Talk:Enharmonic genus

Additional sources
What, where, and why does this article need additional sources? Hyacinth (talk) 13:02, 25 March 2010 (UTC)
 * The banner was not placed by me, but I have marked quite a few places that need sources, with annotations in hidden text for some of them explaining why. As to "what" sources this article needs, I would have to guess reliable, third-party ones were meant.—Jerome Kohl (talk) 16:17, 25 March 2010 (UTC)

Regarding Jerome Kohl's revision of 29 September 2012‎
1. Genera melorum of Greek music theory (harmonike) are not 'genres'. Greek music did knew genres but this has nothing to do (or rather indirect) with genera. That's why this equalization is misleading. For correct English usage of genera you may check: M.L.West. Ancient Greek Music. Oxford, 1992, pp.162, 250-251 et passim. Or another (even more fundamental) book: T.Mathiesen. Apollo's lyre. Lincoln and London, 1999, pp.30, 65, 73 et passim.

2. Pyknon is not a characteristic feature of enharmonic genus, unlike ditone and diesis. Therefore listing ditone, diesis and pyknon in a row is misleading. (Presence or absence of) pyknon (literally 'compression') is an important criterion of systematization of all different genera, not specifically enharmonic. You may check, what the pyknon is, in the same books (and many others). Olorulus (talk) 05:12, 30 September 2012 (UTC)
 * (edit conflict) Oddly enough, I am very familiar with the book by West which you cite, as well as the one by Mathiesen. In fact, these were the sources for almost all of the material which you are contesting here. The word normally used in English for genera is, oddly enough, genera (Latin singular: genus), for the simple reason that there is no suitable English word to substitute for it. What English word would you suggest should be used in its place? This would of course involve renaming this article. As for pyknon, I must once again refer to West and Mathiesen, both of whom use this word to describe the pair of intervals left after the incomposite larger interval of the chromatic and enharmonic tetrachords are subtracted. Of course I agree that it is not specific to the enharmonic genus, though of course it does not exist in the diatonic. How does the present wording of this article suggest otherwise?—Jerome Kohl (talk) 05:34, 30 September 2012 (UTC)
 * (not a conflict at all) Thank you for removing 'genres'. As for 'pyknon', I suggest that you write a special article on pyknon, better after Mathiesen. This my suggestion is not because of laziness (see Пикнон in Russian Wikipedia), it's just because my English is good enough to check sense but not to check (English) style. Olorulus (talk) 08:00, 1 October 2012 (UTC)
 * The "(edit conflict)" was a notification that my reply might not fully address the latest change you made to your message, which arrived after I had already composed my remarks. I had previously thought of writing a separate article on pyknon, but it seemed like such a small subject (no irony intended). You are right to suggest that a better explanation of pyknon is needed and, since it applies to the chromatic genus as well as to the enharmonic, a separate article may be a better solution than repeating the information in both articles.—Jerome Kohl (talk) 16:45, 1 October 2012 (UTC)
 * I disagree about 'small subject'. The pyknon is the only valid criterion for differentiation of γένη τῶν μελῳδουμένων for ca. 900 years of Greek and Roman music theory. Echoes of this differentiation can be traced even in the works of Italian humanists of the 16th and 17th cc. who dreamed of restauration of ancient genera. Olorulus (talk) 07:04, 3 October 2012 (UTC)

Major Third/Ditone
"major third" needs to be explained. Major third cannot be assumed as a (correct) name for the ditone- there were and are times and contexts when the two are the same, and times and when the two are not. — Preceding unsigned comment added by Frank Zamjatin (talk • contribs) 13:26, 17 January 2013 (UTC)
 * Depending on the assumptions of the writer using the terms, of course. I imagine this is why the words are linked to their respective Wikipedia articles on first occurrence. It does not seem appropriate to launch into a detailed explanation of different-sized tones, Pythagorean and other tunings, Greek and Latin terminology, and the various points in history when these terms were used, in the lede section of the article (where these words first occur). Could you suggest an appropriate place for such a discussion, and a way of limiting it so as not to frighten off the less doughty readers?—Jerome Kohl (talk) 22:36, 17 January 2013 (UTC)

Notation
The notation section, which is the section most smacking of original research, overwhelms the article. I am not pointing this out because I disagree with what is written in the notation section (it is fine), but because it needs references and because I think the article as a whole needs to be more balanced.


