183edo

← 182edo

183edo

184edo →

Prime factorization	3 × 61
Step size	6.55738 ¢
Fifth	107\183 (701.639 ¢)
Semitones (A1:m2)	17:14 (111.5 ¢ : 91.8 ¢)
Consistency limit	17
Distinct consistency limit	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 cents 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 temperaments 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.

Prime harmonics

183edo is notable as having especially low error in all prime limits 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

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3	[-290 183⟩	[⟨183 290]]	+0.0996	0.100	1.52
2.3.5	32805/32768, ⟨10 23 -20]	[⟨183 290 425]]	-0.0157	0.182	2.78
2.3.5.7	6144/6125, 16875/16807, 19683/19600	[⟨183 290 425 514]]	-0.1601	0.296	4.51
2.3.5.7.11	540/539, 1375/1372, 5632/5625, 8019/8000	[⟨183 290 425 514 633]]	-0.0993	0.291	4.44
2.3.5.7.11.13	351/350, 540/539, 676/675, 1375/1372, 4096/4095	[⟨183 290 425 514 633 677]]	-0.0295	0.308	4.70
2.3.5.7.11.13.17	351/350, 442/441, 540/539, 561/560, 1375/1372, 4096/4095	[⟨183 290 425 514 633 677 748]]	-0.0240	0.286	4.36

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per octave	Generator (reduced)	Cents (reduced)	Associated ratio	Temperament
1	10\183	65.57	27/26	Luminal
1	17\183	111.48	16/15	Stockhausenic
1	38\183	249.18	15/13	Hemischis
1	58\183	380.33	56/45	Quanharuk
1	59\183	386.89	5/4	Grendel
1	76\183	498.36	4/3	Helmholtz
1	77\183	504.92	104976/78125	Countermeantone
3	21\183	137.70	13/12	Avicenna
3	24\183	157.38	35/32	Nessafof
3	28\183	183.61	10/9	Mirkat
3	76\183 (15\183)	498.36 (98.36)	4/3 (200/189)	Term