away from the root and therefore called the

"seventh" of the chord, and producing a four-note chord, called a "seventh chord".

Depending on the widths of the individual thirds stacked to build the chord, the interval between the root

and the seventh of the chord may be major, minor, or diminished. (The interval of an augmented seventh

reproduces the root, and is therefore left out of the chordal nomenclature.) The nomenclature allows that, by

default, "C7" indicates a chord with a root, third, fifth, and seventh spelled C, E, G, and B. Other types of

seventh chords must be named more explicitly, such as "C Major 7" (spelled C, E, G, B), "C augmented 7"(here the word augmented applies to the fifth, not the seventh, spelled C, E, G, B), etc. (For a more

complete exposition of nomenclature see Chord (music).)

Continuing to stack thirds on top of a seventh chord produces extensions, and brings in the "extended

tensions" or "upper tensions" (those more than an octave above the root when stacked in thirds), the ninths,

elevenths, and thirteenths. This creates the chords named after them. (Note that except for dyads and triads,

tertian chord types are named for the interval of the largest size and magnitude in use in the stack, not for the

number of chord members : thus a ninth chord has five members, not nine.) Extensions beyond the thirteenth

reproduce existing chord members and are (usually) left out of the nomenclature. Complex harmonies based

on extended chords are found in abundance in jazz, late-romantic music, modern orchestral works, filmmusic, etc.

Typically, in the classical Common practice period a dissonant chord (chord with tension) resolves to a

consonant chord. Harmonization usually sounds pleasant to the ear when there is a balance between the

consonant and dissonant sounds. In simple words, that occurs when there is a balance between "tense" and

"relaxed" moments. For this reason, usually tension is 'prepared' and then 'resolved'.[17]

Preparing tension means to place a series of consonant chords that lead smoothly to the dissonant chord. In

this way the composer ensures introducing tension smoothly, without disturbing the listener. Once the piece

reaches its sub-climax, the listener needs a moment of relaxation to clear up the tension, which is obtainedby playing a consonant chord that resolves the tension of the previous chords. The clearing of this tension
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The harmonious major triad is composed of

three tones. Their frequency ratio

corresponds approximately 6:5:4. In real

performances, however, the third is often

larger than 5:4. The ratio 5:4 correspondsto an interval of 386 cents, but an equally

tempered major third is 400 cents and a

Pythagorean third with a ratio of 81:64 is

408 cents. Measurements of frequencies in

good performances confirm that the size of

the major third varies across this range and

can even lie outside it without sounding out

of tune. Thus, there is no simple connection

between frequency ratios and harmonic

function.

usually sounds pleasant to the listener, though this is not always the case in late-nineteenth century music,

such as Tristan und Isolde by Richard Wagner.[17]

Perception of harmony

Harmony is based on consonance, a concept whose definition has changed various times during the history

of Western music. In a psychological approach, consonance is a continuous variable. Consonance can varyacross a wide range. A chord may sound consonant for various reasons.

One is lack of perceptual roughness. Roughness happens when partials (frequency components) lie within a

critical bandwidth, which is a measure of the ear's ability to separate different frequencies. Critical

bandwidth lies between 2 and 3 semitones at high frequencies and becomes larger at lower frequencies. The

roughness of two simultaneous harmonic complex tones depends on the amplitudes of the harmonics and the

interval between the tones. The roughest interval in the chromatic scale is the minor second and its inversion

the major seventh. For typical spectral envelopes in the central range, the second roughest interval is the

major second and minor seventh, followed by the tritone, the minor third (major sixth), the major third

(minor sixth) and the perfect fourth (fifth).

The second reason is perceptual fusion. A chord fuses in

perception if its overall spectrum is similar to a harmonic series.

According to this definition a major triad fuses better than a

minor triad and a major-minor seventh chord fuses better than a

major-major seventh or minor-minor seventh. These differences

may not be readily apparent in tempered contexts but can

explain why major triads are generally more prevalent than

minor triads and major-minor sevenths generally more prevalent

than other sevenths (in spite of the dissonance of the tritone

interval) in mainstream tonal music. Of course these

comparisons depend on style.

