1525edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
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1525edo is consistent to the [[9-odd-limit]], though its approcimation for [[7/4|7]] is worse than for the 5-limit. In higher limits, it is a good 2.3.5.7.13.19.31 system, and an excellent 2.3.5.19 system with an optional addition of [[29/23]]. | 1525edo is consistent to the [[9-odd-limit]], though its approcimation for [[7/4|7]] is worse than for the 5-limit. In higher limits, it is a good 2.3.5.7.13.19.31 system, and an excellent 2.3.5.19 system with an optional addition of [[29/23]]. | ||
In the 5-limit, it tempers out the [[dipromethia]], mapping [[2048/2025]] into [[61edo|1\61]] as well as the [[astro]] comma, {{monzo|91 -12 -31}} and the 25th-octave [[manganese]] comma, {{monzo|211 50 -125}}. In the 7-limit, it tunes [[osiris]], and in the 2.5.7.11.13 subgroup, [[french decimal]]. | In the 5-limit, it tempers out the [[dipromethia]], mapping [[2048/2025]] into [[61edo|1\61]] as well as the [[astro]] comma, {{monzo|91 -12 -31}} and the 25th-octave [[manganese]] comma, {{monzo|211 50 -125}}. In the 7-limit, it tunes [[osiris]], and in the 2.5.7.11.13 subgroup, [[french decimal]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|1525}} | {{Harmonics in equal|1525}} | ||
Latest revision as of 23:13, 20 February 2025
| ← 1524edo | 1525edo | 1526edo → |
1525 equal divisions of the octave (abbreviated 1525edo or 1525ed2), also called 1525-tone equal temperament (1525tet) or 1525 equal temperament (1525et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1525 equal parts of about 0.787 ¢ each. Each step represents a frequency ratio of 21/1525, or the 1525th root of 2.
1525edo is consistent to the 9-odd-limit, though its approcimation for 7 is worse than for the 5-limit. In higher limits, it is a good 2.3.5.7.13.19.31 system, and an excellent 2.3.5.19 system with an optional addition of 29/23.
In the 5-limit, it tempers out the dipromethia, mapping 2048/2025 into 1\61 as well as the astro comma, [91 -12 -31⟩ and the 25th-octave manganese comma, [211 50 -125⟩. In the 7-limit, it tunes osiris, and in the 2.5.7.11.13 subgroup, french decimal.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.053 | +0.047 | -0.170 | +0.289 | -0.134 | -0.300 | -0.070 | -0.340 | -0.331 | -0.118 |
| Relative (%) | +0.0 | -6.8 | +6.0 | -21.6 | +36.7 | -17.1 | -38.1 | -8.9 | -43.2 | -42.1 | -14.9 | |
| Steps (reduced) |
1525 (0) |
2417 (892) |
3541 (491) |
4281 (1231) |
5276 (701) |
5643 (1068) |
6233 (133) |
6478 (378) |
6898 (798) |
7408 (1308) |
7555 (1455) | |
Subsets and supersets
Since 1525 factors as 52 × 61, 1525edo has subset edos 1, 5, 25, 61, 305.