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Message: 11076 - Contents - Hide Contents Date: Sat, 19 Jun 2004 17:14:23 Subject: Re: Paul's nifty fifty From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx Herman Miller <hmiller@I...> wrote:> Paul Erlich wrote: >>>>>> [3, 12, -1, 12, -10, -36] supermajor seconds >>>>>>>> Anyone have another suggestion? >>>>>> Trimeantone? (3 generators = a meantone fifth) >>> Or just plain supermajor? >> >>>> If you ignore the 5 axis, this temperament has been referred to >> as "wonder" and "slendric" -- correct? >> For some reason I have <<3, 17, -1, 20, -10, -50]] listedas "Slendric /> Wonder". But actually <<3, 7, -1, 4, -10, -22]] might be a better fit > for the description on Catalogue of linear temperaments * [with cont.] (Wayb.). Any of > these could be "slendric" or "wonder" (it might be useful to assign each > of these names to a different temperament).But both names apply to a system where there is no prime 5. Hola from Espaņa.
Message: 11077 - Contents - Hide Contents Date: Sat, 19 Jun 2004 17:16:04 Subject: Re: Paul's nifty fifty From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote:> --- In tuning-math@xxxxxxxxxxx.xxxx Herman Miller <hmiller@I...> wrote:>> Paul Erlich wrote: >>>>>>>> [3, 12, -1, 12, -10, -36] supermajor seconds >>>>>>>>>> Anyone have another suggestion? >>>>>>>> Trimeantone? (3 generators = a meantone fifth) >>>> Or just plain supermajor? >>> >>>>>> If you ignore the 5 axis, this temperament has been referred to >>> as "wonder" and "slendric" -- correct? >>>> For some reason I have <<3, 17, -1, 20, -10, -50]] listed as > "Slendric />> Wonder". But actually <<3, 7, -1, 4, -10, -22]] might be a better fit >> for the description on Catalogue of linear temperaments * [with cont.] (Wayb.). Any of >> these could be "slendric" or "wonder" (it might be useful to assign > each>> of these names to a different temperament). >> I'd advise keeping the name "wonder" for <<3 17 -1 20 -10 -50||. This > is clearly much more consistent with what Margo had in mind as a > {2,3,7} linear temperament using 1029/1024. Margo is not much of a fan > of flat fifths, for starters, and the tunings are consistent. Graham's > site seems to be unavailable at the moment, but I have no objections > to "slendric" in place of "supermajor seconds", an ugly name even if I > am responsible for it.Unfortunately, if prime 5 is in there, this is even less like slendro than "pelogic" is like pelog. ________________________________________________________________________ ________________________________________________________________________ ------------------------------------------------------------------------ Yahoo! Groups Links <*> To visit your group on the web, go to: Yahoo groups: /tuning-math/ * [with cont.] <*> 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 * [with cont.] (Wayb.)
Message: 11078 - Contents - Hide Contents Date: Sun, 20 Jun 2004 21:24:00 Subject: Re: Atomic projection From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Paul G Hjelmstad" <paul.hjelmstad@m...> wrote:> --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> > wrote:>> We can define what I've called a "notation"--a pair of unimodular >> matries inverse to each other, one of which is a row matrix of > monzos>> and another a column matrix of vals--for atomic in various ways. The >> simplest is >> >> [|-67 35 5>, |-15 8 1>, |161 -84 -12>] >> [<12 19 28|, <0 -1 7|, <5 8 11|] >> * * * * * > "5-limit commas in atomic" checks out beautifully, but "5-limit ets > in atomic" only works for the initial value (number of steps for 2, > or the octave). Is this intentional?I said "vals", not "ets"; all of them are vals.> >>>> While the most common way to project intervals and vals is to toss >> octaves, we can do an atomic projection for ets by tossing result of >> mapping the atom with an et, and an atomic projection for intervals > by>> ignoring the results of the <5 8 11| val. >> * * * * * > Would it be possible to demonstrate these two cases? (tossing the > result of mapping the atom with an et, and 2) ignoring the results of > the <5 8 11| value?If we set semitone = 2^(1/12) and schisma = (648/625)^(1/32), then the atomic projection for intervals leads to a tempering, which is quite different than octave equivalence classes. Nevertheless, formally they look the same--I take the results of applying <12 19 28| and <0 1 -7| and ignore <5 8 11|, which corresponds to ignoring <1 0 0| when we do octave classes. To get the tempering, take semitone^a schisma^b, where a is the result of applying <12 19 28| to the interval, and b is the result of applying <0 1 -7|. The projection for vals works so long as the val sends the atom to zero--as, for instance, 12-et, 612-et, 4296-et. Otherwise the best you can do is an approximation, which gives floating point results which round off, so long as we don't go too far afield, to the correct et value. You can also toss the result of applying the val to an atom, but the results won't make a whole lot of sense. So, for instance, 612 gives the semitone a value of 51 and the schisma a value of 1, so the projected et is <51 1|. By comparison <22/12, 1/20| works, more or less, like 22, but this isn't algebra, it's an approximation which is only valid after rounding and in a restricted sense.
