From: mclaren
Subject: mystery package
--
Recently a mystery package arrived in my mailbox.
Expecting a mail bomb from the Unatuner,
imagine my surprise to discover....
..That the parcel contained the very nearly complete
text of "acoustique musicale," a French book on
xenharmonics and acoustics from the 1950s.
No return address. No letter inside. On a scale
of 1 to 11, my puzzlement at this package scored
somewhere above 11. Examination of the postmark,
however, revealed that the xenharmonic cipher
who sent this little gem was in fact Kami Rousseau.
The book turns out to be an astoundingly rare
item: the internal collection of the CNRS titled
"Acoustique Musicale," from 1959.
This is treasure, containing worthwhile articles
which have not appeared anywhere else.
Thanks, Kami!
--
The contents of this rare volume are so
interesting that it seemed worthwhile to
post my alleged and highly risible "translation"
of the more important articles. (One
at a time. One now, others later) The book
contains articles by Jacques Chailley,
M. Barkechli, Adriaan Fokker, Jacques
Brillouin, R. Tanner, Robert Dussaut,
P. Riety and Fritz Winckel. Chailley was
a Sorbonne professor and director of
the Institute of Musicology of Paris;
a Sorbonne professor and director of
the Institute of Musicology of Paris;
Winckel was a pioneer psychoacoustician;
Fokker rediscovered 31-tet and founded
the Netherlands Huyghens-Fokker institute;
R. Tanner was attached to the C.R.S.I.M.
in Marseille and did interesting work on
acoustics and tuning; Barkechli was the
director-general for arts in Iran during
the reign of the Shah, and was one of the
few writers in the 1950s to discuss the
contributions of Zalzal, Farabi and other
Medieval arabic scholars to the development
of modern intonation.
--
N.B.: Forum subscribers are warned that
Your Humble E-Mail Correspondent never
took a course in French. So the many ludicrous
errorsin the following muttonheaded "translation"
took a course in French. So the many ludicrous
errorsin the following muttonheaded "translation"
are strictly *MY* fault, not the author's.
--
The first article is "The dynamism of scales
and consonances in the principal acoustical
systems and its influence on the development
of music" by Jacques Chailley. This is the same
Chailley who wrote the excellent "40,000 Years
of Music" in 1964, one of the best books on
music history, period.
"Of the various acoustic systems which involve
physical considerations in some way, three
stand out in western musical practice. Up to
the 16th century, musical practice was primarily
Pythagorean; from the 16th to the 18th century,
it was based on Zarlino's work; and from that
era to the present, on 12-tone equal temperament.
"I. The origins of the Pythagorean intonation are
era to the present, on 12-tone equal temperament.
"I. The origins of the Pythagorean intonation are
empirical. (This is 100% backwards from the
reality; Aristoxenos, the chief intonational
empiricist of ancient times, vehemently disagreed
with the Pythagoreans and make considerable light
of their reliance on the sacred tetraktys as the
source of all music -- but then, no doubt my
"translation" is hog-wild --mclaren) Clearly there's
no truth to the tale of Pythagoras hearing blacksmith's
hammers (John Chalmers has pointed this out, also
why. For one thing, the anvil would ring and not the
hammers just as the clapper does not ring rather
than the bell. For another thing, vibrating masses
follow a different law of musical ratios than
vibrating strings-- mclaren). Instead he established
the relationship between the size of the interval and
the length of string. Pythagoras deduced that the
octave, the fifth and the fourth were the basis of
the length of string. Pythagoras deduced that the
octave, the fifth and the fourth were the basis of
all existing music. (Actually the Pythagoreans
worshipped a numerological pyramid made of
the number 1, 2, 3, and 4, called the tetraktys.
M. Chailley's statement is not quite accurate,
but close. Either he has confused the
ecstatic 3-worship of Holy Trinity-influenced
Medieval music theorists like Jean de Muris with
Pythaogras' writings, or my ludicrous "translation"
is to blame -- mclaren) Pythagoras had no
contact with other cultures which did not use such
intervals--such as the American Indians.
