This is an Opt In Archive . We would like to hear from you if you want your posts included. For the contact address see About this archive. All posts are copyright (c).
Contents Hide Contents S 109000 9050 9100 9150 9200 9250 9300 9350 9400 9450 9500 9550 9600 9650 9700 9750 9800 9850 9900 9950
9850 - 9875 -
Message: 9854 Date: Fri, 06 Feb 2004 08:10:20 Subject: Re: 126 7-limit linears From: Dave Keenan --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote: > 1 [0, 0, 2, 0, 3, 5] 662.236987 77.285947 2.153690 > 2 [1, 1, 0, -1, -3, -3] 806.955502 64.326132 2.467788 > 3 [0, 0, 3, 0, 5, 7] 829.171704 30.152577 3.266201 ... Thanks for the list. I can certainly get it into a spreadsheet and plot it easily, but I have no idea what I'm plotting. I assume the last two columns are error and complexity but I have no idea which is which. Also, I'm not yet up to speed on reading wedgies directly so I have no idea of the identity of the temperaments. Can we please have generators or mappings or comma pairs, if not names (where they exist)? I suppose you figure it was difficult to generate so it should be difficult to interpret as well. ;-)
Message: 9864 Date: Sun, 08 Feb 2004 20:04:48 Subject: Re: Some warped egresses From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx Herman Miller <hmiller@I...> wrote: > I think I've found a couple of good JI approximations for retuning > _Egress_. The first one is a nice symmetrical looking one with lots of > consonances, which looks like it'd work nicely with any of the > pelog-type approximations, and would also work as 14 consecutive steps > of meantone, Fb-B. > > 404 Not Found * Search for http://www.io.com/~hmiller/midi/egress/egress-jimajor.mid in Wayback Machine > > 0 0 0 0 0 ! Bb 5/4 -2 0 1 0 > 1 -2 1 -1 1 ! B > 2 4 -1 -1 0 ! Cb > 3 2 0 -2 1 ! C 7/5 0 0 -1 1 Ab Eb Bb > 4 1 1 -1 0 ! Db 3/2 -1 1 0 0 > 5 3 -2 -1 1 ! D D A E B > 6 2 -1 0 0 ! Eb Fb Cb Gb Db > 7 0 0 -1 1 ! E 7/4 -2 0 0 1 > 8 6 -2 -1 0 ! Fb F C G > 9 4 -1 -2 1 ! F > 10 3 0 -1 0 ! Gb 1/1 1 0 0 0 > 11 1 1 -2 1 ! G > 12 4 -2 0 0 ! Ab > 13 2 -1 -1 1 ! A 7/6 -1 -1 0 1 > 14 1 0 0 0 ! Bb 5/4 -2 0 1 0 > > Does anyone know of any better 14-note block of JI that might be useful > for this purpose? Maybe not, but I did post one or two 14-note blocks once -- they're in Scala. I would search the tuning list for "What's your favorite number?", but it seems the yahoogroups search engine has suddenly become near-useless as it only searches a very small number of posts at a time.
Message: 9865 Date: Sun, 08 Feb 2004 08:50:19 Subject: 23 "pro-moated" 7-limit linear temps, L_1 complex.(was: Re: 126 7-limit linears) From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote: > --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote: > > Since there's a huge empty gap between complexity ~25+ and ~31, I was > > forced to look for a lower-complexity moat (probably a good thing > > anyway). I'll upload a graph showing the temperaments indicated by > > their ranking according to error/8.125 + complexity/25, since I saw a > > reasonable linear moat where this measure equals 1. Twenty > > temperaments make it in: > > Given that we normally relate error and complexity multiplicitively, normally . . . > I > think using log(err) and log(complexity) makes far more sense. I don't think they make more sense practically. > Can you > justify using them additively? Yes, or else some small power of them. Dave and I discussed this in depth. He initially proposed a*error^2 + b*complexity^2, partly because the local minima of harmonic entropy are parabolic.
Message: 9866 Date: Sun, 08 Feb 2004 12:11:14 Subject: Re: Some warped egresses From: Carl Lumma >Maybe not, but I did post one or two 14-note blocks once -- they're >in Scala. I would search the tuning list for "What's your favorite >number?", but it seems the yahoogroups search engine has suddenly >become near-useless as it only searches a very small number of posts >at a time. Also I remember it not enforcing "". I don't find any tuning stuff with this on google. -C.
