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9 Polyharmony and PolytonalityI. Polyharmony involves the simultaneous sounding of two or more tertian chords with distinct roots (poly-

chords). The variables are the quality of the chords, the root relationships, and the spacing or arrangement ofthe chords. Polychords may be used within a diatonic context (Example a) or a chromatic context (Example b).Note the analysis.

a. b.

Chords most often used are major, minor, Mm7, and MM7. Roots may all be similarly related, or there maybe no system for root selection.

The chords in a polychord are kept distinct by spacing, by placing the chords in contrapuntal streams, or

by contrasting orchestration; otherwise, certain spacings will be ambiguous. For example,

is apt to sound like a tall chord, whereas will sound like a cluster.

Polychords may also be expressed in linear fashion:

II. Chord and scale. Diatonic polychords will typically reduce to a simple diatonic scale (major or church mode),and the effect is often like pandiatonicism. Chromatic polychords may reduce to a single exotic scale, fre-quently octatonic.

III. Polytonality involves the simultaneous sounding of two or more distinct areas of tonality, expressed as linesor chords. The variables are the scale or mode of each element and the relationship of the tonics. Traditionalscalar materials are usually used. Each scalar element must be kept distinct by spacing or orchestration.

Tonal areas can be made distinct from one another by selecting keys with the most distant tonal relationshipsto provide the fewest common notes between scales. Occasionally, however, the composer will choose scalesthat provide for common tones; the result is very similar to a synthetic scale or a permutational scale, inwhich certain tones occur in both raised and lowered form.

The following example is both polychordal and polytonal:

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Polytonal passages are usually resolved in one of two ways: into a sonority containing elements of both keysor into a single key. Polytonal material is often used in brief, isolated passages.

IV. Suggestions for class discussion.

A. Analyze the examples in Unit 35 of Music for Analysis. Students may bring additional examples from theliterature into class.

B. Experiment with polychords, trying major triads in various root relationships and spacings. Also try MM7and MMM9 chords.

C. Analyze several polychordal examples. What root relationships are used? Is there a clear rationale for thechord successions and /or root relationships? What qualities of triads seem to work best together?

D. Suggested reading (see the Bibliography): Dallin, Persichetti, Ulehla.

Exercises

1. Experiment with polytonality. Set up a simple accompaniment pattern, keeping to a single tonal area.Write a melody against it that begins in the same key, moves through distinctly contrasting keys, and thenreturns to the original key.

2. Write brief passages for piano that illustrate the following:a. Diatonic polychords within G major, using nonsystematic root relationships.b. Chromatic polychords, using systematic root relationships and/or exact planing.

3. Write a two-voice contrapuntal example using a polyharmonic chordal basis.

4. Write a two-voice example using two modes or synthetic scales having some common tones. If possible,use different key signatures or partial signatures for each voice (in the style of Bartk).

5. Analyze the given material, and complete in the same idiom:

a.

b.

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6. Study the excerpt from Honegger Symphony No. 5 (#432 in Music for Analysis). Then, continue harmo-nizing the following melody employing chromatic polychords.

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