183edo: Difference between revisions
m Moving from Category:Edo to Category:Equal divisions of the octave using Cat-a-lot |
m surprisingly strong no-19's system |
||
| Line 1: | Line 1: | ||
''183edo'' divides the octave into 183 equal parts of 6.557 [[ | ''183edo'' divides the octave into 183 equal parts of 6.557 [[cent]]s each. It is notable as a higher limit system, especially when 7 is left out of the picture. It tempers out the [[schisma|schisma]], 32805/32768, in the [[5-limit|5-limit]]. In the [[7-limit|7-limit]], it tempers out porwell, [[6144/6125]], cataharry, [[19683/19600]] and mirkwai, [[16875/16807]]. In the [[11-limit|11-limit]] it tempers out [[540/539]], [[3025/3024]] and [[8019/8000]]; in the [[13-limit|13-limit]], [[351/350]] and [[676/675]]; in the [[17-limit|17-limit]] 442/441, 561/560 and 715/714; and in the [[19-limit|19-limit]] 456/455. It is the [[Optimal_patent_val|optimal patent val]] for 13-, 17- and 19-limit [[Mirkwai_clan|mirkat temperament]], the 72&183 temperament, and an excellent tuning for the [[rank-three_temperament|rank-three temperament]]s [[The_Archipelago|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]], 4425/4424, 6656/6655, [[936/935]], [[1089/1088]], and 1377/1375. | ||
== Just approximation == | |||
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, 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|prec=3}} | |||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||
Revision as of 05:44, 13 April 2021
183edo divides the octave into 183 equal parts of 6.557 cents each. It 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-three 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.
Just approximation
183edo is notable as having especially low error in all prime limits from 11 to 29 for EDOs in the 100 to 200 range, 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".