source file: mills2.txt Date: Sat, 16 Nov 1996 11:06:04 -0800 Subject: Post from Brian McLaren From: John Chalmers 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; 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" 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 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 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 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, 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 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 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 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 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 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. "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) "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 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 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 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 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 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 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 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) "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 -- 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 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, 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 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 Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sat, 16 Nov 1996 21:29 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA14394; Sat, 16 Nov 1996 21:30:42 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA14346 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id MAA11935; Sat, 16 Nov 1996 12:30:39 -0800 Date: Sat, 16 Nov 1996 12:30:39 -0800 Message-Id: <199611161530_MC1-C06-32E7@compuserve.com> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu