Talk:Genus (music)

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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}
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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)
replies: text: What about the other, sourced, information you removed? (which I have readded despite one redundancy) Hyacinth 01:23, 30 April 2006 (UTC)
replies: text: I see a lot more redundancies. I'll try to integrate it. —Keenan Pepper 02:12, 30 April 2006 (UTC)

text: ...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)
replies: text: 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)
thread_title: Removed

message: 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)
thread_title: Diatonic and chromatic

message: [I note with some amusement that I have been commenting this article already years ago. I am not particularly interested by Greek genera, but...]
The lede to the article said:
:The tetrachordal system has been inherited by the modal theory of Byzantine music and may have been one source of the later theory of the jins of Arabic music.
without any mention of the Latin theory, which, obviously, did inherit the tetrachordal system as early as Hucbald's Musica in the late 9th century, and which built on it its construction of the musical scale, its solmization system, etc. etc. So, I added a mention of Latin theory.
I don't know enough about Byzantine theory, but I really wonder how its modal theory could be based on the tetrachordal system – unless one equates mode with scale. 
I had already modified the mention of Arabic jins (shouldn't it be ajnas, plural of jins?), to stress that this too was a matter of heritage. I keep wondering when the Arabic theory developed a theory of ajnas (which today form an important part of the teaching of Arabic modal theory in Arabic Conservatoires, I think). I cannot refrain thinking that this was a result of the presence of Western "experts" on Greek theory at the Cairo Congress of 1932, but this is something I was never able to prove – nor any of my Arabic students to disprove.
This all to say that I think that this article might require some attention by people knowing better than I do. — Hucbald.SaintAmand (talk) 20:09, 12 September 2019 (UTC)
thread_title:  Heritage of the Greek tetrachordal system