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

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