2960edo

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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 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

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 (%)	-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)

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)