2960edo

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← 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

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

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)

Scales

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