The third reason is familiarity. Chords that have often been

heard in musical contexts tend to sound more consonant. This

principle explains the gradual historical increase in harmonic

complexity of Western music. For example, around 1600

unprepared seventh chords gradually became familiar and were

therefore gradually perceived as more consonant.

Western music is based on major and minor triads. The reason

why these chords are so central is that they are consonant in

terms of both fusion and lack of roughness. they fuse because

they include the perfect fourth/fifth interval. They lack

roughness because they lack major and minor second intervals.

No other combination of three tones in the chromatic scale

satisfies these criteria.

Consonance and dissonance in balance
http://en.wikipedia.org/wiki/Harmonic_series_(music)http://en.wikipedia.org/wiki/Minor_sixthhttp://en.wikipedia.org/wiki/Major_sixthhttp://en.wikipedia.org/wiki/Harmony#cite_note-Schejtman-17http://en.wikipedia.org/wiki/Cent_(music)http://en.wikipedia.org/wiki/Major_chordhttp://en.wikipedia.org/wiki/File:Major_triad.svg


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Post-nineteenth century music has evolved in the way that tension may be less often prepared and less

formally structured than in Baroque or Classical periods, thus producing new styles such as post-romantic

harmony, impressionism, pantonality, Jazz and Blues, where dissonance may not be prepared in the way

seen in 'common practice' harmony. In a jazz or blues song, the tonic chord may be a dominant seventh

chord.

The creation and destruction of harmonic and 'statistical' tensions is essential to the maintenance

of compositional drama. Any composition (or improvisation) which remains consistent and

'regular' throughout is, for me, equivalent to watching a movie with only 'good guys' in it, or

eating cottage cheese.

Frank Zappa, "The Real Frank Zappa Book" page 181, Frank Zappa and PeterOcchiogrosso, 1990

See also

Chromatic chordChromatic mediantHomophony (music)

List of musical terminologyMathematics of musical scalesMusica universalis

Organum (polyphonic chant)Peter Westergaard's tonal theoryProlongationPhysics of music

Tonality

Unified fieldVoice leading

References

Footnotes

1. ^ Malm, William P. (1996).Music Cultures of the Pacific, the Near East, and Asia, p.15. ISBN 0-13-182387-6.

Third edition. "Homophonic texture...is more common in Western music, where tunes are often built on chords

(harmonies) that move in progressions. Indeed this harmonic orientation is one of the major differences betweenWestern and much non-Western music."

2. ^ Dahlhaus, Car. "Harmony", Grove Music Online, ed. L. Macy (accessed 24 February 2007), grovemusic.com

(http://www.grovemusic.com/) (subscription access).

3. ^ Jamini, Deborah (2005).Harmony and Composition: Basics to Intermediate, p.147. ISBN 1-4120-3333-0.

4. ^ '1. Harmony' The Concise Oxford Dictionary of English Etymology in English Language Reference accessed via

Oxford Reference Online (http://www.oxfordreference.com/) (24 February 2007)

5. ^ Harmonia, Henry George Liddell, Robert Scott, "A Greek-English Lexicon", at Perseus

(http://www.perseus.tufts.edu/cgi-bin/ptext?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3D%2315282)

6. ^ ab Dahlhaus, Carl. "Harmony", Grove Music Online, ed. L. Macy (accessed 24 February 2007), grovemusic.com


7. ^abc

Arnold Whittall, The Oxford Companion to Music, ed. Alison Latham, (Oxford University Press, 2002)(accessed via [Oxford Reference Online], 16 November 2007 is gayubview=Main&entry=t114.e3144

