User:Francium/3593edo
| ← 3592edo | 3593edo | 3594edo → |
3593 equal divisions of the octave (abbreviated 3593edo or 3593ed2), also called 3593-tone equal temperament (3593tet) or 3593 equal temperament (3593et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 3593 equal parts of about 0.334 ¢ each. Each step represents a frequency ratio of 21/3593, or the 3593rd root of 2.
Theory
3593edo is consistent to the 13-limit, tempering out 4096/4095, 6656/6655, 105644/105625, 1063348/1063125 and 21437500/21434787. It supports lafa.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.077 | +0.104 | +0.058 | +0.153 | +0.088 | +0.107 | -0.153 | -0.085 | +0.066 | +0.135 | -0.053 |
| Relative (%) | +23.0 | +31.2 | +17.4 | +45.9 | +26.2 | +32.0 | -45.8 | -25.4 | +19.6 | +40.3 | -15.8 | |
| Steps (reduced) |
5695 (2102) |
8343 (1157) |
10087 (2901) |
11390 (611) |
12430 (1651) |
13296 (2517) |
14037 (3258) |
14686 (314) |
15263 (891) |
15782 (1410) |
16253 (1881) | |
Subsets and supersets
3593edo is the 503rd prime edo.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [5695 -3593⟩ | [⟨3593 5695]] | −0.0242 | 0.0242 | 7.25 |
| 2.3.5 | [77 -31 -12⟩, [19 -116 71⟩ | [⟨3593 5695 8343]] | −0.0311 | 0.0220 | 6.59 |
| 2.3.5.7 | 78125000/78121827, 962072674304/961083984375, 3391115364245/3389154437772 | [⟨3593 5695 8343 10087]] | −0.0285 | 0.0196 | 5.87 |
| 2.3.5.7.11 | 151263/151250, 21437500/21434787, 2097152/2096325, 4274192384/4271484375 | [⟨3593 5695 8343 10087 12430]] | −0.0279 | 0.0176 | 5.27 |
| 2.3.5.7.11.13 | 4096/4095, 6656/6655, 105644/105625, 1063348/1063125, 21437500/21434787 | [⟨3593 5695 8343 10087 12430 13296]] | −0.0280 | 0.0161 | 4.82 |