source file: mills2.txt Subject: Post from McLaren From: John Chalmers From: mclaren Subject: Enrique Moreno's 1995 PhD thesis -- Enrique Moreno wrote a thesis in 1995 entitled "Embedding Equal Pitch Spaces and the Question of Expanded Chromas: An Experimental Approach." This is available as Report No. STAN-M-93 from the Stanford Unviersity Music Dept., CCRMA, Stanford CA 94305-8180. This dissertation is one of the most interesting and provocative theses about microtonality to come out of Stanford. It stands as the equal of Elizabeth Cohen's and Douglas Keislar's fascinating theses (both highly recommended). The heart of the thesis can be found on pages 50 through 52: "We need to see that the tuning has a unique organization, and that its intervals and chords are, in justice, as unique as the tuning itself may be, even when the tuning may contain very closely approximated versions of some familiar intervals. The main difference comes perhaps not so much from the intervals of the tunig t hemsleves but from the *context* that the whole tuning as an entity provides for every interval in it. In this sense, to attempt to classify the new intervals as variations of twelve-tone-to- the-octave equal intervals (or of just intervals) woudl constitute perhaps a reasonable mistake. "It would be reasonable because it is reasonable to attempt to understand unknown things in terms of the things we know, especially if there exists a certain resemblance. It is reasonable to judge the world according tothe categories of our experience, but it is not logical to assume that our categories are the ultimate representation of reality. (..) "Follwoing the same ine of thought, we realize that notating this tuning with the aid of symbols that make reference to our usual twelve-tone-to-the- octave tuning or to historical tunings would be more or less absurd. Imagine having to interepret the signs ^b, ~#, as "not so flat" and "not so sharp", or -b+++ as "quasi-flat plus three syntonic commas," or whatever. In short, regardless that some of the intervals, chords, and even chord progressions may resemble certain well-known intervals, chords, and chord progression,s this tuning and many others (although not necessarily all) deserve a fresh departure point." This is the stronget and clearest statement I have yet found of one extreme of the attitude toward microtonality--namely, that we should approach the intervals and the tunings anew and search our their properties without preconceptions. This is clearly not entirely possibe--it remains a fact that the human ear/brain system has measurable properties and various intervals will have predictable *sensory* effects on the auditory system--but in making this point Enrique gets at an extremely important truth. Namely, that the *sensory* affect of an interval or a tuning is not all necessarily the same as the *musical* affect of that interval or tuning. N0orman Cazden made much the same point in the article "On Sensory Consonance," Int. Journ. of Aesthetics and Art Criticism, 1980, but Cazden was mainly concerned with demolishing Helmhotlz's influence. Enrique's point is much farther-reaching. Now, the other end of the spectrum can be seen in Easley Blackwood's and Paul Rapoport's writings on microtonality. "When investigating a tuning for which there is no repertoire or tradition of any kind, the most illuminating approach is to look for conenctions between the new tuning and 12-note equal. All the other tunings contain many extremely discordant intervals, and are amenable to row music, or to other non-tonal compositional techniques. But hte most interesting are those that include tonal elements--ie., major and minor triads, and seventh chords, which may be arranged in ways similar to, but not exactly like, 12-note equal." [Blackwood, Easley, "Research Notes, NEH Grant RO-29376-78-0642, 1980, page 1] Clearly this approach has a lot of problems. For example, Blackwood reveals fundamental bias when he states that "major and minor triads" are his primary criteria. This causes him to completely overlook the neutral mode and neutral triads on tunings like 17-TET and 21-TET, and as a result Blackwood makes many verifiably false statements--for example, Blackwood discusses *only* the major and minor triads in 17-TET. He never discusses the neutral triad, formed from a third with 5 steps of 70.588235 cents each. Fortunately, Paul Rapoport revises this oversight--but Paul's overall approach remains relentlessly Pythagorean and 12-TET-based, which is simply not appropriate, say, with melodic modes in 19-TET, or harmonies in 21-TET, or with 9-TET or 7-TET or 10-TET or many other tuning which cannot be jammed into the 12-TET mold. In 17-TET, the neutral melodic mode is an important resource. Blackwood completely overlooks it. He does not discuss 8- or 9-tone melodic modes, nor does he discuss pentantonic modes except in 23-TET, to his credit. Thus the great drawback of trying to force all equal temperaments into the conceptual framework of 12-TET is that it leads the composer to completely overlook many useful (but highly non-twelvular) melodic and harmonic resources. On the other hand, Easley Blackwood's and Paul Rapoport's approach to non-12 also has many advantages: by identifying points of similarity with 12, it gives them a place to start analyzing harmonic progressions and melodic modes. The great weakness of Enrique Moreno's position is that he does not provide a conceptual framework for harmonic progressions and melodic modes. The basic idea of Enrique's thesis (to do it gross injustice by boiling it down to a few words) is that non-octave tunings can be characterized by the Nth root of K, where N and K are integers. In many cases, K then takes on the audible characteristics of the 2:1 (octave) ratio in the twelve-tone equal temperament. Thus, Enrique contends--and has data from psychoacoustic experiments to prove--that in many cases the K:1 ratio exhibits many of the properties of the octave 2:1 ratio in 12-tone equal temperament. The particular property on which Enrique concentrates is chroma--that is, the property according to which a perceived pitch remains "the same" perceptually if it is displaced up or down by that ratio. Thus, in 12-TET, a C4 is heard as "the same" as a C3 and a C5; similarly, in the 12th root of 3, Enrique claims (and has data to demonstrate) that a pitch displaced up or down by 3:1 also "sounds the same." This gives a starting point for harmony in non-octave scales, since inversions can now be analyzed, melodic modes can be described, etc. Enrique's approach seems especially praiseworthy because [1] it involves psychoacoustic data, and thus has some connection to the real world--unlike so much mental- masturbation "modern" 12-TET music theory; [2] it has the courage to leave behind 12-TET preconceptions. If it seems utopian that listeners might be expected to utterly abandon 12-TET conventions when listening to mirotonal music, it's well to remember Heinz Werner's paper in the 1940 Journal of Psychology, cited a few posts back. Wener found that, given enough time to familiarize themselves with a microtonal tunings, *every* listener he tested was able to make the leap into hearing the new intervals on their own terms. Further proof is provided by everyday experience--William Schottstaedt, for example, has pointed out that after working with 11-TET for an extended period, he found that 12-TET sounded "strange" when he returned to it. In sum, Enrique's thesis is a major contribution to microtonal theory. It also adventurously extends some of the conventional notions of music theory (i.e., octave equivalence) without becoming a slave to 12-TET ideas. --mclaren