186edo: Difference between revisions

186edo is closely related to 31edo, but the patent vals differ on the mapping for 3. The equal temperament tempers out 67108864/66430125 (misty comma) and 390625000/387420489 (quartonic comma) in the 5-limit, as well as 6115295232/6103515625 (vishnuzma); 3136/3125, 5120/5103 and 117649/116640 in the 7-limit. Using the patent val, it tempers out 385/384, 1331/1323, 2200/2187, and 3773/3750 in the 11-limit; 325/324, 352/351, 847/845, and 1573/1568 in the 13-limit.

Approximation of prime harmonics in 186edo
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	+1.27	+0.78	-1.08	-2.93	-1.82	-1.73	-0.74	-2.47	+2.68	-3.10
Error	Relative (%)	+0.0	+19.7	+12.1	-16.8	-45.4	-28.2	-26.8	-11.5	-38.3	+41.6	-48.1
Steps (reduced)		186 (0)	295 (109)	432 (60)	522 (150)	643 (85)	688 (130)	760 (16)	790 (46)	841 (97)	904 (160)	921 (177)

Since 186 factors into 2 × 3 × 31, 186edo has subset edos 2, 3, 6, 31, 62, and 93.

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 {{Infobox ET}}
-'''186edo''' is the [[EDO|equal division of the octave]] into 186 parts of 6.4516 cents each. It is closely related to [[31edo]], but the patent vals differ on the mapping for 3. It tempers out 67108864/66430125 (misty comma) and 390625000/387420489 (quartonic comma) in the 5-limit, as well as 6115295232/6103515625 (vishnuzma); 3136/3125, 5120/5103 and 117649/116640 in the 7-limit. Using the patent val, it tempers out 385/384, 1331/1323, 2200/2187, and 3773/3750 in the 11-limit; 325/324, 352/351, 847/845, and 1573/1568 in the 13-limit.
+{{EDO intro}}
-{{stub}}
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+edo is closely related to [[31edo]], but the [[patent val]]s differ on the mapping for [[3/1|3]]. The equal temperament [[tempering out|tempers out]] 67108864/66430125 ([[misty comma]]) and 390625000/387420489 ([[quartonic comma]]) in the 5-limit, as well as 6115295232/6103515625 ([[vishnuzma]]); [[3136/3125]], [[5120/5103]] and 117649/116640 in the 7-limit. Using the patent val, it tempers out [[385/384]], 1331/1323, [[2200/2187]], and 3773/3750 in the 11-limit; [[325/324]], [[352/351]], [[847/845]], and [[1573/1568]] in the 13-limit.
+=== Odd harmonics ===
+{{Harmonics in equal|186}}
+=== Subsets and supersets ===
+Since 186 factors into {{factorization|186}}, 186edo has subset edos {{EDOs| 2, 3, 6, 31, 62, and 93 }}.

Revision as of 16:09, 22 April 2024