source file: mills2.txt Date: Mon, 11 Nov 1996 08:32:40 -0800 Subject: from Brian From: John Chalmers 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