Transformation

A while back (Tue Oct 24, 2000 1:34 am, to be exact),
I posted to the tuning list a _Journal of Music Theory_
review of Eric Regener's 1973 book _Pitch notation and
Equal Temperament: A Formal Study_:
/tuning/topicId_14954.html#14995

I asked a question about the math here:
/tuning/topicId_14954.html#15054

Paul's explanation of the math, in answer to that question,
is here:
/tuning/topicId_14954.html#15059

Now I'm making a Tuning Dictionary entry for "Transformation",
and using one of Regener's examples.

http://www.ixpres.com/interval/dict/transform.htm

This is the example which reinterprets coordinates (d,q) in
interval space "I", in terms of (a,b) in interval space K_0.
So the coordinates d(1,0) + q(0,1) define interval space "I",
and the coordinates a(1,0) + b(0,1) define interval space "K_0".

Their relationship is as follows:

> The transformation equation from interval space 'I'
> to interval space K_0, according to Chrisman, would be:
>
> d(1,0) + q(0,1) = a(3,-1) + b(1,2) so
> (d,q) = (3a+b,-a+2b) and
> d = 3a + b
> q = -a + 2b

But isn't that wrong? I can see from a diagram that
some of the signs should be reversed, and the answer should be:

d = 3a - b
q = a + 2b

????

-monz

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If you're interested in Regener, my Master's thesis presents his work,
among other things:

http://xenia.media.mit.edu/~bdenckla/thesis/texts/htthe

I've struggled to get a small subset of this work, in particular my
streamlined presentation of Regener's work, published with no luck.

--- In tuning-math@yahoogroups.com, "monz" <joemonz@y...> wrote:
> A while back (Tue Oct 24, 2000 1:34 am, to be exact),
> I posted to the tuning list a _Journal of Music Theory_
> review of Eric Regener's 1973 book _Pitch notation and
> Equal Temperament: A Formal Study_:
> /tuning/topicId_14954.html#14995
>
>
> I asked a question about the math here:
> /tuning/topicId_14954.html#15054
>
>
> Paul's explanation of the math, in answer to that question,
> is here:
> /tuning/topicId_14954.html#15059
>
>
>
> Now I'm making a Tuning Dictionary entry for "Transformation",
> and using one of Regener's examples.
>
> http://www.ixpres.com/interval/dict/transform.htm
>
>
> This is the example which reinterprets coordinates (d,q) in
> interval space "I", in terms of (a,b) in interval space K_0.
> So the coordinates d(1,0) + q(0,1) define interval space "I",
> and the coordinates a(1,0) + b(0,1) define interval space "K_0".
>
> Their relationship is as follows:
>
> > The transformation equation from interval space 'I'
> > to interval space K_0, according to Chrisman, would be:
> >
> > d(1,0) + q(0,1) = a(3,-1) + b(1,2) so
> > (d,q) = (3a+b,-a+2b) and
> > d = 3a + b
> > q = -a + 2b
>
>
> But isn't that wrong? I can see from a diagram that
> some of the signs should be reversed, and the answer should be:
>
> d = 3a - b
> q = a + 2b
>
>
> ????
>
>
>
> -monz
>
>
>
>
>
>
>
> _________________________________________________________
> Do You Yahoo!?
> Get your free @yahoo.com address at http://mail.yahoo.com

hi Ben,

> From: "bdenckla" <bdenckla@yahoo.com>
> To: <tuning-math@yahoogroups.com>
> Sent: Wednesday, June 11, 2003 12:58 PM
> Subject: [tuning-math] Re: Transformation
>
>
> If you're interested in Regener, my Master's thesis
> presents his work, among other things:
>
> http://xenia.media.mit.edu/~bdenckla/thesis/texts/htthe
>
> I've struggled to get a small subset of this work,
> in particular my streamlined presentation of Regener's
> work, published with no luck.

wow, thanks! i'll enjoy reading this!
good luck with publication ... keep trying.

-monz