729edt: Difference between revisions
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Corrections (same consistency limit as 460edo and same temperament as 460et in the 23-limit) |
m Adopt template: ED intro |
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729edt is closely related to [[460edo]], with the difference of 3/1 instead of 2/1 being just. The mappings match through the 23-limit, where they temper out exactly the same commas. Overall, 729edt approximates harmonics 2, 3, 5, 13, and 17 exceptionally well, while 460edo only has this good of an error on the 19th harmonic. | 729edt is closely related to [[460edo]], with the difference of 3/1 instead of 2/1 being just. The mappings match through the 23-limit, where they temper out exactly the same commas. Overall, 729edt approximates harmonics 2, 3, 5, 13, and 17 exceptionally well, while 460edo only has this good of an error on the 19th harmonic. | ||
Latest revision as of 10:03, 27 April 2024
| ← 728edt | 729edt | 730edt → |
729 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 729edt or 729ed3), is a nonoctave tuning system that divides the interval of 3/1 into 729 equal parts of about 2.61 ¢ each. Each step represents a frequency ratio of 31/729, or the 729th root of 3.
729edt is closely related to 460edo, with the difference of 3/1 instead of 2/1 being just. The mappings match through the 23-limit, where they temper out exactly the same commas. Overall, 729edt approximates harmonics 2, 3, 5, 13, and 17 exceptionally well, while 460edo only has this good of an error on the 19th harmonic.
729edt tempers out the [-81 28 -54⟩ comma which sets 27 intervals of 25/24 equal to the tritave.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.14 | +0.00 | +0.09 | -0.62 | -0.41 | -0.02 | -0.05 | +0.46 | +1.04 | -1.09 | +0.86 |
| Relative (%) | +5.2 | +0.0 | +3.4 | -23.7 | -15.8 | -0.9 | -2.0 | +17.5 | +39.8 | -41.8 | +32.8 | |
| Steps (reduced) |
460 (460) |
729 (0) |
1068 (339) |
1291 (562) |
1591 (133) |
1702 (244) |
1880 (422) |
1954 (496) |
2081 (623) |
2234 (47) |
2279 (92) | |