TWENTIETH- - Synapse Music

Harmonic Progression and Tonality 101
The subject of harmonic progression becomes even murkier when nontenian chords
are considered, because the roots of such chords are not defined by any generally accepted
theory or by the common agreement of listeners. The most successful attempt to develop a
universal theory of chord roots was carried out by Paul Hindemith in his Craft of Musical
Composition,' first published in 1937. Al though his theory does account for al\ possible
chords (with the exception of microtonal chords) and had a certain amount of influence in
the middle of the century, it has since fallen into disfavor. largely because, as Hindemith
himself wrote, ''A true musician believes only in what he hears,"2 and his fellow musicians
remained unconvinccd.
If it is no longer possible to create meaningful harmonic progressions based on
chord roots, are there other possibilities? One would be to arrange a succession of chords
according to some measurement of the tension, or dissonance, that each contains. Again,
Hindemith was one of the few to attempt a systematic approach to harmonic tension that
would account for all possible sonorities. He devised six chord groups, with six subgroups
bringing the total number of classifications to twelve. To most of these was assigned
a relative degree of harmonic tension, which, along with other aspects of his
theory, allowed Hindemith to propose "progressions" of chords arranged according to
theirtension. 3 As with his theory of chord roots, this aspect of Hindemith's theory has not
withstood the test of time. Nevertheless, it wo uld be foolish to dismi ss out of hand the
considered opinions of an accomplished composer, and the interested reader is urged to
study his theory in its entirety'
Even without a universally accepted theory, a composer is, of course, free to attempt
progressions of tension. Other possibilities might include progressions of register, chord
type, density, numbers of pitch classes, and so forth. We are on unfamiliar ground here, as
we often are in approaching lwentieth-century works, and imaginalion and flexibility of
approach are impOitanl analytical tools.
NONHARMONIC MUSIC
In its broadest definition, harmony means the vertical aspect of music, and a harmony, or
chord. is any collcction of pitch classes sounded simultaneously. Such broad definitions
are sometimes useful , but they may also distract us from the fact that a good deal of
twentieth-century music is not harmonic in conception. Sometimes the "simultanei ties" in
a piece are just that- the more or less uncontrolled com ing-together of ve ry independent
lines: Although Schoenberg was certainl y not completely indifferent to the vertical dimcnsion,
it would appear that the primary emphasis in Example 5-2, for instance, is on lines,
rather than the chords that they produce. (Remember that the bass clarinet will sound a
major 9th lower than wri tten.) The term linear counterpoint is often used for music of this
sort, where the compositional method is evidently overwhelmingly linear. This approach is
typical of much atonal music, but it occms in other styles as welL