Talk:Schismatic temperament

message: As I understand it, the story of the different spellings is as follows:
Helmholtz's original German book used the term "schismatische Verwechslung".  I probably got that wrong, but it would naturally fit "schismatic temperament" in English.
Ellis translated it as "skhismatic" using a more modern Greek transliteration.
Other writers (dunno who) called it "schismatic" which is already an English word (a heretical movement that breaks off from the One True Church or somesuch) and consistent with "schism".
John Chalmers used the word "skhismic" to show its Greek roots, leave out the "at" which doesn't mean anything, and avoid unfortunate associations with heretical movements.
I then have to take the blame for introducing a third variant, because there wasn't an established standard, and I wanted a simple, familiar spelling.  I don't think this action really deserves to be recorded in the first paragraph of the actual article.  Whatever spelling you use here will become the standard, no need for apologies.
X31eq 12:56, 17 December 2005 (UTC)
replies: text: I discover this article somewhat late, and my question/comment probably comes too late. However, here it is: I am surprized at the mention that "Helmholtz's original German book used the term schismatische Verwechslung". It is not very easy to check, but it seems that Helmholtz not only didn't say schismatische Verwechslung, but also never used the term schisma. This at least is what Liberty Manik writes in his Das Arabische Tonsystem. If it were not true, I'd be interested to have a more precise reference. Hucbald.SaintAmand (talk) 17:56, 5 June 2015 (UTC)
thread_title:  Spelling 

message: I find this article really hard to understand, and i think this happens because of the lack of  examples. Does a typical schismatic temperament consist of 12 or 24 or 36 tones per octave? Is there  a typical example in the first place? And if there is no typical example, what would just some example be like? i would appreciate the addition of one or two examples to this article by some knowing person very much.
62.134.176.86 23:33, 18 May 2006 (UTC)
replies: text: There are no frequency ratios because schismatic temperament is a temperament, not just intonation, so the intervals don't correspond exactly to rational numbers. There is only one schismatic temperament, and it extends infinitely in both directions. Since there is only one schismatic temperament, it doesn't make sense to provide "examples". Nevertheless, I'll try to improve the article according to your suggestion. —Keenan Pepper 00:45, 19 May 2006 (UTC)
replies: text: Thanks for the fast answer! With frequency ratios i mean in this case an actual rational number or something like 2^(1/12) as a factor between frequencies. But you are right, an irrational ratio is not really a ratio. So what i meant is something like a relative frequency table. So it's your point. Concerning the examples, i still think that a range of the infinitely extending temperament is still an example for a temperament. In my opinion a temperament is something that can be seen on real instruments. But one could argue that an infinitely extending temperament is more something like a temperament, because it's more abstract. 62.134.229.109 11:58, 19 May 2006 (UTC)
thread_title:  lack of examples with frequency-ratios 

