Marchetto everywhere

Gadzooks!

I've been working furiously on my essay describing
a rational interpretation of Marchetto of Padua's
"fifth-tones" so that I could put it up complete
on my website. It's already been there for a
while (albeit unfinished) for those in the know.

I've felt for some time that this is one of my
most original and important papers. Apparently
everyone else who's discussed Marchetto assumed
an equal division of the whole tone into 5 or 9
smaller parts (see, for example, Margo Schulter's
recent posting here).

This didn't make sense to me. A theorist in the
early 1300s would have divided intervals arithmetically
on a monochord, which gives unequal ratio divisions.
This was the point of departure for my analysis.

These ideas appeared in print originally in a chapter
on Marchetto that was in the 1997 draft of my book.
(a real collector's item by now -- I think Kyle Gann
has the only remaining copy in its original form).

Well, today John Chalmers tipped me off that the
issue of MTO (Music Theory Online) that just got
posted today has an article about...
you guessed it. Jay Rahn gives a reading of
Marchetto's theory that's pretty much identical
to mine. Incredible timing.

So, even though there's more to be added to mine,
here are both URLs for your reading enjoyment.

My paper:

http://www.ixpres.com/interval/monzo/marchet.htm

The MTO article:

http://smt.ucsb.edu/cgi-bin/check-browser.pl?rahn+98.4.6

- Joe Monzo
monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html

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Jeff Collins wrote:

> I am new to this list and have been doing a bit of
> lurking around, but today i read a post from Joe Monzo
> who mentioned the Subharmonic scale. This scale
> sounds very interesting to me...but i have absolutely
> no information on it.
> Does anyone possibly have any info they can e-mail
> (or snail) to me? I would really appreciate it.

First, welcome to the List.

I've decided it would be more fruitful to send this
to the List than to you personally. Perhaps others
have comments.

The "subharmonic scale" can be characterized as a
utonal progression, in Partch's terms. It is the
exact inverse of the "harmonic series" of overtones
above a fundamental. In the case of subharmonics,
the "fundamental" is the highest note in the series,
with the subharmonics in reciprocal integer ratios
below it.

The proportions as we used in our improv were as follows,
with pitch progressing from the top down, and with
the equivalent "bottom-up" standard terms given for
the notes which form the "minor triad":

1/3 "fundamental"
1/4 "5th"
1/5 "minor 3rd"
1/6 "root"
1/7
1/8 "5th"
1/9
1/10 "minor 3rd"
1/11
1/12 "root"
1/13
1/14
1/15
1/16 "5th"
1/17
1/18
1/19
1/20 "minor 3rd"
1/21
1/22
1/23
1/24 "root"
1/25
1/26

Note that we normally skip the 1/1 and 1/2 as they
just produce higher octaves of the top 1/3. Intervals
between notes become progressively smaller as you
go down the scale.

The top note, 1/3, was around 3200 Hz. Notes below
1/16 are progressively smaller "semitones" -- the
keyboard tuning went much further than this, but
notes near the bottom were quite low in pitch and
sounded more like rumbles than clear subharmonics.

- Joe Monzo
monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html

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