Re: rothenberg

Carl,

Thanks for the very helpful explaination. I was thinking too much in
terms of a fixed key, whereas a musical style which calls for efficiency
(in contrast to stability) is one which is more likely to frequently
modulate between keys of the same scale. The quality of the efficient
scale is not the ability to establish the key with the fewest possible
notes, but the ability to use the greater part of the scale without being
redundant in terms of key information. This explains why Bach pieces (as
examples of a style which exploits the properties of an efficient scale)
need to modulate before the end of the eighth bar: once the melody has
exhausted the key information it needs to move forward on pain of redundancy.
Of course, scales like 42222, although efficient in theory, are so
unstable that they aren't heard as unique scales (42222 sounds like a whole
tone scale with one note unplayed), and key information doesn't apply when
the scale itself can't be established

I'm not sure about your point on perfectly symmetrical scales, though:
>In fact, since sufficient sets are not defined for scales with perfect
>modal symmetry (like the whole tone scale), neither is efficiency defined,
>and I can see an argument for calling it zero in these cases. But by R.'s
>reasoning (above), 1.0 is probably more intuitive: seeing efficiency as how
>much work the melody will have to do to fix the tonic.

R. lists the efficiency of these scales as 1/n, which is correct according
to his equation if any one note of the scale is a sufficient set. This
makes sense because any note of, say, the whole tone scale C D E F# G# A#
distinguishes it from C# D# F G A B. That's to say nothing about the
_tonic_, however, but tonality is a different and more involed topic (a
sufficient set for C major is also a sufficient set for A natural minor).
I can see the argument for saying that "sufficient sets of the 12-t scale"
is undefined, but to rate this scale high in effiency classes it with the
diatonic and anhemitonic pentatonics scale as high stability + high
efficiency, whereas they clearly belong in the high stability + low
efficiency class. I think you have to say that one note of the 12-t scale
distinguishes it from a 12-t scale at a different pitch level as a
semantical justification for defining a sufficient set for it.

jason

>The quality of the efficient scale is not the ability to establish the key
>with the fewest possible notes, but the ability to use the greater part of
>the scale without being redundant in terms of key information.

Exactly.

>I'm not sure about your point on perfectly symmetrical scales, though:
>
>>In fact, since sufficient sets are not defined for scales with perfect
>>modal symmetry (like the whole tone scale), neither is efficiency defined,
>>and I can see an argument for calling it zero in these cases. But by R.'s
>>reasoning (above), 1.0 is probably more intuitive: seeing efficiency as how
>>much work the melody will have to do to fix the tonic.
>
>R. lists the efficiency of these scales as 1/n, which is correct according
>to his equation if any one note of the scale is a sufficient set. This
>makes sense because any note of, say, the whole tone scale C D E F# G# A#
>distinguishes it from C# D# F G A B. That's to say nothing about the
>_tonic_, however, but tonality is a different and more involed topic (a
>sufficient set for C major is also a sufficient set for A natural minor).

Good points.

>I can see the argument for saying that "sufficient sets of the 12-t scale"
>is undefined, but to rate this scale high in effiency classes it with the
>diatonic and anhemitonic pentatonics scale as high stability + high
>efficiency, whereas they clearly belong in the high stability + low
>efficiency class.

That's right. Looks like I got my situation backwards -- Rothenberg
considers symmetrical scales minimally efficient. It was I who suggested
they could also be considered maximally efficient. So much for memory.
So dis-regard my "correction", and let this statement stand,

>>Rather, in Rothenberg's terms, the movement was about using
>>proper inefficient scales

Hopefully, those who are following this thread will not be confused, but
rather appreciate that there are arguments in favor of calling the
symmetrical scales both maximally and minimally efficient.

-Carl