Tertian harmony is harmony that spaces its notes a third a part from other notes. Additionally, tertian harmony includes the harmonic inversion of thirds. Before one begins their exploration into poly-chords, one should be familiar with tertian harmony in its simplest terms of inversions and through a few applied patterns. From this understanding of tertian harmony through inversions and patterns and after one has accomplished or, in the least, feels comfortable with tertian harmony, one should then attempt to combine more than one chord.
The first step in gaining an understanding tertian ploychords is to write triads and 7th chords in a formulaic fashion. For example, begin by writing each major chord a major second apart (i.e. Cmaj-Dmaj, Ebmaj-Fmaj, etc.) After writing these series of chords, write out triads that are minor third apart. For example: Ebmaj-Gbmaj, Amaj-Cmaj, and all other similar progressions. As one can see from the two previous examples, one should continue this process until one has exhausted all the permutations of the triad progression. In a similar fashion, one should continue this writing exercise with seventh chords. The purpose to this writing exercise is for the musician/composer to develop a visual and intellectual connection to the concepts that they will use in a open/free musical environment.
To continue with this process of learning tertian polychords, the next step, after one has learned by rote and memorized the permutations, is to apply their understanding of poly chords to an improvisation setting. Before one begins improvising with other musicians, one should improvise alone. This will familiarize oneself with the polychords without the aid of written materials. One should strive, during this stage, to improvise with polychords without much thought. Other permutations on this stage include the improvising within a strict harmonic setting. For example, one can improvise on chords that are a minor third apart. Similarly, one can improvise on a series of polychords.
In the last stage of development, one should perform with other musicians and observe how polychords affect other musicians playing and one's performance. During this stage, one should apply their polychord knowledge towards Jazz standards, modal tunes, or atonal standards. Each form of Jazz standard offers its own rewards and challenges. Due to the pros and cons of each form of standard, the outcome will greatly differ. In addition to performing Jazz standards, one should attempt create their original composition with polychords. Furthermore, one should attempt to re-harmonize a Jazz standard with their new understanding of polychords.
In the end, this article focused primarily on the practicing and application seventh chords and triads in a polychordal environment. One can venture into larger tertian harmonies or into other harmonic formulations, such as segundel, quartal, quintal, and all other similar formulations. During one's venture into other tertian or non-tertian formulations, one should observe the impact polychords have on one's and other performances. As a reminder to one's practicing of polychords, for one to be successful at polychords, one should remain diligent in their practice and application of tertian polychords. The process of learning polychords can be tedious, but in the long run, the rewards are greater than not learning this harmonic concept. In the next article on polychords, polychord progressions and its application to composition will be discussed.
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.
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