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Dan's formula

🔗Carl Lumma <clumma@xxx.xxxx>

2/18/1999 8:00:48 AM

>It seems more useful to me to know: For a given d-tET, and a given (prime
or >odd) limit for the ratios, what is the maximum error in the most
accurate >*consistent* set of mappings of n steps to ratios? My charts at
>http://dkeenan.com/Music/OpenTunings.htm answer this for many
>important cases.

Thanks, Dave Keenan, for your work on this thread. Dan's formula is very
interesting, and your charts are very handy. I had never noticed how
viable 37tET was a 7-limit...

You and Dan are both prime candidates for Scala. It will approximate any
scale with ratios, and you can restrict the ratios it returns by prime
limit and/or a number of other weighting schemes. Scala will also find ET
approximations to rational scales to an arbitrary degree of accuracy.

Carl