et approximations

Hi Dan,

<<
I'm curious as to how your generating your ET to ratio examples. It would
appear to be something on the order of rendering a given sequence of cents
in the smallest possible ratio representations...[?] What's the
process/method?
>>

I wrote the program back in the summer of 95 using Masm 6, and I didn't stop
to put in comments, so the source is not that easy to read, but I did find
the source code, and I would be happy to mail that and the executable to
anyone who is interested.

Also, I was able to find my explanation of the program in a message I posted
to the list back then:

<<
I have written a program to derive a JI scale that approximates
an ET scale.

I used the following algorithm.

The et scale is expressed in ratios of 12 decimal digit integers.
A series of fractional approximations is derived for each
interval in the scale using multiplication inverses. The first
approximations in this series is the most accurate, and the last
is the least accurate.

Typically, the least accurate approximation will be the same for
several intervals of the scale.

The program checks the least accurate approximations for every
note of the scale. If that approximation is used for only one
note, that approximation is assigned to that note. If it is not
unique, it is assigned to the note that it best represents.

The program then repeats the procedure for the next more
accurate level of approximation until all notes have been
assigned approximations.
>>

Thanks for your interest,

Marion