Talk:Genus (music)

From Wikipedia, the free encyclopedia

Wikipedia:WikiProject Tunings, Temperaments, and Scales This article is part of the WikiProject Tunings, Temperaments, and Scales to improve Wikipedia's articles related to musical tunings, temperaments, and scales.

[edit] Removed

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

Gn = Gn−1 ∪ Gn−2

or

Gn = Gn−1 ∪ (Gn−1 − Gn−2).

So let G1 be a 1-tone scale, then

G2 = G1 ∪ G'1

is a 2-tone scale,

G3 = G2 ∪ G'1

is a 3-tone scale,

G4 = G3 ∪ G'2

is a pentatonic scale,

G5 = G4 ∪ G'2

is a diatonic scale,

G6 = G5 ∪ G'4

is a chromatic scale, and

G7 = G6 ∪ G'4

is an enharmonic scale, or, alternatively,

G7 = G6 ∪ G'5

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

This microtonal 19-tone scale could be followed by

G8 = G7 ∪ G'6

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

G9 = G8 ∪ G'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}

Is this really appropriate for this page? It sounds like Joseph Yasser's Theory of Evolving Tonality (which we need an article on BTW), but it doesn't sound like it has much to do with the Greek genera. The diatonic scale made from the diatonic genus is one step in Yasser's progression, but the chromatic and enharmonic don't have much to do with it — unless I'm missing something? —Keenan Pepper 14:34, 5 December 2005 (UTC)

Also, the link to Harry Partch's 43-tone scale is inappropriate. —Keenan Pepper 14:37, 5 December 2005 (UTC)

What about the other, sourced, information you removed? (which I have readded despite one redundancy) Hyacinth 01:23, 30 April 2006 (UTC)
I see a lot more redundancies. I'll try to integrate it. —Keenan Pepper 02:12, 30 April 2006 (UTC)
...the diatonic contained a minor second at top with two major seconds at the bottom... I was sure (and Chalmers's book backs me up) that the diatonic genus had a major second at the top, and the remaining minor third divided various ways, usually with something like a minor second on the bottom. Luckily, FSU's music library has a copy of Miller and Lieberman, so I'll check it out and see for myself if there's really a conflict. —Keenan Pepper 02:42, 30 April 2006 (UTC)
In the ancient sources, the greek authors often wrote of pitch "upside down" from the way we tend to think of it today, and this may have been the source of some confusion here? Offhand, my copy of "A History of Western Music" (Grout, ed. Palisca, Sixth ed. 2001) lists the Diatonic as "E D C B" descending, Chromatic as "E C-sharp C B" and Enharmonic as "E C C-flat B", which from what I can tell about the text is based on Aristoxenus' writings (which don't refer to tuning in any rigorous mathematical way, as I recall them). A description of the note names (mese, parhypate, etc.) might be in order on this page as well. Rainwarrior 09:30, 30 April 2006 (UTC)

[edit] Diatonic and chromatic

The terms diatonic and chromatic cause serious uncertainties at several Wikipedia articles, and in the broader literature. Some of us thought that both terms needed special coverage, so we started up a new article: Diatonic and chromatic. Why not have a look, and join the discussion? Be ready to have comfortable assumptions challenged! – Noetica♬♩ Talk 22:24, 3 April 2007 (UTC)