User:Francium/4703edo
| ← 4702edo | 4703edo | 4704edo → |
4703 equal divisions of the octave (abbreviated 4703edo or 4703ed2), also called 4703-tone equal temperament (4703tet) or 4703 equal temperament (4703et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 4703 equal parts of about 0.255 ¢ each. Each step represents a frequency ratio of 21/4703, or the 4703rd root of 2.
Theory
4703edo is consistent to the 15-odd-limit, tempering out 6656/6655, 1990656/1990625, 4100625/4100096, 151263/151250 and 109772091/109760000 in the 13-limit; 12376/12375, 14400/14399, 61965/61952, 194481/194480, 1990656/1990625 and 109772091/109760000 in the 17-limit; and 12376/12375, 14400/14399, 13377/13376, 89376/89375, 61965/61952, 104976/104975 and 28900/28899 in the 19-limit. It is strong in the 2.3.5.7.13.19.29 subgroup, tempering out 27000/26999, 23751/23750, 1990656/1990625, 570807/570752, 16385733/16384000 and 12252500/12252303. Using the 2.3.5.7.13.19 subgroup, it tempers out 12636/12635. Its error of the harmonic 19 is remarkably low at 0.3 percent. The equal temperament supports laquinzo-aquadquadgu.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.020 | -0.007 | +0.003 | +0.075 | -0.043 | -0.086 | -0.001 | -0.080 | -0.022 | +0.106 |
| Relative (%) | +0.0 | -7.9 | -2.8 | +1.0 | +29.3 | -16.8 | -33.8 | -0.3 | -31.2 | -8.5 | +41.5 | |
| Steps (reduced) |
4703 (0) |
7454 (2751) |
10920 (1514) |
13203 (3797) |
16270 (2161) |
17403 (3294) |
19223 (411) |
19978 (1166) |
21274 (2462) |
22847 (4035) |
23300 (4488) | |
Subsets and supersets
4703edo is the 635th prime edo.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-7454 4703⟩ | [⟨4703 7454]] | +0.0063 | 0.0063 | 2.47 |
| 2.3.5 | [-90 -15 49⟩, [-86 107 -36⟩ | [⟨4703 7454 10920]] | +0.0052 | 0.0054 | 2.12 |
| 2.3.5.7 | 94143178827/94119200000, 3955078125/3954653486, 281484423828125/281474976710656 | [⟨4703 7454 10920 13203]] | +0.0037 | 0.0054 | 2.12 |
| 2.3.5.7.11 | 151263/151250, 820125/819896, 1019215872/1019046875, 15625959723/15625000000 | [⟨4703 7454 10920 13203 16270]] | −0.0014 | 0.0112 | 4.39 |
| 2.3.5.7.11.13 | 6656/6655, 1990656/1990625, 4100625/4100096, 151263/151250, 109772091/109760000 | [⟨4703 7454 10920 13203 16270 17403]] | +0.0008 | 0.0113 | 4.43 |
| 2.3.5.7.11.13.17 | 12376/12375, 14400/14399, 61965/61952, 194481/194480, 1990656/1990625, 109772091/109760000 | [⟨4703 7454 10920 13203 16270 17403 19223]] | +0.0037 | 0.0127 | 4.98 |
| 2.3.5.7.11.13.17.19 | 12376/12375, 14400/14399, 13377/13376, 89376/89375, 61965/61952, 104976/104975, 28900/28899 | [⟨4703 7454 10920 13203 16270 17403 19223 19978]] | +0.0033 | 0.0119 | 4.66 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 728\4703 | 185.7538 | [24 4 -13⟩ | Pirate |
* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct