Highly composite equal division: Difference between revisions

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== Highly composite edo ==

[[12edo]] is the predominantly used tuning in the world today, ~~and in addition it~~ is the only known so far highly composite edo that's also a zeta edo, and the only one with a step size above [[just noticeable difference]]. Others have not been found yet, and given the lack of such edos until hundreds of thousands it's likely if another one is found, it would not be of any harmonic use since ~~it's~~ amount of steps would be astronomical.

[[12edo]], the predominantly used tuning in the world today, is the only known so far highly composite edo that is also a zeta edo and the only one with a step size above [[just-noticeable difference]], except for the trival ones. Others have not been found yet, and given the lack of such edos until hundreds of thousands it is likely if another one is found, it would not be of any harmonic use since its amount of steps would be astronomical.

=== The first 41 highly composite edos ===

The first 19 highly composite edos are also the first 19 superabundant edos.

{{EDOs|1, 2, 4, 6, 12, 24, 36, 48, 60, 120}},

{{EDOs| 1, 2, 4, 6, 12, 24, 36, 48, 60, 120 }},

{{EDOs|180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 7560}},

{{EDOs| 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 7560 }},

10080, 15120, 20160, 25200, [[27720edo|27720]], 45360, 50400, 55440, 83160, 110880,

166320, 221760, 277200, 332640, 498960, 554400, 665280, 720720, 1081080, 1441440, 2162160.

@@ Line 15: / Line 15: @@
 == Highly composite edo ==
-[[12edo]] is the predominantly used tuning in the world today, and in addition it is the only known so far highly composite edo that's also a zeta edo, and the only one with a step size above [[just noticeable difference]]. Others have not been found yet, and given the lack of such edos until hundreds of thousands it's likely if another one is found, it would not be of any harmonic use since it's amount of steps would be astronomical.
+[[12edo]], the predominantly used tuning in the world today, is the only known so far highly composite edo that is also a zeta edo and the only one with a step size above [[just-noticeable difference]], except for the trival ones. Others have not been found yet, and given the lack of such edos until hundreds of thousands it is likely if another one is found, it would not be of any harmonic use since its amount of steps would be astronomical.
 === The first 41 highly composite edos ===
 The first 19 highly composite edos are also the first 19 superabundant edos.
-{{EDOs|1, 2, 4, 6, 12, 24, 36, 48, 60, 120}}, <br>
+{{EDOs| 1, 2, 4, 6, 12, 24, 36, 48, 60, 120 }}, <br>
-{{EDOs|180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 7560}}, <br>
+{{EDOs| 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 7560 }}, <br>
 , 15120, 20160, 25200, [[27720edo|27720]], 45360, 50400, 55440, 83160, 110880, <br>
 , 221760, 277200, 332640, 498960, 554400, 665280, 720720, 1081080, 1441440, 2162160.