1240edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|1240}} 1240edo is consistent in the 7-odd-limit, though the error on harmonic 3 is quite large. It is a strong tuning for 5-limit sov..." |
m changed EDO intro to ED intro |
||
| (One intermediate revision by one other user not shown) | |||
| Line 1: | Line 1: | ||
{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
1240edo is [[consistent]] in the 7-odd-limit, though the error on harmonic [[3/1|3]] is quite large. It is a strong tuning for 5-limit [[soviet ferris wheel]], ({{monzo|-171 20 60}}), and a good tuning for [[dodifo]], ({{monzo|-67 -9 35}}). | 1240edo is [[consistent]] in the [[7-odd-limit]], though the error on [[harmonic]] [[3/1|3]] is quite large. It is a strong tuning for 5-limit [[soviet ferris wheel]], ({{monzo|-171 20 60}}), and a good tuning for [[dodifo]], ({{monzo|-67 -9 35}}). | ||
Beyond the 7-odd-limit, there is a number of mappings to be considered. In the 2.7.23 | Beyond the 7-odd-limit, there is a number of mappings to be considered. In the 2.27.7.23.29 [[subgroup]], it is a flat system, and in 2.9.11.13.15, it is a sharp system. In the 2.5.11.13.29, it tunes the [[genojacobin]] temperament. | ||
=== Odd harmonics === | === Odd harmonics === | ||
{{ | {{Harmonics in equal|1240|columns=14}} | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
Since 1240 factors as {{Factorization|1240}}, | Since 1240 factors as {{Factorization|1240}}, 1240edo has subset edos {{EDOs| 2, 4, 5, 8, 10, 20, 31, 40, 62, 124, 155, 248, 310, 620 }}. | ||
Latest revision as of 05:43, 21 February 2025
| ← 1239edo | 1240edo | 1241edo → |
1240 equal divisions of the octave (abbreviated 1240edo or 1240ed2), also called 1240-tone equal temperament (1240tet) or 1240 equal temperament (1240et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1240 equal parts of about 0.968 ¢ each. Each step represents a frequency ratio of 21/1240, or the 1240th root of 2.
1240edo is consistent in the 7-odd-limit, though the error on harmonic 3 is quite large. It is a strong tuning for 5-limit soviet ferris wheel, ([-171 20 60⟩), and a good tuning for dodifo, ([-67 -9 35⟩).
Beyond the 7-odd-limit, there is a number of mappings to be considered. In the 2.27.7.23.29 subgroup, it is a flat system, and in 2.9.11.13.15, it is a sharp system. In the 2.5.11.13.29, it tunes the genojacobin temperament.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | 25 | 27 | 29 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.342 | -0.185 | -0.116 | +0.284 | +0.295 | +0.440 | +0.441 | -0.439 | -0.416 | -0.458 | -0.210 | -0.369 | -0.059 | +0.100 |
| Relative (%) | -35.4 | -19.1 | -12.0 | +29.3 | +30.5 | +45.5 | +45.6 | -45.4 | -43.0 | -47.4 | -21.7 | -38.2 | -6.1 | +10.4 | |
| Steps (reduced) |
1965 (725) |
2879 (399) |
3481 (1001) |
3931 (211) |
4290 (570) |
4589 (869) |
4845 (1125) |
5068 (108) |
5267 (307) |
5446 (486) |
5609 (649) |
5758 (798) |
5896 (936) |
6024 (1064) | |
Subsets and supersets
Since 1240 factors as 23 × 5 × 31, 1240edo has subset edos 2, 4, 5, 8, 10, 20, 31, 40, 62, 124, 155, 248, 310, 620.