321edo: Difference between revisions
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→Scales: Added a corresponding temperament for the Blastoff scale. |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
321edo 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]] | 321edo 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 === | === Prime harmonics === | ||
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== Interval table == | == Interval table == | ||
{{ | {{main|Table of 321edo intervals}} | ||
== Scales == | |||
[[JUMBLE]]'s Blastoff scale (9L 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 == | == Music == | ||
; [[JUMBLE]] | ; [[JUMBLE]] | ||
* [https://www.youtube.com/watch?v=4HT5onKQaz0 ''Sun Through The Window''] (2023) | * [https://www.youtube.com/watch?v=4HT5onKQaz0 ''Sun Through The Window''] (2023) – ambient | ||
* [https://www.youtube.com/watch?v=cQoWVBbKnuA ''BLASTOFF!''] (2023) | * [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]] | |||
Latest revision as of 10:46, 23 May 2025
| ← 320edo | 321edo | 322edo → |
321 equal divisions of the octave (abbreviated 321edo or 321ed2), also called 321-tone equal temperament (321tet) or 321 equal temperament (321et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 321 equal parts of about 3.74 ¢ each. Each step represents a frequency ratio of 21/321, or the 321st root of 2.
Theory
321edo is inconsistent in the 5-odd-limit. The patent val 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
| 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 |
| 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) | |
Interval table
Scales
JUMBLE's Blastoff scale (9L 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 secundly (or lower limit secund) temperament.
Music
- Sun Through The Window (2023) – ambient
- BLASTOFF! (2023) – synthwave, 9L 8s scale
- Infinity (2023)
- Greige City (2023) – synthwave, 9L 8s scale
- So Long, San Diego (2024)
- Ten Day Forecast (2024) – ambient
- Frozen Star (2024)