183edo: Difference between revisions

Line 4:

| Fifth = 107\183 (701.64¢)

| Major 2nd = 31\183 (203¢)

| ~~Minor 2nd~~ = 14~~\183~~ (92¢)

| Semitones = 17:14 (111¢ : 92¢)

| ~~Augmented 1sn~~ = 17~~\183 (111¢)~~

| Consistency = 17

}}

The '''183 equal divisions of the octave''' ('''183edo'''), or the '''183(-tone) equal temperament''' ('''183tet''', '''183et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 183 [[equal]] parts of about 6.56 [[cent]]s each, a size close to [[243/242]], the rastma.

== 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]] ~~and~~ [[676/675]]; 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&~~183~~ 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]], 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]].

As a no-sevens temperament, it tempers out [[32805/32768]], 5632/5625, [[8019/8000]], [[676/675]], ~~4425~~/~~4424~~, 6656/6655, [[936/935]], [[1089/1088]], and 1377/1375.

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.

=== Prime harmonics ===

@@ Line 4: / Line 4: @@
 | Fifth = 107\183 (701.64¢)
 | Major 2nd = 31\183 (203¢)
-| Minor 2nd = 14\183 (92¢)
+| Semitones = 17:14 (111¢ : 92¢)
-| Augmented 1sn = 17\183 (111¢)
+| Consistency = 17
 }}
 The '''183 equal divisions of the octave''' ('''183edo'''), or the '''183(-tone) equal temperament''' ('''183tet''', '''183et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 183 [[equal]] parts of about 6.56 [[cent]]s each, a size close to [[243/242]], the rastma.
 == 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]] and [[676/675]]; 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;183 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]], 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]].
-As a no-sevens temperament, it tempers out [[32805/32768]], 5632/5625, [[8019/8000]], [[676/675]], 4425/4424, 6656/6655, [[936/935]], [[1089/1088]], and 1377/1375.
+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.
 === Prime harmonics ===