2960edo
| ← 2959edo | 2960edo | 2961edo → |
2960 equal divisions of the octave (2960edo), or 2960-tone equal temperament (2960tet), 2960 equal temperament (2960et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 2960 equal parts of about 0.405 ¢ each.
Theory
2960edo is a dual-fifth system that is also an excellent 2.5.9.11.17.19 subgroup tuning.
2960dh val ⟨2960 4691 6873 8309 10240 10953 12099 12573] is the unique mapping that supports both the 80th-octave temperament called mercury, and the coincidentally similarly named mercury meantone, which tunes the meantone steps to 19/17 and 15/14.
In this case, 19/17 is mapped to 474 steps and 15/14 is mapped to 295 steps. This means that the fifth is mapped to 1717 steps, being 14 steps below the patent val fifth, therefore also meaning if such a temperament is realized via the regular temperament perspective, it will not be mapped to 3\2.
From a regular temperament perspective, mercury meantone in 2960edo can be potentially realized as 893 & 2960dh temperament in the 19-limit, as it maps two generators to 19/17 and 2955 generators to 15/14, which is circularly equivalent to 5 steps down in 2960edo (2955 + 5 = 2960), corresponding to Phrygian and Locrian modes. Eliora proposes the name quicksilvertone for this regular temperament.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | -0.198 | +0.038 | +0.093 | +0.009 | +0.033 | -0.122 | -0.161 | +0.045 | +0.055 | -0.105 | +0.104 |
| relative (%) | -49 | +9 | +23 | +2 | +8 | -30 | -40 | +11 | +13 | -26 | +26 | |
| Steps (reduced) |
4691 (1731) |
6873 (953) |
8310 (2390) |
9383 (503) |
10240 (1360) |
10953 (2073) |
11564 (2684) |
12099 (259) |
12574 (734) |
13001 (1161) |
13390 (1550) | |
Scales
- 474 474 295 474 474 474 295 - mercury meantone (major scale)