definitely efficient confusion [Rothenberg]

Thanks to Carl Lumma for explaining Rothenberg's concept of
"efficiency...":

> You're right -- the least symmetrical (most individual) scales are the
> most efficient (quickest) in determining their tonics. But that's not how Rothenberg uses the word "efficient". He uses it to mean the amount of key-locating information, per tone, that a scale can provide. Which means that the most individual scales are the _least_ efficient, since it doesn't take much before the listener knows the key. IOW, efficient scales are the _slowest_ at telling you their key.

Perhaps I'm just not getting this... but it seems that this concept is a
little "backwards" in terminology (??) What exactly is an efficient
scale "efficient" in?? Not revealing itself? Not doing anything... so
that the composer has to do it?? Why on earth would that be
"efficient??" This seems a little peculiar to me, but, then, this is
totally taken out of context of the articles...

Speaking of which, where can one find the Rothenberg articles or books?
I'm not finding anything on line on John Starrett's site or anyplace...

Thanks again for the help!!!

__________ ____ ___ __ _
Joseph Pehrson

It's a confusing topic,

>Thanks to Carl Lumma for explaining Rothenberg's concept of "efficiency...":

and I'm not sure I'm helping, writing these posts between waking and going
to work.

>Perhaps I'm just not getting this... but it seems that this concept is a
>little "backwards" in terminology (??) What exactly is an efficient
>scale "efficient" in?? Not revealing itself?

At not revealing its key, yes!

>Not doing anything... so that the composer has to do it?? Why on earth
>would that be "efficient??"

What does it mean to know that we are in the A-major key of the diatonic
scale? Rothenberg wants to know. He thinks that all scales are not
created equal here -- that it means more to know the key of the diatonic
scale, than say, of the harmonic minor. In this sense, the diatonic
scale is called more "efficient", because you get more key information out
of it. Efficiency is a measure of key information per note of the scale.

>Speaking of which, where can one find the Rothenberg articles or books?
>I'm not finding anything on line on John Starrett's site or anyplace...

Go to: http://www.egroups.com/group/tuning/

...and put message number "4044" in the "jump to" box. If anything's still
unclear, post your question to the list.

-Carl