2960edo

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2960edo

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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

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 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

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)