Ives 1/8-tone scale

> [Johnny Reinhard, TD 424.19]
>
> Joe, I'm not sure it's fruitful to analyze 24-TET and 48-TET
> with the same notation rules for extended Pythagorean. It
> seems to be a contradiction in terms. They are all part of
> the smorgasbord that Ives flirts with.
>

Well, this was just an afterthought I had while I was pondering
Ives's use of both D# and Eb in that scale diagram.

It struck me that, except for the top Eb in that 1/8-tone
scale, all the other chromatic semitones were marked as sharps.
(Of course, that's assuming that was what published is
exactly what Ives wrote.)

This gave me the thought that perhaps Ives was thinking of
the chromatic scale he outlined as his basis, and called the
'old scale', in Pythagorean terms rather than in 12-tET.

So for that particular posting, I calculated all the
micro-intervals as subdivisions of a Pythagorean 12-tone
scale - actually 13-tone including the Eb, because it's
a Pythagorean comma flatter than D#.

I have no argument beyond that for this interpretation.
It was just an idea.

Actually, I probably thought of it because it's very much
along the lines of my new interpretation of Aristoxenus's
intervals.

BTW, in my Tuning Digest this morning, that last diagram
(on Ives) *did* get mangled by extra carriage returns being
inserted, as I had prophesied might happen. Sorry about that.
The diagram can be seen correctly on my webpage:
http://www.ixpres.com/interval/monzo/ives/48tet.htm

Can anyone give me the information for the book from which
I copied this diagram? Is it the _Memos_, or is it some
other book containing Ives's writings? I have the _Essays
Before a Sonata_, and I thought those two were the only
ones.

-monz

Joseph L. Monzo Philadelphia monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
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