Talk:31 equal temperament

message: Please see Wikipedia talk:WikiProject Tunings, Temperaments, and Scales#External links to music. —Keenan Pepper 19:46, 3 September 2006 (UTC)
thread_title:  External links to music 

message: What the hell does this mean? :
The single most important fact about 31-et is that it equates to the unison, or tempers out, the syntonic comma of 81/80. It is therefore a meantone temperament. It also tempers the 5-limit intervals 393216/390625, known as the Würschmidt comma after music theorist José Würschmidt, and 2109375/2097152, known as the semicomma.
More significantly, perhaps, it tempers out 126/125, the septimal semicomma or starling comma. Because it tempers out both 81/80 and 126/125, it supports septimal meantone temperament. It also tempers out 1029/1024, the gamelan residue, and 1728/1715, the Orwell comma. Consequently it supports a wide variety of linear temperaments.
—The preceding unsigned comment was added by 71.102.186.234 (talk • contribs) 08:05, 22 November 2006  (UTC)
:I agree that it's pretty confusing. I don't even know what the Würschmidt comma or semicomma is, or what significance they have, or the gamelan residue and Orwell comma. However, I will attempt to explain, and we should probably also amend the article:
:Some people like to classify temperaments based on the commas they "temper out"; which means that using this kind of tuning, a particular disagreement between two intervals that would be constructed with just intonation, called a comma, is eliminated by modifying each of those intervals slightly so that they line up. Interestingly, temperaments that have "tempered out" similar commas often have an easier time of converting music from one to the other, which is why it was written that this temperament might "support" other temperaments.
:Now, the article doesn't do anything to explain this. Musical temperament explains it only a little. This kind of information is rather obscure (of the handfull of people that actuall play with temperaments, how many of them are interested in comma-compatibility? and how many of them would come to wikipedia for that information?). I'm not sure if it really belongs in the article. - Rainwarrior 17:04, 22 November 2006 (UTC)
thread_title:  Clarity

message: Why are equal temperaments called "31 equal temperament" and "53 equal temperament" on Wikipedia, without the word "tone"? CKL  —Preceding signed but undated comment was added at 15:58, 25 September 2007 (UTC)
replies: text: There are a lot of ways to name the scale. "31 tone equal temperament" is also valid. Some like "31 equal divisions of the octave". It's just a matter of preference which one to use. - Rainwarrior 05:21, 13 November 2007 (UTC)

text: The term "tone" is commonly reserved for intervals close to the 9:8 or 10:9 diatonic whole tones, whereas the steps of other equal divisions may or may not be of a comparable size.  69.7.77.20 (talk) 16:05, 8 March 2012 (UTC)
thread_title:  no "tone" 

message: There is unfortunately room for subjectivity in determining which intervals to include in the table on this page, as well as other pages such as 19 equal temperament, 22 equal temperament, 53 equal temperament, etc.  While I admit this, I think it's hard to justify including ratios for large numbers like the just intonation for seconds.  Joel Mandelbaum, who has worked with this tuning system more than most composers, once commented that a close match to just tuning was very important when it came to consonant intervals, but was of little importance in dissonant intervals.  He uses this system mainly because it allows one to include the 7th and 11th partials of the harmonic series.  I have never read (or heard) anything to suggest that the higher ratios play any meaningful role in the perception and use of these tuning systems.  Cazort 20:15, 12 November 2007 (UTC)
thread_title:  Which intervals to include in table? 

message: Please see for example, page 875, vol 11, of The New Grove (1995), or MGG, on "meantone" before stating the "fact" that 31-tET "is" a meantone tuning. (It can function as one, or "correspond closely" to use the term in Grove's, but to say that it "is" a meantone tuning is simply provincial.)
: I agree too, I think "can function as" or "can be viewed as" would be better.  69.182.126.165 (talk) 13:25, 27 April 2008 (UTC)
replies: text: I agree.  69.182.126.165 (talk) 13:25, 27 April 2008 (UTC)
replies: text:  The whole point of 'meantone' is that a major third is equal to two 'whole tones'. That's all it means. Anyone can click on that article and read it; there's no reason to duplicate all that stuff here.  —Preceding unsigned comment added by 166.84.1.1 (talk) 04:30, 24 May 2009 (UTC)
thread_title:  Check your "facts" 

message: How is emphasizing septimal minor third and other intervals in the interval size table an improvement? Hyacinth (talk) 23:47, 7 June 2009 (UTC)
replies: text: I don't fully understand the question, as the septimal minor third has not been emphasised as far as I can see. However, as to "other intervals", I agree entirely: it made the table look messy, and I cannot see how it helped, so I have reverted it. JamesBWatson (talk) 12:48, 10 June 2009 (UTC)
thread_title: Improvement?

message: Why, where, and how does this article contain too much jargon or need explanation or simplification? Hyacinth (talk) 01:49, 28 June 2009 (UTC)
thread_title: Too much jargon

message: On the french version, it talks about some crazy multiple possibilities (such as 19, 31, 43, 53)...
So as I moved towards the english version, hoping for more detailed information and possibly an EXAMPLE of music composed in such intervals, I was quite surprised to see that that article doesn't even have a general title: "31 equal temperament", that doesn't even suggest if the actual translation for "tempérament par divisions multiples" is indeed "equal temperament".
So I guess, two things disappointed me: first, the article has no generalization of the notion of "temperament division" (I don't even know if you could actually call it that). And second, I can't seem to find any kind of content regarding this alternative division, not even on Google. I mean, of course some websites mention it here and there, but no serious example, discussion, or even a complete explanation.
I can imagine this subject might not be very popular, but if there is a reason for it (for instance, if all the possible combinations other than 12 don't make any kind of harmony -don't ask me), well at least write it down somewhere, let me know if it is worth it to continue look for answers...
This is not a wild critique, I am sincerely looking forward to completing the article, but I have almost no understanding of that field.
I am deeply interested by the idea of alternative temperament divisions (or whatever is right to call it). I simply have a little trouble finding answers...  — Preceding unsigned comment added by 220.110.185.240 (talk) 01:36, 30 September 2011 (UTC)
thread_title:  Why 31? 

message: Why and where does this article need additional citations for verification? What references does it need and how should they be added? Hyacinth (talk) 00:34, 7 July 2012 (UTC)
thread_title: Additional citations

message: It is curious that Diccionario de la Real Academia Española defines musical intervals following 31 equal temperament. The article "semítono" states: . That is: semitone=one of two unequal parts to which a whole tone is divided, diatonic semitone=3 commas, chromatic semitone=2 commas. So whole tone=5 commas, perfect fourth=13 commas, perfect fifth=18 commas and perfect octave=31 commas. Burzuchius (talk) 14:27, 28 January 2013 (UTC)
replies: text: Interesting! I suppose this is because 31 equal temperament can basically be equated with quarter-comma meantone, which was once a common tuning. Double sharp (talk) 12:36, 19 January 2016 (UTC)
thread_title:  Curiosity