Here is my 1st patch, a little tool for working with equal temperament tunings. It allows you to find the closest match to a specific ratio within any equal temperament tuning. Instructions available on website at http://www.bwong.ca

I am sure others have made far better utilities, but it is my first attempt at working with pd. Comments and suggestions for improvement welcome.

http://www.pdpatchrepo.info/hurleur/etrcalc.pd

Attached is a copy of etrcalc2.pd, remade using Maelstorm's equation. This version also gives the note number, and runs much faster than the previous version. Thanks again Maelstorm!

http://www.pdpatchrepo.info/hurleur/etrcalc2.pd

Nice solution Maelstorm! By simply rounding the result of your equation to the nearest integer we have our solution, expressed as a scale degree. Actual scale ratio and variance values can then be directly calculated as in my original design. The elegance of your solution should also make expansion of the patch for multiple targets much easier, as well as obviously being much faster, particularly as the number of scale degrees rises.

Thanks very much, I will start working on etrcalc2!

Thanks arif, I will check out [until].

Terminology for general equal temperament tunings is a bit vague, I used "interval" to describe the frequency being divided up, while using "target ratio" to describe the desired target number. In this I was taking the 1978 article "A Theory of Equal-Tempered Scales", by Kees van Prooijen as a precedent.

BTW, I just released a new piece yesterday called "Tritium Tea" which is composed in three different tritave equal temperaments. You can find it on my website at http://bwong.ca

Well, what it does is find the closest match to a particular ratio in any equal temperament tuning. For example, to find the closest match to an octave in the Bohlen-Pierce 13 tone equal temperament, you would enter an interval of 3, divisions of 13, and a target of 2, then hit run. After a couple of seconds it will return the closest match (1.96613) and a variance value (0.033866). This type of tool would be useful in analyzing new equal temperament tunings, and is inspired by the work described by Wendy Carlos in development of the Alpha, Beta, and Gamma tunings.

I used [pulse] as a way to get it to run through the operations the appropriate number of times for the tuning (ie 13 times maximum for BP13TET), and [counter] to help keep track of finding the closest match below and above the target ratio. It is probably more convoluted than it needs to be; keep in mind this is my first pd patch.

I don't doubt that a simpler and cleaner solution could be found and would be certainly be interested to see any improvements more experienced pd users can come up with. Expansion to deal with multiple target ratios would obviously be useful.