749edo
Jump to navigation
Jump to search
Prime factorization
7 × 107
Step size
1.60214¢
Fifth
438\749 (701.736¢)
Semitones (A1:m2)
70:57 (112.1¢ : 91.32¢)
Consistency limit
7
Distinct consistency limit
7
| ← 748edo | 749edo | 750edo → |
749 equal divisions of the octave (abbreviated 749edo or 749ed2), also called 749-tone equal temperament (749tet) or 749 equal temperament (749et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 749 equal parts of about 1.6 ¢ each. Each step represents a frequency ratio of 21/749, or the 749th root of 2.
The equal temperament is most notable for tempering out the schisma, 32805/32768, and provides the optimal patent val for the 5-limit schismatic (helmholtz) temperament.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.219 | -0.199 | +0.466 | -0.183 | +0.594 | +0.786 | +0.484 | -0.237 | +0.596 | +0.492 |
| Relative (%) | +0.0 | -13.7 | -12.4 | +29.1 | -11.4 | +37.1 | +49.0 | +30.2 | -14.8 | +37.2 | +30.7 | |
| Steps (reduced) |
749 (0) |
1187 (438) |
1739 (241) |
2103 (605) |
2591 (344) |
2772 (525) |
3062 (66) |
3182 (186) |
3388 (392) |
3639 (643) |
3711 (715) | |
Subsets and supersets
Since 749 factors into 7 × 107, 749edo contains 7edo and 107edo as subsets.