1240edo

← 1239edo

1240edo

1241edo →

Prime factorization	23 × 5 × 31
Step size	0.967742¢
Fifth	725\1240 (701.613¢) (→145\248)
Semitones (A1:m2)	115:95 (111.3¢ : 91.94¢)
Dual sharp fifth	726\1240 (702.581¢) (→363\620)
Dual flat fifth	725\1240 (701.613¢) (→145\248)
Dual major 2nd	211\1240 (204.194¢)
Consistency limit	7
Distinct consistency limit	7

1240 equal divisions of the octave (abbreviated 1240edo or 1240ed2), also called 1240-tone equal temperament (1240tet) or 1240 equal temperament (1240et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1240 equal parts of about 0.968 ¢ each. Each step represents a frequency ratio of 2^1/1240, or the 1240th root of 2.

1240edo is consistent in the 7-odd-limit, though the error on harmonic 3 is quite large. It is a strong tuning for 5-limit soviet ferris wheel, ([-171 20 60⟩), and a good tuning for dodifo, ([-67 -9 35⟩).

Beyond the 7-odd-limit, there is a number of mappings to be considered. In the 2.27.7.23.29 subgroup, it is a flat system, and in 2.9.11.13.15, it is a sharp system. In the 2.5.11.13.29, it tunes the genojacobin temperament.

Odd harmonics

Approximation of odd harmonics in 1240edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23	25	27	29
Error	Absolute (¢)	-0.342	-0.185	-0.116	+0.284	+0.295	+0.440	+0.441	-0.439	-0.416	-0.458	-0.210	-0.369	-0.059	+0.100
	Relative (%)	-35.4	-19.1	-12.0	+29.3	+30.5	+45.5	+45.6	-45.4	-43.0	-47.4	-21.7	-38.2	-6.1	+10.4
Steps (reduced)		1965 (725)	2879 (399)	3481 (1001)	3931 (211)	4290 (570)	4589 (869)	4845 (1125)	5068 (108)	5267 (307)	5446 (486)	5609 (649)	5758 (798)	5896 (936)	6024 (1064)

Subsets and supersets

Since 1240 factors as 2³ × 5 × 31, 1240edo has subset edos 2, 4, 5, 8, 10, 20, 31, 40, 62, 124, 155, 248, 310, 620.