message: I wonder whether the time would not be ripe for a more thorough revision of the article. Schismatic temperament significantly improved these last days, despite (or, I hope, partly thanks to) our somewhat cahotic exchanges. Yet, I think it could become even clearer if it took better account of the history of what is called schismatic temperament today. It already is obvious that two different tuning systems are involved, which I'll discuss in turn below.
* 1. The tuning by schismatic exchange, which Ellis unfortunately named skhismatic tuning. This is an obsolete tuning system, first documented in Arabic treatises of the 13th century (among which Safi al-Din al-Urmawi). The aim of al-Urmawi was to provide a Pythagorean explanation of the "quarter tones" (the "Zalzalian" intervals of music of the Near and Middle East). To achieve this, he extended the series of "just" fifths from G to A, 17 degrees, in an attempt to equate the difference of a "half flat" or "half sharp" between degrees of the Oriental system with the difference between Pythagorean enharmonies (G/F, D/C, etc.). This was justified by the enormous faith in Pythagorean theory, even in Persia and as late as the 13th century. The attempt failed, however, because Zalzalian intervals differ from the diatonic ones by about two commas, while Pythagorean enharmonies differ by only one comma. This tuning system is documented among others in R. G. Kiesewetter, Die Musik der Araber, 1842, the principal source of Helmhotz, and later in L. Manik, Das Arabische Tonsystem im Mittelalter, 1969, and many others in more recent times. So far as I can tell, Manik is responsible for the expression Schismatische Verwechslung, that I translate here as Schismatic exchange; "commatic exchange" might be more appropriate, but it sounds somewhat funny.
:A similar tuning has been in use in Occident in the late 14th and the 15th century, as described among others by M. Lindley in several papers available on his webpage on Academia.edu (this is a long list; one of the most directly relevant papers is "Pythagorean Intonation and the Rise of the Triad", 1980). This keyboard tuning was limited to 12 keys in the octave and knew several forms; in all cases, the keys tuned by enharmony were black keys. Once again, this tuning originated in a reluctance to abandon Pythagorean theory; that the theory eventually was abandoned is linked to the important changes by which the Western world passed from the Middle Ages to the Renaissance. The tuning by schismatic exchange did not survive these changes and was superseded by meantone tunings early in the 16th century (and, in theory at least, by just intonation at some later point in the century).
* 2. The Helmholtzian temperament was proposed by Helmholtz as a revivification of the Arabic tuning; Helmholtz was not aware of the Western version. The idea was to slightly temper the fifths of Pythagorean tuning so as to end after 8 fifths, not on a slightly detuned major third by enharmony (say, C-F for C-E), but on a "just" one (5:4). The difference to be gained is a schisma, so that each fifth had to be tempered by 1/8-schisma. Helmholtz however, oddly enough, apparently was not aware of anything named a "schisma", so that he said that the amount by which each fifth was to be tempered was 1/8 the difference between a "just" fifth and a tempered one in 12t-ET. Ellis, Helmholtz' English translator, gave a more exact description of this temperament, which he called "Helmholtzian".
:Note that the present article states that "eighth-schisma has much much more accurate perfect fifths and minor thirds". I presume that this is a slip of the pen for "major third". It is not true for the minor one, unless this also is taken by enharmony, say C-D for C-E, which means 9 fifths on the sharp side; a schismatic tuning (or Helmholtzian temperament) that would produce both good major and minor thirds above C would have to extend from F to D, and if it wanted also A to be a good minor third, and A a goor major third below C, it would have to extend from B to G, etc. — this is the reason why schismatic tunings (like just intonation) are hardly more than utopies: they can produce very good approximations of many intervals, but very few diatonic scales coherent withing themselves. [This confines to the complexities that I wanted to avoid. One may get an intuition of this in the idea that a coherent diatonic scale in schismatic intonation should have all its degrees taken as enharmonies with respect to its "tonic", something like C E F E or G, F or A, G or B, C...]
Helmholtz' temperament does not seem to have been widely used, but recent webpages oddly describe it (not that it'd be odd to describe the tuning, but the descriptions are odd). A few comments about these:
:— the unsigned page at x31eq.com oddly decides to call s and r (for the Greek letters sigma and rho — ???) what everybody else would call the major and minor semitones. It then gives a confused explanation of 7+5 and 5+7 scales, which boils down to stating whether it is the major or the minor semitone which is the diatonic one (and the other the chromatic one). It is well known that meantone temperaments have the diatonic semitone as the major one and that the Pythagorean tuning has it the other way around; but x31eq apparently prefers complex explanations (why make things simple if making them complex gives the impression that you are more intelligent?). To explain this in a manner that anyone with elementary musical formation will understand, the tone is said to be made up of 9 commas (let's assume that this is true); the semitone is either 4 commas or 5 commas. Now, a diatonic octave is made of five tones, each of 9 commas, 45 commas together, and two semitones which can be either 5 commas, with a total of 55 commas (5x9 + 2x5; this is the Holder scale properly speaking, with commas of 1/55-octage), or 4 commas, 53 in total (5x9 + 2x4; this gives a good approximation of 1/4-comma meantone). If one compares this with the image given by Hyacinth in the previous section of this talk page, the lines on this image that go up from left to right have a diatonic semitone that is the major semitone; the lines that go down produce the minor semitone as diatonic semitone. To call the first "schismatic"... well, why not?
:— the "xenharmonic" page on what is called "[schismatic family]" uses a langage that I don't understand, or that I prefer not to understand.
:— the tonalsoft pages make a clear difference between what they call schismic tuning (my "tuning by schismatic exchange") and schismic temperament, which it does not really describe. Then it turns to the same language as xenharmonic.
I offer the above as suggestions for a revision of the article (which, I add, may have an opportunity to disentangle the whole matter by making it simple). But I won't rewrite the article myself for these reasons: (1) I do not have the time just now to check all needed references; (2) I cannot understand the "xenharmonic" language, which to me seems to come from another planet (or to have come after some schism 😊); (3) my own idea would be that this whole affair ends with Helmholtz/Ellis and subsequently can only be treated as a historical phenomenon (as did L. Manik, M. Lindley, and some of the Arabic researchers that I know).
Hucbald.SaintAmand (talk) 10:58, 7 June 2015 (UTC)
replies: text: This article could probably be trimmed and merged with Schisma. Hyacinth (talk) 16:57, 7 June 2015 (UTC)
replies: text: Yes, why not? But then, if possible, without the phrase "Tempering out the schisma leads to schismatic temperament". I had not seen that article either, and I find most interesting to read that the musical sense of "schisma" was introduced by Ellis — this probably requires a reference, but it makes sense in view of my description above. I'd also like to see the mention of grad, as a unit defined by Werckmeister, checked in the treatises of this author — it is so much better to refer to the primary sources. Unfortunately, Werckmeister's treatises probably were published in Frakturschrift (Gothic font), which for the time being makes OCR difficult. I'll see what I can do. Hucbald.SaintAmand (talk) 17:30, 7 June 2015 (UTC)
thread_title:  A revision of the article? 

message: Hyacinth, I saw your recent change to the article. You are right that the name "skhismic temperament" is Ellis'; but this tuning nevertheless had been described by Helmholtz, p. 280 ff of the translation, and Helmholtz [rightly] described it as "the Arabic and Persian musical system". As said above, this is a 13th-century tuning system. All this will be resolved, of course, with the possible rewriting of the article and/or its possible merging with Schisma... Hucbald.SaintAmand (talk) 19:29, 7 June 2015 (UTC)
thread_title:  Skhismic temperament: Helmholtz or Ellis? (or al-Urmawi?)