# 2960edo

← 2959edo | 2960edo | 2961edo → |

^{4}× 5 × 37**2960 equal divisions of the octave** (abbreviated **2960edo** or **2960ed2**), also called **2960-tone equal temperament** (**2960tet**) or **2960 equal temperament** (**2960et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2960 equal parts of about 0.405 ¢ each. Each step represents a frequency ratio of 2^{1/2960}, or the 2960th root of 2.

## Theory

2960edo is inconsistent to the 5-odd-limit and harmonic 3 is about halfway between its steps. Otherwise it is excellent in approximating harmonics 5, 9, 11, 17, and 19, making it suitable for a 2.9.5.11.17.19 subgroup interpretation, with optional additions of 7 and 23, or 21 and 13.

The 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 mercurial comma, which is the difference between a stack of 5 19/17 and 2 15/14 with the octave. These can be arranged in diatonic pattern to sound like a meantone scale. In this case, 19/17 is mapped to 474 steps and 15/14 is mapped to 295 steps.

From a regular temperament perspective, this 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 (%) | -48.9 | +9.3 | +22.9 | +2.2 | +8.2 | -30.2 | -39.6 | +11.0 | +13.5 | -26.0 | +25.7 | |

Steps (reduced) |
4691 (1731) |
6873 (953) |
8310 (2390) |
9383 (503) |
10240 (1360) |
10953 (2073) |
11564 (2684) |
12099 (259) |
12574 (734) |
13001 (1161) |
13390 (1550) |

### Subsets and supersets

Since 2960 factors into 2^{4} × 5 × 37, 2960edo has subset edos 2, 4, 5, 8, 10, 16, 20, 37, 40, 74, 80, 148, 185, 296, 370, 592, 740 and 1480.

## Scales

- 474 474 295 474 474 474 295 - mercury "meantone" (major scale)