317edo: Difference between revisions
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Created page with "{{Infobox ET}} {{EDO intro|317}} == Theory == 317et tempers out 589824/588245, 16875/16807, 65625/65536 and 49009212/48828125 in the 7-limit; 1835008/1830125, 14700/14..." |
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|2.9 | |2.9 | ||
|{{monzo|1005 -317}} | |{{monzo|1005 -317}} | ||
|{{ | |{{mapping|317 1005}} | ||
| -0.0799 | | -0.0799 | ||
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|2.9.5 | |2.9.5 | ||
|{{monzo|-53 5 16}}, {{monzo|33 -17 9}} | |{{monzo|-53 5 16}}, {{monzo|33 -17 9}} | ||
|{{ | |{{mapping|317 1005 736}} | ||
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|2.9.5.7 | |2.9.5.7 | ||
|420175/419904, 703125/702464, 33554432/33480783 | |420175/419904, 703125/702464, 33554432/33480783 | ||
|{{ | |{{mapping|317 1005 736 890}} | ||
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|2.9.5.7.11 | |2.9.5.7.11 | ||
|6250/6237, 12005/11979, 46656/46585, 151263/151250 | |6250/6237, 12005/11979, 46656/46585, 151263/151250 | ||
|{{ | |{{mapping|317 1005 736 890 1097}} | ||
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|2.9.5.7.11.13 | |2.9.5.7.11.13 | ||
|1575/1573, 4459/4455, 6250/6237, 67392/67375, 190125/189728 | |1575/1573, 4459/4455, 6250/6237, 67392/67375, 190125/189728 | ||
|{ | |{{mapping|317 1005 736 890 1097 1173}} | ||
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|2.9.5.7.11.13.17 | |2.9.5.7.11.13.17 | ||
|936/935, 1225/1224, 1575/1573, 12376/12375, 17920/17901, 34000/33957 | |936/935, 1225/1224, 1575/1573, 12376/12375, 17920/17901, 34000/33957 | ||
|{ | |{{mapping|317 1005 736 890 1097 1173 1296}} | ||
| -0.1109 | | -0.1109 | ||
| 0.1587 | | 0.1587 | ||
| 4.19 | | 4.19 | ||
|} | |} | ||
== Music == | |||
; [[Francium]] | |||
* "Narrator Of Myths" from ''Mysteries'' (2023) [https://open.spotify.com/track/6AYSSw1kVKDDzWVYMyxafv Spotify] | [https://francium223.bandcamp.com/track/narrator-of-myths Bandcamp] | [https://www.youtube.com/watch?v=fNmEjgVonHk YouTube] | |||
Revision as of 05:40, 20 November 2023
| ← 316edo | 317edo | 318edo → |
Theory
317et tempers out 589824/588245, 16875/16807, 65625/65536 and 49009212/48828125 in the 7-limit; 1835008/1830125, 14700/14641, 2097152/2096325, 4000/3993, 2734375/2725888, 1953125/1951488, 172032/171875, 441/440, 5767168/5764801, 825000/823543, 537109375/536870912, 134775333/134217728, 160083/160000, 16808715/16777216, 539055/537824 and 3294225/3294172 in the 11-limit.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.64 | -0.19 | +0.26 | +0.51 | +1.36 | -0.15 | -1.83 | +1.04 | +1.54 | -1.38 | +0.12 |
| Relative (%) | -43.3 | -5.1 | +6.8 | +13.4 | +36.0 | -3.9 | -48.4 | +27.4 | +40.7 | -36.5 | +3.1 | |
| Steps (reduced) |
502 (185) |
736 (102) |
890 (256) |
1005 (54) |
1097 (146) |
1173 (222) |
1238 (287) |
1296 (28) |
1347 (79) |
1392 (124) |
1434 (166) | |
Subsets and supersets
317edo is the 66th prime edo. 634edo, which doubles it, gives a good correction to the harmonic 3.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.9 | [1005 -317⟩ | [⟨317 1005]] | -0.0799 | 0.0799 | 2.11 |
| 2.9.5 | [-53 5 16⟩, [33 -17 9⟩ | [⟨317 1005 736]] | -0.0254 | 0.1009 | 2.67 |
| 2.9.5.7 | 420175/419904, 703125/702464, 33554432/33480783 | [⟨317 1005 736 890]] | -0.0422 | 0.0921 | 2.43 |
| 2.9.5.7.11 | 6250/6237, 12005/11979, 46656/46585, 151263/151250 | [⟨317 1005 736 890 1097]] | -0.1126 | 0.1631 | 4.31 |
| 2.9.5.7.11.13 | 1575/1573, 4459/4455, 6250/6237, 67392/67375, 190125/189728 | [⟨317 1005 736 890 1097 1173]] | -0.0871 | 0.1594 | 4.21 |
| 2.9.5.7.11.13.17 | 936/935, 1225/1224, 1575/1573, 12376/12375, 17920/17901, 34000/33957 | [⟨317 1005 736 890 1097 1173 1296]] | -0.1109 | 0.1587 | 4.19 |