"Concerning the list of resonances, Pythagoreans
started their investigation at the second and
stopped at the fourth harmonic. They ignored,
evidently, the harmonic principle discovered
during the 17th century, namely that of the
relationship between consecutive harmonics which
during the 17th century, namely that of the
relationship between consecutive harmonics which
transformed simultaneous consonances into
a posteriori operation. (Hard to see what he's
getting at here. Probably my nonexistent French
is bamboozling me. --mclaren) Superparticularity
was considered the most important relationship,
not the proximity of the sounds in a list of
harmonics--which was ignored when the first
frequencies were calculated. (I've probably got
it scrambled. The gist seems to be that absolute
frequencies are not important but rather their
relationships--which is to say, ratios, and
that superparticular ratios are considered the
most important. --mclaren) And so the 9/8
interval is not defined as the ratio twixt
harmonics 8 and 9, but the difference betwene
the 3/2 fifth and the 4/3 fourth. There was
no consideration of the 5/4 "natural" third,
the 3/2 fifth and the 4/3 fourth. There was
no consideration of the 5/4 "natural" third,
although it was superparticular, because
the Pythagoreans stopped their investigations
at harmonic 4.
"In arresting his observations at the number 4,
Pythagoras conformed to the most primitve
classification of consonance: category1 (unison,
ocrtave) represents perfect consonance,
while category 2 (fifth, fourth) consists of
imperfect consonances. In the melodic
art of music, this results in a scale whose
structure in the sound-universe of Pythagorean
theory is based exclusively on the cycle of
fifths:
(Here M. Chailley gives an unfortunately
misleading 5-line staff with 7 musical
pitches notated as the conventional 12-TET
notes. The naive reader might be deceived
pitches notated as the conventional 12-TET
notes. The naive reader might be deceived
by this diagram into imagining that the final
B in M. Chailley's diagram--starting pitch
F, ending pitch after 6 just 3/2s B--
corresponds to the familiar B on the piano
keyboard, ratio 2^[6/12] = 1.41414... or
600 cents. In fact, in the Pythagorean
tuning this pitch pitch is not the familiar B
above F but a pitch above F = (3/2)^6 =
11.390625 = 11.390625/8 = 611.73 cents.
The difference between this "B" and the
B on the piano keyboard is clearly audible.
12 cents is not a subtle or indetectable
interval. The point here is that Mssr.
Chailley's diagram entirely leaves out the
fact that in a Pythagorean tuning the
pitches rise by 1.995 cents for each note
prdouced by a leap of a just perfect fifth
pitches rise by 1.995 cents for each note
prdouced by a leap of a just perfect fifth
as compared to 12-tet. After 6 notes this
adds up to 6*1.995 cents = about 12 cents,
a non-trivial difference. --mclaren)
"The system is fundamentally a succession
of fifths producing 1, 2 and eventually all 7
of the notes of the diatonic scale.
"The cycle stops at 7 notes. Chromaticism
becomes a question of physics in the
continuation of the cycle of just perfect
fifths, rather than a matter of convention
and musical language.
"And so Pythagorean intonation is perfectly
suited to melody, and C-E-G-C' are perfectly
in tune. In the middle ages western
music was melodic and Pythagorean tuning
was popular, but did not last beyond the
16th century. The intonation was
was popular, but did not last beyond the
16th century. The intonation was
prediminantly minor, since in hexatonic
Pythgorean tuning, the minor Pythagorean
third is much more a point of acoustic rest
than the Pythagorean major third, and
the pentatonic mode was primarily used.
