From: mclaren
Subject: Paul Erlich's suggestions for teaching
intonation
--
Paul Erlich on 15 August offered a suggested
curriculum for a 15-week course in tunings.
This took a lot of courage on his part, and
also a lot of careful thought. Kudos are due
to him on both counts, since in setting down
plenty of hard details and carefully-thought-out
ideas, he laid himself open to the verbal assaults
so beloved of an unfortunate minority on this tuning
forum.
Paul Erlich's proposed 15-week course in
tuning seems excellent--*if* the purpose is
to indoctrinate the student in Pythagorean
tuning theory, with other tunings considered
as deviations therefrom.
This might not be the best way to introduce
students to tuning theory, insofar as they
are already brainwashed into the Pythagorean
mindset. Our overwhelmingly Pythagorean
music notation and terminology pretty
much assure that by the time students reach
Erlich's putative course, they'll have long since
followed Alexander Pope's dictum: "A little
knowledge is a dangerous thing; drink deep or
foreswear that Pierian spring."
If we are going to teach people about tuning
theory we may want to give them a sense that
other structures and harmonies are possible than
those considered standard in western Pythagorean
musical paradigms.
Who knows? We might even to reveal to them (gasp!)
that most of the world's musical cultures are
*not* based on Pythagorean paradigms.
However, if Pythagorean zombification is the intent,
the course seems well structured *except* for
the strange introduction of "7-TET representations
of pentatonic scales allowing modulational freedom."
Alas, 7-TET *cannot* be understand in Pythagorean
terms. Attempts to force the neutral triad typical
of and the sole consonant harmony in 7-TET into
a Pythagorean mold produces Easley Blackwood's
unfortunate gaffes: EB states that "the only
consonant harmony in 20-TET is a kind of sixth
chord," untrue, since the neutral chord (which cannot
be explained in a Ptyhagorean framework) is one
of only 2 consonant triadic structures in 20-TET.
Blackwood also states that "there is no
consonant vertical triad in 17-TET," also untrue.
In both cases the primary consonant vertical
triad is a *neutral chord*--the *same* kind of
structure which forms the *sole consonant
vertical triadic structure* in 7-TET.
In 17-TET the neutral triad occurs on
scale degrees 1-6-11; in 20-TET the neutral
triad occurs on scale degrees 1-7-13; in
7-TET the neutral triad occurs on scale degrees
1-3-5. (Numbering scale degrees from 1 to
N where N is the equal tempered division of
the octave.)
If we approach these equal temperaments in
Pythagorean terms we cannot recognize or
acknowledge the existence of neutral triads
or neutral modes, since Pythagorean 3-limit
theory has no place for the 11-limit neutral
comma.
(See my upcoming serialized set of posts
which set forth my article "The Sound and
Structure of the Equal Temperaments," in
which the neutral comma is defined,
quantified, and used to describe the
properties of scales like 7-TET which
can be understood or approach in 3-
or 5-limit terms.)
Clearly 7-TET is completely out of place
in any discussion of Pythagorean tunings.
--
Introducing NJ NET scales between
a discussion of the Pythagorean comma
and schismatic tunings of the late middle
ages also seems strange. NJ NET scales
come out of left field, then vanish.
Perhaps they would be better placed off by
themseves as a separate block?
Paul Erlich's "10. Just intonation--
Indian Music" propounds the pervasive
and dubious claim that "Indian
music" is based small integer ratios.
In fact there are at least two kinds
of "indian music"--North Indian music,
which uses 9 of 22 just srutis theoretically
but does not appear to follow them at all in
actual practice; and South Indian music,
which uses 12 tweaked pitches (*NOT* the
same as those in western music) with
extensive highly microtonal inflexions around
these pitches.
Be it noted that the fount of Indic music
theory, the Natya Sastra, is primarily a
book on drama: only 3 chapters deal exclusively
with music. Moreover, the purported integer ratios
are nowhere written down in the Natya Sastra (according
to the books I've read--I can't read Sanskrit, alas),
and thus the just intonation Indian tunings are in
fact inferred and derived from the text, rather than
being explicitly calculated and written down outright
as columns of numbers and ratios.
Some highly respected Indian musical
scholars claim that the 9 of 22 sruti model
is universal in Indian music, but it is
not clear whether they are talking about
the prescriptions of the classic Indian
musical texts from hundreds (often
thousands) of years ago, or whether they
are describing what most Indian musicians
actually do *today.*
There is so much controversy, so many
dubious claims, and so much bad data about
both types of "Indian music" that it would
be better to leave this topic off entirely.
It is clear that western theorists do *not*
understand the nature of the intonation
used in either North or South Indian music,
if indeed a single type of intonation is
used in either (there may be as many
intonations as there are pandits). In fact
there is violent and ongoing controversy
among both North and South Indian music
theorists, as well as *between* them,
primarily because of the British Raj.
