# 2960edo

 ← 2959edo 2960edo 2961edo →
Prime factorization 24 × 5 × 37
Step size 0.405405¢
Fifth 1731\2960 (701.757¢)
Semitones (A1:m2) 277:225 (112.3¢ : 91.22¢)
Dual sharp fifth 1732\2960 (702.162¢) (→433\740)
Dual flat fifth 1731\2960 (701.757¢)
Dual major 2nd 503\2960 (203.919¢)
Consistency limit 3
Distinct consistency limit 3

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 21/2960, 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

Approximation of odd harmonics in 2960edo
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 24 × 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)