Temperaments vs. Overtones

I’m building a string instrument that makes music with the strings’ harmonic tones as well as their fundamentals.  And, for hard-to-explain reasons, it’s going to have more than 12 fundamental tones per octave.  So I needed to figure out which tuning system has the best overlap between its equally-tempered fundamentals and their respective overtone sequences.  This is exactly the kind of massive combinatorics problem I don’t know how to solve in my head.  So I wrote some software to help me visualize it.

It’s written in SVG and Javascript.  Firefox: definitely.  IE: definitely not.  I haven’t yet checked if Safari and Chrome support these features.

http://web.media.mit.edu/~hellyeah/crunch.svg

The + and – buttons* change the number of notes in the temperament. Each circle in the top row is a note in the selected equal temperament.  Each row is an overtone series.

Hover over a note to see some information about it.  Click on any note to see the distribution of notes that closely match simple musical intervals. Lighter green indicates a better match.

Enjoy!

* If clicking the buttons doesn’t seem to be working, try clicking their edges.  And be aware that it takes a second or 2 to re-render the whole grid.