953edt
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Prime factorization
953 (prime)
Step size
1.99576¢
Octave
601\953edt (1199.45¢)
Consistency limit
2
Distinct consistency limit
2
| ← 952edt | 953edt | 954edt → |
953 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 953edt or 953ed3), is a nonoctave tuning system that divides the interval of 3/1 into 953 equal parts of about 2 ¢ each. Each step represents a frequency ratio of 31/953, or the 953rd root of 3. It corresponds to 601.27470edo.
Theory
953edt is strong in the 3.5.7.11.13.19.23.29.31 subgroup, tempering out 91125/91091, 60025/60021, 256025/255879, 4125/4123, 9317/9315, 16445/16443, 30625/30613 and 130977/130975. Using the 3.5.7.11.13.19.23 subgroup, it tempers out 110565/110561.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.551 | +0.000 | +0.894 | -0.239 | -0.551 | +0.009 | +0.343 | +0.000 | -0.790 | -0.146 | +0.894 |
| Relative (%) | -27.6 | +0.0 | +44.8 | -12.0 | -27.6 | +0.5 | +17.2 | +0.0 | -39.6 | -7.3 | +44.8 | |
| Steps (reduced) |
601 (601) |
953 (0) |
1203 (250) |
1396 (443) |
1554 (601) |
1688 (735) |
1804 (851) |
1906 (0) |
1997 (91) |
2080 (174) |
2156 (250) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.028 | -0.542 | -0.239 | -0.208 | +0.612 | -0.551 | -0.353 | +0.655 | +0.009 | -0.697 | +0.181 | +0.343 | -0.478 | -0.523 | +0.000 |
| Relative (%) | +1.4 | -27.1 | -12.0 | -10.4 | +30.6 | -27.6 | -17.7 | +32.8 | +0.5 | -34.9 | +9.1 | +17.2 | -24.0 | -26.2 | +0.0 | |
| Steps (reduced) |
2225 (319) |
2289 (383) |
2349 (443) |
2405 (499) |
2458 (552) |
2507 (601) |
2554 (648) |
2599 (693) |
2641 (735) |
2681 (775) |
2720 (814) |
2757 (851) |
2792 (886) |
2826 (920) |
2859 (0) | |