The psychological effect that polytonality can have on the listener is often governed by the relationship between the keys that are presented. Vincent Persichetti elaborates:
“The fundamental quality of polytonal texture is determined by the key relationship set up by the tonics. In major-key combinations, a polytonal order of tension from consonant to dissonant is secured by combining two keys that lie a perfect fifth, major ninth, major sixth, major third, major seventh apart – and so on up the cycle of fifths . . . Those keys that are not closely related according to the circle of fifths will more easily set apart the tonal key spheres.” 1
The following is an elaboration of Persichetti’s visual representation of his theory with regard to the consonance or dissonance of key combinations:
Although the case can be made that this is a subjective classification system, and although Persichetti does not provide a definition of or reasoning with regard to how he defines resonance within the confines of polytonality, the examples provided in the chapter of his book display a thorough understanding of his experience with polytonality. If I can offer a criticism, it is that I feel as if Persichetti could have provided a much more in depth analysis of why certain key relationships are more consonant, dissonant, or resonant than others, rather than mere stating that this is so.
1 Persichetti, Vincent, “Polytonality.” Twentieth-Century Harmony: Creative Aspects and Practice. New York: Norton, 1961, p. 255-261.
In the following examples, repeated melodic fragments (motives) factor importantly in how new keys are introduced into an established tonal environment. Further, one of the tonal environments (either the established or the newly introduced) can be purposefully ambiguous, suggesting perhaps two or more tonal possibilities.
In what is one of Lennie Tristano’s most widely acclaimed improvised melodies, the chord progression to All of Me is visited with a torrent of running eight-note lines at a fast-paced tempo. By the beginning of the third chorus, the listener has had ample opportunity to have become acclimated to the chordal framework of the composition, complete with solo material that has been largely diatonic to the key of B-flat major. It is at this moment, however, that Tristano chooses to briefly introduce a repeating motive, beginning in the key of B major and again in the parent key of the composition.
While the tempo and usage of continuous eighth notes (common throughout the entire solo) provides the melody with a definite sense of momentum, it is the repetition of a six-beat motive, once in the foreign key and again in the original key that provides the listener with a fragment to identify with. Additionally, the fact that this motive crosses the bar line adds to the sense of momentum.
Leading up to the excerpt above from Kneebody’s Clime Pt. 2, the melody establishes itself as being firmly within an E minor or G mixolydian tonality. This is reinforced by the eight-measure ostinato in the bass, repeated throughout the five-minute composition. Once established, however, the melody briefly visits the keys of C major, A-flat lydian, and D-flat major, using the repeated ascending scale, descending arpeggio motive throughout. Once these new keys are introduced, the door is opened for additional tonal environments to be brought in. And while the E and F-sharp major melodic segments do not follow a specific motive, they do maintain the eighth-note triplet momentum of the previous melodies.
While Darius Milhaud was the first to use the term “polytonality” as a means of describing his own compositional styling, it would perhaps be more accurately regarded as instruction toward composers, performers, and listeners alike with regard to this technique’s clear differentiations from strict atonality. Milhaud makes the distinction by pointing out the similarities of his techniques with those of more traditional harmonic environments:
“It is easy to find the sources of polytonality. From the harmonic point of view, they are found in passing tones, unresolved appoggiaturas, and foreign notes of chords that one can consider as members of another key.”1
A clear example of this can be found in the Botafogo from Milhaud’s Saudades do Brasil:
Here we can see a clearly articulated F minor Latin dance ostinato in the left hand, while the right hand begins with the ascending form of the F# melodic minor scale, beginning on C#, and continuing through B, after which alternating F# minor and E# diminished triads explore their respective inversions. It isn’t until the right hand’s C# falls to C natural in measure 13 that a point of resolution is reached between these two conflicting keys.
While Milhaud sought to explain polytonality as a technique he was using at the time, the concept is explored retrospectively in Ludmila Ulehla’s Contemporary Harmony: Romanticism through the Twelve-Tone Row, citing examples in works from Prokofiev, Hindemith, Barber, and others. Her exploration of polytonality focuses primarily on the vertical structures assembled by juxtaposing disparate elements, as seen in Copland’s Piano Sonata2:
While Ulehla points to a simultaneous sounding of B major and D major tonalities with interspersed events in C major throughout these first several measures of the movement, the block chord movement and cluster style voicing of these tonalities make it difficult (if not impossible) to clearly decipher them as anything beyond polychords, the presence of which does not necessarily constitute polytonality. Ulehla calls the cluster in measures three and four an F#13. But without the presence of an A# in this voicing, a crucial tone of this chord is missing, and there is no leading tone to suggest that it belongs to B major. Additionally, none of the tonal environments suggested by Ulehla account for the E# in measure 14.
