Tuesday, January 11, 2011

The connection between Musical Scales and Modular Arithmetic

Pythagoras' musical scale is based on a geometric sequence and can be viewed as a type of modular arithmetic. Whenever we get out of the ratio interval 1 to 2, we divide by a power of two to find out the corresponding number within the interval.

In Pythagoras' scale the ratio of 3:2 corresponds to the fifth note (V) in the scale.

Looking in terms of the scale numbers,since note VIII is like the first note I, we can view the numbering of these scale notes has a modular system with modulo number 7 just like how a clock is a modular system with a of modulo 12.

Understanding that we can identify the first tone I with 0,II with 1 …, VII is 6.
Therefore the tone ( V ) is adding 4 and modulo 7. Understanding the way modular arithmetic works and it's direct connection in the way scales are shaped. Can lead to better computer based scale creation systems.

No comments:

Post a Comment