Talk:Genus (music)

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

G_n = G_n−1 ∪ G_n−2

or

G_n = G_n−1 ∪ (G_n−1 − G_n−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)

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)

Revised article as of July 2014

Jerome, this revision seems excellent. It deserves careful reading and the article probably must be considered rather specializer; but why not? There is no reason to present complex matters as if they were simple: the presentation must be as simple as can be, but at the same time show the complexity of the topic under discussion. I think that you achieve that excellently.

I have one (first) question. You write at some point that "Archytas used the simpler and more consonant 9/7", and your example shows that it corresponds to 435 cents. It what sense is this "more consonant"? Don't you equate "more consonant" with "simpler"? Would you consider that the simpler a ratio, the more "consonant" it is? Archytas may have thought so, but only because "consonant", for him, meant something utterly different from what it means to us... it probably meant to him "corresponding to a simpler ratio", which leads us to a circular argument.

What I mean with this is that, so far as we can tell, the whole question of "genre" was, for the Ancient Greek, a matter of ratios, of whole-number arithmetics. Your article begins speaking of "certain classes of intonations"; but what kind of intonations? Can we be sure that this whole discussion concerned actual intonations for the practice of music? Where these Greek intellectuals really interested in performed music? We cannot know, but that would seem rather doubtful (I don't know whether Matthiesen has anything to say about this). It seems to me, therefore, that the lead of the article should raise this question and state that we cannot know whether this whole affair was one of abstract discussion about ratios of whole numbers (which, for Pythagoreans and Platonicians, as they probably all where, entailed fundamental questions of ontology), or about practical music and 'real' intonations.

I don't think that raising such a question would augment the difficult of the article to excessive levels. On the other hand, it may be difficult to document it with precise references. I won't therefore change anything at this point (I'd lack the time, anyway), but I'd like to know your opinion. – Hucbald.SaintAmand (talk) 20:41, 22 July 2014 (UTC)

Thanks, Hucbald, though I did not write all of this material. Although I have contributed to all three of them, at this point I have merely conflated the articles "Diatonic genus", "Chromatic genus", and "Enharmonic genus" into this one article, and written a new lede for it. I think the Archytas claim may originally have been inserted by another editor, though I recall checking on this at the time, and I believe it was I who added the reference to Barbera's NG article. I haven't gone back to verify this, but I believe he does say that Archytas's solution is "more consonant". While it is likely that we think of consonance in a different way than the Greeks did, I don't think it is an entirely separate conception. Mathiesen certainly doesn't think so, either, to judge from many of his comments on Aristoxenus who, as an Aristotelian, was very suspicious of explaining everything in terms of numerical ratios. The Greeks were certainly capable of sounding two notes simultaneously—in fact, it is impossible to imagine they tuned their lyres in any other way, even if their music was strictly monophonic (a rather hotly contested issue these days, by the way). In fact, the sharp differences between the Pythagorean and Aristoxenian traditions is one of the major problems I see with this article as it now stands. In spite of what it says in the introductory section to the "Tetrachord" section (which I wrote), the remainder of the article is heavily biased toward the Pythagoreans, with all of that tuning stuff with number ratios (which I did not write, but do not disagree with, as far as it goes). More needs to be said about Aristoxenus's "dynamic" concept within the sections on the individual genera.

This is also why I have stopped short of filling up the "Shades" subsections with the easiest material to insert, which are the numerical tables from Cleonides (who, despite his clear debt to Aristoxenus is also infected by enthusiasm for number ratios), Ptolemy, and others. I would rather have something there first on the more difficult conceptions outlined by Aristoxenus and explained by Mathiesen and other modern writers. This is also the reason I chose to say in the lede "certain classes of intonations" instead of "certain proportional divisions" or "certain intervallic relations". This would apply to the Pythagorean conception, but not the Aristoxenian one—which is extremely important historically, and not only for music of the ancient world.

