source file: mills2.txt Date: Tue, 26 Nov 1996 08:09:20 -0800 Subject: From Brian McLaren From: John Chalmers From: mclaren Subject: sensory versus musical consonance -- Kami Rousseau has suggested stretching just intonation scales so that the octaves will be heard as perceptual octaves, the fifths as perceptually "pure" fifths, and so on. This idea is interesting and innovative. However, it's important to point out a source of possible confusion here. My posts on pyschoacoustics have described in detail the fact that the mathematical and perceptual octave are different entities, especially when the octave is heard as an isolated interval. Psychoacoustic experiments do indeed show that isolated intervals are heard as "too flat" and "too narrow" and "impure" when they are tuned to a precise 2:1 ratio, whereas an interval of approximately 1208-1215 cents is heard as "pure" and "in tune" and "just." However, what we are discussing here is *sensory consonance.* This is consonance as measured by psychoacoustic experiments. It is the consonance perceived by observers under experimental conditions. It is consonance of isolated intervals in a non-musical setting. This is not necessarily the same thing as *musical consonance.* Musical consonance is dependent on *context*. It is judged in a musical setting. Musical consonance is dependent not only on timbre and beats and the width of the critical band, it is also dependent on the preceding harmonies, the nature of the music's melodic stucture, and most importantly it is determined by the intonation itself. It is very important to make this distinction between *sensory consonance* and *musical consonance* because the two are not generally distinguished in music theory. In fact Hermann Helmholtz intentionally and purposely conflated the two--Helmholtz claimed that sensory consonance was completely equivalent to musical consonance. Yet it is clear that this is often not the case. One of the best examples is the stretched Balinese octave. Heard as an isolated interval, this 1215-cent octave can sound questionable. But it is never played in isolation in Balinese music. When a Balinese gamelan plays, there's a constant tinkling shimmering gonging interplay of partials that make the partials seem to sizzle in the air, and the beats thus produced are integral to the musical effect. Individual intervals sound quite different in terms of their consonance from the same intervals played in rhythmic counterpoint with mass masses of other notes, whose timbre blends into one huge shimmering klangfarbenmelodie. Indonesian gamelan tuners know this so well that they point out that an individual metallophone cannot be fully tuned until the entire gamelan has been rough-tuned; the entire timbral wash is needed to fine-tune any one metallophone in the ensemble. This is a *very* important point. Our ears have a remarkable ability to pick up on the structure embedded within an intonation and to fit various harmonic and melodic progressions into that embedded structure. A great deal of subconscious processing goes on when we listen to music; our ear/brain system is extraordinarily sophisticated at extracting and recognizing patterns buried in the intonation of the music to which we listen. The net result is that we must be careful not to pursue sensory consonance at the expense of musical consonance. While as Johan Sundberg points out it is vital not to mistake mathematical for perceptual intervals, it is even more vital *not* to give up musical consonance in the pursuit of sensory consonance. Thus Kami's suggestion of stretching just intonation tunings makes good sense as far as increasing the sensory consonance of the intervals. However, stretching the intervals in a just array disarranges most of the mathematical relationships between the octave and the component just intervals. This can be a significant loss if those relationships are used musically. Moreover, this is not just a matter of mathematics; the ear can hear the musical structure embedded with a just intonation scale. Disjointing this structure for the sake of improving sensory consonance might prove musically successful--or it might not. My guess is that it will depend on the musical context. -- On another point: An extremely superficial understanding of my criticisms of theories of just intonation on this forum leads to the false conclusion that I am out to debunk just intonation. Nothing could be further from the truth. If this is what people have come away with by reading my posts on psychoacoustics then they have completely misunderstood my point. Instead, my point is that the arguments used by JI advocates in favor of just intonation do not hold water. Hermann Helmholtz and Partch (following Helmholtz's lead) both tried to claim that western music was based on the harmonic series, and that therefore sensory consonance could be directly equated to musical consonance, and that therefore just intonation is musically superior and musically preferable to any other system because just intonation offers maximal sensory consonance and direct use of the harmonic series in music. These arguments in favor of just intonation have actually been extremely damaging to the cause of JI. As psychoacoustics and digital synthesis have progressed by leaps and bounds, it has become increasingly clear over the last 100 years that sensory consonance is not at all necessarily