397edo: Difference between revisions
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis begin}} | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| Line 44: | Line 36: | ||
| 0.2859 | | 0.2859 | ||
| 9.46 | | 9.46 | ||
{{comma basis end}} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {{rank-2 begin}} | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 84: | Line 70: | ||
| 7/5 | | 7/5 | ||
| [[Cotritone]] (397cd) | | [[Cotritone]] (397cd) | ||
{{rank-2 end}} | |||
{{orf}} | |||
== Music == | == Music == | ||
; [[Francium]] | ; [[Francium]] | ||
* "Mysteries Within Us" from ''End Of Sartorius Membranes'' (2024) | * "Mysteries Within Us" from ''End Of Sartorius Membranes'' (2024) – [https://open.spotify.com/track/4fbOQF5p1YITudOw866GvH Spotify] | [https://francium223.bandcamp.com/track/mysteries-within-us Bandcamp] | [https://www.youtube.com/watch?v=kDdh9XZ4UNE YouTube] | ||
[[Category:Listen]] | [[Category:Listen]] | ||
Revision as of 02:48, 16 November 2024
| ← 396edo | 397edo | 398edo → |
Theory
397edo is only consistent to the 5-odd-limit, with three mappings possible for the 7-limit:
- ⟨397 629 922 1115] (patent val)
- ⟨397 629 922 1114] (397d val)
- ⟨397 629 921 1114] (397cd val)
Using the patent val, it tempers out 129140163/128000000 and [55 -1 -23⟩ in the 5-limit; 6144/6125, 16875/16807 and 129140163/128000000 in the 7-limit; supporting grendel.
Using the 397d val, it tempers out 129140163/128000000 and [55 -1 -23⟩ in the 5-limit; 3136/3125, 420175/419904 and 33756345/33554432 in the 7-limit; supporting sengagen.
Using the 397cd val, it tempers out 390625000/387420489 and [-55 23 8⟩ in the 5-limit; 2401/2400, 390625/387072 and 14348907/14336000 in the 7-limit; supporting cotritone.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.70 | +0.59 | +1.45 | -1.19 | -0.23 | +0.84 | -1.29 | +0.44 | +1.15 | +0.56 |
| Relative (%) | +0.0 | -23.0 | +19.5 | +48.0 | -39.4 | -7.5 | +27.7 | -42.7 | +14.6 | +38.2 | +18.4 | |
| Steps (reduced) |
397 (0) |
629 (232) |
922 (128) |
1115 (321) |
1373 (182) |
1469 (278) |
1623 (35) |
1686 (98) |
1796 (208) |
1929 (341) |
1967 (379) | |
Subsets and supersets
397edo is the 78th prime edo. 1588edo, which quadruples it, gives a good correction to the harmonic 7.
Regular temperament properties
Template:Comma basis begin |- | 2.3 | [-629 397⟩ | [⟨397 629]] | 0.2194 | 0.2195 | 7.26 |- | 2.3.5 | 129140163/128000000, [55 -1 -23⟩ | [⟨397 629 922]] | 0.0618 | 0.2859 | 9.46 Template:Comma basis end
Rank-2 temperaments
Template:Rank-2 begin |- | 1 | 8\397 | 24.18 | 686/675 | Sengagen (397d) |- | 1 | 37\397 | 111.84 | 16/15 | Vavoom |- | 1 | 128\397 | 386.90 | 5/4 | Grendel (397) |- | 1 | 171\397 | 516.88 | 27/20 | Gravity |- | 1 | 193\397 | 583.38 | 7/5 | Cotritone (397cd) Template:Rank-2 end Template:Orf