27720edo
Jump to navigation
Jump to search
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
| ← 27719edo | 27720edo | 27721edo → |
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
| 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
| 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 |