Suppose p>5 is prime and q is the next largest prime. For any p-limit linear temperament wedgie, we can project down to a q-limit wedgie by for instance taking...
This gives part of the family tree of the meantone family; I don't go into cousins such as the various 11-limit versions of flattone or dominant sevenths. In...
Here we have a 7-limit system with the same TOP generators as in the 5-limit, and an 11-limit system with nearly identical generators. However, the -41-nexial...
The 5 to 7 limit choice is not as clear as I was thinking, because Number 91 intrudes itself, so I withdraw my objection to keeping "hanson" only as a 5-limit...
... This family stuff looks awesome. I wish I understood the half of it. I'm surprised you're using generator sizes. How do you standardize the generator...
... How do you get a unique set of generators out of the TOP tuning? My miserable notes offer... ... """ ...which makes it sound as if 'tis predicated on mere...
One way to sort out the family relationships is to use a comma scheme which I have intended for some time to discuss, but which I may have neglected to do....
... One way is to apply the TOP tuning to a rational number generator which works as a reduced generator. For instance, with meantone that would be 4/3, with...
... <gwsmith@s...> ... rudimentary. ... the ... (a,b) ... by ... orthogonal ... Hate to be a pain, but I obtain: [(a+4b)/17, (4a+16b)/17, c] Am I missing...
... This immediately appeals to me more than generators. I wonder how it relates to Paul's tratios. They involve the LCM... I wonder what good that is. Also,...
... It's a different reduction--sequential reduction or something. ... This won't work. It doesn't even work if you replace TM reduction with sequential...
... Hmm, I must have the brackets backward on my web page; I have meantone as [1, 4, 10, 4, 13, 12>. I can never remember which way they go. But is there any...
... This is an 11-limit version of orwell that I've been playing with from time to time, although I've mostly been using 7-limit scales recently. You can...
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