RE: Scales and Numerology

Paul Hahn wrote,

>Interesting. I've lately been toying with a 9-out-of-31 scale.

Care to let us in on it?

On Thu, 6 Aug 1998, John Chalmers wrote:
> As for 9-tone scales in 31-tet, David Rothenberg and Connie Chan studied
> this one: 5 3 3 3 3 5 3 3 3, generated by a chain of 14 degrees of 31-tet.
> This scale is an MOS, is strictly proper,

Call me a heretic, but I'm beginning to wonder if these properties
aren't as important as I'd once thought they were. Look at the success
of the minor pentatonic in Japan, for example.

> has "stability" of 1.0 and
> "efficiency" of .7407.

Shame on me, but I don't even know what these measure signify. Help,
please.

--pH http://library.wustl.edu/~manynote
O
/\ "Churchill? Can he run a hundred balls?"
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NOTE: dehyphenate node to remove spamblock. <*>

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>> This scale is an MOS, is strictly proper,

>Call me a heretic, but I'm beginning to wonder if these
properties
>aren't as important as I'd once thought they were. Look at the
success
>of the minor pentatonic in Japan, for example.

The minor pentatonic scale is MOS and strictly proper, but other
Japanese scales are among the most important examples of scales that are
not MOS, proper, or distributionally even (John Clough's term for a
scale with two step sizes and no more than two specific sizes for each
generic interval). Other important examples are the jazz (ascending)
melodic minor scale and the various scales containing augmented seconds.

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On Mon, 10 Aug 1998, Paul H. Erlich wrote:
>>> This scale is an MOS, is strictly proper,
>
>>Call me a heretic, but I'm beginning to wonder if these properties
>>aren't as important as I'd once thought they were. Look at the success
>>of the minor pentatonic in Japan, for example.
>
> The minor pentatonic scale is MOS and strictly proper, but other
> Japanese scales are among the most important examples of scales that are
> not MOS, proper, or distributionally even (John Clough's term for a
> scale with two step sizes and no more than two specific sizes for each
> generic interval).

?? I don't think we're talking about the same scale. I mean the one
that's approximated in 12TET by 2-1-4-1-4.

--pH http://library.wustl.edu/~manynote
O
/\ "Churchill? Can he run a hundred balls?"
-\-\-- o
NOTE: dehyphenate node to remove spamblock. <*>