Omnitetrachordality

I searched the group as far back as Yahoo has it without finding a
definition. I think perhaps Joe should put one in his dictionary.

--- In tuning@y..., genewardsmith@j... wrote:
> I searched the group as far back as Yahoo has it without finding a
> definition. I think perhaps Joe should put one in his dictionary.

It means that every octave species of the scale has two identical
~4:3 spans, which are either a ~4:3 apart (conjuct tetrachords) or a
~3:2 apart (disjunct tetrachords). For example, the diatonic scale:

A B C D E F G A
|-4:3-|-4:3-| LsL

B C D E F G A B
|-4:3-|-4:3-| sLL

C D E F G A B C
|-4:3-| |-4:3-| LLs

D E F G A B C D
|-4:3-| |-4:3-| LsL

E F G A B C D E
|-4:3-| |-4:3-| sLL

F G A B C D E F
|-4:3-|-4:3-| LLs

G A B C D E F G
|-4:3-|-4:3-| LsL

This property guarantees that, in addition to being invariant to
transpositions by ratios of 2, it's nearly invariant to
transpositions by ratios of 3.

Another example is my pentachordal decatonic scale (LsssLsssss). In
this case, we have identical pentachords, not tetrachords, but the
term "omnitetrachordality" is probably clearest.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., genewardsmith@j... wrote:

> It means that every octave species of the scale has two identical
> ~4:3 spans, which are either a ~4:3 apart (conjuct tetrachords) or
a
> ~3:2 apart (disjunct tetrachords.

Would it help to have theorems about when you will get
omnitetrachordality?

--- In tuning@y..., genewardsmith@j... wrote:

> Would it help to have theorems about when you will get
> omnitetrachordality?

Sure!