Message: 11079 - Contents - Hide Contents Date: Sun, 20 Jun 2004 21:36:51 Subject: Re: Atomic projection From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote: By comparison <22/12, 1/20| works, more or> less, like 22, but this isn't algebra, it's an approximation which is > only valid after rounding and in a restricted sense.<22/12 1/16| might be better: (22/12)<12 19 28| + (1/16)<0 1 -7| = <22 34.896 50.896| If you round off, it has a limited ability to act like 22; what good this is, if any, is another question.
Message: 11080 - Contents - Hide Contents Date: Sun, 20 Jun 2004 22:03:29 Subject: Re: Atomic projection From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote:> <22/12 1/16| might be better: > > (22/12)<12 19 28| + (1/16)<0 1 -7| = <22 34.896 50.896| > > If you round off, it has a limited ability to act like 22; what good > this is, if any, is another question.There's another approach, which would work in any practical case, which is to lift the atomic projection back to the 5-limit first. This becomes easier to do the more accurate the temperament, since the lifting involves finding the preimage value with the least height. In the case of atomic, for any reasonable situation there will be only one lifted value which makes sense, because the numerator and denominator of the atom is so large. For instance, 27/25 is |1 17> in terms of the atomic projection, meaning one semitone of st = |-65 35 5> and 17 schismas (32805/32768.) If we look at st * schisma^17 * atom^i for various i, only i=2 leads to a value which does not have huge numerators and denominators, so we lift |1 17> easily to 27/25. We can likewise lift anything with numerators and denominators less than 48 digits by this means. Once lifted, of course, we can do anything we like with it, such as find out its value in 22-equal. For less accurate temperaments, or higher limit temperaments, this will of course not work in quite this strong a way. For instance ennealimmal, with commas of 2401/2400 and 4375/4374, can lift products of (27/25)^a (21/20)^b to the 7-limit so long as the numerator and denominator are three digits or less.
Message: 11084 - Contents - Hide Contents Date: Thu, 24 Jun 2004 19:49:25 Subject: Re: File missing From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Paul G Hjelmstad" <paul.hjelmstad@m...> wrote:> All, > > Does anyone know what happened to the nifty file listing all the > commas? (Including "Atom of Kirkenburger")? > > Paul Hi Paul,I think it's still fine: Sign In - * [with cont.] (Wayb.) method=reportRows&tbl=10&sortBy=3 -the other paul
Message: 11085 - Contents - Hide Contents Date: Thu, 24 Jun 2004 21:13:53 Subject: Re: Paul's nifty fifty From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote:> Here is what I am suggesting for names for Paul's list of 50 > temperaments. Septischismic in place of schismic, augie in the place > of augmented, and erethezontic in the place of biporky have been > discussed. Minorsemi from the approximate 21/20 generator, and > duodecal because like waage it's got 12 on the brain. > > In the 5-limit, the names minorsemi and tertiatonic come from the > discussion of 12-note 5-limit Fokker blocks around tuning-math 8300 to > 8400. Superpythagorean corresponds to the 7-limit name, and corrects a > typo for the comma. > > [6, 5, 3, -6, -12, -7] kleismic > [10, 9, 7, -9, -17, -9] nonkleismicI'm very unenthusiastic about these names.
