213edo: Difference between revisions
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So, I've never really gotten behind the high-level math stuff, so I don't know if I will add more stuff later. |
m lc monzo |
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213edo is the equal division of the octave into 213 parts of 5.6338 cents each. It is (uniquely) consistent through the [[7-limit|7-odd-limit]] and tempers out the following commas up to the [[13-limit]]: {{ | 213edo is the equal division of the octave into 213 parts of 5.6338 cents each. It is (uniquely) consistent through the [[7-limit|7-odd-limit]] and tempers out the following commas up to the [[13-limit]]: {{monzo| 3 -10 11 }} in the [[5-limit]]; {{monzo| 6 -5 -4 4 }}, {{monzo| 10 -11 2 1 }} and 6144 / 6125 in the [[7-limit]]; 896/891 in the [[11-limit]]; {{monzo| 12 -7 0 1 0 -1 }}, 325 / 324, 352 / 351 and 364 / 363 in the [[13-limit]]. The patent val for 213-EDO is <213 338 495 598|. The general approximations to pure 3- and 5-limit intervals are quite bad, but 7-limit intervals are slightly better tuned. However, intervals involving a factor of 5/3 or 3/5 are quite well approximated. Thus it makes sense to view this as a 2.5/3.7 subgroup temperament. | ||
Revision as of 12:36, 17 January 2021
213edo is the equal division of the octave into 213 parts of 5.6338 cents each. It is (uniquely) consistent through the 7-odd-limit and tempers out the following commas up to the 13-limit: [3 -10 11⟩ in the 5-limit; [6 -5 -4 4⟩, [10 -11 2 1⟩ and 6144 / 6125 in the 7-limit; 896/891 in the 11-limit; [12 -7 0 1 0 -1⟩, 325 / 324, 352 / 351 and 364 / 363 in the 13-limit. The patent val for 213-EDO is <213 338 495 598|. The general approximations to pure 3- and 5-limit intervals are quite bad, but 7-limit intervals are slightly better tuned. However, intervals involving a factor of 5/3 or 3/5 are quite well approximated. Thus it makes sense to view this as a 2.5/3.7 subgroup temperament.