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As a result of this labeling process, one will see that polychordal units are symmetrical as opposed to Persichetti’s polychordal principle. Due to this second labeling process, one can see that extreme dissonance in this case, would be a polychordal unit that consists of C and F#. The next descending unit of dissonance would be one of following: C & Db or C & B. On extreme end of this dissonance, extreme consonance would be C & C and next ascending order of dissonance would be either C & F or C & G.
The second approach to polychordal dissonance/consonance, tend to lend itself to improvisers and composers whom process information in a mathematical or analytical sense.
In end, composer and/or improviser has two methods in developing polychordal dissonance and consonance for their respective genre. In artistic terms, one is left to determine if either approach is conducive for themselves. One will determine which approach is ideal for them through practice and experience. To apply these ideals to an improvisation setting, one could follow methods as laid out in Polychords and Jazz Improviser. In contrast to improvisers, composers should start with a four bar phrase that has four or five polychordal units. From this example, one should then begin to compose through this predetermined chord progression.
Andrew Hanna is the CEO & Production Manager of At Hand Productions, Inc. At Hand Productions is a leading Philadelphia concert and theatrical production company. Andrew Hanna has 20 years of composition experience and 16 years of performance experience. His compositions range from duets to large theatrical productions such as My Journal, Requiem for the Now, and Prophecies of War.