Before we consider a few examples, let's begin with the following quotation from This is Your Brain on Music by Daniel Levitin (p. 257):
Classical music as most of us think of it - say, from 1575 to 1950, from Monteverdi to Mozart to Bach to Stravinsky, Rachmaninoff, and so on - is no longer being written. Contemporary composers in music conservatories are not creating this sort of music as a rule, but rather, they are writing what many refer to as twentieth- century (now twenty-first-century) art music. And so we have Philip Glass and John Cage and more recent, lesser-known composers whose music is rarely performed by our symphony orchestras. When Copeland and Bernstein were composing, orchestras played their works and the public enjoyed them. This seems to be less and less the case in the past forty years. Contemporary "classical" music is practiced mostly in universities; it is listened to by almost no one; it deconstructs harmony, melody, and rhythm, rendering them all but unrecognizable; it is a purely intellectual exercise, and save for the rare avant-garde ballet company, no one dances to it either.
Although this cri-de-couer (some would say "rant") would no doubt be disputed in the academic music world, there is also no doubt that it expresses the overwhelming majority opinion among the general population of music lovers. We will begin by illustrating how it is possible to appreciate some aspects of avant-garde music (and why composers such as Cage are performed and appreciated).
Example 1. Cage string quartet
In the figure below we show a spectrogram for a passage from a string quartet by John Cage (String Quartet IV). The rectangle on the left shows considerable structure (triangle shaped contours) and there is a dialectic in this passage between sharp attacked string notes and longer bowed notes. This structure is repeated (with some variations) in the second larger rectangle. Adjacent to these rectangles are regions marked as ovals, where there is much less structure, only random contours (with some slight, partial repetions of structure). The overall effect is a dialectic between structure (in the rectangularly marked regions) versus chaos (or randomness) in the regions marked by ovals. (A possible, external, metaphor is that we have some dancing music (of a baroque sounding type) interspersed with periods where there is no dancing, only some reflections in people's thoughts of the previous music.)
Stravinsky String Quartet
The spectrogram below shows a portion of Stravinsky's Three Pieces for String Quartet, Movement II (analyzed in detail in New Images of Musical Sound). This piece exhibits a dialectic between sharp attacks of string notes (section A), versus longer pizzicato pluckings (section B), and then contains a blend of the two types of notes in section AB, and finally longer contoured pitches in section C. There is also a hierarchy of silences, short spaces of silence in the sections A through C, interspersed with longer periods of silence between the sections. This piece could be interpreted with the following external metaphor (remember that it premiered in 1914 on the eve of the first world war): section A is the marching of troops, section B is bullets ricocheting (say in target practice), section AB is a battle (troops marching and bullets flying), and section C is the mourning that follows a battle. For a more poetic set of metaphors, see the Amy Lowell poem (especially the Movement II stanza).
|--------------- A -------------| |----- B ----| |------------------------------------- AB -------------------------------| |----------- C -------------|
Piano passage by Milton Babbitt
As an example that perhaps illustrates best what Levitin says in the quote above, we show below a spectrogram of a passage from the Milton Babbitt piece Three Compositions for Piano. As explained in Chapter 5 of The Math Behind the Music, Babbitt is using a cycle of group theory transformations on notes of a 12-tone piano scale to generate this passage. Although this is an abstract structural method, notice that the spectrogram does not contain identifiable structures to its patterns of notes, and indeed most listeners are baffled by the complete absence of melodic contour in the piece.
Bell Tower Ringings
This fourth example is not an example of avant-garde music. It is the spectrogram of an excerpt from a set of Bell tower ringings, described in Chapter 5 of The Math Behind the Music as an illustration of a cycle of group-theoretic transformations applied to the notes. Unlike the Babbitt example, however, this passage has a more musical sound. And, in fact, as we show in the spectrogram below there is a repetition of similar structures of downward descending notes in the first two parallelograms, and a repetition with overlay of such descending pattern in the third parallelogram. This provides the explanation for the musicality of the piece.
This
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