103edo: Difference between revisions
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis begin}} | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
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| 0.595 | | 0.595 | ||
| 5.10 | | 5.10 | ||
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=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {{rank-2 begin}} | ||
|- | |- | ||
| 1 | | 1 | ||
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| 7/5 | | 7/5 | ||
| [[Neptune]] | | [[Neptune]] | ||
{{rank-2 end}} | |||
{{orf}} | |||
== Music == | == Music == | ||
; [[Francium]] | ; [[Francium]] | ||
* "Forest Tribe Dance" from ''Mysteries'' (2023) | * "Forest Tribe Dance" from ''Mysteries'' (2023) – [https://open.spotify.com/track/0lPUfgduKoJliGbU3kcow0 Spotify] | [https://francium223.bandcamp.com/track/forest-tribe-dance Bandcamp] | [https://www.youtube.com/watch?v=5pbnmzXAFcM YouTube] | ||
[[Category:Benediction]] | [[Category:Benediction]] | ||
[[Category:Listen]] | |||
[[Category:Miracle]] | [[Category:Miracle]] | ||
Revision as of 04:50, 16 November 2024
| ← 102edo | 103edo | 104edo → |
Theory
In 103edo, all intervals within the 17-odd-limit are consistent, with the sole exception of 9/8 and its octave complement 16/9, which barely miss (relative error 50.2%). Its closest zeta peak index, 596zpi, stretches the octave by +0.739 cents. This expansion is uniquely consistent within the 15-integer-limit.
103edo is a good miracle tuning, especially for the 7-limit, and for benediction and hemisecordite, two of the 13-limit extensions of miracle. It tempers out 78732/78125 in the 5-limit; 225/224, 1029/1024 and 2401/2400 in the 7-limit; 243/242, 441/440 and 540/539 in the 11-limit; 351/350 and 847/845 in the 13-limit. In the 13-limit it provides the optimal patent val for marvel temperament as well as benediction and hemisecordite.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -2.93 | -1.85 | -1.84 | -3.75 | -1.69 | -0.10 | +5.40 | +0.85 | -4.33 | -3.29 |
| Relative (%) | +0.0 | -25.1 | -15.9 | -15.8 | -32.1 | -14.5 | -0.9 | +46.3 | +7.3 | -37.2 | -28.2 | |
| Steps (reduced) |
103 (0) |
163 (60) |
239 (33) |
289 (83) |
356 (47) |
381 (72) |
421 (9) |
438 (26) |
466 (54) |
500 (88) |
510 (98) | |
Subsets and supersets
103edo is the 27th prime edo, following 101edo and before 107edo.
Intervals
Regular temperament properties
Template:Comma basis begin |- | 2.3 | [-163 103⟩ | [⟨103 166]] | +0.923 | 0.924 | 7.92 |- | 2.3.5 | 78732/78125, 34171875/33554432 | [⟨103 166 239]] | +0.881 | 0.757 | 6.49 |- | 2.3.5.7 | 225/224, 1029/1024, 78732/78125 | [⟨103 166 239 289]] | +0.824 | 0.663 | 5.68 |- | 2.3.5.7.11 | 225/224, 243/242, 385/384, 43923/43750 | [⟨103 166 239 289 356]] | +0.876 | 0.602 | 5.16 |- | 2.3.5.7.11.13 | 225/224, 243/242, 351/350, 385/384, 847/845 | [⟨103 166 239 289 356 381]] | +0.806 | 0.571 | 4.90 |- | 2.3.5.7.11.13.17 | 225/224, 243/242, 273/272, 351/350, 375/374, 847/845 | [⟨103 166 239 289 356 381 421]] | +0.694 | 0.595 | 5.10 Template:Comma basis end
Rank-2 temperaments
Template:Rank-2 begin |- | 1 | 3\103 | 34.951 | 1990656/1953125 | Gammy |- | 1 | 5\103 | 58.252 | 27/26 | Hemisecordite |- | 1 | 9\103 | 104.854 | 17/16 | Septendesemi |- | 1 | 10\103 | 116.505 | 15/14~16/15 | Miracle / benediction |- | 1 | 16\103 | 186.408 | 10/9 | Mintone |- | 1 | 20\103 | 233.010 | 8/7 | Slendric |- | 1 | 21\103 | 244.660 | 15/13 | Subsemifourth |- | 1 | 26\103 | 303.013 | 25/21 | Quinmite |- | 1 | 31\103 | 361.165 | 16/13 | Phicordial |- | 1 | 37\103 | 431.06 | 77/60 | Lockerbie |- | 1 | 38\103 | 442.708 | 162/125 | Sensei |- | 1 | 39\103 | 454.369 | 13/10 | Fibo |- | 1 | 40\103 | 466.019 | 55/42 | Hemiseptisix |- | 1 | 42\103 | 489.320 | 65/49 | Catafourth |- | 1 | 45\103 | 524.272 | 65/48 | Widefourth |- | 1 | 47\103 | 547.573 | 11/8 | Heinz |- | 1 | 48\103 | 559.223 | 242/175 | Tritriple |- | 1 | 50\103 | 582.524 | 7/5 | Neptune Template:Rank-2 end Template:Orf