From the recording Polyrythmic Overtone Beating


Polyrythmic overtone beating - Brian Baumbusch

This piece was developed based on specific microtonal scales which are used to determine the composition, and in many ways act as key elements of the composition. It involves retuning sine wave samples in order to create symmetrical scales which produce polyrhythmic tone beats because of their parallel relationship. For example, a scale that has ratios 1/1, 9/8, 5/4 3/2, 7/4, 2/1, teamed with difference tones separated by parallel commas, will create polyrhythms of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, etc... This is because the size in hertz between the just ratios and their parallel difference tones is exactly proportional to the just ratio and the fundamental. The piece introduces the just tones with slight pitch bending, then mixes in different registers of these parallel beatings. At certain points, a new beat is introduces and pitch bent on either end of the standing beat in order to produce a swirling acceleration of beating. The oscillators were created defined as ratios using the program "Little Miss Scale Oven" which in this case has retuned sine wave generators in Logic.
The specific scale that was used is listed below, defined in ratios: 1/1, 4718592/4251528, 9/8, 2621440/2125764, 5/4, 2097152/1594233, 4/3, 1572864/1062822, 3/2, 3670016/2125644, 7/4, 1048576/531411  
In simple terms, this is a justly tuned hexatonic scale with parallel difference tones tuned flat from each pitch by a pythagorean comma.