(The Pythagorean major third so-called
is usually calculated as (3/2)^4, = 81/64
= 1.2625625 = 407.82 cents, while
the Pythagorean minor third is usually
calculated as the difference twixt the
9/8 and the 4/3 or 8/9*4/3 = 32/27 =
1.185185 = 294.1349 cents. -- mclaren)
"As far as polyphony goes, the Pythagorean
system was not favorable to the development
of triadic harmony based on its
fundamental intervals, since perfect
consonance was restricted to only two
fundamental intervals, since perfect
consonance was restricted to only two
of these. It was favorable to the
development of counterpoint in independent
lines, where the requirement for perfect
consonance was not great: aside
from the unison and octave, and the
two imperfect consonanances, it was
a matter of indifference in which of the
two classes (fifth or fourth) the intervals
fell. Practically speaking, this made for
primitive polypohony, and throughout the
Middle Ages polyphony was restricted
to such counterpoint, in which all parts
were composed so as to proceed together,
rather than various lines in contrary motion.
(Mssr. Chailley is alluding to fauxbourdon
here, along with plainchant. In fauxbordon
an upper voice duplicates the lower at the
here, along with plainchant. In fauxbordon
an upper voice duplicates the lower at the
interval of a just fourth, which in plainchant
duplication at the octave was allowed -- mclaren)
In conclusion, the Pythagorean system had
the characteristic, that the semitones
were enlarged compared to the other
intervals and were not considered proper
consonances. The resulting tendency was
for very strongly consonant intervals to
sound on the fifth, the minor third
and the unison, the major sixth above
the octave, the minor sixth above the
fifth or the fourth.
"Plagal cadences were typical. As a result,
Pythagorean intonation was a dynamic system,
whose accentuation of the differences between
intervals emphasized dissonance more than
consonance.
intervals emphasized dissonance more than
consonance.
"As a result, certain pitches were often made
more attractive by modification to their
consonance in performance (musica falsa),
and this was the primary function of
chromaticism. Marchetto of Padua (in
the 16th century) used the 5/4 as a chromatic
alteration in this manner instead of the 81/64.
"This could be considered an early Medieval
use of temperament. The Pythagorean major
third is a true dissonance, whose tendency
toward resolution is very strong. Thus
Pythagorean chromaticism represents the
triumph of the large interval as one of
maximum attraction. (Presumably Mssr.
Chailley means here that the 407.8-cent
P maj 3rd tended to resolve to the just
3/2 701.955 cent fifth. -- mclaren)
P maj 3rd tended to resolve to the just
3/2 701.955 cent fifth. -- mclaren)
"Pythagorean triadic harmony was not
consonant; the P maj 3rd was constantly
drawn along a line of strong attraction to
the fifth. The music of the Middle Ages
was characterized by primitive polyphony
and strong dynamism.
"II. Zarlino held a contrary view. He adopted
the major third as a basic consnance, using
harmonic 5 to make three fundamental
consonances instead of 2. (That is, 5/4
along with 2/1 and 3/2 -- mclaren)
"The result was that consonance was extended
to triads, and a major third over the fundamental
satisfied the requirements of proper sonority
in accordance with the model of resonance.
(Presumably this refers obliquely to the fact
that all the members of a just 4:5:6 chord are
(Presumably this refers obliquely to the fact
that all the members of a just 4:5:6 chord are
harmonics of an unheard fundamental. Or it
might simply refer to the fact that when
just intonation is used, there in a noticeable
increase in the resonance of chords played on
instruments with strictly integer harmonics.
-- mclaren) Harmony in the 16th century
accreted bit by bit from counterpoint and
progressively deviated from a strict adherence
to consonance. The harmonic progressions
did not solely rest on consonances, but did
exhibit a constant relationship to a bass line.
"Zarlino's system was therefore static.
The chromaticism of Zarlino's system
accentuated the character of individual
keys. The chromatic tetrachord of the Greeks
was identified through an error of orthogoraphy
with a description by Boethius, instead of
was identified through an error of orthogoraphy
with a description by Boethius, instead of
the intervals of Zarlino's system. (Eh? This
is probably me scrambling the translation...
