203edo: Difference between revisions
Same fifth as 29edo, which is pretty good. Don't see a point to consider an alt fifith. It's not mentioned in the following sentences either. |
ArrowHead294 (talk | contribs) mNo edit summary |
||
| Line 1: | Line 1: | ||
{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
203 = 7 × 29, | Since {{nowrap|203 {{=}} 7 × 29}}, 203edo shares its [[3/2|fifth]] with [[29edo]]. It is in[[consistent]] to the [[5-odd-limit]] and higher limits, with two mappings possible for the 7-limit: {{val| 203 322 471 570 }} ([[patent val]]), {{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]]) 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. The alternative 203cef val is also worth considering, which tempers out [[441/440]], [[896/891]], and [[3388/3375]] in the 11-limit; and [[196/195]], 352/351, [[364/363]], and 676/675 in the 13-limit. | ||
=== Odd harmonics === | === Odd harmonics === | ||
Latest revision as of 19:27, 20 February 2025
| ← 202edo | 203edo | 204edo → |
203 equal divisions of the octave (abbreviated 203edo or 203ed2), also called 203-tone equal temperament (203tet) or 203 equal temperament (203et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 203 equal parts of about 5.91 ¢ each. Each step represents a frequency ratio of 21/203, or the 203rd root of 2.
Since 203 = 7 × 29, 203edo shares its fifth with 29edo. It is inconsistent to the 5-odd-limit and higher limits, with two mappings possible for the 7-limit: ⟨203 322 471 570] (patent val), ⟨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) 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. The alternative 203cef val is also worth considering, which tempers out 441/440, 896/891, and 3388/3375 in the 11-limit; and 196/195, 352/351, 364/363, and 676/675 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) | |
Subsets and supersets
Since 203 factors into 7 × 29, 203edo contains 7edo and 29edo as its subsets.