This I think has a great deal to do with what you ask about the relationship between theory and practice. On the one hand, it is easy to suspect the Pythagoreans of a pie-in-the-sky belief in their numbers; on the other, while it may be easier to believe Aristoxenus was more interested in practical music making, it is also much more difficult to understand exactly what his verbal explanations are describing, at such a distance in time. I once bought a book at one of those clearance sales, where books stamped with very low prices are piled up on a table. It attracted me because it was completely unintelligible to me. I could not even figure out what language it was in (many years later I learned it was in Armenian). I would occasionally show it to people, to whom I would explain that "only the page numbers are in English". From this, I learned that mathematics are easy and universal, while languages are difficult and particular.—Jerome Kohl (talk) 22:47, 22 July 2014 (UTC)

Eisagogê Armonikê

Jerome, if you saw the original of Jon Solomon's PhD, I have nothing to add: I didn't see it myself and don't intend to. It strikes me however that his title page probably gave these words in Greek, and that several secondary sources give this extremely odd transliteration, which I cannot believe is Solomon's own. This may have started in the University of North Carolina itself, which might explain why you saw alternative title pages with this obviously incorrect transliteration; they are also found on standard websites, but which may be copying each other. I merely wonder whether it is wise to continue on the same line, while Solomon himself might prefer a better title... – Hucbald.SaintAmand (talk) 21:33, 23 July 2014 (UTC)

I too would like to see this abomination changed. Since you do not have access to the dissertation and I have it open on my computer screen before me, here is the situation. The ProQuest initial cover page with "Information to Users" is headed with the title (in full caps):

• CLEONIDES: "ISAYOYI ARMONIKI"; CRITICAL EDITION, TRANSLATION, AND CO [it is cut off exactly like this].

This is followed by the actual UMI cover page, which looks as if it had been typed onto a University Microfilms form by Solomon himself. Here the title is not truncated, and reads:

• CLEONIDES: "ISAYOYI ARMONIKI"; CRITICAL EDITION, TRANSLATION, AND COMMENTARY

Next comes the dissertation title page, typed also in full caps, with the Cleonides title in Greek letters, lacking polytonic markings, thus:

• CLEONIDES: ΕΙΣΑΓΩΓΗ ΑΡΜΟΝΙΚΗ; / CRITICAL EDITION, TRANSLATION, AND COMMENTARY

(The solidus indicates a line break in the title, it does not appear as part of it.) The title page is followed by the abstract, where the title is given all over again, this time in caps/lc format, and with one of the Greek polytonic markings (the varia over the final eta in the first word) drawn in by hand:

• JON SOLOMON: Cleonides: Είσαγωγὴ ὰρμονική; Critical Edition, Translation, and Commentary (Under the direction of PHILIP STADTER)

I would have supposed the erroneous substitution of oxia for smooth breathing and varia for rough breathing is a product of the typewriter font available to Solomon in 1980, only in the text of the abstract itself these markings are correctly rendered in two further occurrences of the Greek title, as they are also throughout the text of the dissertation (I am inspecting the text at 600% magnification). The varia on eta, however, is always drawn in by hand. How far do you think we can go toward rectifying the orthography, without actually misrepresenting the title as it actually appears in the dissertation? When there are multiple title occurrences like this, the usual authority is the half-title page (in a published book), which in a dissertation is the same as the title page. Because in this case the title is typed in full caps, of course it must be changed to normal caps/lc for the bibliographical entry. Do you think it is legitimate to silently supply the correct polytonics and, if so, should the correctly transliterated title be added in brackets (instead of the lousy transliteration found in the UMI cover sheet, apparently typed by Solomon himself), or just leave the Greek?—Jerome Kohl (talk) 01:03, 24 July 2014 (UTC)

Solomon apparently intended to have the title in Greek. He apparently tried to reproduce the Greek with Latin letters on UMI forms. This then was taken over by such repertories as Worldcat, etc. But it remains that the true title is ΕΙΣΑΓΩΓΗ ΑΡΜΟΝΙΚΗ, or Είσαγωγὴ ὰρμονική. The WP article rightly gives it in Greek, since that is now possible. In addition, it should give a correct transliteration in brackets – not as the transliteration of the author, but as a help for WP readers, as would be done without question if it were not for this old, unfortunate attempt by Solomon himself (or by some editor). This, at least, is what I'd recommend – Hucbald.SaintAmand (talk) 10:43, 24 July 2014 (UTC)

Yes, this sounds like a plausible explanation, and a reasonable suggestion. I shall implement it immediately.—Jerome Kohl (talk) 16:35, 24 July 2014 (UTC)

Now corrected, as well as the typo in the Greek title, since obviously Solomon knew it was a rough-breathing mark, not a varia.—Jerome Kohl (talk) 16:48, 24 July 2014 (UTC)

Heritage of the Greek tetrachordal system

[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)