321edo: Difference between revisions

Approximation of prime harmonics in 321edo
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	+0.85	-1.27	-0.60	-1.79	+0.59	-0.28	+1.55	-0.24	-1.54	-1.11
Error	Relative (%)	+0.0	+22.7	-33.9	-16.1	-47.8	+15.9	-7.6	+41.5	-6.3	-41.2	-29.7
Steps (reduced)		321 (0)	509 (188)	745 (103)	901 (259)	1110 (147)	1188 (225)	1312 (28)	1364 (80)	1452 (168)	1559 (275)	1590 (306)

Music

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 {{Infobox ET}}
-The 321 equal division divides the octave into 321 equal parts of 3.738 cents each. The patent val tempers out 2401/2400, 5120/5103 and 10976/10935 in the 7-limit, supporting hemififths temperament. In the 11-limit it tempers out 385/384 and 1375/1372, and in the 13-limit 325/324, 352/351, 847/845 and 2080/2079,  providing the [[Optimal_patent_val|optimal patent val]] for 11- and 13-limit [[Hemifamity_family#Akea|akea temperament]].
+{{EDO intro|321}}
+== Theory ==
+edo is in[[consistent]] in the [[5-odd-limit]]. The [[patent val]] [[Tempering out|tempers out]] [[2401/2400]], [[5120/5103]] and [[10976/10935]] in the 7-limit, supporting [[hemififths]]. In the 11-limit it tempers out [[385/384]] and 1375/1372, and in the 13-limit [[325/324]], [[352/351]], [[847/845]] and [[2080/2079]],  providing the [[optimal patent val]] for 11- and 13-limit [[akea]] temperament.
+=== Prime harmonics ===
+{{Harmonics in equal|321}}
 == Music ==
-; JUMBLE
+; [[JUMBLE]]
 * [https://www.youtube.com/watch?v=4HT5onKQaz0 ''Sun Through The Window''] (2023)
 * [https://www.youtube.com/watch?v=cQoWVBbKnuA ''BLASTOFF!''] (2023)
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->