16625edo: Difference between revisions
m Sort key |
ArrowHead294 (talk | contribs) mNo edit summary |
||
| (5 intermediate revisions by 4 users not shown) | |||
| Line 1: | Line 1: | ||
{{ | {{Infobox ET}} | ||
{{ED intro}} | |||
16625edo is [[consistent]] in the 29-odd-limit. It tempers out the comma {{monzo| 802 -799 200 }} which equates a stack of two hundred [[syntonic comma]]s with [[12/1]], and supports the rank-2 {{nowrap|6862 & 9763}} temperament tempering out this comma. | |||
{{ | |||
=== Prime harmonics === | |||
{{Harmonics in equal|16625}} | |||
16625edo has | === Subsets and supersets === | ||
16625edo has subset edos {{EDOs| 5, 7, 19, 25, 35, 95, 125, 133, 175, 475, 665, 875, 2375, and 3325 }}, of which 665 is a continued fraction approximant to the perfect fifth 3/2. | |||
Latest revision as of 17:41, 20 February 2025
| ← 16624edo | 16625edo | 16626edo → |
16625 equal divisions of the octave (abbreviated 16625edo or 16625ed2), also called 16625-tone equal temperament (16625tet) or 16625 equal temperament (16625et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 16625 equal parts of about 0.0722 ¢ each. Each step represents a frequency ratio of 21/16625, or the 16625th root of 2.
16625edo is consistent in the 29-odd-limit. It tempers out the comma [802 -799 200⟩ which equates a stack of two hundred syntonic commas with 12/1, and supports the rank-2 6862 & 9763 temperament tempering out this comma.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | -0.0001 | -0.0039 | -0.0199 | -0.0037 | +0.0137 | -0.0050 | +0.0148 | -0.0157 | +0.0048 | +0.0351 |
| Relative (%) | +0.0 | -0.2 | -5.5 | -27.6 | -5.1 | +19.0 | -7.0 | +20.5 | -21.8 | +6.6 | +48.6 | |
| Steps (reduced) |
16625 (0) |
26350 (9725) |
38602 (5352) |
46672 (13422) |
57513 (7638) |
61520 (11645) |
67954 (1454) |
70622 (4122) |
75204 (8704) |
80764 (14264) |
82364 (15864) | |
Subsets and supersets
16625edo has subset edos 5, 7, 19, 25, 35, 95, 125, 133, 175, 475, 665, 875, 2375, and 3325, of which 665 is a continued fraction approximant to the perfect fifth 3/2.