27720edo: Difference between revisions
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== Theory == | == 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. | |||
27720edo | |||
The prime subgroups best represented by this EDO are 2, 3, 5, 7, 13, 23, 37, 43, 53, 59, 61, 67, 71, 73, 87. As a whole, 27720 does a remarkable job supporting the 2.3.5.7.13 subgroup, being most likely the first highly melodic EDO to do so since [[12edo]]. The mapping for 3/2 in 27720edo derives from [[1848edo]]. | The prime subgroups best represented by this EDO are 2, 3, 5, 7, 13, 23, 37, 43, 53, 59, 61, 67, 71, 73, 87. As a whole, 27720 does a remarkable job supporting the 2.3.5.7.13 subgroup, being most likely the first highly melodic EDO to do so since [[12edo]]. The mapping for 3/2 in 27720edo derives from [[1848edo]]. | ||
=== Prime harmonics === | |||
{{Harmonics in equal|27720}} | |||
== Contorsion table == | == Contorsion table == | ||
{| class="wikitable" | {| class="wikitable" | ||
Revision as of 01:41, 18 March 2023
| ← 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. As a whole, 27720 does a remarkable job supporting the 2.3.5.7.13 subgroup, being most likely the first highly melodic EDO to do so since 12edo. 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 |