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Message: 11005 Date: Wed, 02 Jun 2004 00:50:09 Subject: Re: Family commas From: Carl Lumma >> Also, when you say "given that all the previous commas are >> fixed", does this imply any relation to TM-reduction? > >It's a different reduction--sequential reduction or something. > >> The words that are coming to mind are, temperament n should >> be considered an extension of temperament m if m's TM-reduced >> basis is a subset of n's. Does that make any sense? > >This won't work. It doesn't even work if you replace TM reduction with >sequential reduction, though that is better for this. The nexial >approach does it, however. Noted. >> >> >> 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 representation? Forgive >> >> >> me if this is old stuff, I haven't kept up. >> >> > >> >> >It's just the TOP tuning for the generators. >> >> >> >> How do you get a unique set of generators out of the TOP >> >> tuning? >> > >> >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 miracle 15/14 or 16/15, >> >> This is apparently not giving unique generators... > >Sure it does; miracle(15/14) = [0, 1] = miracle(16/15) Right you are. -Carl ________________________________________________________________________ ________________________________________________________________________ ------------------------------------------------------------------------ Yahoo! Groups Links <*> To visit your group on the web, go to: Yahoo groups: /tuning-math/ * <*> To unsubscribe from this group, send an email to: tuning-math-unsubscribe@xxxxxxxxxxx.xxx <*> Your use of Yahoo! Groups is subject to: Yahoo! Terms of Service *
Message: 11008 Date: Wed, 02 Jun 2004 00:06:58 Subject: Re: Family commas From: Carl Lumma > ... defining a linear temperament in terms of a > sequence of commas, each at a succesively higher prime limit, > and each with a minimal Tenney height given that all the > previous commas are fixed. This sort of whatzit reduction, > for meantone, would say meantone is the 81/80-temperament, > dominant sevenths the [81/80, 36/35] temperament, septimal > meantone the [81/80, 126/125]-temperament, flattone the > [81/80, 525/512]-temperament. Then 11-limit meantone is > the [81/80, 126/125, 385/384]-temperament and huygens the > [81/80, 126/125, 99/98]-temperament. And so forth. 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, when you say "given that all the previous commas are fixed", does this imply any relation to TM-reduction? The words that are coming to mind are, temperament n should be considered an extension of temperament m if m's TM-reduced basis is a subset of n's. Does that make any sense? > It should be noted that while this keeps track of the familial > relationships, we don't necessarily get corresponding > generators in these family trees, nor do we necessarily get > rid of contorsion. 7-limit ennealimmal is the [ennealimma, > breedsma]- temperament, but the wedge product of this has a > common factor of 4. Rats. -Carl
Message: 11009 Date: Wed, 02 Jun 2004 00:16:28 Subject: Re: The hanson family From: Carl Lumma >> >> 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 representation? Forgive >> >> me if this is old stuff, I haven't kept up. >> > >> >It's just the TOP tuning for the generators. >> >> How do you get a unique set of generators out of the TOP >> tuning? > >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 miracle 15/14 or 16/15, This is apparently not giving unique generators... -Carl ________________________________________________________________________ ________________________________________________________________________ ------------------------------------------------------------------------ Yahoo! Groups Links <*> To visit your group on the web, go to: Yahoo groups: /tuning-math/ * <*> To unsubscribe from this group, send an email to: tuning-math-unsubscribe@xxxxxxxxxxx.xxx <*> Your use of Yahoo! Groups is subject to: Yahoo! Terms of Service *
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