from Brian

From: mclaren
Subject: Partch's heirs
--
An interesting question.
Theoretically, Partch's heirs are James
Tenney, Ben Johnston and pre-eminently
Erv Wilson. He is the foremost tuning
theorist at work in the U.S. and probably
the world, and he has pushed ji scale
construction significantly beyond Partch's
crucial insight of the tonality diamond
(an insight first gleaned by Augusto Novaro
in 1927, true--but Partch carried out the
full implications of the diamond, which Novaro
never did, to my knowledge. Partch built
instruments and compositions embodying the
diamond. Novaro did not).
Tenney's and Johnston's main claim to fame is
that they supposedly introduced the idea of ratio
space into ji music; but since Adriaan Fokker
actually introduced 3-D ratio space in his book
"Just Intonation and the Combination of Harmonic
Diatonic Melodic Blocks," The Hague: Martinus
Nijhoff, 1949 and specifically presented a ratio-
sapce lattice in his 1951 article "31 Tone
Temperament," Tenney and Johnston in fact
contributed relatively little to post-Partch
JI *theory.* (Their *musical* accomplishments
are an entirely different matter, of course.)
Erv Wilson took the idea behind the tonality
diamond--a 2-dimensional permutational
method of generating ji arrays which was
self-limiting and self-coherent--and he
extended the idea into n dimensions. Wilson
CPSs are N-dimenional permutational methods
of generating ji arrays. Like the tonality
diamond method, Wilson CPSs produce ji arrays
which inherently limit the number of scale
pitches (thus solving one of just intonation's
greatest potential problems....where do you
stop when building a ji scale?) and produced
a rich emergent order (in Partch's case,
utonalities and otonalities and the possibility
of taking N-limit chords in two different
senses; in Erv's CPS case many different types
of "x"-tonalities with the possibility of
taking N-limit chords in many different senses,
depending on whether the CPS is stellated,
whether its facets are inverted, etc., etc.).
For an article which bears on post-Partch
theoretical extensions of ji, see
"Changing the Metaphor: Ratios in the
Music of Partch, Tenney and Johnston" by
Bob Gilmore in Vol. 39, Nos. 1&2 of
Perspectives of New Music, 1995.
In terms of instrument-building, yes, Gary
Morrison is exactly right that Cris Forster is
probably the finest ji instrument builder
alive and likely an even better instrument
builder than Partch ever was. Alas, like Partch,
Forster is hard to get along with. Unlike
Partch, he has done his utmost to make sure that
no one gets to hear his remarkable instruments.
In terms of performance, Johnny Reinhard and
Jonathan Szanto and Dean Drummond and the
rest of the people making Partchian music are
Partch's heirs. No doubt this includes myself
and Jonathan Glasier, inasmuch as we performed
in Partch 43-tone monophonic fabric in our
most recent Sonic Arts Gallery concert but one.
--
In Topic 1 of Digest 821 Paul Erlich wrote that
when it occurs in the context of a 4:5:6:7 chord
the seventh is consonant, while if it occurs
in a diatonic scale with six consonant triads,
it is dissonant.
Paul's statement builds on Kami Rousseau's
query as to what to make of the seventh.
This is an old old old old old controversy,
and methinks we shan't solve it here.
For an interesting theoretical discussion of
seven ratios & various 7-commas for aug 6ths,
see "The Number Seven In the Theory of
Intonation," Eric Regener, Journal of Music
Theory, Vol. 19, 1975, pp. 140-153.
The best discussion of 7 ratios re: the history
of music remains Martin Vogel's 1955 German-
language PhD thesis "Zahl Sieben in der Spekul-
ativen Musiktheorie." Hard to get hold of and
harder to plow through, alas.
Lippius and Zarlino militantly contended
that the just seventh was a consonance,
while Prosdocimus and Tinctoris contended
with equal vehemence that it was a dissonance.
We don't know what Aristoxenos or the
Pythaogrean thought, but we can guess:
since the 7:4 could not be found in the sacred
tetraktys, the Pythagoreans would have classed
it as a dissonance, while Artistoxenos with
full confidence in his ears might well have
classed the just seventh as a consonance.
The controversy continued into the 18th
century. Helmholtz contended 7/4 it was
a consonance, while Riemann and
Schenker treated it as a dissonance.
There is a precedent for such theoretical
confusion over how to classify a musical
interval. The fourth was classified in
Boethius' day as "an imperfect perfect
consonance."
The just seventh would appear to fall
into the same category: depending on
context, it can function as either a
consonance or a dissonance. For example,
the bare 7/6 by itself is often heard as
a dissonance in lower registers; as the
just 7th of a 4:5:6:7 chord whose root
is above about 1500 Hz, the seventh is
usually heard as a very smooth consonance.
There is a psychoacoustic reason for this
which might prove of interest:
The interval between the 6th and 7th
members of the harmonic series falls just
barely within the width of the critical
band above 500 Hz. This means that at
low fundametal frequencies the 7/6 will
be heard as dissonant because most of
the harmonic partials of the harmonic
series timbres will interfere within
the critical band, and many of them will
interfere within 1/4 of the critical
band, producing sensory dissonance
according to Plomp & Levelt's & Kameoka
& Kuriyagawa's definition.
However, if the fundamental is above 1500
Hz, then the harmonics of a timbre which
sits at an interval of 7:4 above 2000 Hz very
quickly exceed the range of audibility. If
the fundamental of a 4:5:6:7 chord is 2000 Hz,
then the fundamental of the timbre which
plays at a 7:4 to 2000 Hz is 3500 Hz. If the
limit of pitch discrimination is 17 khz (mine is),
and the limit of audibility 19 khz (mine is), then
all harmonics above the 5th of the timbre
which sits a 7:4 above the fundamental of the
4:5:6:7 chord will beat supersonically. That is,
the component sine waves will be above the
range of audibility and thus their beats will
be a matter of little concern since the sine
waves themselves are too high to be heard.
(Beats are periodic fluctuations in the loudness
of periodic signals. If a sine wave above the
range of audibility varies periodically in
loudness, it is a matter of little concern,
since regardless how loud or soft the sine
wave, it cannot be heard.)
This explains from a psychoacoustic standpoint
the long-standing controversy over the just 7th.
When played in a high register, the 7:4 exhibits
sensory consonance. When played in a low
register, the 7:4 exhibit sensory dissonance.
The just seventh interval is therefore unique
in that its consonance depends crucially on
the range in which it is played. (Other intervals
can be made into sensory consonances if
played at very high frequencies, but
the 7:6 is unique in that its width nearly
matches that of the critical band. Thus it
is uniquely sensitive to the exact position
in the frequency spectrum at which it is
played.)
The question of the musical consonance
(and of the musical concordance) of the just
seventh is an entirely different question,
and one about which there has been at least
as much controversy.
Alas, to date no one has yet come up with a
convincing theory of basing tunings on just
sevenths. It simply takes too many of them
to produce small intervals with sensory
consonance, and thus 7-commas and 7-ratio
scale pitches tend to have enormous numerators
and denominators...destroying the theoretic
advantages of tuning the 7-ratio just.
--mclaren


Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Mon, 11 Nov 1996 17:37 +0100
Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA04317; Mon, 11 Nov 1996 17:38:53 +0100
Received: from eartha.mills.edu by ns (smtpxd); id XA04352
Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI)
for id IAA11477; Mon, 11 Nov 1996 08:38:50 -0800
Date: Mon, 11 Nov 1996 08:38:50 -0800
Message-Id:
Errors-To: madole@ella.mills.edu
Reply-To: tuning@eartha.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@eartha.mills.edu