Bozu's opinions of various edos: Difference between revisions

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4. Hypopent. If X is divisible by seven, X edo is "hypopent". The elemental basis of hypopent is 7edo.

If X is not divisible by three, four, five, or seven, then X edo is a composite type. However, if X can be expressed as X = 5A + 7B, where A and B are natural numbers, X edo will be a composite hyperpent (if A>B) or composite hypopent (otherwise, i.e. A<B or A=B). With larger edo's, there is the possibility of a hybrid tuning with both hyperpent and hypopent characteristics, when X can be expressed as X = 5A + 7B and also as X = 5C + 7D, where either A>B AND C<=D or A<=B AND C>D, with A, B, C, and D being non-negative integers.

If X is not divisible by three, four, five, or seven, then X edo is a composite type. However, if X can be expressed as X = 5A + 7B, where A and B are natural numbers, X edo will be a composite hyperpent (if A>B) or composite hypopent (otherwise, i.e. A>B AND C<=D or A<=B AND C>D, with A, B, C, and D being non-negative integers.

There are also a couple of cases in which X edo has no relation to any of these elements. One special case is 2edo, which I classify as 0th order diminished type. The other cases are 11edo, 13edo, and 23edo, which are not divisible by 3, 4, 5, nor 7, and cannot be expressed as 5A + 7B with any non-negative integers A and B.

Thus...

== Sizes of edo's ==

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 . Hypopent.  If X is divisible by seven, X edo is "hypopent".  The elemental basis of hypopent is 7edo.
-If X is not divisible by three, four, five, or seven, then X edo is a composite type.  However, if X can be expressed as X = 5A + 7B, where A and B are natural numbers, X edo will be a composite hyperpent (if A>B) or composite hypopent (otherwise, i.e. A<B or A=B).  With larger edo's, there is the possibility of a hybrid tuning with both hyperpent and hypopent characteristics, when X can be expressed as X = 5A + 7B and also as X = 5C + 7D, where either A>B AND C<=D or A<=B AND C>D, with A, B, C, and D being non-negative integers.
+If X is not divisible by three, four, five, or seven, then X edo is a composite type.  However, if X can be expressed as X = 5A + 7B, where A and B are natural numbers, X edo will be a composite hyperpent (if A>B) or composite hypopent (otherwise, i.e. A>B AND C<=D or A<=B AND C>D, with A, B, C, and D being non-negative integers.
 There are also a couple of cases in which X edo has no relation to any of these elements.  One special case is 2edo, which I classify as 0th order diminished type.  The other cases are 11edo, 13edo, and 23edo, which are not divisible by 3, 4, 5, nor 7, and cannot be expressed as 5A + 7B with any non-negative integers A and B.
 Thus...
 == Sizes of edo's ==