183edo: Difference between revisions

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== Theory ==

183edo is notable as a higher limit system, especially when 7 is left out of the picture. It tempers out the [[schisma]]~~, 32805/32768,~~ in the [[5-limit]]. In the [[7-limit]], it tempers out porwell, [[6144/6125]], cataharry, [[19683/19600]] and mirkwai, [[16875/16807]]. In the [[11-limit]], it tempers out [[540/539]], [[3025/3024]] and [[8019/8000]]; in the [[13-limit]], [[351/350]], [[676/675]], [[1001/1000]], [[2080/2079]] ~~and~~ [[4096/4095]]; in the [[17-limit]] 442/441, 561/560 ~~and~~ [[715/714]]; and in the [[19-limit]] 456/455. It is the [[optimal patent val]] for 13-, 17~~- and 19~~-limit [[mirkat]] ~~temperament~~, the 72&111 temperament, and an excellent tuning for the [[rank-3 temperament]]s [[madagascar]] and [[borneo]].

183edo is notable as a higher limit system, especially when 7 is left out of the picture. It tempers out the [[schisma]] in the [[5-limit]]. In the [[7-limit]], it tempers out porwell, [[6144/6125]], cataharry, [[19683/19600]] and mirkwai, [[16875/16807]]. In the [[11-limit]], it tempers out [[540/539]], 1375/1372, [[3025/3024]], 5632/5625, and [[8019/8000]]; in the [[13-limit]], [[351/350]], [[676/675]], [[729/728]], [[1001/1000]], [[1573/1568]], [[2080/2079]], [[4096/4095]], [[4225/4224]], and [[6656/6655]]; in the [[17-limit]] 442/441, 561/560, [[715/714]], [[936/935]], [[1089/1088]], and [[1156/1155]]; and in the [[19-limit]] 456/455. It is the [[optimal patent val]] for 13- and 17-limit [[mirkat]], the 72&111 temperament, and an excellent tuning for the [[rank-3 temperament]]s [[madagascar]] and [[borneo]]. It allows [[essentially tempered chord]] including [[ratwolf triad]], [[swetismic chords]], [[squbemic chords]], [[sinbadmic chords]], and [[lambeth chords]] in the 13-odd-limit, in addition to [[island chords]] in the 15-odd-limit.

As a no-sevens temperament, it tempers out ~~[[32805/32768]],~~ 5632/5625, [[8019/8000]], [[676/675]], [[4225/4224]], [[6656/6655]], [[936/935]], [[1089/1088]], and 1377/1375.

As a no-sevens temperament, it tempers out 5632/5625, 8019/8000, 676/675, 4225/4224, 6656/6655, 936/935, 1089/1088, and 1377/1375.

=== Prime harmonics ===

183edo is notable as having especially low error in ''all'' [[prime limit]]s from 11 to 29 for EDOs in the 100 to 200 range, compared using a variety of metrics (prime error punishments), although it has a bad 19 which causes it to fail to be consistent in the [[19-odd-limit]]. It is however a strong no-19's system, being consistent in the no-19's no-35's 29-prime-limited 45-odd-limit add-43. (The prime 43 is added in the set of odd harmonics due to its essentially perfect accuracy. The harmonic 35 is excluded due to the sharpness of 7 compounding and causing inconsistency in ''some'' cases such as for 39/35.) It can also be considered to model the 2.17.29.43 subgroup with extreme accuracy.

== Regular temperament properties ==

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 == Theory ==
-edo is notable as a higher limit system, especially when 7 is left out of the picture. It tempers out the [[schisma]], 32805/32768, in the [[5-limit]]. In the [[7-limit]], it tempers out porwell, [[6144/6125]], cataharry, [[19683/19600]] and mirkwai, [[16875/16807]]. In the [[11-limit]], it tempers out [[540/539]], [[3025/3024]] and [[8019/8000]]; in the [[13-limit]], [[351/350]], [[676/675]], [[1001/1000]], [[2080/2079]] and [[4096/4095]]; in the [[17-limit]] 442/441, 561/560 and [[715/714]]; and in the [[19-limit]] 456/455. It is the [[optimal patent val]] for 13-, 17- and 19-limit [[mirkat]] temperament, the 72&amp;111 temperament, and an excellent tuning for the [[rank-3 temperament]]s [[madagascar]] and [[borneo]].
+edo is notable as a higher limit system, especially when 7 is left out of the picture. It tempers out the [[schisma]] in the [[5-limit]]. In the [[7-limit]], it tempers out porwell, [[6144/6125]], cataharry, [[19683/19600]] and mirkwai, [[16875/16807]]. In the [[11-limit]], it tempers out [[540/539]], 1375/1372, [[3025/3024]], 5632/5625, and [[8019/8000]]; in the [[13-limit]], [[351/350]], [[676/675]], [[729/728]], [[1001/1000]], [[1573/1568]], [[2080/2079]], [[4096/4095]], [[4225/4224]], and [[6656/6655]]; in the [[17-limit]] 442/441, 561/560, [[715/714]], [[936/935]], [[1089/1088]], and [[1156/1155]]; and in the [[19-limit]] 456/455. It is the [[optimal patent val]] for 13- and 17-limit [[mirkat]], the 72&amp;111 temperament, and an excellent tuning for the [[rank-3 temperament]]s [[madagascar]] and [[borneo]]. It allows [[essentially tempered chord]] including [[ratwolf triad]], [[swetismic chords]], [[squbemic chords]], [[sinbadmic chords]], and [[lambeth chords]] in the 13-odd-limit, in addition to [[island chords]] in the 15-odd-limit.
-As a no-sevens temperament, it tempers out [[32805/32768]], 5632/5625, [[8019/8000]], [[676/675]], [[4225/4224]], [[6656/6655]], [[936/935]], [[1089/1088]], and 1377/1375.
+As a no-sevens temperament, it tempers out 5632/5625, 8019/8000, 676/675, 4225/4224, 6656/6655, 936/935, 1089/1088, and 1377/1375.
 === Prime harmonics ===
 edo is notable as having especially low error in ''all'' [[prime limit]]s from 11 to 29 for EDOs in the 100 to 200 range, compared using a variety of metrics (prime error punishments), although it has a bad 19 which causes it to fail to be consistent in the [[19-odd-limit]]. It is however a strong no-19's system, being consistent in the no-19's no-35's 29-prime-limited 45-odd-limit add-43. (The prime 43 is added in the set of odd harmonics due to its essentially perfect accuracy. The harmonic 35 is excluded due to the sharpness of 7 compounding and causing inconsistency in ''some'' cases such as for 39/35.) It can also be considered to model the 2.17.29.43 subgroup with extreme accuracy.
-{{Primes in edo|183|columns=10}}
+{{Harmonics in equal|183}}
 == Regular temperament properties ==