User:Aura/762148edo: Difference between revisions
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Prime factorization
22 × 190537
Step size
0.0015745 ¢
Fifth
445828\762148 (701.955 ¢) (→ 111457\190537)
Semitones (A1:m2)
72204:57304 (113.7 ¢ : 90.22 ¢)
Consistency limit
17
Distinct consistency limit
17
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== Theory == | == Theory == | ||
This EDO has a consistency limit of 17, but seems to be at its best in the 11-limit. It tempers out the [[Archangelic comma]] in the 3-limit. | This EDO has a consistency limit of 17, but seems to be at its best in the 11-limit. It tempers out the [[Archangelic comma]] in the 3-limit, as well as [22953, -14473, 0, 0, -4> in the 2.3.11 subgroup. | ||
{{Harmonics in equal|762148}} | {{Harmonics in equal|762148}} | ||
[[Category:Equal divisions of the octave|######]] <!-- 6-digit number --> | [[Category:Equal divisions of the octave|######]] <!-- 6-digit number --> | ||
Revision as of 16:28, 7 September 2025
| ← 762147edo | 762148edo | 762149edo → |
762148 equal divisions of the octave (abbreviated 762148edo or 762148ed2), also called 762148-tone equal temperament (762148tet) or 762148 equal temperament (762148et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 762148 equal parts of about 0.00157 ¢ each. Each step represents a frequency ratio of 21/762148, or the 762148th root of 2.
Theory
This EDO has a consistency limit of 17, but seems to be at its best in the 11-limit. It tempers out the Archangelic comma in the 3-limit, as well as [22953, -14473, 0, 0, -4> in the 2.3.11 subgroup.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000000 | +0.000000 | +0.000230 | +0.000096 | +0.000174 | +0.000425 | +0.000583 | -0.000722 | +0.000476 | -0.000786 | +0.000300 |
| Relative (%) | +0.0 | +0.0 | +14.6 | +6.1 | +11.1 | +27.0 | +37.0 | -45.9 | +30.2 | -49.9 | +19.0 | |
| Steps (reduced) |
762148 (0) |
1207976 (445828) |
1769653 (245357) |
2139620 (615324) |
2636599 (350155) |
2820283 (533839) |
3115252 (66660) |
3237549 (188957) |
3447624 (399032) |
3702500 (653908) |
3775831 (727239) | |