Message: 11086 - Contents - Hide Contents Date: Thu, 24 Jun 2004 21:28:28 Subject: Re: Paul's nifty fifty From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:>> [6, 5, 3, -6, -12, -7] kleismic >> [10, 9, 7, -9, -17, -9] nonkleismic >> I'm very unenthusiastic about these names.How about some alternatives?
Message: 11087 - Contents - Hide Contents Date: Thu, 24 Jun 2004 21:42:25 Subject: Re: Paul's nifty fifty From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote:> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote: >>>> [6, 5, 3, -6, -12, -7] kleismic >>> [10, 9, 7, -9, -17, -9] nonkleismic >>>> I'm very unenthusiastic about these names. >> How about some alternatives?The field of drosophila genetics makes use, in addition to porcupine and hedgehog, of the terms armadillo and pangolin. Perhaps these could be called into service?
Message: 11089 - Contents - Hide Contents
Date: Thu, 24 Jun 2004 23:45:50
Subject: The tertiaseptal family
From: Gene Ward Smith
If we do a search for {2,5,7}-commas of size less than 50 cents and
epimericity less than 0.6, the complete list seems to be 128/125,
50/49, 3136/3125, 2100875/2097152; all of which except for the last
are quite familiar. I've mentioned it on occasion, but this is may be
the first close look anyone has given.
The {2,5,7} linear temperament has generator an approximate 256/245,
three of which make up a septimal tone of 8/7, this relationship
defining the comma. Among the DE scales are 15, 16, and 31 notes.
The 7-limit temperament with TM basis 2401/2400 and 65625/65536 has
essentially the same TOP generator of 77.2 cents, and I propose naming
both the {2,5,7} temperament and its extension to the 7-limit by the
name "tertiaseptal", meaning the generator is 1/3 of a septimal tone
of 8/7. Now would be a good time to suggest a better name.
Tertiaseptal is an excellent high-complexity temperament, especially
if we stick to the 7 odd limit and forgo 9, which 171-et does a good
job for.
If we have a {2,5,7} linear temperament, we can do something like the
nexial business, except that we use <<a2 0 0 -a5 -a7 0|| where
<a2 a5 a7| is a {2,5,7}-val belonging to the comma. Using this
definition of family relationship, we find valentine belongs to the
same family:
{2,5,7}-comma tertiaseptal 2100875/2097152
[1200.073, 77.200]
7-limit family
0: <<22 -5 3 -59 -57 21|| tertiaseptal {2401/2400, 65625/65536}
[1200.074, 77.199]
-16: <<6 -5 3 -22 -12 21|| {49/48, 3584/3375}
[1198.126, 80.798]
-31: <<9 5 -3 -13 -30 -21|| valentine {126/125, 1029/1024}
[1199.793, 77.833]
Message: 11090 - Contents - Hide Contents Date: Thu, 24 Jun 2004 23:51:08 Subject: Re: Paul's nifty fifty From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:> --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> > wrote:>> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> > wrote: >>>>>> [6, 5, 3, -6, -12, -7] kleismic >>>> [10, 9, 7, -9, -17, -9] nonkleismic >>>>>> I'm very unenthusiastic about these names. >>>> How about some alternatives? >> The field of drosophila genetics makes use, in addition to porcupine > and hedgehog, of the terms armadillo and pangolin. Perhaps these > could be called into service?I've heard they give weird names to friutfly genes, such as "fruitless" for the gene which makes male fruitflies gay (and no, I am not making that up.) Are these examples? How about "armadillo" in place of "kleismic", and "pangolin" in place of "nonkleismic"?