(http://www.oxfordreference.com/views/ENTRY.html?this) )
http://www.oxfordreference.com/views/ENTRY.html?thishttp://en.wikipedia.org/wiki/Harmony#cite_ref-oxfordcompanion_7-2http://en.wikipedia.org/wiki/Harmony#cite_ref-oxfordcompanion_7-1http://en.wikipedia.org/wiki/Harmony#cite_ref-oxfordcompanion_7-0http://www.grovemusic.com/http://en.wikipedia.org/wiki/Grove_Dictionary_of_Music_and_Musicianshttp://en.wikipedia.org/wiki/Harmony#cite_ref-grovelead_6-1http://en.wikipedia.org/wiki/Harmony#cite_ref-grovelead_6-0http://www.perseus.tufts.edu/cgi-bin/ptext?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3D%2315282http://en.wikipedia.org/wiki/Harmony#cite_ref-5http://www.oxfordreference.com/http://en.wikipedia.org/wiki/Harmony#cite_ref-4http://en.wikipedia.org/wiki/Special:BookSources/1412033330http://en.wikipedia.org/wiki/Harmony#cite_ref-Jamini_3-0http://www.grovemusic.com/http://en.wikipedia.org/wiki/Grove_Dictionary_of_Music_and_Musicianshttp://en.wikipedia.org/wiki/Harmony#cite_ref-2http://en.wikipedia.org/wiki/Special:BookSources/0131823876http://en.wikipedia.org/wiki/Harmony#cite_ref-1http://en.wikipedia.org/wiki/Voice_leadinghttp://en.wikipedia.org/wiki/Unified_fieldhttp://en.wikipedia.org/wiki/Tonalityhttp://en.wikipedia.org/wiki/Physics_of_musichttp://en.wikipedia.org/wiki/Prolongationhttp://en.wikipedia.org/wiki/Peter_Westergaard%27s_tonal_theoryhttp://en.wikipedia.org/wiki/Organumhttp://en.wikipedia.org/wiki/Musica_universalishttp://en.wikipedia.org/wiki/Mathematics_of_musical_scaleshttp://en.wikipedia.org/wiki/List_of_musical_terminologyhttp://en.wikipedia.org/wiki/Homophony_(music)http://en.wikipedia.org/wiki/Chromatic_medianthttp://en.wikipedia.org/wiki/Chromatic_chordhttp://en.wikipedia.org/wiki/Frank_Zappahttp://en.wikipedia.org/wiki/Blueshttp://en.wikipedia.org/wiki/Jazzhttp://en.wikipedia.org/wiki/Impressionist_musichttp://en.wikipedia.org/wiki/Classical_Musichttp://en.wikipedia.org/wiki/Baroque_Music


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8. ^ Harmony, 3: Historical development. "Carl Dahlhaus", Grove Music Online, ed. L. Macy (accessed 16 November

2007), grovemusic.com (http://www.grovemusic.com/) (subscription access).

9. ^ see also Whitall 'Harmony: 4. Practice and Principle', Oxford Companion to Music

10. ^ Regula Qureshi. "India, I, 2(ii): Music and musicians: Art music", Grove Music Online, ed. L. Macy (accessed 16

November 2007), grovemusic.com (http://www.grovemusic.com/) (subscription access). and Catherine Schmidt

Jones, 'Listening to Indian Classical Music', Connexions, (accessed 16 November 2007) [1]

(http://cnx.org/content/m12502/latest/)

11. ^ Harold S. Powers/Richard Widdess. "India, III, 2: Theory and practice of classical music: Rga", Grove Music

Online, ed. L. Macy (accessed 16 November 2007), grovemusic.com (http://www.grovemusic.com/) (subscription

access).

12. ^ Harold S. Powers/Richard Widdess. "India, III, 3(ii): Theory and practice of classical music: Melodic

elaboration", Grove Music Online, ed. L. Macy (accessed 16 November 2007), grovemusic.com


13. ^ Rob C. Wegman. "Improvisation, II: Western art music", Grove Music Online, ed. L. Macy (accessed 16

November 2007), grovemusic.com (http://www.grovemusic.com/) (subscription access).

14. ^ Robert D Levin. "Improvisation, II, 4(i): The Classical period in Western art music: Instrumental music", Grove

Music Online, ed. L. Macy (accessed 16 November 2007), grovemusic.com (http://www.grovemusic.com/)

(subscription access).

15. ^ Bruno Nettl. "Improvisation, I, 2: Concepts and practices: Improvisation in musical cultures", Grove MusicOnline, ed. L. Macy (accessed 16 November 2007), grovemusic.com (http://www.grovemusic.com/) (subscription

access).