the same thing as musical consonance, and that as a result many exotic and beuatiful yet inharmonic timbres and intonations can be developed which nonetheless sound musically effective and very beautiful. The problem with the Helmholtz/Partch/ Johnston/Doty argument in favor of just intonation is that it creates a Manichean dichotomy: once we accept the premise that the harmonic series is the end-and and the be-all of music, all musical structures not based on the harmonic/subharmonic series must be regarded as musically inferior, to be purged, expurgated, reviled, cast down into darkness. This is a big problem because it immediately puts the listener in the position of having to revile and abjure all the music s/he has heard over a lifetime...since virtually all of the music all of us hear while we grow up is, of course, 12 tone equal temperament. Yet anyone interested enough to spend years studying music theory must love 12-tet music dearly indeed. So this creates a huge problem for the just intonation advocate: you are now in the position to having to convince your audience that all the music they love is a debased abomination, a falling-away from the true faith of the harmonic series. This is not a good way to attract converts and gain followers. The sensory consonance argument for JI is also lethally flawed, because anyone with a reasonable knowledge of pyschoacoustics can destroy it by citing the experimental evidence. For that matter, you can utterly annihilate the Helmholtz/Partch sensory consonance argument simply by playing pieces of music by Risset, Chowning, Dashow, Harvey, et al. which use extremely inharmonic timbres but which nonetheless sounds beautiful. Inharmonic digitally-generated timbres and computer-produced and -controlled inharmonic series could not be heard prior to the mid-1970s. The computer power to produce such music was simply not available. Now that everyone can hear and experiment with such musical timbres and inharmonic series tunings, it has become starkly apparent that arguments for just intonation on the basis of sensory consonance do *not* necessarily lead to the harmonic series, and (conversely) that the harmonic series does *not* necessarily lead to sensory consonance. (Inharmonic timbres with harmonic series chords produce musical effects completely *unlike* those of just intonation. John R. Pierce, Max Mathews, William Sethares, myself and many others have produced demonstation tapes showing this effect.) The point of all this is that my systematic demolition of the sensory consonance argument for just intonation is in fact necessary to create a firm foundation for the musical use of JI. Otherwise, we are building on a foundation of quicksand. As for the the claim that the harmonic series is the basis of all consonance intervals and timbres, and that sensory consonance can best be obtained from the members of the harmonic series, and that therefore JI is the most musical intonation because it maximizes sensory consonance... Well, as we have seen, all of these arguments are incorrect because all of the premises are false. And so, to use these lethally flawed arguments for just intonation is merely to create a wonderful oportunity for those hostile to new music to shoot down just intonation wthout even hearing it. A much more powerful argument for just intonation is the "Mount Everest" argument. Like Everest, just intonation is there-- why not explore it? While it's extremely easy for any narrow- minded conservative hater of new music like the abysmally ignorant Paul Griffiths (current music critic for the New Yorker) to demolish the "natural interval" or "harmonic series" or "sensory consonance" justification of JI, it's extremely hard for even the most narrow-minded musical reactionary to convince anyone that we'd all be better off if we didn't open our ears and explore potentially beautiful new JI harmonies and melodies. This argument for JI puts the shoe on the other foot--reactionaries like Griffiths must now show their true colors and argue against open- mindedness if they want to prevent anyone from trying JI on this basis. -- To return to the original point, then, Kami's idea of stretching JI scales is an interesting one. However, it's important not to confuse sensory consonance with musical consonance, and not to confuse either of those with musical concordance. Stretching a JI scale might heighten the perceptual purity of intervals while lowering the musical utility of those intervals. If stretching the scale warps or destroys the internal structure of the intonation, sensory consonance might be enhanced at the price of creating musical discordance. As always, all three quantities must be balanced, and they are inextricably bound up with the musical context in which this occurs. It would be nice to give a simpler or shorter evaluation of Kami's idea...but given the complexity of human hearing and the subtlety of even the simplest-sounding intonation, that just isn't possible. --mclaren Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Tue, 26 Nov 1996 17:27 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA08530; Tue, 26 Nov 1996 17:29:21 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA08622 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id IAA27803; Tue, 26 Nov 1996 08:29:18 -0800 Date: Tue, 26 Nov 1996 08:29:18 -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