Message: 11091 - Contents - Hide Contents Date: Thu, 24 Jun 2004 23:55:28 Subject: Re: Paul's nifty fifty From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote:> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:>> --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> >> wrote:>>> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> >> wrote: >>>>>>>> [6, 5, 3, -6, -12, -7] kleismic >>>>> [10, 9, 7, -9, -17, -9] nonkleismic >>>>>>>> I'm very unenthusiastic about these names. >>>>>> How about some alternatives? >>>> The field of drosophila genetics makes use, in addition to porcupine >> and hedgehog, of the terms armadillo and pangolin. Perhaps these >> could be called into service? >> I've heard they give weird names to friutfly genes, such as > "fruitless" for the gene which makes male fruitflies gay (and no, I am > not making that up.) Are these examples? Yes. > How about "armadillo" in place of "kleismic", and "pangolin" in place > of "nonkleismic"?Fine. Anyone have a problem with this? Only a few days left.
Message: 11092 - Contents - Hide Contents Date: Thu, 24 Jun 2004 21:50:40 Subject: Re: Paul's nifty fifty From: Herman Miller Paul Erlich wrote:>> How about "armadillo" in place of "kleismic", and "pangolin" in > > place > >> of "nonkleismic"? > >> Fine. Anyone have a problem with this? Only a few days left.If 5-limit kleismic is "hanson", what about "keenan" for what we've been calling 7-limit kleismic, <<6, 5, 3, -6, -12, -7]]? (Larry Hanson's paper implies a "catakleismic" 7-limit mapping, <<6, 5, 22, -6, 18, 37]]: see http://www.anaphoria.com/hanson.PDF - Type Ok * [with cont.] (Wayb.), fig. 12, which implies a mapping of [0, 6, 5, 22], while on the other hand Dave Keenan's page at 11 note chain-of-minor-thirds scale * [with cont.] (Wayb.) implies a [0, 6, 5, 3] mapping.) Admittedly, "nonkleismic" isn't a very good name, especially for something that extends to a (theoretically) good 11-limit and even a reasonably good 13-limit version. <<10, 9, 7, 25, -9, -17, 5, -9, 27, 46]] <<10, 9, 7, 25, -5, -9, -17, 5, -45, -9, 27, -45, 46, -40, -110]] So something like that deserves a pretty unique and memorable name, and a pangolin is a pretty unique and memorable sort of animal.
Message: 11093 - Contents - Hide Contents Date: Fri, 25 Jun 2004 22:41:53 Subject: Re: The Keyboard Temperament of J. S. Bach From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Charles" <Francis@d...> wrote:> For those interested in this topic, new findings are available at: > J.S. Bach Tuning * [with cont.] (Wayb.) > > > Regards > CharlesI find these conclusions insupportable. That C-A would be a Pythagorean major sixth (27:16), while A-F# would be just (5:3) or near-just major sixths, goes against the key-gradation pattern that all well-temperaments of the time exhibit. C-A and G-E are the major sixths closest to just (or very nearly so) in all of them, since they occur most frequently in the keys with the fewest accidentals in their key signatures. But this topic is better for the tuning list, not this list.
Message: 11094 - Contents - Hide Contents Date: Fri, 25 Jun 2004 22:57:16 Subject: Re: Paul's nifty fifty From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote:> [1, -8, -14, -15, -25, -10] septischismic?Continuing on our kick of naming after people, I might call this Garibaldi, since Eduardo Sabat-Garibaldi gave names to 5120/5103 ("Beta 5") and 33554432/33480783 ("Beta 2") in his study which yielded the 1/9-schisma, pure-octave version of this temperament. 4000/3969, though, may have escaped his attention (at least Manuel doesn't list any other "Beta"s, or any name for 4000/3969 at all).> 32805/32768 schismicAnd this would be Helmholtz (I've seen it referred to as Helmholtzian temperament in the past, though of course it's Groven's too).
Message: 11095 - Contents - Hide Contents Date: Fri, 25 Jun 2004 20:55:21 Subject: Re: Paul's nifty fifty From: Herman Miller Paul Erlich wrote:> --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> > wrote: > >>> [1, -8, -14, -15, -25, -10] septischismic? > >> Continuing on our kick of naming after people, I might call this > Garibaldi, since Eduardo Sabat-Garibaldi gave names to 5120/5103 > ("Beta 5") and 33554432/33480783 ("Beta 2") in his study which > yielded the 1/9-schisma, pure-octave version of this temperament. > 4000/3969, though, may have escaped his attention (at least Manuel > doesn't list any other "Beta"s, or any name for 4000/3969 at all). >That also fits the trend of animal names, since a garibaldi is a kind of fish (Hypsypops rubicundus). But is anything wrong with plain "schismic" for this one?
