27720edo

← 27719edo

27720edo

27721edo →

Prime factorization	23 × 32 × 5 × 7 × 11 (highly composite)
Step size	0.04329 ¢
Fifth	16215\27720 (701.948 ¢) (→ 1081\1848)
Semitones (A1:m2)	2625:2085 (113.6 ¢ : 90.26 ¢)
Consistency limit	9
Distinct consistency limit	9

The 27720 equal divisions of the octave (27720edo), or the 27720(-tone) equal temperament (27720tet, 27720et) when viewed from a regular temperament perspective, divides the octave into 27720 equal parts of about 43 millicents, or exactly 10/231 of a cent each.

Theory

27720edo is the 23rd superabundant EDO, counting 95 proper divisors, and 25th highly composite EDO, with a proper index of about 3.05. 27720 is the least common multiple of integers of 1 through 12, with a large jump from 2520edo caused by the prime factor 11.

The prime subgroups best represented by this EDO are 2, 3, 5, 7, 13, 23, 37, 43, 53, 59, 61, 67, 71, 73, 87. The mapping for 3/2 in 27720edo derives from 1848edo.

Prime harmonics

Approximation of prime harmonics in 27720edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.0000	-0.0069	+0.0066	+0.0053	-0.0192	-0.0082	-0.0203	+0.0195	-0.0059	-0.0101	-0.0139
	Relative (%)	+0.0	-16.1	+15.3	+12.2	-44.4	-18.9	-47.0	+44.9	-13.7	-23.3	-32.2
Steps (reduced)		27720 (0)	43935 (16215)	64364 (8924)	77820 (22380)	95895 (12735)	102576 (19416)	113304 (2424)	117753 (6873)	125393 (14513)	134663 (23783)	137330 (26450)

Contorsion table

For 2.prime subgroups

Prime p	Contorsion order for 2.p subgroup	Meaning that the mapping derives from
3	15	1848edo
5	4	6930edo
7	60	462edo
11	45	616edo
13	24	1155edo
17	24	1155edo