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Message: 8886 Date: Tue, 30 Dec 2003 08:56:52 Subject: Re: Meantone reduced blocks From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote: > It would be nice to classify 12-note, 5-limit Fokker blocks at least > up to meantone reduction. While pondering that, I thought I'd see how > an example which does not reduce to Meantone[12] worked out. > > The "thirds" scale, the genus derived from 6/5 and 5/4, can be > analyzed as a Fokker block using the method I've given as > > thirds[i] = (25/24)^i (128/125)^round(i/3) (648/625)^round(i/4+1/8) > > In meantone, 25/24 maps to 7, and 128/125 and 648/625 to -12. > > The > meatone reduction therefore is > > 7i - 12(round(i/3) + round(i/4+1/8)) Please express this meantone scale in conventional letter-name-and- accidental notation.
Message: 8887 Date: Tue, 30 Dec 2003 16:54:18 Subject: Re: 5-limit, 12-note Fokker blocks (attn Manuel) From: Manuel Op de Coul I've paid attention. It will be a useful addition, so I've put it on the todo list. Manuel ________________________________________________________________________ ________________________________________________________________________ ------------------------------------------------------------------------ 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: 8889 Date: Wed, 31 Dec 2003 22:52:19 Subject: Re: The Two Diadie Scales From: Carl Lumma >The two scales using the DIAschisma and the DIEsis of 128/125 are >both known, and this seems like a Carl Lumma speciality. They don't >reduce to Meantone[12], but 22-et, pajara or orwell seem more to the >point. Reduction by 22-et or pajara leads to Pajara[12], but >reduction by orwell leads to two interesting new scales. Or at least >one is new, reducing the first diadie scale gives us something quite >close to lumma.scl, which Carl presented back in 1999. I did a non-thorough by-hand search for 12-tone 5- and 7-limit 'Fokker blocks' (before I knew the term, and before the subject had been explored by the list -- I certainly wasn't checking for epimorphism or monotonicity). Some of this was done before I joined the list, on paper with the rectangular lattices I'd learned about from Doty's JI Primer. -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: 8895 Date: Thu, 01 Jan 2004 20:54:55 Subject: Re: The Two Diadie Scales From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote: > Let me start out by saying that 81/80 with either the schisma or the > pythagorean commas (or those two taken together) give us the 12- note > Pythagorean scale, and that this completes the classification for > scales using 81/80, unless you want to go past 0.75 in epimericity. > > The two scales using the DIAschisma and the DIEsis of 128/125 are > both known, and this seems like a Carl Lumma speciality. They don't > reduce to Meantone[12], but 22-et, pajara or orwell seem more to the > point. Reduction by 22-et or pajara leads to Pajara[12], Gene -- you keep saying Pajara but don't you mean Diaschismic?
Message: 8898 Date: Thu, 01 Jan 2004 21:20:33 Subject: Re: The Two Diadie Scales From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote: > --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> > wrote: > > > > The two scales using the DIAschisma and the DIEsis of 128/125 are > > > both known, and this seems like a Carl Lumma speciality. They > don't > > > reduce to Meantone[12], but 22-et, pajara or orwell seem more to > > the > > > point. Reduction by 22-et or pajara leads to Pajara[12], > > > > Gene -- you keep saying Pajara but don't you mean Diaschismic? > > I'm assuming that in 22-equal, it is more correctly called Pajara. No, Pajara is simply the 7-limit extension of Diaschsimic that you do get in 22-equal (and pretty much in no other ET): GX Networks * As long as you're talking 5-limit though, there's no reason to bring Pajara into it.
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