203edo: Difference between revisions
m Intro & harmonics |
m Cleanup |
||
| Line 2: | Line 2: | ||
{{EDO intro}} | {{EDO intro}} | ||
203edo is in[[consistent]] to the [[5-odd-limit]] and higher, with three mappings possible for the 7-limit: {{val| 203 322 471 570 }} ([[patent val]]), {{val| 203 '''321''' 471 '''569''' }} (203bd), and {{val| 203 322 '''472''' 570 }} (203c). Using the patent val, it [[tempering out|tempers out]] 2109375/2097152 ([[semicomma]]) and {{monzo| 4 -23 14 }} in the 5-limit; [[4000/3969]], [[10976/10935]], and [[2100875/2097152]] in the 7-limit; [[385/384]], 1331/1323, and [[4000/3993]] in the 11-limit; [[352/351]], [[676/675]], [[1573/1568]], and 1625/1617 in the 13-limit. Using the 203c val, it tempers out 78732/78125 ([[sensipent comma]]) and [[29-comma]] in the 5-limit; [[5120/5103]], [[50421/50000]], and 110592/109375 in the 7-limit; [[176/175]], 1331/1323, [[8019/8000]], and 26411/26244 in the 11-limit. Using the 203ce val, it tempers out [[441/440]], [[896/891]], and [[3388/3375]] in the 11-limit. Using the 203cef val, it tempers out [[196/195]], 352/351, [[364/363]], 676/675, and 78732/78125 in the 13-limit. | |||
== | === Odd harmonics === | ||
{{Harmonics in equal|203}} | {{Harmonics in equal|203}} | ||
Revision as of 12:08, 13 April 2024
| ← 202edo | 203edo | 204edo → |
203edo is inconsistent to the 5-odd-limit and higher, with three mappings possible for the 7-limit: ⟨203 322 471 570] (patent val), ⟨203 321 471 569] (203bd), and ⟨203 322 472 570] (203c). Using the patent val, it tempers out 2109375/2097152 (semicomma) and [4 -23 14⟩ in the 5-limit; 4000/3969, 10976/10935, and 2100875/2097152 in the 7-limit; 385/384, 1331/1323, and 4000/3993 in the 11-limit; 352/351, 676/675, 1573/1568, and 1625/1617 in the 13-limit. Using the 203c val, it tempers out 78732/78125 (sensipent comma) and 29-comma in the 5-limit; 5120/5103, 50421/50000, and 110592/109375 in the 7-limit; 176/175, 1331/1323, 8019/8000, and 26411/26244 in the 11-limit. Using the 203ce val, it tempers out 441/440, 896/891, and 3388/3375 in the 11-limit. Using the 203cef val, it tempers out 196/195, 352/351, 364/363, 676/675, and 78732/78125 in the 13-limit.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.49 | -2.08 | +0.63 | -2.92 | -1.56 | -1.12 | -0.58 | +1.45 | -1.95 | +2.13 | -1.67 |
| Relative (%) | +25.3 | -35.1 | +10.7 | -49.5 | -26.5 | -18.9 | -9.9 | +24.5 | -32.9 | +36.0 | -28.3 | |
| Steps (reduced) |
322 (119) |
471 (65) |
570 (164) |
643 (34) |
702 (93) |
751 (142) |
793 (184) |
830 (18) |
862 (50) |
892 (80) |
918 (106) | |