Message: 11096 - Contents - Hide Contents Date: Fri, 25 Jun 2004 21:33:51 Subject: Re: Names for important high-complexity temperaments From: Herman Miller Gene Ward Smith wrote:> While we are on the subject of names, a less urgent question which now > would nevertheless be a good time to bring up is what people think of > the names I've hung on some important temperaments over Paul's cutoff. > > <<22 -5 3 -59 -57 21|| tertiaseptal > > <<16 2 5 -34 -37 6|| hemiwuerschmidt > > <<2 25 13 35 15 -40|| hemififths > > <<5 13 -17 9 -41 -76|| amity > > <<40 22 21 -58 -79 -13|| tritonic? > > <<4 -32 -15 -60 -35 55|| sesquiquartififths? > > The name "tritonic" I'm suggesting since 7/5 is a poptimal generator > (though not, as one might have guessed, because it is minimax.) > Sesquiqartififths is not a very elegant name, but (3/2)^(1/4) is a > poptimal generator for this temperament. Sesquiquarschismic or > something of that sort might be another approach. Or we could be to go > the zoo and pick an animal.I think it could make a certain amout of sense to use "hemi-" for related temperaments with half-size generators (hemiwuerschmidt actually contains wuerschmidt in the same way as hemikleismic contains kleismic and superpelog contains mavila, so superpelog might be "hemimavila"). "Amity" is familiar by now and I can't think of anything better. Is "tritonic" a better name for <<40, 22, 21, -58, -79, -13]] than for <<5, -11, -12, -29, -33, 3]] ? <<4, -32, -15, -60, -35, 55]] came up in my 11-limit temperament search as <<4, -32, -15, 10, -60, -35, 2, 55, 134, 80]]. It has some resemblance to vulture without being related, so I'll suggest "buzzard". Specifically, they both have 48-note MOS scales, the step size ratio is fairly similar (around 2.6 - 2.7 between large and small steps), and the generator of vulture is the fourth root of 3/1 (compared to the fourth root of 3/2).
Message: 11097 - Contents - Hide Contents Date: Fri, 25 Jun 2004 20:51:57 Subject: Re: Paul's nifty fifty From: Herman Miller Paul Erlich wrote:> --- In tuning-math@xxxxxxxxxxx.xxxx Herman Miller <hmiller@I...> > wrote: >>> a pangolin is a pretty unique and memorable sort of animal. > >> Well, it's related to an armadillo, so it might be nice to use the > two names for related temperaments. Let's see . . .Similar, but not closely related (armadillos are related to sloths). Still, it would be nice to use the name "armadillo" for something. It would be even better if there was something related to the number 9 in the temperament, since one of the more common kinds of armadillo is a nine-banded armadillo.
Message: 11098 - Contents - Hide Contents Date: Fri, 25 Jun 2004 00:06:22 Subject: Re: Paul's nifty fifty From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:> Fine. Anyone have a problem with this? Only a few days left.Yipe! Don't we get to see your draft before you submit it?
Message: 11099 - Contents - Hide Contents Date: Fri, 25 Jun 2004 22:39:44 Subject: Re: Paul's nifty fifty From: Herman Miller Herman Miller wrote:> Paul Erlich wrote: >>> --- In tuning-math@xxxxxxxxxxx.xxxx Herman Miller <hmiller@I...> >> wrote: >> >>>>> a pangolin is a pretty unique and memorable sort of animal. >> >>>> Well, it's related to an armadillo, so it might be nice to use the >> two names for related temperaments. Let's see . . . > >> Similar, but not closely related (armadillos are related to sloths). > Still, it would be nice to use the name "armadillo" for something. It > would be even better if there was something related to the number 9 in > the temperament, since one of the more common kinds of armadillo is a > nine-banded armadillo.I just realized that nonkleismic is a starling temperament (126/125). So maybe a bird-related name would be better. Myna? <<3, 5, 9, 1, 6, 7]] is also a starling temperament.
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