3600edo: Difference between revisions

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== Theory ==

[[Category:Equal divisions of the octave|####]]

3600edo is consistent in the 5-limit and it is a good 2.3.5.11.17.23.31.37.41 subgroup tuning.

In the 5-limit, 3600edo [[support|supports]] the [[ennealimmal temperament]], tempering out the ennealimma, {{monzo| 1 -27 18 }}, and (with the [[patent val]]) 2401/2400 and 4375/4374 in the [[7-limit]]. Via the 3600e [[val]] {{val| 3600 5706 8359 10106 12453}}, 3600edo also supports the [[hemiennealimmal temperament]] in the 11-limit.

An alternative 7-limit mapping is 3600d, with the 7 slightly sharp rather than slightly flat; this no longer supports ennealimmal, but it does temper out 52734375/52706752; together with the ennealimma that leads to a sort of strange sibling to ennealimmal temperament, more accurate but also more complex.

One step of 3600edo is close to the [[landscape comma]].

=== ~~Number description~~ ===

=== Prime harmonics ===

=== Subsets and supersets ===

[[Category:Equal divisions of the octave|####]]

3600edo's prime factorization is

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A cent is therefore represented by three steps; and the Dröbisch angle, which is [[360edo|logarithmically 1/360 of the octave]], is ten steps. EDOs corresponding to other notable divisors include [[72edo]], which has found a dissemination in practice and one step of which is represented by 50 steps, and [[200edo]], which holds the continued fraction expansion record for the best perfect fifth and its step is represented by 18 steps.

~~=== Prime harmonics ===~~

~~{{Harmonics in equal|3600}}~~

Aside from its relationship to cents, it is of interest as a system [[support|supporting]] [[ennealimmal temperament]], tempering out the ennealimma, {{monzo| 1 -27 18 }}, in the [[5-limit]] and (with the [[patent val]]) 2401/2400 and 4375/4374 in the [[7-limit]]. An alternative 7-limit mapping is 3600d, with the 7 slightly sharp rather than slightly flat; this no longer supports ennealimmal, but it does temper out 52734375/52706752; together with the ennealimma that leads to a sort of strange sibling to ennealimmal temperament, more accurate but also more complex. Via the [[val]] {{val| 3600 5706 8359 10106 12453 13318 }}, 3600edo also supports [[hemiennealimmal temperament]].

~~One step of 3600edo is close to the [[landscape comma]].~~

[[Category:Equal divisions of the octave|####]]

[[Category:Ennealimmal]]

@@ Line 3: / Line 3: @@
 == Theory ==
+[[Category:Equal divisions of the octave|####]]
+edo is consistent in the 5-limit and it is a good 2.3.5.11.17.23.31.37.41 subgroup tuning.
+In the 5-limit, 3600edo [[support|supports]] the [[ennealimmal temperament]], tempering out the ennealimma, {{monzo| 1 -27 18 }}, and (with the [[patent val]]) 2401/2400 and 4375/4374 in the [[7-limit]]. Via the 3600e [[val]] {{val| 3600 5706 8359 10106 12453}}, 3600edo also supports the [[hemiennealimmal temperament]] in the 11-limit.
+An alternative 7-limit mapping is 3600d, with the 7 slightly sharp rather than slightly flat; this no longer supports ennealimmal, but it does temper out 52734375/52706752; together with the ennealimma that leads to a sort of strange sibling to ennealimmal temperament, more accurate but also more complex.
+One step of 3600edo is close to the [[landscape comma]].
-=== Number description ===
+=== Prime harmonics ===
+{{Harmonics in equal|3600}}
+=== Subsets and supersets ===
 [[Category:Equal divisions of the octave|####]]
 edo's prime factorization is
@@ Line 10: / Line 20: @@
 A cent is therefore represented by three steps; and the Dröbisch angle, which is [[360edo|logarithmically 1/360 of the octave]], is ten steps. EDOs corresponding to other notable divisors include [[72edo]], which has found a dissemination in practice and one step of which is represented by 50 steps, and [[200edo]], which holds the continued fraction expansion record for the best perfect fifth and its step is represented by 18 steps.
-=== Prime harmonics ===
-{{Harmonics in equal|3600}}
-Aside from its relationship to cents, it is of interest as a system [[support|supporting]] [[ennealimmal temperament]], tempering out the ennealimma, {{monzo| 1 -27 18 }}, in the [[5-limit]] and (with the [[patent val]]) 2401/2400 and 4375/4374 in the [[7-limit]]. An alternative 7-limit mapping is 3600d, with the 7 slightly sharp rather than slightly flat; this no longer supports ennealimmal, but it does temper out 52734375/52706752; together with the ennealimma that leads to a sort of strange sibling to ennealimmal temperament, more accurate but also more complex. Via the [[val]] {{val| 3600 5706 8359 10106 12453 13318 }}, 3600edo also supports [[hemiennealimmal temperament]].
-One step of 3600edo is close to the [[landscape comma]].
 [[Category:Equal divisions of the octave|####]]<!-- 4-digit number -->
 [[Category:Ennealimmal]]