168edo: Difference between revisions
m Added link to whitewood, added mention of dotcom |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro}} | |||
It is closely related to [[84edo]], but the patent vals differ on the mapping for 11 and 17. It is [[contorted]] in the 7-limit, tempering out 225/224, 1728/1715, and 78732/78125. Using the patent val, it tempers out 243/242, 2420/2401, 3025/3024, and 43923/43750 in the 11-limit; 351/350, 625/624, 640/637, 847/845, and 1573/1568 in the 13-limit; 375/374, 561/560, 715/714, 891/884, 936/935, and 1331/1326 in the 17-limit. Using the 168d val, it tempers out 3136/3125, 19683/19600, and 33075/32768 in the 7-limit; 243/242, 385/384, 3773/3750, and 9801/9800 in the 11-limit. | |||
Stacking alternating steps of 43 and 53 produces an optimal [[whitewood]] [14] scale of 19 5 19 5 19 5 19 5 19 5 19 5 19 5 that spreads the overall flatness evenly between the major and minor thirds. [[Substitute harmonic#Dotcom|dotcom]] is also supported. | Stacking alternating steps of 43 and 53 produces an optimal [[whitewood]] [14] scale of 19 5 19 5 19 5 19 5 19 5 19 5 19 5 that spreads the overall flatness evenly between the major and minor thirds. [[Substitute harmonic#Dotcom|dotcom]] is also supported. | ||
Revision as of 22:56, 3 February 2024
| ← 167edo | 168edo | 169edo → |
It is closely related to 84edo, but the patent vals differ on the mapping for 11 and 17. It is contorted in the 7-limit, tempering out 225/224, 1728/1715, and 78732/78125. Using the patent val, it tempers out 243/242, 2420/2401, 3025/3024, and 43923/43750 in the 11-limit; 351/350, 625/624, 640/637, 847/845, and 1573/1568 in the 13-limit; 375/374, 561/560, 715/714, 891/884, 936/935, and 1331/1326 in the 17-limit. Using the 168d val, it tempers out 3136/3125, 19683/19600, and 33075/32768 in the 7-limit; 243/242, 385/384, 3773/3750, and 9801/9800 in the 11-limit.
Stacking alternating steps of 43 and 53 produces an optimal whitewood [14] scale of 19 5 19 5 19 5 19 5 19 5 19 5 19 5 that spreads the overall flatness evenly between the major and minor thirds. dotcom is also supported.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.96 | -0.60 | +2.60 | +3.23 | -1.32 | +2.33 | -2.55 | +2.19 | +2.49 | +0.65 | +0.30 |
| Relative (%) | -27.4 | -8.4 | +36.4 | +45.3 | -18.5 | +32.6 | -35.8 | +30.6 | +34.8 | +9.1 | +4.2 | |
| Steps (reduced) |
266 (98) |
390 (54) |
472 (136) |
533 (29) |
581 (77) |
622 (118) |
656 (152) |
687 (15) |
714 (42) |
738 (66) |
760 (88) | |