189/187

189/187, or the chouten comma is a 17-limit or 3.7.11.17-subgroup comma of about 18.42 cents.

Interval information

Ratio	189/187
Factorization	33 × 7 × 11-1 × 17-1
Monzo	[0 3 0 1 -1 0 -1⟩
Size in cents	18.41756¢
Name	chouten comma
FJS name	[math]\displaystyle{ \text{A1}^{7}_{11,17} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	15.1091
Weil norm (log2 max(n, d))	15.1245
Wilson norm (sopfr(nd))	44
Comma size	small
Open this interval in xen-calc

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:

• 56/55 and 136/135
• 81/80 and 561/560
• 91/90 and 2431/2430

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.