User:Eliora/2026edo: Difference between revisions
Created page with "{{Infobox ET|2026edo}} {{ED intro|2026edo}} 2026edo is consistent in the 5-odd-limit. Overall though, it has a substantially poor harmonic quality. The best harmonic up to 101st harmonic is 13th. Nonetheless, despite inconsistency, in the 23-limit, the patent val beats all the others in accuracy. Some commas it tempers out are: [2, -1, 4, -2, 0, 0, -1, 0, 0⟩ (2500:2499) [2, 2, 1, -1, 0, 0, 1, -1, -1⟩ (3060:3059) [0, 1, 1, -1, 0, 1, 0, 1, -2⟩ (3705:3703) [-1, -1,..." |
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{{Harmonics in equal|2026|prec=3|columns=13}} | {{Harmonics in equal|2026|prec=3|columns=13}} | ||
{{Harmonics in equal|2026|prec=3|columns=13|start=14|collapsed=true|title=Approximation of prime harmonics in | {{Harmonics in equal|2026|prec=3|columns=13|start=14|collapsed=true|title=Approximation of prime harmonics in 2026edo (continued)}} | ||
Latest revision as of 19:57, 28 August 2026
| ← 2025edo | 2026edo | 2027edo → |
2026 equal divisions of the octave (abbreviated 2026edo or 2026ed2), also called 2026-tone equal temperament (2026tet) or 2026 equal temperament (2026et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2026 equal parts of about 0.592 ¢ each. Each step represents a frequency ratio of 21/2026, or the 2026th root of 2.
2026edo is consistent in the 5-odd-limit. Overall though, it has a substantially poor harmonic quality. The best harmonic up to 101st harmonic is 13th.
Nonetheless, despite inconsistency, in the 23-limit, the patent val beats all the others in accuracy.
Some commas it tempers out are: [2, -1, 4, -2, 0, 0, -1, 0, 0⟩ (2500:2499) [2, 2, 1, -1, 0, 0, 1, -1, -1⟩ (3060:3059) [0, 1, 1, -1, 0, 1, 0, 1, -2⟩ (3705:3703) [-1, -1, 0, -1, -2, 1, 1, 0, 1⟩ (5083:5082) [4, -1, -2, -1, -1, 0, 0, 2, 0⟩ (5776:5775) [0, -3, 2, 0, 0, -1, 1, 1, -1⟩ (8075:8073) [-10, -1, 1, -1, 1, 0, 1, 0, 1⟩ (21505:21504) [3, -3, -1, -1, 1, 1, 0, 1, -1⟩ (21736:21735) [-6, 0, 2, 1, 1, 1, -1, 0, -1⟩ (25025:25024) [8, -2, 0, 0, -1, 2, 0, -1, -1⟩ (43264:43263) [1, -2, 4, -3, -2, 1, 0, 0, 1⟩ (373750:373527) [0, 0, -1, 2, 0, 4, 0, 0, -4⟩ (1399489:1399205) [-1, 0, 4, -4, 2, -1, 0, 1, -1⟩ (1436875:1435798)
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.079 | -0.134 | +0.177 | +0.113 | -0.054 | -0.118 | -0.178 | +0.156 | -0.160 | -0.119 | -0.209 | -0.237 |
| Relative (%) | +0.0 | -13.4 | -22.6 | +29.9 | +19.2 | -9.1 | -20.0 | -30.1 | +26.3 | -26.9 | -20.2 | -35.3 | -40.0 | |
| Steps (reduced) |
2026 (0) |
3211 (1185) |
4704 (652) |
5688 (1636) |
7009 (931) |
7497 (1419) |
8281 (177) |
8606 (502) |
9165 (1061) |
9842 (1738) |
10037 (1933) |
10554 (424) |
10854 (724) | |
| Harmonic | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | 83 | 89 | 97 | 101 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.230 | +0.239 | +0.138 | -0.139 | +0.193 | +0.061 | -0.230 | +0.246 | -0.272 | +0.101 | +0.097 | -0.251 | +0.275 |
| Relative (%) | +38.8 | +40.3 | +23.3 | -23.5 | +32.6 | +10.3 | -38.8 | +41.5 | -46.0 | +17.0 | +16.4 | -42.3 | +46.4 | |
| Steps (reduced) |
10994 (864) |
11254 (1124) |
11605 (1475) |
11918 (1788) |
12016 (1886) |
12290 (134) |
12459 (303) |
12541 (385) |
12771 (615) |
12916 (760) |
13120 (964) |
13371 (1215) |
13490 (1334) | |