3600edo: Difference between revisions

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The '''3600edo''' divides the octave into 3600 equal parts of 0.33333 (exactly 1/3) of a [[cent]] each. A cent is therefore three steps; also, the Dröbisch Angle which is 1/360 octave is ten steps. It also has the advantage of expressing the steps of [[72edo]] in whole numbers. Aside from its relationship to cents, it is of interest as a system 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]].

The '''3600edo''' divides the octave into 3600 equal parts of 0.33333 (exactly 1/3) of a [[cent]] each. A cent is therefore three steps; also, the Dröbisch Angle which is 1/360 octave is ten steps.

== ~~Divisors~~ ==

== Theory ==

~~The~~ prime factorization is

It also has the advantage of expressing the steps of [[72edo]] in whole numbers. Aside from its relationship to cents, it is of interest as a system 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 also close to the [[landscape comma]].

3600edo's prime factorization is

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-The '''3600edo''' divides the octave into 3600 equal parts of 0.33333 (exactly 1/3) of a [[cent]] each. A cent is therefore three steps; also, the Dröbisch Angle which is 1/360 octave is ten steps. It also has the advantage of expressing the steps of [[72edo]] in whole numbers. Aside from its relationship to cents, it is of interest as a system 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]].
+The '''3600edo''' divides the octave into 3600 equal parts of 0.33333 (exactly 1/3) of a [[cent]] each. A cent is therefore three steps; also, the Dröbisch Angle which is 1/360 octave is ten steps.
-== Divisors ==
+== Theory ==
-The prime factorization is
+It also has the advantage of expressing the steps of [[72edo]] in whole numbers. Aside from its relationship to cents, it is of interest as a system 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 also close to the [[landscape comma]].
+edo's prime factorization is
 <math>3600 = 2^{4} \cdot 3^{2} \cdot 5^{2}</math>