Category: ideas

12th root of 2

The note relationships in a chromatic scale are based on the 12th root of 2.

An octave has a ratio of 2. An octave is divided into 12 equal steps.

For example, to find the ratio of one semi-tone (half step), on a scientific calculator, use this button:

Screen Shot 2015-03-23 at 12.36.27 PM

Here’s the result where x = 2 and y = 12

Screen Shot 2015-03-23 at 12.47.48 PM

In a computer program, you could use the pow() function calculate 2 to the 1/12 power. Here’s an example in javascript:

Screen Shot 2015-03-23 at 12.44.03 PM

This Max patch shows the relationships between any two notes and how to calculate the pitch of a note based on the semi-tone interval. You might use it as a starting point to design your own scales. For example, a 13 note chromatic scale.  Or relationships based on randomness.

Screen Shot 2015-03-23 at 12.32.36 PM


folder: 12throotof2

patch: 12throotof2.maxpat

Portrait series

Optical flow, a depth camera, and edge detection.

By Matt Romein


Portrait of Margo Cramer from

The programming uses the following external code: – Rob Ramirez
ab.hsflow.jxs – Andrew Benson
jit.openni – DiabloDale
cv.jit – Jean-Marc Pelletier