83edo: Difference between revisions
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The 83 equal temperament divides the octave into 83 equal parts of 14.458 cents each. The 3 is six and a half cents sharp and the 5 four cents sharp, with 7, 11, and 13 more accurate but a little flat. It tempers out 15625/15552 in the 5-limit and 686/675, 4000/3969 and 6144/6125 in the 7-limit, and provides the optimal patent val for the 7-limit 27&56 temperament with wedgie <<5 18 17 17 13 -11||. In the 11-limit it tempers out 121/120, 176/175 and 385/384, and in the 13-limit 91/90, 169/168 and 196/195, and it provides the optimal patent val for the 11-limit 22&61 temperament and the 13-limit 15&83 temperament. 83 is the 23rd prime number. | The 83 equal temperament divides the octave into 83 equal parts of 14.458 cents each. The 3 is six and a half cents sharp and the 5 four cents sharp, with 7, 11, and 13 more accurate but a little flat. It tempers out 15625/15552 in the 5-limit and 686/675, 4000/3969 and 6144/6125 in the 7-limit, and provides the optimal patent val for the 7-limit 27&56 temperament with wedgie <<5 18 17 17 13 -11||. In the 11-limit it tempers out 121/120, 176/175 and 385/384, and in the 13-limit 91/90, 169/168 and 196/195, and it provides the optimal patent val for the 11-limit 22&61 temperament and the 13-limit 15&83 temperament. 83 is the 23rd prime number. | ||
[[Category:Edo]] | |||
[[Category:Prime edo]] | |||
[[Category:todo:expand]] | |||
[[Category:todo:explain its xenharmonic value]] | |||
[[Category:todo:add sound examples]] | |||
Revision as of 15:17, 28 October 2018
The 83 equal temperament divides the octave into 83 equal parts of 14.458 cents each. The 3 is six and a half cents sharp and the 5 four cents sharp, with 7, 11, and 13 more accurate but a little flat. It tempers out 15625/15552 in the 5-limit and 686/675, 4000/3969 and 6144/6125 in the 7-limit, and provides the optimal patent val for the 7-limit 27&56 temperament with wedgie <<5 18 17 17 13 -11||. In the 11-limit it tempers out 121/120, 176/175 and 385/384, and in the 13-limit 91/90, 169/168 and 196/195, and it provides the optimal patent val for the 11-limit 22&61 temperament and the 13-limit 15&83 temperament. 83 is the 23rd prime number.