107edo: Difference between revisions
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Revision as of 21:13, 30 May 2023
| ← 106edo | 107edo | 108edo → |
Theory
107edo is inconsistent to the 5-odd-limit and higher limits, with four mappings possible for the 7-limit: ⟨107 170 248 300] (patent val), ⟨107 169 248 300] (107b), ⟨107 170 249 300] (107c), and ⟨107 170 249 301] (107cd).
Using the patent val, it tempers out 3125/3072 (magic comma) and 33554432000/31381059609 in the 5-limit; 1029/1024, 2240/2187, and 3125/3087 in the 7-limit; 100/99, 1232/1215, and 1331/1323 in the 11-limit.
Using the 107b val, it tempers out 81/80 (syntonic comma) and [-61 -1 27⟩; in the 5-limit; 2401/2400, 2430/2401, and 234375/229376 in the 7-limit; 385/384, 1350/1331, 1375/1372, and 1944/1925 in the 11-limit.
Using the 107c val, it tempers out 1638400/1594323 (immunity comma) and 1990656/1953125 (valentine comma) in the 5-limit; 126/125, 1029/1024, and 307328/295245 in the 7-limit; 121/120, 176/175, 441/440, and 184877/177147 in the 11-limit.
Using the 107cd val, it tempers out 1728/1715, 4000/3969, and 28672/28125 in the 7-limit; 121/120, 896/891, 1375/1372, and 3168/3125 in the 11-limit.
Subsets and supersets
107edo is the 28th prime edo.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +4.59 | -5.01 | -4.34 | -2.04 | -1.79 | +0.59 | -0.42 | -4.02 | +5.29 | +0.25 | -0.24 |
| Relative (%) | +40.9 | -44.6 | -38.7 | -18.2 | -15.9 | +5.3 | -3.7 | -35.9 | +47.2 | +2.2 | -2.1 | |
| Steps (reduced) |
170 (63) |
248 (34) |
300 (86) |
339 (18) |
370 (49) |
396 (75) |
418 (97) |
437 (9) |
455 (27) |
470 (42) |
484 (56) | |
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.9 | [339 -107⟩ | ⟨107 339] | +0.322 | 0.322 | 2.87 |
| 2.9.5 | 9765625/9565938, [-34 10 1⟩ | ⟨107 339 248] | +0.933 | 0.904 | 8.06 |
| 2.9.5.7 | 225/224, 84035/82944, [14 -6 7 -4⟩ | ⟨107 339 248 300] | +1.087 | 0.827 | 7.37 |
| 2.9.5.7.11 | 225/224, 441/440, 26411/26244, 161280/161051 | ⟨107 339 248 300 370] | +0.973 | 0.774 | 6.90 |
| 2.9.5.7.11.13 | 225/224, 325/324, 441/440, 847/845, 24500/24167 | ⟨107 339 248 300 370 396] | +0.783 | 0.823 | 7.33 |
| 2.9.5.7.11.13.17 | 170/169, 225/224, 325/324, 441/440, 847/845, 2000/1989 | ⟨107 339 248 300 370 396 437] | +0.812 | 0.765 | 6.82 |