Composer Adrian Allen similarly states in the Polytonality volume of Harmonic and Melodic Music Theory and Method for the 21st Century3 in that, by stacking block chords with notes from different keys, clear, discernable polytonality is evident. Throughout the volume, Allen operates solely within the vacuum of his own compositions to reinforce his theorem, as seen below:
Allen’s String Quartet No. 2 is meant to illustrate how voices derived from different keys can be used for a desired polytonal effect. However, with the ensemble key signature changing at every measure for the first five measures of the piece, there is no opportunity for the establishment of a stable environment with which to contrast any others. Further, as established in the earlier Copland example, block chord movement between voices makes it more likely that the combined sonorities of the ensemble will form little more than unrelated polychords or, as is the case in measure three above, simple triads that, given a slightly more stable backdrop, would be diatonic to a single given key.
In his book Polytonal Triad Etudes4, Ed Byrne offers a practical approach to his method, in that he would hope that playing through the etudes themselves would provide the wisdom needed to distinguish polytonality, as there is no explanation in his volume with regard to how the studies in his book are polytonal. An excerpt follows:
This eight-measure excerpt, being nothing more than a string of major triad arpeggios with a passing tone thrown in as the second-to-last note, is part of a study in which several nearly identical iterations of the same triads in the same places of each measure are repeated ad nausea. Composed and performed without accompaniment, a stable tonal environment is never established (which begs the question, “Why the B-flat key signature?”). Further, this method is notably similar to George Garzone’s Triadic Chromatic Approach, a method that has gained a reputation within jazz pedagogical circles as being a revolutionary method for ear training and improvising.5 Garzone’s method, while making ample use of linking strings of non-related triads as a rule, makes no claims with regard to polytonality.6
For the sake of comparison, an excerpt of Garzone’s contrafact written over the chord progression to Have You Met Miss Jones is below:
By virtue of the fact that Garzone’s triadic treatment of a pre-existing tonal landscape is meant to be performed within a tonally stable chordal accompaniment, this melody is actually more polytonal than Byrne’s, which has no such harmonic association.
In his book Twentieth-Century Harmony, Vincent Persichetti defines polytonality as, “a procedure in which two or more keys are combined simultaneously.” He goes on to specify, “Each melodic line should retain its own individuality.” And, while I don’t want to be so bold as to put words into Persichetti’s mouth, I would choose to expound on his definition/instruction by stating that polytonality is the horizontal manifestation of multiple ideas, or multiple iterations of a single idea, clearly articulated in multiple distinguishable keys, modes, or tonalities.
Continuing with Persichetti’s advice regarding effective execution of polytonal situations, he states, “For maximum clarity in the projection of different tonalities, one key is introduced and as the next key is added.” In summary, polytonal events are most effectively implemented after a single tonal environment (key) has been well established, so as to provide adequate contrast between existing and new material. An example from Bob Brookmeyer follows:
The tonal environment, clearly defined with a ii – V7 – I – VI7 – ii – V7 – I progression in E-flat major, only appears to be clearly honored in the melody as a point of resolution during the last two measures. This is possibly due not only to the commonality of the diatonic progression, but also because this particular improvised melody occurs after several iterations (choruses) of the same progression, providing the listener with an ingrained, expected harmonic environment.
Analysis of the excerpt above will show a half-step relationship between different environments, somewhat reminiscent in the Milhaud example above. And while there are substitution-based occurrences of multiple key events, I would like to also bring the reader’s attention to the asterisks, demarcating a downward, Schenkerian-esque “züge-like” pull towards the tonic, which may account for Brookmeyer’s selection of notes more so than a deliberate “key-against-key” technique.
1 Milhaud, Darius, “La Mêlodie,” Melos 3 (1922): p. 195.
2 Ulehla, Ludmila, “Bichordal Writing and Polytonality.” Contemporary Harmony: Romanticism through the Twelve-Tone Row. Advance (1994). p. 284-286.
3 Allen, Adrien, “Polytonality.” Harmonic and Melodic Music Theory and Method for the 21st Century. Vol. 10. Maestro Press, 2014. p. 59.
4 Byrne, Ed, Polytonal Triad Etudes, ByrneJazz, 2008. Linear Jazz Improvisation.
5 Garzone’s method, while not copyrighted or trademarked, is documented by himself in the DVD, The Music of George Garzone & the Triadic Chromatic Approach (Jody Jazz, Inc., 2008). The year of publication of this DVD is the same as that of Ed Byrne’s Polytonal Triadic Etudes.
6 I feel as if this can be said with some authority, having studied the Triadic Chromatic Approach method with Garzone in a private-lesson and ensemble format over the course of two years, and having received positive feedback on multiple occasions from Garozne with regard to my grasp of his concept.