![]() ![]() The series that determines the order of all twelve pitch classes is called a tone row this will always be a listing of all twelve pitch classes with a fixed interval order. There are a variety of ways in which composers have employed this, but in its strictest form, all twelve pitches must be used before a pitch can be repeated. (Although set theory can be used to study any type of music as long as it uses the twelve pitches from the chromatic scale.) Serialism is any music in which some aspect of the composition is based on a pre-defined repeatable pattern this can be the melodic intervals, harmonic intervals, harmonies, rhythm, or any other aspect of music that could be described in a series.ġ2-tone music is a sub-genre within serialism in which a fixed series of all twelve pitches is used to generate both the melodic and harmonic content of the piece. Tone rows, serialism, and 12-tone musicīefore we go further, we should briefly define the genre of music most associated with set theory and matrices. As you begin searching pieces for set classes, you will appreciate not having to transpose and invert every time it is much easier to have a complete list for reference, and you could use our new (013) trichord “matrix” for this purpose. Rather than only looking for intervallic patterns, you could quickly refer to your chart to identify whether a specific trichord belongs to this set class. (Note that to create this chart, the inverted form of the pc set is written in descending form rather than ascending form, so you must read it backwards to find its normal form.) You can make a chart like this for any pc set, and this would extremely helpful if you were analyzing a piece of music that had this trichord present. Here, the “common pc” column shows the pitch class that is common to both the inversion and the transposition pc sets. If you wanted to represent this visually, you could plot each transposition and inversion on a chart, on which this central, shared pitch for each transposition shows the inversion and transposition branching out. ![]() (The interval of transposition is the “0” in T 0.) If you look at each pair of transposed and inverted pc sets, you will notice the same thing they always center the interval of transposition. The only obvious correlation between the actual pitch classes is that both of the pc sets contain 0–which happens to be the interval of transposition for those two sets. In the above example, you could describe T 0 and T 0I as the reverse order of the same intervals moving away from a central pitch. Of course, for each of these, you should normalize the pc set after inversion.Įach one of these twenty-four pc sets contains a unique collection of pitch classes. There are a further twelve unique pc sets that result from inverting our prime form pc set. We can represent these using transposition notation. Because each of the pc sets will be in normal form, we know that there is only one pc set for each possible starting pitch. ![]() Conclusionīecause of your study of prime form, you probably realized that there are twenty-four possibilities. You can also think of this as listing every pc set represented by a single prime form. Use your ability to transpose and invert that pc set to find them quickly. To do this, start by writing out each unique, normal-form pc set represented in the set class of (013). Let’s use set classes as a way to build up to understanding tone rows. Luckily, your newfound understanding of set theory help in comprehending tone rows and their manipulation. For many people, the terms tone row and matrix are synonymous with post-tonal theory.
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