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On Analysis

by William Harris

   I have always been interested by Schenker analysis of music, after a protreptic from Larry Read on Salzer's development and interpretation of Schenker ideas, I plunged into this area again and burned some midnight oil with a stack of formidable reading. Some things were so good that I cannot help commenting; other aspects do not seem pertinent to modern composition. Putting together my thoughts as a way of clarifying myself, I come up with an approach for my own use, based indirectly on Schenker's visual graphing system.

   A quick look at Schenker's Five Graphic Music Analyses with introduction by Felix Salzer (Dover reprint 1969 from the 1933 edition from the Mannes College of Music) shows a brilliant visual way of approaching music. Not only does a passage have a natural and intuitive beginning and End, as every teacher inculcates, but there are inner sections which fold out, and within each are smaller coherences, down to slurs and even ties. Understanding the building blocks of a passage, from minor phrases to the overall contour is essential for sensitive interpretation, and Schenker has laid out a method of visual patterning to show both the macro and micro structure at one glance. Actually it takes a lot of glances, but if you look carefully it is all in there.

   This was especially interesting to me because for years I was doing a very similar poetry graphing for literature students, with events contoured on a ten foot long roll of 12-inch paper in colored lines, the vertical axis representing strength of effect and the horizontal axis representing time. When more than a handful of the "contour lines" congregated about a given point, we always found there a special focus of intensity, a poetic node. The students made their own graphs, which opened their eyes to what was going into good poetry, but my colleagues passed the wall where our streams of graphs were posted with a sneer and never had a notion of what we were doing. So with Schenker, with a novel and complex approach of this kind one can easily be set off miss the point.

   Reading the detailed commentaries in Salzer's Structural Hearing (2 vols. 1952, Dover 1962), one comes to the conclusions that:

  1. Music can be taken apart this way, but probably not put together thus, as Salzer openly admits. This is a method for analysis, not for composition.
  2. The approach to the leading of inner voices, brilliant as it is, is harmonic and based on examples from the Eighteenth and Nineteenth centuries. Detailed, terribly precise and academically professional, this type of analysis does not apply to music outside its sphere. But the overall sense of form and orientation is generic, fascinating and well worth study.

   In order to clear my mind, I started putting together a different system for my own use, but within Schenkerís notion of micro-to-macro in the framework of a graphical layout. This is a beginning, so I will compress my thinking into a few paragraphs:

   Starting with a general music base rather than a harmonic predisposition, I state:

  1. Music is composed of tones and of non-tones, which are empty spaces. (I avoid the word "note" which refers to a mark on paper rather than sound.)
  2. A tone can be followed by another tone or by a space.
  3. Tones and spaces can have varying lengths, which when taken in a series will produce rhythm.
  4. Tones in a matrix of rhythm are heard as "tone-series" or voices, which will often be taken as what we call melodies.
  5. Arrays of voices in the same time-space produce two very different sorts of polyphony:
    • Dynamic polyphony in which voice-leading rules, all voices being theoretically equal although some may be taken as dominating for special effects.
    • Static or block polyphony, in which tones are intended to sound simultaneously, producing chordal effects. This is quite different from the designed chords which are simply tones occupying the same space.
  6. Tones progress in a time-frame, varying in both pitch and duration simultaneously. Pitch can go up, down or repeat. Durations can be located on a binary framework by halving, as we conventionally do in Western music, or there can be a free time designation based on real-time.
  7. In close formation, tones can be seen as forming scales, which can be eighth-tones, quarter tones, chromatics, diatonics, whole tones, or arpeggiated series. In contra-distinction, non-scalar series do form the fabric of most music, offering many melodic options for the ear.
  8. Tones stand at the basic structural level, but they cannot exist without further definition as to:
    • Register, or where the tones falls in the range of human hearing, with fundamentals from 60 Hz to near 3500 Hz. This is a basic factor, like as pitch but involving timbre.
    • Amplitude or loudness, from barely perceptibly to thunderous. This is a variable and secondary factor.
    • Timbre, or the display of partials of the sound over the spectrum of hearing, which defines the musical instrument used, leads to the art of orchestration. This is very important in composing music, but in a sense secondary, since it comes after the initial definition of tone and register.

   Salzer's Harmony may be limited and historically based, but harmony does exist naturally in music. If tones are simultaneous, we have either harmonic chordal displays, or if sequential, voices leading in and out of harmonic arrays. If two or more tones are leading in time, they can progress in and out of each othersí "envelopes", or they can be separate and detached and in a sense "syncopating" harmonically either accidentally or intentionally. But memory will associate dynamic tones over a considerable passage of time, and consider them part of overall structure.

   Summary: Certain basic features must exist. There must be tones and optionally spaces. There must be more than one tone, thus series or voice or melody-line, which will have some sort of rhythm, stretching from perfectly even to incomprehensibly variable. Register will exist as a variant of pitch, since mono-tone music is invariably monotonous. Right after this we will want to specify the kind of sound, that is instrumentation and orchestration.

