Beethoven JI tuning experiment & 'lateral' harmonies

[Paul Erlich, TD 188.8]
> Many classical pieces have been analyzed in just intonation and
> almost invariably they have a net downward drift in JI, sometimes
> by as much as half an octave.

Altho this statement by Paul is correct, I must take issue
with the methods of analysis he's referring to.

I have been doing an experiment in 'justification',
using the Scherzo of Beethoven's piano sonata #9 (op. 14 # 1).
Of course it was written originally for a 12-tone fixed tuning,
which may have been 12-eq but was more probably either
a well-temperament or a meantone.

(Considering the extraordinarily high quality of his overall
output, I have seen shamefully little regarding Beethoven's
conception of tuning - in part, that's the reason I picked *this*
piece for the experiment; it's also a great piece. Ed Foote's
CD _Beethoven in the Temperaments_, which was released about
a year ago, is the only investigation I know of, and it was criticized
a bit in this forum, altho I liked it.)

What I found in this experiment, and which surprised me,
is that, contrary to just about anything you'll read anywhere,
including some of my own stuff, 12:15:18 is *NOT* an accurate
analysis of a Dominant [V] chord.

The (culturally-conditioned?) preference for a sharpened
Pythagorean 'leading-tone' makes this chord sound flat, at
least in this piece, and to my ears. It sounds a lot better
using the Pythagorean pitch for the leading tone, and choosing
the 'root' and '5th' which make a nice 4:5:6 triad with it,
in the corresponding area of the harmonic lattice.

This requires a 'root-movement' in the chord progression which
is quite a bit more complex than the typically Pythagorean
'root-movement' which is usually assumed.

Also, the proportions of some chords that are used in passing
is considerably more complex than those usually found in
a JI analysis of music from this period.

The only reason I haven't said anything about this until now is
because the MIDI file is still unfinished and I wanted to put
the completed analysis and sequence up on my website, but
since Ray Tomes rekindled discussion of it, I decided to work
a bit more on what I already had, and put it online 'in progress':

http://www.ixpres.com/interval/monzo/beethove/son9schz.htm

-monz

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

___________________________________________________________________
You don't need to buy Internet access to use free Internet e-mail.
Get completely free e-mail from Juno at http://www.juno.com/getjuno.html
or call Juno at (800) 654-JUNO [654-5866]

Joe Monzo wrote,

> What I found in this experiment, and which surprised me,
> is that, contrary to just about anything you'll read anywhere,
> including some of my own stuff, 12:15:18 is *NOT* an accurate
> analysis of a Dominant [V] chord.

> The (culturally-conditioned?) preference for a sharpened
> Pythagorean 'leading-tone' makes this chord sound flat, at
> least in this piece, and to my ears. It sounds a lot better
> using the Pythagorean pitch for the leading tone, and choosing
> the 'root' and '5th' which make a nice 4:5:6 triad with it,
> in the corresponding area of the harmonic lattice.
>
> This requires a 'root-movement' in the chord progression which
> is quite a bit more complex than the typically Pythagorean
> 'root-movement' which is usually assumed.

George Kahrimanis, who has (questionably) backed up his theories with experimental
observations on preferences in synthesized performances, analyzes the dominant in
minor as a utonal chord, the dominant seventh being tuned 1/9:1/7:1/6:1/5 and with
its lowest note on the regular dominant. That gives a highly raised leading tone
much in accord with the modern practice of a typical string quartet playing
Beethoven.