30631edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ED intro}} | {{ED intro}} | ||
30631edo is [[consistent]] in the [[35-odd-limit]] and is a [[zeta peak integer edo]]. | |||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|30631| | {{Harmonics in equal|30631|columns=11}} | ||
{{Harmonics in equal|30631|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 30631edo (continued)}} | |||
{{Stub}} | |||
Latest revision as of 11:21, 15 January 2026
| ← 30630edo | 30631edo | 30632edo → |
30631 equal divisions of the octave (abbreviated 30631edo or 30631ed2), also called 30631-tone equal temperament (30631tet) or 30631 equal temperament (30631et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 30631 equal parts of about 0.0392 ¢ each. Each step represents a frequency ratio of 21/30631, or the 30631st root of 2.
30631edo is consistent in the 35-odd-limit and is a zeta peak integer edo.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | +0.0005 | +0.0008 | -0.0035 | +0.0059 | -0.0066 | -0.0029 | -0.0105 | -0.0089 | +0.0072 | +0.0005 |
| Relative (%) | +0.0 | +1.4 | +2.1 | -8.9 | +15.0 | -16.9 | -7.4 | -26.8 | -22.6 | +18.4 | +1.3 | |
| Steps (reduced) |
30631 (0) |
48549 (17918) |
71123 (9861) |
85992 (24730) |
105966 (14073) |
113348 (21455) |
125203 (2679) |
130118 (7594) |
138561 (16037) |
148805 (26281) |
151752 (29228) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0092 | -0.0069 | +0.0033 | +0.0152 | +0.0027 | -0.0094 | -0.0163 | -0.0148 | +0.0038 | +0.0190 | -0.0042 |
| Relative (%) | +23.4 | -17.5 | +8.4 | +38.9 | +6.9 | -23.9 | -41.5 | -37.8 | +9.6 | +48.4 | -10.8 | |
| Steps (reduced) |
159571 (6416) |
164107 (10952) |
166212 (13057) |
170143 (16988) |
175452 (22297) |
180191 (27036) |
181664 (28509) |
185810 (2024) |
188373 (4587) |
189601 (5815) |
193091 (9305) | |
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