187edo: Difference between revisions

Revision as of 16:06, 22 April 2024

Prime factorization

11 × 17

Step size

6.41711 ¢

Fifth

109\187 (699.465 ¢)

Semitones (A1:m2)

15:16 (96.26 ¢ : 102.7 ¢)

Dual sharp fifth

110\187 (705.882 ¢) (→ 10\17)

Dual flat fifth

109\187 (699.465 ¢)

Dual major 2nd

32\187 (205.348 ¢)

Consistency limit

7

Distinct consistency limit

7

This edo is a bit of a chimera. It has a fifth which is 2.9 cents flat and a classical major third 1.3 cents flat, but the 7, 11 and 13 are more accurate. The equal temperament tempers out 78732/78125 (sensipent comma) in the 5-limit and 225/224 in the 7-limit, providing the optimal patent val for sensei which tempers out both. In the 11-limit it tempers out 441/440, 1375/1372 and 4000/3993 and in the 13-limit 351/350, 625/624, 1188/1183, 1716/1715 and 2200/2197.

Approximation of odd harmonics in 187edo
Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-2.49	-1.29	+0.16	+1.44	+0.55	+0.11	+2.64	-2.28	-2.33	-2.33	+0.60
Error	Relative (%)	-38.8	-20.1	+2.5	+22.4	+8.6	+1.8	+41.1	-35.6	-36.2	-36.3	+9.4
Steps (reduced)		296 (109)	434 (60)	525 (151)	593 (32)	647 (86)	692 (131)	731 (170)	764 (16)	794 (46)	821 (73)	846 (98)

Since 187 factors into 11 × 17, 187edo contains 11edo and 17edo as its subsets.

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-The 187 equal temperament, which divides the octave into 187 parts of 6.417 cents each, is a bit of a chimera. It has a fifth which is 2.9 cents flat and a major third 1.3 cents flat, but the 7, 11 and 13 are more accurate. It tempers out 78732/78125, the sensipent comma, in the 5-limit and 225/224 in the 7-limit, providing the optimal patent val for [[Sensipent_family#Sensei|sensei temperament]] which tempers out both. In the 11-limit it tempers out 441/440, 1375/1372 and 4000/3993 and in the 13-limit 1188/1183, 351/350, 625/624, 1716/1715 and 2200/2197.
+{{EDO intro}}
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+This edo is a bit of a chimera. It has a [[3/2|fifth]] which is 2.9 cents flat and a [[5/4|classical major third]] 1.3 cents flat, but the [[7/1|7]], [[11/1|11]] and [[13/1|13]] are more accurate. The equal temperament [[tempering out|tempers out]] 78732/78125 ([[sensipent comma]]) in the 5-limit and [[225/224]] in the 7-limit, providing the [[optimal patent val]] for [[sensei]] which tempers out both. In the 11-limit it tempers out [[441/440]], 1375/1372 and [[4000/3993]] and in the 13-limit [[351/350]], [[625/624]], [[1188/1183]], [[1716/1715]] and [[2200/2197]].
+=== Odd harmonics ===
+{{Harmonics in equal|187}}
+=== Subsets and supersets ===
+Since 187 factors into {{factorization|187}}, 187edo contains [[11edo]] and [[17edo]] as its subsets.