463edo
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Prime factorization
463 (prime)
Step size
2.59179¢
Fifth
271\463 (702.376¢)
Semitones (A1:m2)
45:34 (116.6¢ : 88.12¢)
Consistency limit
11
Distinct consistency limit
11
| ← 462edo | 463edo | 464edo → |
463 equal divisions of the octave (abbreviated 463edo or 463ed2), also called 463-tone equal temperament (463tet) or 463 equal temperament (463et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 463 equal parts of about 2.59 ¢ each. Each step represents a frequency ratio of 21/463, or the 463rd root of 2.
Theory
The equal temperament tempers out the amity comma in the 5-limit; 420175/419904 and 703125/702464 in the 7-limit; 3025/3024, 4000/3993, 6250/6237, 19712/19683, and 117649/117612 in the 11-limit. It supports amity, trinity and undesemi.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.00 | +0.42 | -0.14 | +0.50 | +0.73 | -0.79 | -1.28 | +0.54 | -1.06 | -0.64 | +0.54 |
| relative (%) | +0 | +16 | -5 | +19 | +28 | -30 | -50 | +21 | -41 | -25 | +21 | |
| Steps (reduced) |
463 (0) |
734 (271) |
1075 (149) |
1300 (374) |
1602 (213) |
1713 (324) |
1892 (40) |
1967 (115) |
2094 (242) |
2249 (397) |
2294 (442) | |
Subsets and supersets
463edo is the 90th prime edo.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [734 -463⟩ | [⟨463 734]] | -0.1328 | 0.1327 | 5.12 |
| 2.3.5 | 1600000/1594323, [91 -12 -31⟩ | [⟨463 734 1075]] | -0.0689 | 0.1411 | 5.44 |
| 2.3.5.7 | 420175/419904, 703125/702464, 1600000/1594323 | [⟨463 734 1075 1300]] | -0.0966 | 0.1313 | 5.07 |
| 2.3.5.7.11 | 3025/3024, 4000/3993, 19712/19683, 117649/117612 | [⟨463 734 1075 1300 1602]] | -0.1197 | 0.1262 | 4.87 |
| 2.3.5.7.11.13 | 676/675, 1716/1715, 3025/3024, 4000/3993, 4096/4095 | [⟨463 734 1075 1300 1602 1713]] | -0.0643 | 0.1691 | 6.52 |
| 2.3.5.7.11.13.17 | 442/441, 595/594, 676/675, 2500/2499, 3025/3024, 4096/4095 | [⟨463 734 1075 1300 1602 1713 1892]] | -0.0103 | 0.2051 | 7.91 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 31\463 | 80.35 | 22/21 | Undesemi |
| 1 | 51\463 | 132.18 | 27/25 | Astro |
| 1 | 131\463 | 339.52 | 243/200 | Amity (5-limit) |
| 1 | 176\463 | 456.16 | 125/96 | Qak |
| 1 | 198\463 | 513.17 | 121/90 | Trinity (463fg) |
Music
- For Amity (2023) – amity in 463edo tuning