This page was originally created using Internet Explorer 5 for Macintosh to check for proper rendering, and has seen only minor edits since that time. In its current form, it does not validate as either HTML 4 or XHTML 1 (with the appropriate DOCTYPE statement inserted). Evenso, Camino (a Gecko-based browser that uses Mac OS X's Cocoa Framework) renders it entirely correctly. (No longer true, the 1/1 key is supposed to be the full height of all the rows it lies between.) As of 11June2010, I've repaired it so that it now renders almost perfectly in Safari.

-7-6-5-4-3-2-1 0 +1+2+3+4+5+6+7

latest/current note



base frequency



top of stack


least terms

While it may not be obvious, this is intended to be a simulation of a musical instrument, even if one more useful in composition than in performance. The numbers calculated are intended to be the frequencies of musical tones.

I origianlly wrote this during the summer of 2001, and have made very few changes since then. As such it represents an early stage in my gradual (and still incomplete) assimilation of a musical theory called Just Intonation. In particular I had still not learned about harmonic series when writing this page. Rather than try to explain Just Intonation, let me simply direct you to the website of The Just Intonation Network.

The inclusion of a stack for base frequencies is my own addition, and not part of any current musical tradition, so far as I am aware. The point of it being there is to support the process of diverging from and then returning to a theme.

Since writing this page I've spent many hours learning C, Objective-C, the basics of Cocoa, and at least an outline view of CoreAudio, with the intention of implementing something like what you see here on Mac OS X, complete with sound. After that, who knows...

John T. Payne
a.k.a. satyr@well.com