183edo: Difference between revisions
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{{Primes in edo|183|columns=10}} | {{Primes in edo|183|columns=10}} | ||
== Regular temperament properties == | |||
{| class="wikitable center-4 center-5 center-6" | |||
! rowspan="2" | Subgroup | |||
! rowspan="2" | [[Comma list]] | |||
! rowspan="2" | [[Mapping]] | |||
! rowspan="2" | Optimal<br>8ve stretch (¢) | |||
! colspan="2" | Tuning error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |||
| 2.3 | |||
| {{monzo| -290 183 }} | |||
| [{{val| 183 290 }}] | |||
| +0.0996 | |||
| 0.100 | |||
| 1.52 | |||
|- | |||
| 2.3.5 | |||
| 32805/32768, {{val| 10 23 -20 }} | |||
| [{{val| 183 290 425 }}] | |||
| -0.0157 | |||
| 0.182 | |||
| 2.78 | |||
|- | |||
| 2.3.5.7 | |||
| 6144/6125, 16875/16807, 19683/19600 | |||
| [{{val| 183 290 425 514 }}] | |||
| -0.1601 | |||
| 0.296 | |||
| 4.51 | |||
|- | |||
| 2.3.5.7.11 | |||
| 540/539, 1375/1372, 5632/5625, 8019/8000 | |||
| [{{val| 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 | |||
| [{{val| 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 | |||
| [{{val| 183 290 425 514 633 677 748 }}] | |||
| -0.0240 | |||
| 0.286 | |||
| 4.36 | |||
|} | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all right-3 left-5" | |||
|+Table of rank-2 temperaments by generator | |||
! Periods<br>per octave | |||
! Generator<br>(reduced) | |||
! Cents<br>(reduced) | |||
! Associated<br>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<br>(15\183) | |||
| 498.36<br>(98.36) | |||
| 4/3<br>(200/189) | |||
| [[Term]] | |||
|} | |||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||
Revision as of 09:33, 16 July 2021
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 6.557 cents each.
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.
Script error: No such module "primes_in_edo".
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
| 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 |