Talk:Decaononic: Difference between revisions

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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. [[User:FloraC|FloraC]] ([[User talk: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. --[[User:VIxen|VIxen]] ([[User talk:VIxen|talk]]) 00:57, 24 November 2021 (UTC)

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 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. [[User:FloraC|FloraC]] ([[User talk: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. --[[User:VIxen|VIxen]] ([[User talk:VIxen|talk]]) 00:57, 24 November 2021 (UTC)