163edo
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Prime factorization
163 (prime)
Step size
7.36196¢
Fifth
95\163 (699.387¢)
Semitones (A1:m2)
13:14 (95.71¢ : 103.1¢)
Dual sharp fifth
96\163 (706.748¢)
Dual flat fifth
95\163 (699.387¢)
Dual major 2nd
28\163 (206.135¢)
Consistency limit
5
Distinct consistency limit
5
| ← 162edo | 163edo | 164edo → |
163 equal divisions of the octave (abbreviated 163edo or 163ed2), also called 163-tone equal temperament (163tet) or 163 equal temperament (163et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 163 equal parts of about 7.362 ¢ each. Each step represents a frequency ratio of 21/163, or the 163rd root of 2.
Theory
163edo tempers out 15625/15552 (kleisma) and 22876792454961/21990232555520 in the 5-limit. Using the patent val, it tempers out 1728/1715, 3125/3087, and 413343/409600 in the 7-limit; 2187/2156, 2420/2401, 2835/2816 and 4375/4356 in the 11-limit; 351/350, 640/637, 975/968, 1188/1183, and 1573/1568 in the 13-limit.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | -2.57 | -3.49 | +2.95 | +2.22 | +0.83 | -1.26 | +1.30 | -1.89 | -3.03 | +0.38 | -2.51 |
| relative (%) | -35 | -47 | +40 | +30 | +11 | -17 | +18 | -26 | -41 | +5 | -34 | |
| Steps (reduced) |
258 (95) |
378 (52) |
458 (132) |
517 (28) |
564 (75) |
603 (114) |
637 (148) |
666 (14) |
692 (40) |
716 (64) |
737 (85) | |
Miscellany
163edo is the 38th prime edo.