367edo: Difference between revisions
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis begin}} | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
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| 0.3688 | | 0.3688 | ||
| 11.28 | | 11.28 | ||
{{comma basis end}} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {{rank-2 begin}} | ||
|- | |- | ||
| 1 | | 1 | ||
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| 6/5 | | 6/5 | ||
| [[Hanson]] | | [[Hanson]] | ||
{{rank-2 end}} | |||
{{orf]} | |||
== Music == | == Music == | ||
; [[Francium]] | ; [[Francium]] | ||
* "Loss" from ''End Of Sartorius Membranes'' (2024) | * "Loss" from ''End Of Sartorius Membranes'' (2024) – [https://open.spotify.com/track/0fZfyXdtSonjGHoTSQu5O5 Spotify] | [https://francium223.bandcamp.com/track/loss Bandcamp] | [https://www.youtube.com/watch?v=5UmRUMSzoHM YouTube] | ||
[[Category:Listen]] | [[Category:Listen]] | ||
Revision as of 02:07, 16 November 2024
| ← 366edo | 367edo | 368edo → |
Theory
367et is only consistent to the 5-odd-limit, with three mappings possible for the 7-limit:
- ⟨367 582 852 1030] (patent val)
- ⟨367 582 852 1031] (367d val)
- ⟨367 582 853 1031] (367cd val)
Using the patent val, it tempers out 15625/15552 and [102 -57 -5⟩ in the 5-limit; 5120/5103 and 40353607/39858075 in the 7-limit.
Using the 367d val, it tempers out 15625/15552 and [102 -57 -5⟩ in the 5-limit; 2460375/2458624 and 2097152/2083725 in the 7-limit.
Using the 367cd val, it tempers out 268435456/263671875 and [33 -34 9⟩ in the 5-limit; 5120/5103, 7558272/7503125 and 235298/234375 in the 7-limit.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.04 | -0.48 | -0.98 | -1.19 | +1.27 | -0.20 | +0.56 | -0.32 | +0.03 | +0.06 | -0.48 |
| Relative (%) | +31.9 | -14.8 | -29.9 | -36.2 | +38.9 | -6.1 | +17.1 | -9.9 | +1.1 | +2.0 | -14.7 | |
| Steps (reduced) |
582 (215) |
852 (118) |
1030 (296) |
1163 (62) |
1270 (169) |
1358 (257) |
1434 (333) |
1500 (32) |
1559 (91) |
1612 (144) |
1660 (192) | |
Subsets and supersets
367edo is the 73rd prime edo. 1101edo, which triples it, gives a good correction to the harmonic 7.
Regular temperament properties
Template:Comma basis begin |- | 2.3 | [582 -367⟩ | [⟨367 582]] | -0.3288 | 0.3287 | 10.05 |- | 2.3.5 | 15625/15552, [102 -57 -5⟩ | [⟨367 582 852]] | -0.1500 | 0.3688 | 11.28 Template:Comma basis end
Rank-2 temperaments
Template:Rank-2 begin |- | 1 | 28\367 | 91.55 | [46 -7 -15⟩ | Gross |- | 1 | 97\367 | 317.17 | 6/5 | Hanson Template:Rank-2 end {{orf]}