4079edo
| ← 4078edo | 4079edo | 4080edo → |
4079 equal divisions of the octave (abbreviated 4079edo or 4079ed2), also called 4079-tone equal temperament (4079tet) or 4079 equal temperament (4079et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 4079 equal parts of about 0.294 ¢ each. Each step represents a frequency ratio of 21/4079, or the 4079th root of 2.
Theory
4079edo is consistent to the 17-odd-limit, tempering out 14400/14399, 123201/123200, 121875/121856, 37180/37179, 3536379/3536000 and 2100875/2100384. The equal temperament is strong in the 2.3.5.11.13.31 subgroup, tempering out 196625/196608, 1830519/1830400, 140625/140608, 492075/492032 and 54925000/54918391. Using the 2.3.5.7.11.37 subgroup, it tempers out 12321/12320.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.018 | -0.043 | -0.059 | -0.006 | -0.028 | +0.070 | -0.087 | +0.115 | +0.087 | -0.049 |
| Relative (%) | +0.0 | -6.2 | -14.5 | -20.1 | -2.2 | -9.4 | +23.9 | -29.6 | +39.1 | +29.6 | -16.7 | |
| Steps (reduced) |
4079 (0) |
6465 (2386) |
9471 (1313) |
11451 (3293) |
14111 (1874) |
15094 (2857) |
16673 (357) |
17327 (1011) |
18452 (2136) |
19816 (3500) |
20208 (3892) | |
Subsets and supersets
4079edo is the 562nd prime edo.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-6465 4079⟩ | [⟨4079 6465]] | +0.0058 | 0.0058 | 1.97 |
| 2.3.5 | [-105 -7 50⟩, [-123 82 -3⟩ | [⟨4079 6465 9471]] | +0.0100 | 0.0076 | 2.58 |
| 2.3.5.7 | 78125000/78121827, 13841287201/13839609375, [-57 16 10 3⟩ | [⟨4079 6465 9471 11451]] | +0.0127 | 0.0081 | 2.75 |
| 2.3.5.7.11 | 151263/151250, 21437500/21434787, 14348907/14348180, 1879453125/1879048192 | [⟨4079 6465 9471 11451 14111]] | +0.0105 | 0.0085 | 2.89 |
| 2.3.5.7.11.13 | 123201/123200, 4100625/4100096, 196625/196608, 151263/151250, 5175625/5174928 | [⟨4079 6465 9471 11451 14111 15094]] | +0.0100 | 0.0078 | 2.65 |
| 2.3.5.7.11.13.17 | 14400/14399, 123201/123200, 121875/121856, 37180/37179, 3536379/3536000, 2100875/2100384 | [⟨4079 6465 9471 11451 14111 15094 16673]] | +0.0061 | 0.0120 | 4.08 |