Whole generations of South & North Indian
music theorists and researchers travelled
to Britain to absorb a "modern" education
and in the process they were brainwashed
by the very strong British just intonation
movement of the 1910s-1930s. (B.
Chaitandra Deva is the most glaring
example, but there are many others.) Thus
a great many of the texts written by
Indian music theorists about Indian music
in English between the 1930s and the 1970s
are in fact regurgitations of the British just
intonation theories by way of Perronet Thompson,
Kathleen Schlesinger, Poole, et alii.
I've read the texts of these Anglicized Indian music
theorists *and* those of foreigners who claim to
"explain" the "true" intonation system used in
North or South India. The purported "limit" and number
of pitches used in Indian JI is in every case different
(Danielou claims 11-limit, B. C. Deva claims 31-limit,
Dudon claims 7-limit, Jhairazbhoy claims it's non-JI,
and so on). For a convincing debunking of these "just
intonation Indian tuning" claims, read "Intonation in
present day North Indian Classical music," Bulletin
of the School of Oriental and African Studies,
University of London, 1963, vol. 26, pp. 118-132.
For an equally convincing and authoritative description
of the classical just 9 of 22 sruti Indian tuning
system by an eminent Indian scholar, see the web
page for Indian music. (I won't give you the URL
because it is of course dead with a 404 by now.
At the rate telcos are being taken over, URLs
last about 2 weeks nowadays.)
Alas, B. C. Deva's text "Psychoacoustics
and Music" provides no experimental or
theoretical justification for his claim of
a 31-limit JI North Indian classic tuning,
though it does provide strong evidence for
a link between the timbre of the tambura
drone and the pitches of the scale.
Deva's book could be the result of his
absorption in Britain of British ji theories
about India. Or it might be an accurate and
factual description. "Perceptual, Acoustical and Musical
Apsects of the Tambura Drone" is perhaps the
best serious and worthwhile modern study
using scientific methods (Carterette et al. in
"Music Perception," 7(2), 1989, 75-108) written
in English by an Indian music theorist. Krumhansl's
"studies" on North Indian classical music are worthless
inasmuch as Prof. Krumhansl claims that the 7
modal pitches of North Indian classic music
are identical to the 7 white keys of the piano.
Right.
Put on *your* CDs of North Indian classical
music, and tell me *you* believe that.
The only conclusive result of all these studies and
claims and theories is that no one, Anglo-Saxon
or Indian, has made a convincing case
for just intonation or any other specific
intonational model in the actual performance
of contemporary present-day Indian music. The
measured data from oscillographs and
melographs, where they exist, (in the Jairazbhoy
1963 article, in particular) systematically
contradict all the proposed intonational
models.
In "12. Equal-tempered versions of meantone,"
Paul Erlich has gotten very close. However,
(Salinas' 1/3-comma meantone) should be
supplemented with 55-TET, which the German
composers considered the acme of intonational
perfection. Froberger, Handel and in particular
Georg Philip Telemann considered a subset of 55-TET
supremely musical: Georg Andreas Sorge mentions
Telemann by name in his 1748 text "Gespra"ch
zwischen einem musico theoretico und einmen
studioso musices" (Conversation between a
music theorist and a student of music):
"Besser gefa"llt mir das beru"hmten Herrn
Capellmeister Telemanns `Systema Intervallorum'
also welcher die Octav in 55. geometrische
Beschnitte (commata) die von Stufe zu
Stufe keiner werdern, theilet." (A rough
translation: "The well-known Herr Cappelmeister
Telemann's `Systema intervallorum' pleases me
better, in which the octave is sliced up into 55
units [commata] which become smaller from
top to bottom.")
Erlich's idea of comparing 22-equal with the
22 theoretical ji sruti is excellent. Side-by-
side *audible* comparison are *extremely*
important; words on a page or figures
on a chart are cold and deaf and silent.
Words & diagrams don't do nearly as much as
sound examples to clarify these musically
important differences.
The progression from "introduce the 7-limit
consonances" in #17 to "equal-tempered
representations of higher consonances"
in #20 to "inharmonic timbres" and then
"non-octave scales" seems haphazard, but
in #20 to "inharmonic timbres" and then
"non-octave scales" seems haphazard, but
perhaps given a Pythagorean model there is
no straightforward way to proceed from the
7-limit to inharmonic non-Pythagorean
anti-western models of harmony/melody.
--
Overall, Paul Erlich's proposed course would
prove useful in teaching students about
harmony from a western Pythagorean
viewpoint and then gently extending it
in modest ways.
As far as breaking students out of their
Pythagorean zombification and leading them
to discover alternative melodic and
harmonic paradigms, Erlich's might not be
the best curriculum.
--
An alternative curriculum could be
--
An alternative curriculum could be
constructed historically. Starting
with the neolithic bone flute recently
discovered in an archaeological dig
in France, microtonality could be
shown to predate the invention of
writing, and xenharmonics could
be demonstrated as one of the oldest
human activities (the 15,000-year-old
bone flutes do not appear to have used
12 equal tempered tones. Gosh, what a
surprise, eh?).
