743edo
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Prime factorization
743 (prime)
Step size
1.61507¢
Fifth
435\743 (702.557¢)
Semitones (A1:m2)
73:54 (117.9¢ : 87.21¢)
Dual sharp fifth
435\743 (702.557¢)
Dual flat fifth
434\743 (700.942¢)
Dual major 2nd
126\743 (203.499¢)
Consistency limit
3
Distinct consistency limit
3
| ← 742edo | 743edo | 744edo → |
743 equal divisions of the octave (abbreviated 743edo or 743ed2), also called 743-tone equal temperament (743tet) or 743 equal temperament (743et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 743 equal parts of about 1.62 ¢ each. Each step represents a frequency ratio of 21/743, or the 743rd root of 2.
Theory
743et is only consistent to the 3-odd-limit and its harmonic 3 is about halfway its steps. It can be used in the 2.9.5.7.11.13.17.19.23.29 subgroup, tempering out 2025/2024, 1089/1088, 67392/67375, 35750/35721, 14400/14399, 15840/15827, 3520/3519, 1521/1520 and 2465/2464.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.602 | -0.311 | +0.219 | -0.411 | -0.578 | -0.689 | +0.291 | +0.024 | -0.339 | -0.794 | -0.011 |
| Relative (%) | +37.3 | -19.3 | +13.5 | -25.4 | -35.8 | -42.7 | +18.0 | +1.5 | -21.0 | -49.2 | -0.7 | |
| Steps (reduced) |
1178 (435) |
1725 (239) |
2086 (600) |
2355 (126) |
2570 (341) |
2749 (520) |
2903 (674) |
3037 (65) |
3156 (184) |
3263 (291) |
3361 (389) | |
Subsets and supersets
743edo is the 132nd prime edo. 1486edo, which doubles it, gives a good correction to the harmonic 3.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.9 | [-2355 743⟩ | [⟨743 2355]] | 0.0648 | 0.0648 | 4.01 |
| 2.9.5 | 32805/32768, [-120 -83 165⟩ | [⟨743 2355 1725]] | 0.0878 | 0.0621 | 3.85 |
| 2.9.5.7 | 32805/32768, 30517578125/30474952704, 247669456896/247165842875 | [⟨743 2355 1725 2086]] | 0.0464 | 0.0897 | 5.55 |
| 2.9.5.7.11 | 32805/32768, 1890625/1889568, 539055/537824, 102487/102400 | [⟨743 2355 1725 2086 2570]] | 0.0705 | 0.0936 | 5.80 |
| 2.9.5.7.11.13 | 67392/67375, 35750/35721, 32805/32768, 91125/91091, 557568/557375 | [⟨743 2355 1725 2086 2570 2749]] | 0.0898 | 0.0957 | 5.93 |
| 2.9.5.7.11.13.17 | 1089/1088, 67392/67375, 35750/35721, 14400/14399, 61965/61952, 75735/75712 | [⟨743 2355 1725 2086 2570 2749 3037]] | 0.0761 | 0.0947 | 5.86 |