Message: 9867 Date: Sun, 08 Feb 2004 08:52:11 Subject: Re: Comma reduction? From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Paul G Hjelmstad" <paul.hjelmstad@u...> wrote: > --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> > wrote: > > --- In tuning-math@xxxxxxxxxxx.xxxx "Paul G Hjelmstad" > > <paul.hjelmstad@u...> wrote: > > > --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> > > > wrote: > > > > --- In tuning-math@xxxxxxxxxxx.xxxx "Paul G Hjelmstad" > > > > <paul.hjelmstad@u...> wrote: > > > > > --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" > > > > <gwsmith@s...> > > > > > wrote: > > > > > > --- In tuning-math@xxxxxxxxxxx.xxxx "Paul G Hjelmstad" > > > > > > <paul.hjelmstad@u...> wrote: > > > > > > > > > > > > > Thanks. Are they called 2-val and 2-monzo because they > > > > > are "linear" > > > > > > > or is there some other reason? > > > > > > > > > > > > 2-vals are two vals wedged, 2-monzos are two monzos wedged. > > The > > > > > former > > > > > > is linear unless it reduces to the zero wedgie, the latter > is > > > > linear > > > > > > only in the 7-limit. > > > > > > > > > > Thanks! So the latter is linear in the 7-limit because the 7- > > > limit > > > > is > > > > > formed from two commas...I see. > > > > > > > > The 7-limit is 4-dimensional, so if you temper out 2 commas > > you're > > > > left with a 2-dimensional system, which is what we usually > refer > > to > > > > as "linear". Is that what you meant? > > > > > > Yes, I guess so. Why does tempering out two commas in a 4- > > dimensional > > > system leave a 2-dimensional system? > > > > Roughly: the two commas in addition to two other basis vectors will > > span the 4-dimensional system (only if the four vectors are > linearly > > independent). If you temper out the two commas, the remaining two > > basis vectors will form a basis for the entire resulting system of > > pitches, which we therefore regard as two-dimensional. > > Got it. How does one find the "remaining two basis vectors?" Is it > with Graham's matrix method? I suppose, or with Gene's algorithm, in which he uses Hermite reduction.
Message: 9870 Date: Sun, 08 Feb 2004 08:55:36 Subject: Re: Basis change for monzos, vals and wedgies From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote: > For whatever insight it may bring, here is an example. Suppose instead > of 2,3,5,7 as a basis for 7-limit, we use 27/25, 21/20, 2401/2400 and > 4375/4374. Paul Hj., this would interest you. Then the corresponding basis for vals is > <19 13 19 24|, <0 2 3 2|, <-1 -2 -3 -3| and <4 6 9 11|. The > definitions for bimonzo, bival and compliment Why, thank you :) > are the same, giving a > new basis there as well. We have > > 441-et: <49 31 0 0| > 612-et: <68 43 0 0| > > ennealimmal: <<1 0 0 0 0 0|| > > This can aslo be computed from > > 2401/2400: |0 0 1 0> > 4375/4374: |0 0 0 1> > > For miracle, we have > > 225/224: |-5 8 -2 -1> > 1029/1024: |-5 8 -1 -1> > > miracle: <<1 0 8 0 5 0|| > > We could also have used, for instance > > 72-et: <8 5 0 0| > 175-et: <19 12 0 1| > > I'm fond of 12-et in this system: > > 12-et: <1 1 1 1| ________________________________________________________________________ ________________________________________________________________________ ------------------------------------------------------------------------ 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: 9872 Date: Sun, 08 Feb 2004 20:30:18 Subject: Re: Jamesbond in 14-et From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote: > The jamesbond temperament, from the 007 in the wedgie <0 0 7 0 11 16|, > has TM basis {25/24, 81/80}. If you look at the TOP tuning of its > generator pair, you find one generator is almost exacly twice another; > this strongly suggests we may effectively identify jamesbond with an > et--but what et? Did you see the horagram I posted?
Message: 9874 Date: Sun, 08 Feb 2004 20:33:28 Subject: 23 "pro-moated" 7-limit linear temps, L_1 complex.(was: Re: 126 7-limit linears) From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote: > --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote: > > > > I > > > think using log(err) and log(complexity) makes far more sense. > > > > I don't think they make more sense practically. > > I think they probably will make more sense both practically and > theoretically, As I see it, no way. Example: when you look at the graph with log (err) as one of the axes, the indication is that JI is infinitely far away. This is ridiculous. The JI line should be right there, with some temperaments many times more distant from it than others. Otherwise, you're operating in the realm of hopelessly impractical abstraction. > but you've been ignoring this issue. Are you going to > think about it, at least? Countless hours already spent thinking about it, and discussing it here.
9000 9050 9100 9150 9200 9250 9300 9350 9400 9450 9500 9550 9600 9650 9700 9750 9800 9850 9900 9950
9850 - 9875 -