dissertation on Early Tonality

In a search for web references to Norton's book (_Tonality in
Western Culture_), I found this dissertation which should prove
interesting to many folks here (especially Margo):

http://web.presby.edu/~danderso/diss/index.html

-monz
http://www.ixpres.com/interval/monzo/homepage.html
'All roads lead to n^0'

Monz wrote,

>In a search for web references to Norton's book (_Tonality in
>Western Culture_), I found this dissertation which should prove
>interesting to many folks here (especially Margo):

>http://web.presby.edu/~danderso/diss/index.html

This looks very interesting, and I'll be sure to digest the whole article,
but immediately it is clear that the author is pretty naive in the
mathematics of tuning theory, saying that the ratio of the equal tempered
major third is four times the twelfth root of two!

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:

> http://www.egroups.com/message/tuning/16034
>
> Monz wrote,
>
> > In a search for web references to Norton's book (_Tonality in
> > Western Culture_), I found this dissertation which should prove
> > interesting to many folks here (especially Margo):
>
> > http://web.presby.edu/~danderso/diss/index.html
>
> This looks very interesting, and I'll be sure to digest the
> whole article, but immediately it is clear that the author is
> pretty naive in the mathematics of tuning theory, saying that
> the ratio of the equal tempered major third is four times the
> twelfth root of two!

Yes, after I posted the URL I noticed that too! The interval
actually expressed by this formula used by Anderson is two '8ves'
plus a 12-tET semitone, or 2500 cents... quite incorrect!

I don't know why authors who write about 12-tET still insist
on using the square root sign either. I know it's mathematically
correct and quickly recognizable, and I used it myself in
my earliest writings, but in this age of Excel spreadsheets
it's so much easier and (IMO) more sensible to use the fractional
exponent form of the notation.

Of course, the correct formula for the 12-tET 'major 3rd' which
Anderson really meant was: 2^(4/12), or, in the ASCII equivalent
of his root-sign notation, 12thROOT(2^4).

Other than that, my first perusal seems to indicate that he's
done quite a bit of scholarship. I've printed and bound the
whole thing and look forward to reading it all.

-monz
http://www.ixpres.com/interval/monzo/homepage.html
'All roads lead to n^0'