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Miscellaneous Observations — Musical Scales

By James Staub for Boston Compass (#129)

November 23, 2020

Mexican-American composer Erv Wilson developed vast and complex microtonal tuning systems and alternative musical scales. Often his work was derived from geometric or other mathematical structures such as the Meru Prastarah (aka Pascal's triangle). The Meru Prastarah is a triangular structure of integers where each number is the sum of the 2 numbers above it.

In standard western tuning, the circle of fifths is a pattern where a particular musical interval (the perfect fifth or 3:2 ratio) can be superimposed again and again to determine all 12 notes in the chromatic scale.

From the ratios between adjacent numbers in the Meru Prastarah, a similar process can be performed to build new musical scales where the distance between notes is different from the 12 tone system, and which do not necessarily repeat on the octave.


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