787edo

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787edo

788edo →

Prime factorization	787 (prime)
Step size	1.52478 ¢
Fifth	460\787 (701.398 ¢)
Semitones (A1:m2)	72:61 (109.8 ¢ : 93.01 ¢)
Dual sharp fifth	461\787 (702.922 ¢)
Dual flat fifth	460\787 (701.398 ¢)
Dual major 2nd	134\787 (204.32 ¢)
Consistency limit	7
Distinct consistency limit	7

Theory

787edo is consistent to the 7-odd-limit and the error of its harmonic 3 is large. The accuracy of the equal temperament is higher in the upper harmonics, making it strong in the 2.17.19.23.31 subgroup, tempering out 151604477/151519232, 573114368/572870539, 68939809/68876792 and 4127463571456/4124314002323. It can also be used in the 2.3.5.7.13.41.43.47 subgroup, tempering out 729/728, 2401/2400, 1025/1024, 8127/8125, 1601613/1600000, 40625/40608 and 546875/545792.

Odd harmonics

Approximation of odd harmonics in 787edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.557	-0.545	-0.592	+0.410	+0.652	-0.375	+0.423	+0.254	-0.181	+0.375	-0.066
	Relative (%)	-36.5	-35.7	-38.8	+26.9	+42.7	-24.6	+27.7	+16.7	-11.9	+24.6	-4.3
Steps (reduced)		1247 (460)	1827 (253)	2209 (635)	2495 (134)	2723 (362)	2912 (551)	3075 (714)	3217 (69)	3343 (195)	3457 (309)	3560 (412)

Subsets and supersets

787edo is the 138th prime edo. 1574edo, which doubles it, gives a good correction to its harmonic 3.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.9	[2495 -787⟩	[⟨787 2495]]	–0.0647	0.0647	4.24