Talk:Equal temperament

22-EDO

The section § Various Western equal temperaments needs to mention the 22 equal temperament, which:

• provides good approximations to some 5-limit, 7-limit and 11-limit just intonation ratios (better than 12-EDO does);
• represents the syntonic comma by a single step; and thus
• provides two versions of diatonic notes (differing by a single step) for different harmonies in the same key.

yoyo (talk) 02:09, 18 March 2020 (UTC)

"9 equal temperament" listed at Redirects for discussion

A discussion is taking place to address the redirect 9 equal temperament. The discussion will occur at Wikipedia:Redirects for discussion/Log/2020 August 1#9 equal temperament until a consensus is reached, and readers of this page are welcome to contribute to the discussion. 1234qwer1234qwer4 (talk) 14:23, 1 August 2020 (UTC)

"10 equal temperament" listed at Redirects for discussion

A discussion is taking place to address the redirect 10 equal temperament. The discussion will occur at Wikipedia:Redirects for discussion/Log/2020 August 1#10 equal temperament until a consensus is reached, and readers of this page are welcome to contribute to the discussion. 1234qwer1234qwer4 (talk) 14:25, 1 August 2020 (UTC)

Arabic Maqam Music vs. 24 EDO

It's worth noting that use of ostensibly 24-TET in Arabic music is simply a notational convention, but that the music as played and performed is very much not EDO in any sense. This article gives a false impression that Arabic music uses a 24 EDO system whereas in fact it actually uses a microtonal system where so-called "quarter-tones" are represented using using half-sharps & half-flats, but only as a notational convention.

To call this 24-TET is a confusion; just because the notational system uses 24 tones for convenience doesn't mean that the music itself is in any sense equal tempered. For comparison, Thomas Tallis (for example) used the western 12 notes system to notate his music, but we wouldn't say that he used 12TET just because of the fact that his notational system usualyl used 12 notes (in actuality of course the performance practice at that time would be to use something approximating a meantone temperament, which a subset of 31TET represents far closer than 12TET).

I haven't updated the article because I don't have time right now to find a reliable source to cite for this and rewrite the relevant section to a high enough standard, so I thought I'd leave this here as a comment, I hope it's helpful.

Re: how this is handled in other wikipedia articles (something to draw from perhaps) the article Arabic Maqam correctly outlines this distinction, as does the subsection Quarter tone#Quarter-tone_scale, but the former gives no source, and the latter one which I have no access to. The article at Arab tone system is contradictory, the rest of the article seeming to disagree with its opening line about 50 cents. It could do with a rewrite, or possibly merging into Arabic Maqam.

In summary then, there is much confusion and contradiction on this subject on wikipedia. The article for quarter tone could probably do with a rewrite too, to more clearly disambiguate from the mathematical "quarter tone" as in 24EDO's +/-50 cents vs. the much more common use of quarter tone to indicate a quarter of a tone in any context regardless of temperament (or lack thereof), but that's another issue (i.e. much as how a semitone is only 100 cents in 12TET, a quarter tone is a much much broader term than the narrow (and rare) context of 24TET. Sometimes the article makes this clear, other times it conflates them.)

--Tomatoswoop (talk) 19:35, 20 October 2020 (UTC)

Would someone please clean up this mess of an article

This good person could begin by removing all irrelevant or utterly false details about other systems. Chinese music is based on semitones, as is 12ET. It generally uses the 'circle of fifths' method of tuning. Comments about Balinese Pelog and Slendro are also completely false.

An explanation of why the Chinese did not use 12ET, after having invented it, would be worthy of inclusion.Luo Shanlian (talk) 09:18, 1 November 2020 (UTC)

Comparison with JI

The original comparison with just intervals that I found here used various 17 and 19-limit intervals for comparison, which I feel is a bit silly, since both historically and in common usage, 12 equal is popular for being a decent compromise at representing 5-limit intervals while not having too many notes. 12 equal doesn't represent nearly enough of the intervals you'd want to do justice to 17 or 19 limit harmony, so making those comparisons is a bit strange.

I changed the table so that it lists the just intervals that are most likely to be the intention behind a given interval in 12 equal in 5-limit harmony. For the tritone, I went with 64/45 because that is the interval between the (5/4) major third and (4/3)^2 = 16/9 minor seventh in a (justly tuned) dominant seventh chord, perhaps the most common application of the tritone. It would also be possible to make an argument for comparing the tritone against 7/5, which is a simpler ratio and thus more relevant to the interactions between low harmonics, but 12 equal does not approximate that ratio as well, and a similar argument about not having good enough approximations to enough other 7-limit intervals applies. People writing music in 12 equal usually appreciate the strong tension created by dominant seventh chords and don't usually regard them as a best attempt at a stable 4:5:6:7 harmonic seventh chord, so that interpretation would be a bit strange.

Cgibbard (talk) 01:10, 10 August 2021 (UTC)

Equal temperament versus well temperament

This article says

Some of the first Europeans to advocate equal temperament were lutenists Vincenzo Galilei, Giacomo Gorzanis, and Francesco Spinacino, all of whom wrote music in it. [15][16][17][18]

while the article Vincenzo Galilei says

"Galilei anticipated Bach's The Well-Tempered Clavier in promoting well temperament (not equal temperament)."

So, what is it? Did Vincenzo Galilei advocate equal temperament, well temperament or both?

The article was in error, corrected.-Aristophile (talk) 14:23, 25 December 2023 (UTC)

A problem with Boiles 1969

There a reference to Boiles 1969 in the Equal temperament#7-tone equal temperament section, which I've just rescued the cite for (Boiles, J. (1969). "Terpehua though-song", Ethnomusicology, 13, 42-47). This comes second hand from "Burns, Edward M. (1999). 'Intervals, Scales, and Tuning', The Psychology of Music", but I can't find anything that matches from Ethnomusicology. The listing for Ethnomusicology from 1969 lists a different paper in those page numbers, there is Tepehua Thought-Song: A Case of Semantic Signaling by Charles L. Boilés in 1967 but I lack the subject knowledge to determine if this is what Burns was actually referring to.
Could someone with such knowledge verify the details and what exactly not should be referenced to? I could have missed something or Burns could have made a mistake. -- LCU ActivelyDisinterested «@» °∆t° 16:15, 25 January 2024 (UTC)