Comparing Intervals

Here is a new piece in the equal-tempered Bohlen-Pierce scale.

This is my first use of a new interval comparison method. My algorithmic composition software is built on a cost function. Pitches are chosen at random, using a probability distribution function determined by the cost function. The pitch to be played, by a particular voice at a particular time, is related to other pitches, those played by other voices at the same time, and by the same voice at different times. The probability for choosing a pitch is higher if the pitch fits well with these other related pitches. The cost function defines what fitting well means.

The diagram above shows two short snippets to be played by the same voice. The snippet a1, a2, a3, a4 is a sequence of notes played at one time, and b1, b2, b3, b4 is a sequence played at a different time, but that is to be some sort of variation closely related to the first snippet.

Suppose the pitch to be played at position a2 is to be chosen. The cost function includes terms to prefer that the pitch at a2 is consonant with those at a1 and a3, the notes immediately before and after a2. Another term encodes a preference for a2 to be consonant with b2.

For the snippets a and b to sound similar, the interval from a1 to a2 should be similar to the interval from b1 to b2. The way I have encoded this is to look at the difference between the two intervals, to treat this difference as yet another interval, and to evaluate the consonance of this difference interval. If one has heard the snippet a and is now hearing the snippet b, one might anticipate b2, expecting the interval from b1 to b2 to be the same interval as from a1 to a2. The actual pitch at b2 versus the anticipated pitch at b2: these two pitches should be closely related. That's my logic behind looking at the difference between the intervals.