omnitetrachordal conversion

[from MMM]
>> >Each of these scales can be
>> >altered slightly so as to make them omnitetrachordal (instead of
>> >having a 'bitonal' symmetry at the half-octave as they do in the
>> >horagram);
>>
>> What is the method for doing so?
>
>If you understand, in 22-equal, how to change a symmetrical decatonic
>to a pentachordal decatonic, and a symmetrical dodecatonic to a
>hexachordal dodecatonic, you're most of the way there. If you want
>more on this, please post a question to one of the other lists.

I know what those scales are, but not how to do the coversion...

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
>
> [from MMM]
> >> >Each of these scales can be
> >> >altered slightly so as to make them omnitetrachordal (instead
of
> >> >having a 'bitonal' symmetry at the half-octave as they do in
the
> >> >horagram);
> >>
> >> What is the method for doing so?
> >
> >If you understand, in 22-equal, how to change a symmetrical
decatonic
> >to a pentachordal decatonic, and a symmetrical dodecatonic to a
> >hexachordal dodecatonic, you're most of the way there. If you want
> >more on this, please post a question to one of the other lists.
>
> I know what those scales are, but not how to do the coversion...
>
> -Carl

In those cases, you just move one instance of the rarer step size
over one step (switching it with a neighboring instance of the more
common step size), and you're done. For larger scales, you'll do this
with the whole clump of steps that adds up to what is the rarer step
size in these smaller scales (switch it with a neighboring instance
of a clump of steps that adds up to what is the more common step size
in the smaller scale). So:

(10) ssssLssssL -> sssssLsssL
(12) LLLLLsLLLLLs -> LLLLLLsLLLLs
(22) LsLsLsLsLsLLsLsLsLsLsL -> LsLsLsLsLsLsLLsLsLsLsL
(34) sLssLssLsLssLssLssLssLssLsLssLssLs ->
sLssLssLssLsLssLssLssLssLsLssLssLs

etc. There are many ways to interpret what I wrote above but all the
interpretations seem to work to give you omnitetrachordal scales.

>> [from MMM]
>> >> >Each of these scales can be
>> >> >altered slightly so as to make them omnitetrachordal (instead
>of
>> >> >having a 'bitonal' symmetry at the half-octave as they do in
>the
>> >> >horagram);
>> >>
>> >> What is the method for doing so?
>> >
>> >If you understand, in 22-equal, how to change a symmetrical
>> >decatonic to a pentachordal decatonic, and a symmetrical dodecatonic
>> >to a hexachordal dodecatonic, you're most of the way there. If you
>> >want more on this, please post a question to one of the other lists.
>>
>> I know what those scales are, but not how to do the coversion...
>>
>> -Carl
>
>In those cases, you just move one instance of the rarer step size
>over one step (switching it with a neighboring instance of the more
>common step size), and you're done. For larger scales, you'll do this
>with the whole clump of steps that adds up to what is the rarer step
>size in these smaller scales (switch it with a neighboring instance
>of a clump of steps that adds up to what is the more common step size
>in the smaller scale). So:
>
>(10) ssssLssssL -> sssssLsssL
>(12) LLLLLsLLLLLs -> LLLLLLsLLLLs
>(22) LsLsLsLsLsLLsLsLsLsLsL -> LsLsLsLsLsLsLLsLsLsLsL
>(34) sLssLssLsLssLssLssLssLssLsLssLssLs ->
>sLssLssLssLsLssLssLssLssLsLssLssLs
>
>etc. There are many ways to interpret what I wrote above but all the
>interpretations seem to work to give you omnitetrachordal scales.

Gotcha.

-Carl