PURE DATA forum~

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.

I think "interval" might be a confusing word choice here. It probably should be something like "ratio". The octave is a 2:1 ratio, but Bohlen-Pierce is based on the tritave, which is 3:1. Equal temperament just means every interval is equally spaced. So with BP, it's a 3:1 ratio divided into 13 equal steps.

By the way, bwong, I've enjoyed your Csound contributions. Welcome to the world of Pd!

bwong, I was just thinking about this today, and I think this could be made more efficient by running the target through an inverse equation like this:

[expr (log($f1)/log($f2))*$f3]

where $f1 is the target, $f2 is the interval, and $f3 is the divisions. Then you can get the int of the output (you could even do that within the [expr]), run that answer and that answer + 1 through you original pow() equation and compare those two numbers. I don't really have time to patch this together right now, but I think you can get the idea.

The way you are doing it now is kind of a "brute force" approach where you go through every one until you find a match. Doing it the above way would be more like finding a name in a phone book and going straight to the part of the alphabet you're looking for.

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!