   Now we come to the critical area. Salzer's harmonic spectrum has at its core a small cluster of tone-relationships, the beatless octave, relatively pure fifth and fourth, rich and buzzy third/sixth, while the rest fall in the class of the so-called dissonances of various sorts. Triadic at heart, this layout is beautiful, and has served the West well for centuries, but after the turn of this century, it was felt to be restrictive in a culture where everything else from Einsteinian relativity to Cubism was going through radical change.

   Look for a moment at the intervals of the scales we use in the West. The octave was known from antiquity for its peculiar quality of beatlessness, in Just Intonation fifth and fourth shared this quality, adjusting by ear for ensemble playing. In the 14th Century, the Church finally permitted use of thirds and sixths, which had been outlawed because of their disturbing, high beat rate. With the development of equal temperament for piano and organ, small amounts of beat were introduced for fourths and fifths, slightly enriching these intervals (at the cost of the old purity). By the 17th Century, thirds/sixths with their fast and exciting beat rates, were established as central to music which became triadic by rule. An open octave or open fifth/fourth were not to be used without a major/minor third inserted, and we became used to this as The Sound of Music. On the one side of this musical spectrum stood, aloof and unused, the pure octaves, just fifth and fourth. The mid-range of triadic combinations was now basic, to be pointed-up here and there with seconds in a triadic display, or for momentary passing effect. On the other end of our spectrum stood the dissonances, the major and minor seconds, the tritone, timbral clashes, and arpeggios of fourths as a sort of scale replacement -- all used most cautiously in the last century, but coming to the fore with this century's New Music, with its anti-triadic obsessions.

   Two tone harmonies, simultaneous or sequential, can range from pure and beatless in their charming emptiness, through the rich, chocolatey, piled-up thirds and sixths, on to the world of dissonance which can be sly and intuitive, dynamic and shocking, or as novel to our ears as a melodic run of parallel tritones. Register and timbre from many instruments complexify this greatly, so it is no longer a question of what series of Schoenbergian notes we use, but a matter of how wide our spectrum of pitch, register, instrumental timbre, and neo-harmonic beating-richness can be. Add to this the tone-slides of the violin, trombone or synth., and the quarter tones of Indian music, and we have more than enough for New Music in New Directions.

   But form remains. There is still beginning and end, even if they don't sound like it any more. There are still scale series, and chordal effects even if they come from voices bumping each other in time. And there are micro-relationships all over the page of score which build into musical paragraphs, and finally define the total musical display, as in Schenker's overall, condensed Ur-linie. Schenker said, you do not compose to this Ur-linie, rather it is the analytical statement of what an intuitive musician with Improvising Mind (it is his word here, not mine) fits together with craft as his work.

   Turn to Schenker's graphical display (Five Graphic Music Analyses, ed Salzer., 1933, Dover reprint 1969) with its wonderful sense of inner structure and overall form. Here we can see the analysis of where the voices come from and where they are leading to, and what inner relationships they have, but in a specialized way. Things were seen by Schenker as forever referring to a triadic display or listed as dissonant, that is, outside the harmonic series (the minor second, the tritone, distant parallel fifths). But they now can all be taken as the tones of Conscious Design and Intent. Scales built on fourths, or pentatonically, or a Lydian sequence are open for our use. Nor do we have to end a piece with a dominant-to-tonic resolution, or even a tonic-like finale. We can flirt with tonic for a while, then end on the seventh, effectively. Tones four octaves apart have strikingly different timbral properties.

   We have to rethink the whole gamut of available beat-relationships, which become available as we leave the tempered piano and organ for wind instruments, string and synth. These Neo-harmonic relationships become the basis for a new kind of analysis, but one which we can still insert within the framework of a Schenkerian visual and graphical display. There is a reason for use of graphic display, as Salzer notes: There are relationships which the ear hears well, but the eye understands quite differently, and in some ways more coherently.

   I am not thinking of abandoning Salzer's harmonic analysis. It would be the worst kind of snobbery to think that Modern Music must construct its melodic-notions, as often happens, out of continual minor seconds and augmented fourths. To outlaw a major triad from new music, would be like rejecting the reds and yellows from a painter's palette. By expanding our notion of sound, we can use, with relish, the traditional harmonic world , and at the same time work with sound-relationships which Classical composers could not have imagined or heard.

   Would such mixed music, spanning in its tone-relationships from Gregorian through developed Diatonic and on to the options we have at hand, sound odd and idiosyncratic? It is to be hoped so, because the Greek word idio-syncratic means literally a private-mixture, a personal way of putting things together. In a highly social world where everyone, including many a composer, is busy trying to look like everyone else, having a Private Mixture in mind is perhaps the most important thing one can do in so vital a discipline as the art of music.