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Encyclopedia > Genus (music)
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In ancient Greek music there were three genera (singular: genus) for classifying musical scales: Wikibooks Wikiversity has more about this subject: School of Music Look up Music on Wiktionary, the free dictionary Wikisource, as part of the 1911 Encyclopedia Wikiproject, has original text related to this article: Music MusicNovatory: the science of music encyclopedia The Virginia Tech Multimedia Music Distionary, with definitions, pronunciations, examples... In music, a scale is a set of musical notes in order by pitch, either ascending or descending. ...

  1. diatonic
  2. chromatic
  3. enharmonic,

diatonic being the simplest and enharmonic the most complex. The chromatic scale is an extension of the diatonic scale: it can be generated by combining the diatonic scale with a complementary pentatonic scale. The enharmonic scale is an extension of the chromatic scale, in which pairs of enharmonic notes are distinguished from each other. In Music theory, the diatonic major scale (also known as the Guido scale), from the Greek diatonikos or to stretch out, is a fundamental building block of the European-influenced musical tradition. ... In music, chromatic indicates the inclusion of notes not in the prevailing scale and is also used for those notes themselves (Shir-Cliff et al 1965, p. ... In music, an enharmonic is a note which is the equivalent of some other note, but spelled differently. ... Jump to: navigation, search In music, a pentatonic scale is a scale with five notes per octave. ... In music, an enharmonic is a note which is the equivalent of some other note, but spelled differently. ...


The Greeks analzyed genera using various terms, including diatonic, enharmonic, and chromatic, the latter being the color between the two other types of modes which were seen as being black and white. Scales are constructed from conjunct or disjunct tetrachords: the tetrachords of the chromatic genus contained a minor third on top and two semitones at the bottom, the diatonic contained a minor second at top with two major seconds at the bottom, and the enharmonic contained a major third on top with two quarter tones at the bottom, all filling in the perfect fourth (Miller and Lieberman, 1998) of the fixed outer strings. However, the closest term used by the Greeks to our modern usage of chromatic is pyknon or the density ("condensation") of chromatic or enharmonic genera. Jump to: navigation, search A minor third is the smaller of two commonly occuring musical intervals that span three diatonic scale degrees. ... The musical interval of a half step, semitone, or minor second is the relationship between the leading tone and the first note (the root or tonic) in a major scale. ... Jump to: navigation, search A minor second is the smallest of three commonly occuring musical intervals that span two diatonic scale degrees; the others being the major second and the augmented second, which are larger by one and two semitones respectively. ... Jump to: navigation, search A major third is the larger of two commonly occuring musical intervals that span three diatonic scale degrees. ... A quarter tone is an interval half as wide (aurally, or logarithmically) as a semitone, which is half a whole tone. ... The perfect fourth or diatessaron, abbreviated P4, is the interval between the first note (the root or tonic) and the fourth note (subdominant) in a major scale. ... Jump to: navigation, search Density (symbol: ρ - Greek: rho) is a measure of mass per unit of volume. ... Condensation can refer to: The change in phase of a substance to a denser phase, such as gas to a liquid. ...

Didymos chromatic tetrachord 16:15, 25:24, 6:5
Eratosthenes chromatic tetrachord 20:19, 19:18, 6:5
Ptolemy soft chromatic 28:27, 15:14, 6:5
Ptolemy intense chromatic 22:21, 12:11, 7:6
Archytas enharmonic 28:27, 36:35, 5:4
(ibid)

The pentatonic scale is one subset of the diatonic scale, its complementary subset being the trivial 2-tone scale, in which the octave is divided into a perfect fifth and a perfect fourth. In music, an octave (sometimes abbreviated 8ve or 8va) is the interval between one musical note and another with half or double the frequency. ... The musical interval of a perfect fifth is the relationship between the first note (the root or tonic) and the fifth note in a major scale. ... The perfect fourth or diatessaron, abbreviated P4, is the interval between the first note (the root or tonic) and the fourth note (subdominant) in a major scale. ...


It is possible to generalize this concept of genus by establishing a hierarchy of genera G1, G2, G3, et cetera, such that either

Gn = Gn−1Gn−2

or

Gn = Gn−1 ∪ (Gn−1Gn−2).

So let G1 be a 1-tone scale, then

G2 = G1G'1

is a 2-tone scale,

G3 = G2G'1

is a 3-tone scale,

G4 = G3G'2

is a pentatonic scale,

G5 = G4G'2

is a diatonic scale,

G6 = G5G'4

is a chromatic scale, and

G7 = G6G'4

is an enharmonic scale, or, alternatively, An enharmonic scale is a musical scale in which there is no exact equivalence between a sharpened note and the flattened note it is enharmonically related to. ...

G7 = G6G'5

could be a microtonal scale with 19 tones in the octave.


This microtonal 19-tone scale could be followed by Microtonal music is music using microtones -- intervals of less than a semitone, or as Charles Ives put it, the notes between the cracks of the piano. ...

G8 = G7G'6

which would be a microtonal 31-tone scale (19 + 12 = 31),

G9 = G8G'6

which would be a microtonal 43-tone scale (31 + 12 = 43).


Examples:

  • G1 = {C}
  • G2 = {C,G} = {C} ∪ {G}
  • G3 = {C,F,G} = {C,G} ∪ {F}
  • G4 = {C,D,F,G,A} = {C,F,G} ∪ {D,A}
  • G5 = {C,D,E,F,G,A,B} = {C,D,F,G,A} ∪ {E,B}
  • G6 = {C,C#,D,D#,E,F,F#,G,G#,A,A#,B} = {C,D,E,F,G,A,B} ∪ {C#,D#,F#,G#,A#}
  • G7 = {C,C#,Db,D,D#,Eb,E,F,F#,Gb,G,G#,Ab,A,A#,Bb,B} = {C,C#,D,D#,E,F,F#,G,G#,A,A#,B} ∪ {Db,Eb,Gb,Ab,Bb}

Source

  • Miller, Leta E. and Lieberman, Frederic (1998). Lou Harrison: Composing a World. Oxford University Press. ISBN 0195110226.

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