6664edo: Difference between revisions
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6664edo is the unique system tempering out both the [[barium comma]], which maps [[81/80]] into [[56edo|1\56]], and the [[septendecima]], which maps [[25/24]] into [[17edo|1\17]]. Therefore in 6664edo steps of 56edo and 17edo can be used as chromas in this particular fashion. | 6664edo is the unique system tempering out both the [[barium comma]], which maps [[81/80]] into [[56edo|1\56]], and the [[septendecima]], which maps [[25/24]] into [[17edo|1\17]]. Therefore in 6664edo steps of 56edo and 17edo can be used as chromas in this particular fashion. | ||
=== Odd harmonics === | === Odd harmonics === | ||
{{harmonics in equal|6664}} | {{harmonics in equal|6664}} | ||
=== Subsest and supersets === | === Subsest and supersets === | ||
6664edo has subset edos {{EDOs|1, 2, 4, 7, 8, 14, 17, 28, 34, 49, 56, 68, 98, 119, 136, 196, 238, 392, 476, 833, 952, 1666, 3332}}. | 6664edo has subset edos {{EDOs|1, 2, 4, 7, 8, 14, 17, 28, 34, 49, 56, 68, 98, 119, 136, 196, 238, 392, 476, 833, 952, 1666, 3332}}. | ||
Latest revision as of 17:42, 20 February 2025
| ← 6663edo | 6664edo | 6665edo → |
6664 equal divisions of the octave (abbreviated 6664edo or 6664ed2), also called 6664-tone equal temperament (6664tet) or 6664 equal temperament (6664et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 6664 equal parts of about 0.18 ¢ each. Each step represents a frequency ratio of 21/6664, or the 6664th root of 2.
6664edo is the unique system tempering out both the barium comma, which maps 81/80 into 1\56, and the septendecima, which maps 25/24 into 1\17. Therefore in 6664edo steps of 56edo and 17edo can be used as chromas in this particular fashion.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.0342 | -0.0592 | -0.0384 | -0.0685 | +0.0626 | +0.0486 | +0.0866 | +0.0266 | -0.0340 | -0.0726 | -0.0030 |
| Relative (%) | -19.0 | -32.9 | -21.3 | -38.0 | +34.8 | +27.0 | +48.1 | +14.8 | -18.9 | -40.3 | -1.7 | |
| Steps (reduced) |
10562 (3898) |
15473 (2145) |
18708 (5380) |
21124 (1132) |
23054 (3062) |
24660 (4668) |
26036 (6044) |
27239 (583) |
28308 (1652) |
29270 (2614) |
30145 (3489) | |
Subsest and supersets
6664edo has subset edos 1, 2, 4, 7, 8, 14, 17, 28, 34, 49, 56, 68, 98, 119, 136, 196, 238, 392, 476, 833, 952, 1666, 3332.