27720edo: Difference between revisions

(2 intermediate revisions by the same user not shown)

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 43 [[cent|millicent]]s, 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 ===

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 [[12edo]]. The mapping for 3/2 in 27720edo derives from [[1848edo]].

== Contorsion table ==

@@ Line 1: / Line 1: @@
+{{Infobox ET}}
 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 ==
+edo 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 ===
 {{Harmonics in equal|27720}}
-edo 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 [[12edo]]. The mapping for 3/2 in 27720edo derives from [[1848edo]].
 == Contorsion table ==