111edo: Difference between revisions
m →Music: cleanup |
→Regular temperament properties: +23-limit |
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| Line 358: | Line 358: | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{ | | {{Monzo| 176 -111 }} | ||
| {{ | | {{Mapping| 111 176 }} | ||
| −0.236 | | −0.236 | ||
| 0.236 | | 0.236 | ||
| Line 366: | Line 366: | ||
| 2.3.5 | | 2.3.5 | ||
| 78732/78125, 67108864/66430125 | | 78732/78125, 67108864/66430125 | ||
| {{ | | {{Mapping| 111 176 258 }} | ||
| −0.570 | | −0.570 | ||
| 0.510 | | 0.510 | ||
| Line 373: | Line 373: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 1728/1715, 3136/3125, 5120/5103 | | 1728/1715, 3136/3125, 5120/5103 | ||
| {{ | | {{Mapping| 111 176 258 312 }} | ||
| −0.797 | | −0.797 | ||
| 0.591 | | 0.591 | ||
| Line 380: | Line 380: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 176/175, 540/539, 1331/1323, 5120/5103 | | 176/175, 540/539, 1331/1323, 5120/5103 | ||
| {{ | | {{Mapping| 111 176 258 312 384 }} | ||
| −0.639 | | −0.639 | ||
| 0.615 | | 0.615 | ||
| Line 387: | Line 387: | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 176/175, 351/350, 540/539, 676/675, 1331/1323 | | 176/175, 351/350, 540/539, 676/675, 1331/1323 | ||
| {{ | | {{Mapping| 111 176 258 312 384 411 }} | ||
| −0.655 | | −0.655 | ||
| 0.562 | | 0.562 | ||
| Line 394: | Line 394: | ||
| 2.3.5.7.11.13.17 | | 2.3.5.7.11.13.17 | ||
| 176/175, 256/255, 351/350, 442/441, 540/539, 715/714 | | 176/175, 256/255, 351/350, 442/441, 540/539, 715/714 | ||
| {{ | | {{Mapping| 111 176 258 312 384 411 454 }} | ||
| −0.672 | | −0.672 | ||
| 0.523 | | 0.523 | ||
| Line 401: | Line 401: | ||
| 2.3.5.7.11.13.17.19 | | 2.3.5.7.11.13.17.19 | ||
| 176/175, 256/255, 286/285, 324/323, 351/350, 400/399, 476/475 | | 176/175, 256/255, 286/285, 324/323, 351/350, 400/399, 476/475 | ||
| {{ | | {{Mapping| 111 176 258 312 384 411 454 472 }} | ||
| −0.740 | | −0.740 | ||
| 0.521 | | 0.521 | ||
| 4.83 | | 4.83 | ||
|- | |||
| 2.3.5.7.11.13.17.19.23 | |||
| 176/175, 253/252, 256/255, 276/275, 286/285, 324/323, 351/350, 400/399 | |||
| {{Mapping| 111 176 258 312 384 411 454 472 502 }} | |||
| −0.628 | |||
| 0.586 | |||
| 5.43 | |||
|} | |} | ||
* 111et has lower absolute errors than any previous equal temperaments in the 13-, 17-, 19-, and 23-limit, beating [[94edo|94]] and [[103edo|103h]] before being superseded by [[121edo|121i]]. | * 111et has lower absolute errors than any previous equal temperaments in the 13-, 17-, 19-, and 23-limit, beating [[94edo|94]] and [[103edo|103h]] before being superseded by [[121edo|121i]]. | ||
| Line 414: | Line 421: | ||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
|- | |- | ||
! Periods<br | ! Periods<br>per 8ve | ||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br | ! Associated<br>ratio* | ||
! Temperament | ! Temperament | ||
|- | |- | ||
| Line 529: | Line 536: | ||
|- | |- | ||
| 3 | | 3 | ||
| 23\111<br | | 23\111<br>(14\111) | ||
| 248.65<br | | 248.65<br>(151.35) | ||
| 15/13<br | | 15/13<br>(12/11) | ||
| [[Hemimist]] | | [[Hemimist]] | ||
|- | |- | ||
| 3 | | 3 | ||
| 46\111<br | | 46\111<br>(9\111) | ||
| 497.30<br | | 497.30<br>(97.30) | ||
| 4/3<br | | 4/3<br>(18/17~19/18) | ||
| [[Misty]] | | [[Misty]] | ||
|} | |} | ||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | <nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | ||
== Scales == | == Scales == | ||