Genus (music)

In ancient Greek music there were three genera (singular: genus) for classifying musical scales:\n# diatonic \n# chromatic \n# enharmonic,\ndiatonic 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. 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. It is possible to generalize this concept of genus by establishing a hierarchy of genera G₁, G₂, G₃, et cetera, such that either\n: G_n = G_n−1 ∪ G_n−2\nor\n: G_n = G_n−1 ∪ (G_n−1 − G_n−2). So let G₁ be a 1-tone scale, then\n: G₂ = G₁ ∪ G'₁\nis a 2-tone scale,\n: G₃ = G₂ ∪ G'₁\nis a 3-tone scale,\n: G₄ = G₃ ∪ G'₂\nis a pentatonic scale,\n: G₅ = G₄ ∪ G'₂\nis a diatonic scale,\n: G₆ = G₅ ∪ G'₄\nis a chromatic scale, and\n: G₇ = G₆ ∪ G'₄\nis an enharmonic scale, or, alternatively,\n: G₇ = G₆ ∪ G'₅\ncould be a microtonal scale with 19 tones in the octave. This microtonal 19-tone scale could be followed by\n: G₈ = G₇ ∪ G'₆\nwhich would be a microtonal 31-tone scale (19 + 12 = 31),\n: G₉ = G₈ ∪ G'₆\nwhich would be a microtonal 43-tone scale (31 + 12 = 43). Examples:\n* G₁ = {C}\n* G₂ = {C,G} = {C} ∪ {G}\n* G₃ = {C,F,G} = {C,G} ∪ {F}\n* G₄ = {C,D,F,G,A} = {C,F,G} ∪ {D,A}\n* G₅ = {C,D,E,F,G,A,B} = {C,D,F,G,A} ∪ {E,B}\n* 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#}\n* 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} Category:Musical scales