403edo
|
This page presents a novelty topic.
It may contain ideas which are less likely to find practical applications in music, or numbers or structures that are arbitrary or exceedingly small, large, or complex. Novelty topics are often developed by a single person or a small group. As such, this page may also contain idiosyncratic terms, notation, or conceptual frameworks. |
|
This page is a stub. You can help the Xenharmonic Wiki by expanding it. |
| ← 402edo | 403edo | 404edo → |
Theory
403et tempers out 134217728/133984375, 78125000/78121827 and 2100875/2097152 in the 7-limit; 100663296/100656875, 806736/805255, 2097152/2096325, 12005/11979, 7168000/7144929, 131072/130977, 107495424/107421875, 42875/42768, 1684375/1679616, 3025/3024, 766656/765625, 4108797/4096000 and 644204/643125 in the 11-limit.
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.77 | +0.78 | -1.08 | -1.43 | -0.45 | -0.83 | -1.42 | -0.74 | +0.25 | -0.31 | +0.01 |
| Relative (%) | +26.0 | +26.3 | -36.4 | -48.0 | -15.1 | -27.7 | -47.7 | -24.8 | +8.5 | -10.4 | +0.5 | |
| Steps (reduced) |
639 (236) |
936 (130) |
1131 (325) |
1277 (68) |
1394 (185) |
1491 (282) |
1574 (365) |
1647 (35) |
1712 (100) |
1770 (158) |
1823 (211) | |
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [639 -403⟩ | ⟨403 639] | -0.2443 | 0.2443 | 8.20 |
| 2.3.5 | [9 -13 5⟩, [81 -13 -26⟩ | ⟨403 639 936] | -0.2753 | 0.2042 | 6.86 |
| 2.3.5.7 | 3136/3125, 1600000/1594323, 2100875/2097152 | ⟨403 639 936 1131] | -0.3751 | 0.2473 | 8.31 |
| 2.3.5.7.11 | 3025/3024, 3388/3375, 42875/42768, 131072/130977 | ⟨403 639 936 1131 1394] | -0.0621 | 0.3160 | 10.61 |
| 2.3.5.7.11.13 | 2080/2079, 3025/3024, 3388/3375, 4096/4095, 42875/42768 | ⟨403 639 936 1131 1394 1491] | -0.0146 | 0.3074 | 10.32 |
| 2.3.5.7.11.13.17 | 2080/2079, 595/594, 1225/1224, 3025/3024, 4096/4095, 3388/3375 | ⟨403 639 936 1131 1394 1491 1647] | +0.0133 | 0.2927 | 9.83 |
Rank-2 temperaments
| Periods per 8ve |
Generator (reduced) |
Cents (reduced) |
Associated ratio |
Temperaments |
|---|---|---|---|---|
| 1 | 53\403 | 157.82 | 36756909/33554432 | Hemiegads |
| 1 | 106\403 | 315.63 | 6/5 | Egads |
| 1 | 114\403 | 339.45 | 243/200 | Amity |