--mclaren)
"The chromaticism of Zarlino represents the
triumph of the small interval. (Presumably
this refers to the fact that Zarlino's theory
brought thirds into music as consonances and
respectable members of chords -- mclaren)
"Concerning melodic construction, the advent
of Zarlino's system required the modification
of the concept of intonational structure. The
hierarchy of the cycle of fifths must needs be
finite if modulation is to be effected. Thus,
based on classical ideas, Zarlino's method
effected a radical transformation.
"Zarlino divided consonances into three
categories. Harmonic 7 did not fit into
"Zarlino divided consonances into three
categories. Harmonic 7 did not fit into
any of these; in fact, the just seventh
was incompatible with the rest of 16th century
theory and practice. As the seventh became
more and more used in music through the 18th
century, it posed grave problems as to its
correct resolution: Rameau's theory dealt
with this question (among others).
"III. It is impossible to construct a practical
system of just intonation using only the first
4 integers. (The organ builders of the 10th through
15th centuries would have been greatly surprised
to hear this. In fact a tenth-century text
lays out the rules in exact Pythagorean fashion:
start with a pipe of whatever length and call
it C, divide ito four parts and remove one--
that's low F. Divide the C pipe into three,
toss out one part, and you have the fifth above
that's low F. Divide the C pipe into three,
toss out one part, and you have the fifth above
C or G. And so on. Duke Philip's organ designer
Henri Arnaut, around 1450, used a slightly
modified Pythagorean system which concentrated
the dissonance into the interval twixt B and F-sharp.
Under Arnaut's system, only 4 thirds out of the 12
were consonant and the bad fifth is amazingly
awful--a true wolf. Nonetheless, Arnaut's system
represented a workable compromise for the period.
To call a system of tuning employed on organs from
the 10th through the 15th centuries "impractical"
tells me Mssr. Chailley didn't do his homework
here -- mclaren)
"Logically, it is suitable to divide consonances
into four categories, the fourth accomodating
the 7th harmonic. This is not in accord with
Zarlino's 3 categories of consonances.
"That, incidentally, is why the 7th harmonic was
Zarlino's 3 categories of consonances.
"That, incidentally, is why the 7th harmonic was
never accepted as a consonance in western
music. (Mssr. Chailley may be barking up the wrong
tree here--the 7th was never accepted as a
consonance because the interval between
harmonic 7 and harmonic 6 is the first interval
in successive members of the harmonic series
which falls within the critical band. The reason
is psychoacoustic, not historical. However, my
alleged and preposterous "translation" might
well be the culprit instead of M. Chailley -- mclaren)
"The sounding of the chord C-E-G-B creates a
dissonance which fails to resolve. The musican,
in assimilating harmonic 7, creates attractive
new intervals but cannot resolve these chords
within the conventional western system. The
7th harmonic does not correspond to any
degree in the western scale; moreover, the
7th harmonic does not correspond to any
degree in the western scale; moreover, the
resolution of seventh chords has contributed
to the tyranny of the dominant chord. (vii
usually resolves to V in classical harmony --
mclaren) In classical tonal music, the just seventh
cannot coexist with usual melodies, and is
only found as a suggestion in the traditional
seventh chords.
"IV. Pythagorean intonation is dynamic, while
Zarlino's just triadic harmonic intonation is static.
Equal temperament is neither one nor the other.
It is a compromise, whose intervals do not partake
entirely of either of these systems, and thus
is a somewhat neutral system whose employment
was spurred by the need to find a correct middle
ground between Pythagorean intonation's excellence
for melody and Zarlino's just intonation system's
excellence in harmony. Equal temperament was
for melody and Zarlino's just intonation system's
excellence in harmony. Equal temperament was
not imposed by fiat, but arose from the nature
of the music being made.
"The result is a certain musical ambiguity; the
possibilitity that a given pitch may be taken
in more than one sense. (Das Wohltempierte
Klavier of Bach is an example.)