 * Yes, not only is it unsourced, but it doesn't seem relevant either. It's appropriate for a musical style guide, but not Wikipedia. At the very least it should go below the tuning section, but removing it would improve the article. 150.199.138.219 (talk) 22:48, 1 May 2013 (UTC)


 * As a matter of fact that section is not unsourced: it bears two of the five references in the article. However, the second half of it is not about notation at all, but rather about scale structure. Separating that from the material actually on notation will still leave one reference (to Gardner Read's well-known book). The substance of course is relevant only to the novice reader who otherwise might be unable to understand the special symbols used in the examples. But is Wikipedia intended only for adepts? I don't think so.—Jerome Kohl (talk) 23:02, 1 May 2013 (UTC)

Infix in music
If "infix" is from M. L. West, Ancient Greek Music either it is a non-standard use of the word or the article Infix should have an additional definition. As it stands, there's nothing there that would help. The link to it might as well be taken away. But maybe "note C inserted between two notes A and B that divides the interval A-B into two smaller intervals A-C and C-B" would do the job. Could be a footnote in this article, not necessarily a new paragraph in the Infix article. Contact Basemetal   here  00:29, 20 May 2013 (UTC)
 * Indeed the word comes from M. L. West who, as a philologist, is accustomed to specialist linguistic terms, and probably used this one on the assumption that "everyone knows" what it means, or at least can figure it out from the context, which is:

"The interval of the fourth has an important structural role in the music of many peoples, particularly in certain geographical zones: Scotland and Ireland, eastern and southeastern Europe, northern Africa, southern Asia as far east as Indonesia, and Indian North America. Here and there melodies can be found based wholly on two notes a fourth apart with no (or only occasional) intermediate notes to bridge the gap. More usually there is at least one 'infix', an additional note dividing the fourth into smaller steps. The steps are always unequal, the larger one being anything between a minor and a major third, and the smaller one accordingly something between a tone and a semitone." "In this case, where there is just one infix in the fourth, we have a scale of the type called pentatonic, because in an octave constructed in this way there will be just five steps, for example, A c d e g a, or e f a b c e. Pentatonic systems are found in the folk music of many parts of the world, including these islands; many Scottish melodies in particular are pentatonic."
 * Notice that West nonetheless uses "scare quotes" (as does this article) to indicate this is not a standard term in a musical context. I have endeavoured to make clear the meaning here (by adding the explanation that F is an "infix" dividing the fourth A–E). It seems to me that adding a footnote repeating this explanation would be excessive. I also think it would be a mistake to add a separate sense to the article "Infix", since this word is not a common musical term, but rather is one being borrowed here from linguistics. In fact, as far as I am aware, West's book is the sole example of this usage. However, I cannot think of an equivalent, standard musical term, either.—Jerome Kohl (talk) 00:50, 20 May 2013 (UTC)

Didymus's use of arithmetic mean between string lengths of 5/4 and 4/3
Regarding my edits of the text equating the arithmetic mean of the string lengths with the harmonic mean of the frequencies, as well as with the reciprocal of the arithmetic mean of the frequencies: The arithmetic mean is, of course, the sum of all the terms, divided by the number of terms. The harmonic mean is defined as the reciprocal of the arithmetic mean of the reciprocals of the terms.

For two terms, as in this example of splitting the interval between two strings of different frequencies: Arithmetic mean A = (x1 + x2)/2 Harmonic mean  H = 1/[ ( 1/x1 + 1/x2 )/2 ] = 2 / ( 1/x1 + 1/x2 )

Frequency and string length are inversely related. For this example, it is assumed that string width and linear density, and all other factors that can influence frequency, remain constant, so that only string length and frequency vary. (In reality however, on an ancient greek lyre, wouldn't it be the tension and perhaps the linear density that vary rather the length??? - I don't the answer to this, but perhaps someone more knowledgeable does). In this case string length is the reciprocal of the frequency, or L = 1/f L1 = 4/3;  L2 = 5/4 f1 = 1/L1 = 3/4; f2 = 1/L2 = 4/5

A(L1, L2) = (4/3 + 5/4 ) / 2 = ( 16/12 +15/12 ) / 2 = 31/24 H(f1, f2) = 2 / ( 4/3 + 5/4 )  =  24/31 therefore A(L1, L2) = 1 / H(f1,f2)

A(f1, f2) = ( 3/4 + 4/5 ) / 2 = ( 15/20 + 16/20) / 2 = 31/40 A(L1, L2) ≠ 1 / A(f1, f2) ≠ H(f1, f2)

Derekhmartin (talk) 00:42, 12 November 2013 (UTC)


 * I can only assume that you know what you are talking about, and will not interfere with your edit.—Jerome Kohl (talk) 01:21, 12 November 2013 (UTC)

I thought more about this, and now I think I misunderstood the intent of the original statement. It's not that it is equating the arithmetic mean of the string lengths with the harmonic mean of the frequencies, but rather that, just as the string length interval is split by the arithmetic mean, the frequency interval is split by the harmonic mean. I've changed the language to make this clear. Derekhmartin (talk) 03:47, 12 November 2013 (UTC)
 * My brain hurts ;-) I'm pleased to hear that this is not entirely plain to you as well. Thanks for your expert attention.—Jerome Kohl (talk) 06:29, 12 November 2013 (UTC)