27720edo: Difference between revisions
need to subst for millicents |
No edit summary |
||
| Line 1: | Line 1: | ||
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 {{ | 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 [[cent|millicent]]s, or exactly 10/231 of a cent each. | ||
== Theory == | |||
{{Harmonics in equal|27720}} | |||
27720edo is a [[highly melodic EDO]]. It 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, and with a large jump from 2520 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 [[72edo|12edo]]. The mapping for 3/2 in 27720edo derives from [[1848edo]]. | |||
== Contorsion table == | |||
{| class="wikitable" | |||
|+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 | |||
|} | |||