1419edo: Difference between revisions
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1419edo is [[consistent]] in the [[25-odd-limit]], and with excellent representation of [[31/16]] it is a strong no-29's 37-limit tuning. It is also an impressive system in even higher limits, with good tunings on [[harmonic]]s [[43/1|43]], [[47/1|47]], and [[53/1|53]]. | |||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|1419}} | {{Harmonics in equal|1419}} | ||
=== Subsets and supersets === | |||
Since 1419 factors into {{factorization|1419}}, 1419edo has subset edos {{EDOs| 3, 11, 33, 43, 129, and 473 }}. | |||
Latest revision as of 17:13, 20 February 2025
| ← 1418edo | 1419edo | 1420edo → |
1419 equal divisions of the octave (abbreviated 1419edo or 1419ed2), also called 1419-tone equal temperament (1419tet) or 1419 equal temperament (1419et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1419 equal parts of about 0.846 ¢ each. Each step represents a frequency ratio of 21/1419, or the 1419th root of 2.
1419edo is consistent in the 25-odd-limit, and with excellent representation of 31/16 it is a strong no-29's 37-limit tuning. It is also an impressive system in even higher limits, with good tunings on harmonics 43, 47, and 53.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.052 | +0.156 | +0.307 | +0.056 | +0.064 | -0.093 | +0.161 | +0.055 | -0.402 | -0.004 |
| Relative (%) | +0.0 | -6.2 | +18.4 | +36.3 | +6.7 | +7.6 | -11.0 | +19.1 | +6.6 | -47.5 | -0.5 | |
| Steps (reduced) |
1419 (0) |
2249 (830) |
3295 (457) |
3984 (1146) |
4909 (652) |
5251 (994) |
5800 (124) |
6028 (352) |
6419 (743) |
6893 (1217) |
7030 (1354) | |
Subsets and supersets
Since 1419 factors into 3 × 11 × 43, 1419edo has subset edos 3, 11, 33, 43, 129, and 473.