16. ^ see Whitall, 'Harmony'

17. ^ ab Schejtman, Rod (2008). The Piano Encyclopedia's "Music Fundamentals eBook", p.20-43 (accessed 10 March

2009). PianoEncyclopedia.com (http://PianoEncyclopedia.com)

Notations

Dahlhaus, Carl. Gjerdingen, Robert O. trans. (1990). Studies in the Origin of Harmonic Tonality,

p. 141. Princeton University Press. ISBN 0-691-09135-8.van der Merwe, Peter (1989). Origins of the Popular Style: The Antecedents of Twentieth-CenturyPopular Music. Oxford: Clarendon Press. ISBN 0-19-316121-4.Nettles, Barrie & Graf, Richard (1997). The Chord Scale Theory and Jazz Harmony. Advance Music,

ISBN 3-89221-056-X

External links

Chord Geometry - Graphical Analysis of Harmony Tool

(http://music.princeton.edu/%7Edmitri/ChordGeometries.html)

Interactive Lessons about harmonizing melodies and scales using different Musical Styles(http://pianoencyclopedia.com)Harmonic Progressions with demos and how to harmonize a melody (http://www.harmony.org.uk)

General Principles of Harmony by Alan Belkin (http://alanbelkinmusic.com/bk.H/index.html)Morphogenesis of chords and scales (http://www.lamadeguido.com/morphogenesis.htm) Chords andscales classification

A Beginner's Guide to Modal Harmony (http://www.standingstones.com/modeharm.html)Posts about traditional and jazz harmony (http://www.elsaposabio.com/musica)Sonantometry as Natural Harmony Algebra (http://sonantometry.blogspot.com)Chord Harmonization Tool (http://www.scales-chords.com/chordscalefinder.php) Online tool that

automates chord progression analysis to identify underlying scales and related chords
http://www.scales-chords.com/chordscalefinder.phphttp://sonantometry.blogspot.com/http://www.elsaposabio.com/musicahttp://www.standingstones.com/modeharm.htmlhttp://www.lamadeguido.com/morphogenesis.htmhttp://alanbelkinmusic.com/bk.H/index.htmlhttp://www.harmony.org.uk/http://pianoencyclopedia.com/http://music.princeton.edu/~dmitri/ChordGeometries.htmlhttp://en.wikipedia.org/wiki/Special:BookSources/389221056Xhttp://en.wikipedia.org/wiki/Special:BookSources/0193161214http://en.wikipedia.org/wiki/Special:BookSources/0691091358http://pianoencyclopedia.com/http://en.wikipedia.org/wiki/Harmony#cite_ref-Schejtman_17-1http://en.wikipedia.org/wiki/Harmony#cite_ref-Schejtman_17-0http://en.wikipedia.org/wiki/Harmony#cite_ref-16http://www.grovemusic.com/http://en.wikipedia.org/wiki/Grove_Dictionary_of_Music_and_Musicianshttp://en.wikipedia.org/wiki/Harmony#cite_ref-15http://www.grovemusic.com/http://en.wikipedia.org/wiki/Grove_Dictionary_of_Music_and_Musicianshttp://en.wikipedia.org/wiki/Harmony#cite_ref-14http://www.grovemusic.com/http://en.wikipedia.org/wiki/Grove_Dictionary_of_Music_and_Musicianshttp://en.wikipedia.org/wiki/Harmony#cite_ref-13http://www.grovemusic.com/http://en.wikipedia.org/wiki/Grove_Dictionary_of_Music_and_Musicianshttp://en.wikipedia.org/wiki/Harmony#cite_ref-12http://www.grovemusic.com/http://en.wikipedia.org/wiki/Grove_Dictionary_of_Music_and_Musicianshttp://en.wikipedia.org/wiki/Harmony#cite_ref-11http://cnx.org/content/m12502/latest/http://www.grovemusic.com/http://en.wikipedia.org/wiki/Grove_Dictionary_of_Music_and_Musicianshttp://en.wikipedia.org/wiki/Harmony#cite_ref-10http://en.wikipedia.org/wiki/Harmony#cite_ref-9http://www.grovemusic.com/http://en.wikipedia.org/wiki/Grove_Dictionary_of_Music_and_Musicianshttp://en.wikipedia.org/wiki/Harmony#cite_ref-8


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Further reading

Prout, Ebenezer,Harmony, its Theory and Practice (1889, revised 1901)

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