189/187: Difference between revisions
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'''189/187''', or the '''chouten comma''' is a [[17-limit]] or 3.7.11.17-subgroup [[comma]] of about 18.42 [[cent]]s. | '''189/187''', or the '''chouten comma''' is a [[17-limit]] or 3.7.11.17-subgroup [[comma]] of about 18.42 [[cent]]s. | ||
This comma is the difference between [[21/11]] and [[17/9]], or [[11/9]] and [[21/17]], | This comma is the difference between [[21/11]] and [[17/9]], or [[11/9]] and [[21/17]], [[18/17]] and [[22/21]] etc. | ||
==Commatic relations== | ==Commatic relations== | ||
This comma is the sum of the following comma combinations: | This comma is the sum of the following comma combinations: | ||
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* [[81/80]] and [[561/560]] | * [[81/80]] and [[561/560]] | ||
* [[91/90]] and [[2431/2430]] | * [[91/90]] and [[2431/2430]] | ||
===[[S-expression]]=== | |||
189/187 is a 1/4-square particulars which is S18*S19*S20*S21. | |||
==Temperament== | ==Temperament== | ||
Tempering out this comma in the 3.7.11.17 [[subgroup]] leads to the rank-3 '''chouten temperament'''. | Tempering out this comma in the 3.7.11.17 [[subgroup]] leads to the rank-3 '''chouten temperament'''. | ||
Latest revision as of 07:14, 20 April 2026
| Interval information |
189/187, or the chouten comma is a 17-limit or 3.7.11.17-subgroup comma of about 18.42 cents.
This comma is the difference between 21/11 and 17/9, or 11/9 and 21/17, 18/17 and 22/21 etc.
Commatic relations
This comma is the sum of the following comma combinations:
- 144/143 and 273/272
- 126/125 and 375/374
- 120/119 and 441/440
- 105/104 and 936/935
- 100/99 and 1701/1700
- 343/342 and 210/209
also the difference between following comma pairs:
S-expression
189/187 is a 1/4-square particulars which is S18*S19*S20*S21.
Temperament
Tempering out this comma in the 3.7.11.17 subgroup leads to the rank-3 chouten temperament.
Chouten
rank: 3
subgroup: 3.7.11.17
comma basis: [3 1 -1 -1] 189/187
edts: 5, 22, 17, 12, 27, 26, 7, 9, 48, 31, 21, 6[+17], 53, 43, 16
edt join: 5 & 22 & 48
mapping: [⟨1 1 2 2], ⟨0 1 0 1], ⟨0 0 1 -1]]
preimage: 3, 7/3, 11/9
WE tuning: 1899.601, 1466.758, 355.824
CWE tuning: 1901.955, 1466.397, 355.180
WE errors: -2.354, -2.467, 3.709, 5.181
CWE errors: 0.000, -0.473, 7.772, 10.172
badness(sintel): 0.056
all the patent vals(edo): 2 7 8 10 12 14 16 24 26 28 29 31 33 34 36 40 41 43 50 55 57 60 64 65 67 69 81 88 91 93 98 100 110 117 122 134
Etymology
Chouten is the abbreviation for chouzetsusaikawa tenshi-chan which is a fictional character from the game needy streamer overload. This name was humorously proposed in 2023 within a small online community, and has been introduced to serve as a optional naming for this comma.