(Well, Mssr. Chailley has fallen into the trap
of assuming Bach wrote in 12-tet, but we
must grant him parole for that insofar as he was
writing around 1958. People weren't nearly
as aware of the use of well temperament in
the 17t and 18th century back in the 1950s
as they are today, largely due to the efforts
of pioneers like Johnny Reinhard--whose
remarkable yearly Christmas programs of
well-tempered Bach have detwelvulated ears
far and wide -- mclaren)
well-tempered Bach have detwelvulated ears
far and wide -- mclaren)
"Equal temperament greatly facilitated rapid
modulation (for example, listen to
Bach's Kleine Harmonisches Lanyrinth
for organ) and allowed the employment of
modern harmonies. (Presumably Mssr. Chailley
refers also to the use of diminished, augmented
and seventh chords, which certainly can be
found in profusion in the music of Bach --
mclaren)
"Equal temperament formed the character of
the classical epoch of music. (Alexander
John Ellis disputes this, along with Patrizio
Barbieri. Both these scholars cite sources
to prove that meantone survived on pianos
into the early 1840s, while in some parts
of Europe--Italy, for instance--meantone
was used by orchestras into the 1890s --
of Europe--Italy, for instance--meantone
was used by orchestras into the 1890s --
mclaren)
"By the end of the 19th century, musicians
had begun to explore extremes of ambiguity.
The result was the decadence of fin-de-sicle
tonality. This was a neutral system: it was
opposed to firm tonality. Such departure
from strict tonality led to an increasing
dissolution of the sense of key (for
example, Wagner, Liszt, Debussy). This
ambiguity led to an ensuing agressive
negation of tonality (Schoenberg). The
result was that any combination of
notes was permitted.
"Concerning melodic structure,
temperament proceeded in the same
way. Temperament in and of itself
was not opposed to the continuation of
way. Temperament in and of itself
was not opposed to the continuation of
classical thematicism based on the
C-E-G triad. Moreover, with the
rediscovery and reintroduction of
folk melodies around the end of the
19th century, ancient melodic structures
based on the cycle of pure fifths revived
in popularity. And so some other composers
(Debussy, Bartok, Stravinsky, etc.)
renewed the thematic structure of music
by using harmonies based on primitive
categories of consonance divided into
only 2 classes, highly consonant, and highly
dissonant. (This is an interesting point and
one which I've not seen made before. --mclaren)
"To conclude, equal temperament provided the
necessary conditions (but not sufficient conditions)
for dodecaphonic music. (12-tone serialism,
necessary conditions (but not sufficient conditions)
for dodecaphonic music. (12-tone serialism,
presumably -- mclaren) Temperament was
definitely an acoustic compromise and marked
the starting point of theoretical department from
historical precendents. Once introduced, it was
not possible to retain the resonance principle
(i.e., Rameau's doctrine that a major chord is
based on integer multiples of an unheard
fundamental -- mclaren) and thus there was
successively greater departure from Pythagorean
models. In the absence of consonances typical
of that system, sounds tends to devolve into
chord-complexes without acoustical rationale,
and this led to new concepts of musical
organization (musique concrete, electronic music,
etc.) as well as serial music (Boulez, Barraque,
Stockhausen, etc.) This evolution would have
been impossible without the initial confusion
Stockhausen, etc.) This evolution would have
been impossible without the initial confusion
introduced by equal temperament.
CONCLUSION
"The historical change in music from acoustic
systems to different ones non-acoustic
in nature was not an accident, but a
continuation of historical practice which
began with the study of acoustical phenomena.
"The essential elements of this evolution were
in place when a language of music and a method of
writing down music emerged." M. Chailley,
circa 1958 (?)
(There is no date visible anywhere in the xerox
which was mailed to me, other than circumstantial
evidence from the dates of the citations. The latest
citations appear to be 1957, so presumably "Acoustique
Musicale" dates from 1958-1960 or thereabouts.)
Thanks again, Kami. Sorry about the ludicrously
bad alleged "translation" but, hey...to me, "Prelude a l'apres
midi d'une faun" means "Prelude to an after ski dune faun.")
--mclaren
