3. pctheory module reference
The central classes in pctheory are the Pitch12, Pitch24, PitchClass12, PitchClass24, OTO, and UTO classes. The Pitch12, and Pitch24 classes use integers to represent pitches: C4 is 0, pitches above C4 have positive numbers, and pitches below C4 have negative numbers. Technically, one could use the same class for both the chromatic and microtonal systems, but these two classes inherit from PitchClass12 and PitchClass24. This gives each pitch a pitch-class attribute, since all pitches can be associated with a pitch-class. Therefore, it is necessary to have two separate classes. The PitchClass12 and PitchClass24 classes, of course, represent pitch-classes in the traditional way, where 0 is C.
The “OTOs” (ordered tone operators) and “UTOs” (unordered tone operators) require a bit more explanation. They correspond to the row operators (ROs) and twelve-tone operators (TTOs). However, a “row operator” can be used on any pcseg, whether or not it is a row, and whether or not it is chromatic or microtonal. Also, while the microtonal system can use some of the same TTOs as the chromatic system, it is oxymoronic to operate on microtonal pitch-classes with “twelve-tone” operators. Furthermore, in the microtonal system, there are twice as many indices of transposition, and twice as many multiplicative operators. Therefore, the OTO and UTO classes represent generalized ordered and unordered standard operations and can be used with chromatic and microtonal pitch-classes, pcsets, pcsegs, and posets. The OTO models an operator of the form TnMm or TnRMm. The UTO models an operator of the form TnMm.