189edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
'''189edo''' is the [[EDO|equal division of the octave]] into 189 parts of 6.3492 cents each. It tempers out 15625/15552 (kleisma) and 9007199254740992/8578797170610375 in the 5-limit; 4000/3969, 6144/6125, and 537824/531441 in the 7-limit, supporting the [[Kleismic family|hemikleismic temperament]]. Using the patent val, it tempers out 896/891, 1331/1323, 1375/1372, and 16896/16807 in the 11-limit; 169/168, 352/351, 364/363, and 1001/1000 in the 13-limit.
{{EDO intro}}


[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
The equal temperament [[tempering out|tempers out]] 15625/15552 (kleisma) and 9007199254740992/8578797170610375 in the 5-limit; [[4000/3969]], [[6144/6125]], and 537824/531441 in the 7-limit, supporting the [[hemikleismic]] temperament. Using the [[patent val]], it tempers out [[896/891]], 1331/1323, 1375/1372, and 16896/16807 in the 11-limit; [[169/168]], [[352/351]], [[364/363]], and [[1001/1000]] in the 13-limit.
 
=== Odd harmonics ===
{{Harmonics in equal|189}}
 
=== Subsets and supersets ===
Since 189 factors into {{factorization|189}}, 189edo contains {{EDOs| 3, 7, 9, 21, 27, and 63 }} as its subsets.

Revision as of 15:38, 22 April 2024

← 188edo 189edo 190edo →
Prime factorization 33 × 7
Step size 6.34921 ¢ 
Fifth 111\189 (704.762 ¢) (→ 37\63)
Semitones (A1:m2) 21:12 (133.3 ¢ : 76.19 ¢)
Dual sharp fifth 111\189 (704.762 ¢) (→ 37\63)
Dual flat fifth 110\189 (698.413 ¢)
Dual major 2nd 32\189 (203.175 ¢)
Consistency limit 7
Distinct consistency limit 7

Template:EDO intro

The equal temperament tempers out 15625/15552 (kleisma) and 9007199254740992/8578797170610375 in the 5-limit; 4000/3969, 6144/6125, and 537824/531441 in the 7-limit, supporting the hemikleismic temperament. Using the patent val, it tempers out 896/891, 1331/1323, 1375/1372, and 16896/16807 in the 11-limit; 169/168, 352/351, 364/363, and 1001/1000 in the 13-limit.

Odd harmonics

Approximation of odd harmonics in 189edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +2.81 +0.99 +2.60 -0.74 +1.06 -2.43 -2.55 +2.98 +0.90 -0.94 +0.30
Relative (%) +44.2 +15.6 +41.0 -11.6 +16.7 -38.3 -40.2 +47.0 +14.2 -14.8 +4.7
Steps
(reduced)
300
(111)
439
(61)
531
(153)
599
(32)
654
(87)
699
(132)
738
(171)
773
(17)
803
(47)
830
(74)
855
(99)

Subsets and supersets

Since 189 factors into 33 × 7, 189edo contains 3, 7, 9, 21, 27, and 63 as its subsets.