source file: mills2.txt Date: Wed, 20 Nov 1996 09:07:30 -0800 Subject: From Brian McLaren From: John Chalmers 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"--Karnatic music, which uses 9 of 22 just srutis theoretically but does not appear to follow them at all in actual practice; and Indian music, which uses 12 tweaked pitches (*NOT* the same as those in western music) with extensive highly microtonal inflexions around these pitches. 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, 31-TET (1/4-comma meantone) and 19-TET (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 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 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 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.) 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, 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, 34, 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 Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Wed, 20 Nov 1996 19:55 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA01019; Wed, 20 Nov 1996 19:56:26 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA01017 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id KAA10174; Wed, 20 Nov 1996 10:56:18 -0800 Date: Wed, 20 Nov 1996 10:56:18 -0800 Message-Id: <9611201850.AA03662@sunfish.musclefish.com> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu