Talk:Decaononic

Not a temperament and issues with the orgin section

It's confusing to describe the concept as a temperament. It seems more like a set of tunings, but tbh I doubt the integrity of this concept as is currently documented. A tone can be 9/8, and it can be 10/9. If decaononic entails that 10/9 is the tone, that makes it a interval naming system since it names the intervals. Otherwise, if decaononic entails that 10/9 is emphasised by some means, it's not clear what counts and what doesn't – even qualitative measurements are missing.

"In most musical theory practices, even the most ardent microtonal ones… " This paragraph is quite inaccurate. Tuning-wise, quarter-comma meantone, for example, tunes the tone to exactly halfway between 9/8 and 10/9, and a fifth flatter that tunes the tone closer to 10/9 than 9/8. Temperament-wise, the tone is used as both 10/9 and 9/8, and there is not a discrimination. One of the more popular temperaments, porcupine, uses 10/9 as a generator. So I think some researches, such as asking any JI user if they use 10/9 as an interval of its own, would be helpful to get an accurate impression of the situation.

I'm tempted to also rename pages of all the n/d equal temperaments to n/d equal-step tunings, since that's what all the "equal temperament" pages are about, but it's another topic. FloraC (talk) 22:44, 23 November 2021 (UTC)

I totally agree that the said paragraph is inaccurate. I'm not sure what 'the most ardent' was supposed to mean, but generally, if a 'practice' doesn't even distinguish 10/9 from 9/8, I don't call it microtonal. As an example of a scale that I consider just precise enough to call microtonal, 46edo does distinguish them already - 10/9 ~ 7\46, 9/8 ~ 8\46 - and even tunes 10/9 far preciser than 9/8. Not to mention that 106edo, 111edo, 118edo all map 10/9, a meantone 19/17, and 9/8 to 3 separate steps, and approximate 10/9 well within the JND.

Besides, there's no consensus on how to define decaononicity as the property of a temperament. E.g. I'd use a much stricter definition - only consider a 17+ limit regular temperament decaononic if it tempers out all the commas of the rank-3 17-limit 46 & 72 & 111, as only then does it give accurate, fairly low Tenney height equivalents to the first 8 powers of 10/9 - namely, 10/9, 21/17 (tempered by 1701/1700), 11/8 (by 561/560), 26/17 (by 936/935), 17/10 (by 2601/2600), 17/9, 21/20 (by 1701/1700), 7/3. (This comma basis can be simplified to 351/350, 442/441, 561/560, 715/714.)

The notable rank-2s with this property in 17-limit are hendec (46 & 72) and mirkat (72 & 111). Edo vals with this property include 7dfg, 19df, 46, 65d, 72, 111, 118f, 137, 183, 190ffg, 255f. And even then, 10/9 isn't the only choice of the period in the said rank-2s. In mirkat, 7/5 works well as a period (with 10/9 as the generator), too. --VIxen (talk) 00:57, 24 November 2021 (UTC)

Oh, and of course, then 7/3 * 10/9 ~ 13/5 by 351/350, and 13/5 * 10/9 = 26/9, so those commas give nice JI equivalents to the first 10 powers of 10/9. Tempering the 11th power to 16/5, though, by 325/324, and hence the 12th to 32/9, is quite a concession of accuracy. Hendec does that (and so do the edos supporting it, like 26, 46, 72, 92p, 118f), mirkat doesn't. --VIxen (talk) 01:18, 24 November 2021 (UTC)

Now it's in a much better state. At least it doesn't get labeled a temperament. But this part still doesn't seem right: "in general, when the difference between the two is eliminated, what it really means is that the 'tone' is set to equal to 9/8 and the tuning completely misses 10/9." The term meantone itself means that the tone is between 9/8 and 10/9, and as I have pointed out, any tuning of meantone flatter than quarter-comma tunes the tone closer to 10/9 than 9/8. 19edo is particularly popular among such tuning options. FloraC (talk) 11:36, 24 November 2021 (UTC)

Thanks to Eliora for improving the article. I agree, however, that the statement about the tuning miss of 10/9 needs a correction. Also, regarding the term, maybe there's a need to consult those who speak Greek or Latin on how it would be called in the languages - inserting the 'o' standing for the English word 'over' between Greek or Latin words feels inconsistent. I guess it would be 'decaenatic' / 'decemnonal' if we were to make it fully Greek / fully Latin, but I don't speak the languages. VIxen (talk) 16:30, 24 November 2021 (UTC)