source file: mills2.txt
Date: Wed, 24 Jan 1996 07:56:34 -0800

Subject: Re: Manuel Op de Coul's List

From: COUL@ezh.nl (Manuel Op de Coul)

What comes closest to being an encyclopedia of scales is announced 
in this posting of mine of 12 October 1995:

> The scale archive with the collections of John Chalmers and myself
> has been updated and contains now over 1250 scales.
> The scales.doc file contains the complete listing. It's found here:

> http://www.cs.ruu.nl/pub/MIDI/DOC/scales.doc (readme file, ASCII)
> http://www.cs.ruu.nl/pub/MIDI/DOC/scales.zip (ZIP file, binary)

> Use the "-a" option while unzipping. The size of the ZIP file is about
> 284 Kb. FTP is possible also from ftp.cs.ruu.nl.
> The file format of the scales is that of my tuning program Scala,
> which I hope will be available soon. The files are text files so also
> usable without it. 

Later I found some duplicates in the archive but they will be removed in 
a next version.


> >- have a mode-fitting algorithm operate on a given scale and look
> >if it's similar to a mode (of equal temperament) in the list,
> This is a nice idea. I'd be interested
> in the sort of algorithm you use. It
> will somewhat depend on how similar
> "similar" is, of course.

It's fairly simple. It looks for the best approximation for
successively higher equal divisions. Every time the approximation is
better (having a lower least-squares difference) than the previous
ones, it's printed out with the root-mean-square difference given. So
you can decide, looking at that number whether it's similar enough, or
look closer at deviations of individual pitches. The tricky part is
the procedure to "round off" a pitch to an integer number of equal
tempered steps.
I've done a posting about this on 1 September 1994. It has a
description of the algorithm. 

Manuel Op de Coul    coul@ezh.nl

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