321edo: Difference between revisions

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-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]].
+{{Infobox ET}}
+{{ED intro}}
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+== 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]], [[2080/2079]] and [[4096/4095]], providing the [[optimal patent val]] for 11- and 13-limit [[akea]] temperament.
+=== Prime harmonics ===
+{{Harmonics in equal|321}}
+== Interval table ==
+{{main|Table of 321edo intervals}}
+== Scales ==
+[[JUMBLE]]'s Blastoff scale (9L&nbsp;8s)
+* 25\321
+* 37\321
+* 62\321
+* 74\321
+* 99\321
+* 111\321
+* 136\321
+* 148\321
+* 173\321
+* 185\321
+* 210\321
+* 222\321
+* 247\321
+* 259\321
+* 284\321
+* 296\321
+* 321\321
+This scale may be thought of as a tuning of the [[Greenwoodmic temperaments#Secundly|secundly]] (or lower limit secund) temperament.
+== Music ==
+; [[JUMBLE]]
+* [https://www.youtube.com/watch?v=4HT5onKQaz0 ''Sun Through The Window''] (2023) – ambient
+* [https://www.youtube.com/watch?v=cQoWVBbKnuA ''BLASTOFF!''] (2023) – synthwave, [[9L 8s]] scale
+* [https://www.youtube.com/watch?v=e8hhlQSYqVY ''Infinity''] (2023)
+* [https://www.youtube.com/watch?v=ZW7JyextZoM ''Greige City''] (2023) – synthwave, [[9L 8s]] scale
+* [https://www.youtube.com/watch?v=yIfooPURtYE ''So Long, San Diego''] (2024)
+* [https://www.youtube.com/watch?v=xI0HXnrlSlA ''Ten Day Forecast''] (2024) – ambient
+; [[No Clue Music]]
+* [https://www.youtube.com/watch?v=orjW0qIveqU ''Frozen Star''] (2024)
+[[Category:Akea]]
+[[Category:Listen]]