# 27720edo

 ← 27719edo 27720edo 27721edo →
Prime factorization 23 × 32 × 5 × 7 × 11
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
Special properties

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