174edo: Difference between revisions

Revision as of 10:30, 25 April 2024

174edo is closely related to 87edo, but the patent vals differ on the mapping for 17 and some higher primes. It is contorted in the 13-limit, tempering out 196/195, 245/243, 352/351, 364/363, and 625/624. Using the patent val, it tempers out 289/288 in the 17-limit; 361/360, 476/475, and 665/663 in the 19-limit; 391/390, 392/391, 460/459, 529/528, and 760/759 in the 23-limit; 1309/1305, 1450/1449, and 4147/4140 in the 29-limit; 496/495 and 1365/1364 in the 31-limit.

Approximation of prime harmonics in 174edo
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	+1.49	-0.11	-3.31	+0.41	+0.85	-1.51	-0.96	-0.69	-1.99	-0.21
Error	Relative (%)	+0.0	+21.7	-1.5	-48.0	+5.9	+12.3	-21.9	-13.9	-10.0	-28.9	-3.0
Steps (reduced)		174 (0)	276 (102)	404 (56)	488 (140)	602 (80)	644 (122)	711 (15)	739 (43)	787 (91)	845 (149)	862 (166)

Since 174 factors into 2 × 3 × 29, 174edo has subset edos 2, 3, 6, 29, 58, and 87.

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 {{Infobox ET}}
-'''174edo''' is the [[EDO|equal division of the octave]] into 174 parts of 6.8966 cents each. It is closely related to [[87edo]], but the patent vals differ on the mapping for 17 and some higher primes. It is [[contorted]] in the 13-limit, tempering out 196/195, 245/243, 352/351, 364/363, and 625/624. Using the patent val, it tempers out 289/288 in the 17-limit; 361/360, 476/475, and 665/663 in the 19-limit; 391/390, 392/391, 460/459, 529/528, and 760/759 in the 23-limit; 1309/1305, 1450/1449, and 4147/4140 in the 29-limit; 496/495 and 1365/1364 in the 31-limit.
+{{EDO intro}}
-==Harmonics==
+edo is closely related to [[87edo]], but the [[patent val]]s differ on the mapping for [[17/1|17]] and some higher primes. It is [[contorted]] in the 13-limit, [[tempering out]] [[196/195]], [[245/243]], [[352/351]], [[364/363]], and [[625/624]]. Using the patent val, it tempers out [[289/288]] in the 17-limit; [[361/360]], [[476/475]], and 665/663 in the 19-limit; [[391/390]], [[392/391]], [[460/459]], [[529/528]], and [[760/759]] in the 23-limit; 1309/1305, 1450/1449, and 4147/4140 in the 29-limit; 496/495 and 1365/1364 in the 31-limit.
+=== Odd harmonics ===
 {{Harmonics in equal|174}}
-{{stub}}
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+=== Subsets and supersets ===
+Since 174 factors into {{factorization|174}}, 174edo has subset edos {{EDOs| 2, 3, 6, 29, 58, and 87 }}.