>From there, reference could be made to
the picture of the mouth bow in the
10,000-yr-old paintings on the Trois Freres
caves, and subsequently Otto Neugebauer's
"The Exact Sciences In Antiquity" could
be used along with examples of tunings
"The Exact Sciences In Antiquity" could
be used along with examples of tunings
from Side 2 of tablet U7/80 of the British
Museum.
(This tuning, written in Old Babylonian
is, conveniently, Pythagorean. Say that
five times fast!)
>From there, reference could be made
to 5th-century Greek theories of music--
specifically Artistoxenos' advocacy
of equal temperament contrasted with
the Pythagorean enthusiasm for 3-limit.
(John Chalmers will no doubt point out
that Aristoxenos' famous quotation is
ambiguous, to which I must respond
that there are still UFO conspiracy theories
about JFK's assassination. No evidence
is 100% completely totally unambiguous.
The gist, however, seems clear.)
is 100% completely totally unambiguous.
The gist, however, seems clear.)
Then tetrachords, tonoi, genera, and
onward to the drastic change in limit
from 3 or 7 or11 or 13-limit Greek paradigms
(depending of whether or not you buy
Kathleeen Schlesinger's fanciful ideas,
and how you date the collection of tunings
compiled by Ptolemy) all the way
down to 3-limit 7th-century tunings
as specified in Boethius ca. 600 A.D.
The controversy over dividing the
whole tone could be dealt with as
a continuation of the Aristoxenian/
Pythagorean conflict--these two
attitudes toward music are diametrically
opposed and cannot be resolved; the
Pythagorean view elevates pure theory
and numbers as source of valid intonation,
Pythagorean view elevates pure theory
and numbers as source of valid intonation,
while the Aristoxenian view elevates
the evidence of the senses as the
supreme arbiter of intonation. In fact
these are more than attitudes toward music,
they are fundamental to the antipodally
opposing approaches to science in the western
world--namely, applied science vs. pure
theoretical science.
The vehement controversy between the
followers of Walter of Odington and
the neo-Pythagoreans could be detailed
throughout the 14th century, not neglecting
to mention the role of Odo of Cluny, and
the rich history of Renaissance tunings
(19, 31, 43, 55, many different meantones,
as well as pure ji as advocated by di Doni
and others) following the introduction of
Napier's logarithms could be dealt with.
The supremacy of meantone and its
reign in European music until the 1840s
should be mentioned, as well as the importance
of the Maudslay lathe in dethroning meantone.
(Since you are scholars the connection will
be obvious.) The role of Helmholtz and
his followers should be contrasted with
the British and American ji movements
in the western hemisphere and the
controversy twixt Russian advocates of
pure ji and xenharmonic equal temperaments
in the GKHN during the 1920s. (Since you
are scholars you are of course familiar
with the roles played by Sabaneev and
Avraamov in Russian microtonality during
the 1920s and 1930s, as well as Alexei
Stepanovich Ogolevets' anticipation of Krahenbuehl
& Schmidt in his 1948 text "An Introduction to
Contemporary Musical Thought," which itself
elaborates on Yasser's historical-determination
theory of tunings but in a direction which leads
to 17- & 22-TET rather than 19-TET as the "4th
stage" of musical evolution.)
From there the path would be clear to discuss
the modern history of tuning, which is
inherently polyintonational. The days of
"one tuning ueber alles" are over, despite the
best efforts of the dunderheads at Lincoln
Center. (They should put an iron gate in front
of the door engraved with the words ARBEIT
MACHT FREI.)
--
Jose Antonio-Martin Salinas wanted to know
whether it was appropriate to spend an
entire hour of a 15-hour lecture on tuning
theory discussing non-octave tunings.
Of course it is not at all appropriate to
spend so little time on non-octave tunings;
a full three or four hours should be spent on
non-octave tunings, inasmuch as the set
of non-octave ETs perceptually include all
of the octave = 2.0 scales. (See my paper
"The Uses and Characteristics of Non-Octave
Scales" in Xenharmonikon 14 for more details.)
In all justice, 5 hours ought to be spent on
nj net scales particularly in other cultures
(Balinese, Javanese, African, Guatamalan,
etc.) and 5 hours should to be lavished on
just intonations greater than 3-limit,
with the remaining 5 hours dealing with
octave = 2 and octave <> 2 equal temperaments.
That is, 5 hours each on NJ NET, ET and
ji tunings.
The importance of non-octave scales is
so vast that I would keep the theory to
a minimum and spend most of the time
immersing students in the exotic, delicious
sound of various Nth root of K non-octave
scales. Once they've experienced the richness
and acoustic beauty of non-octave scales,
they'll be irrevocably hooked--it's like living in
a monochromatic desert all your life and
suddenly being transported to the middle of
a technicolor rain forest. Yes, non-octave scales
are *at least* that important.
--mclaren
