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Message: 11050 - Contents - Hide Contents Date: Sat, 12 Jun 2004 02:12:40 Subject: Re: The diaschismic family From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote:> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote: >>> Well enough, but please take a step back, Gene. Herman was starting >> with 7-limit shrutar, and trying to construct 11-limit shrutar from >> it. But the tuning was originally defined as an 11-limit one, and >> that's what I was asking about. Instead of an answer, we're going >> around in circles. All I remember for sure is that 896/891 and >> 2048/2025 vanish. >> It's h46/\h22 =<<4 -8 14 -2 -22 11 -17 55 23 -54||, and 896/891 and > 2048/2025 do indeed vanish, though the TM basis is actually > {121/120, 176/175, 245/243}.Oh, so it's not considered part of the diaschismic family because its generator is only half the diaschismic one (yes?) . . .
Message: 11051 - Contents - Hide Contents Date: Sat, 12 Jun 2004 02:21:40 Subject: Re: Family commas 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: >>>>> How is it possible to get contorsion from commas? I don't think > it is. >>>> Interpreting the GCD > 1 to mean contorsion rather than torsion > seems>> to make the most sense if you are considering it as representing a >> temperament. You get torsion out of 648/625 and 2048/2025, but you >> could also count it as contorsion by taking the <24 38 56| val >> literally, as 24-equal, being contorted 12-equal, so that the > mapping>> of the 5-limit is not surjective. >> Yes, exactly! But this is not coming from commas, it's coming from a > val!!And I got the val from the commas.>>>> Hemiennealimmal is >>>> then the [ennealimma, breedsma, lehmerisma]-temperament, again > with >>> a>>>> common factor of 4, but now with non-corresponding generators. >>>>>> Don't know what "non-corresponding" means. >>>> They are not approxmiately the same, nor are they mapped from the > same >> JI intervals. >> Hmm . . . can you elaborate on this with more detail, please?Ennealimmal has TOP generators [133.337, 49.024], which correspond to 27/25 and 36/35. Hemiennealimmal has TOP generators [66.669, 17.645], which obviously differ, though 66.669-17.645 = 49.024, which we are free to use for the second generator. The first generator, however, is obviously not an approximate 27/25; we may now take the generators as approximations of 80/77 and 99/98.
Message: 11052 - Contents - Hide Contents Date: Sat, 12 Jun 2004 02:32:10 Subject: Re: Family commas 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: >>>>>>> How is it possible to get contorsion from commas? I don't think >> it is. >>>>>> Interpreting the GCD > 1 to mean contorsion rather than torsion >> seems>>> to make the most sense if you are considering it as representing a >>> temperament. You get torsion out of 648/625 and 2048/2025, but you >>> could also count it as contorsion by taking the <24 38 56| val >>> literally, as 24-equal, being contorted 12-equal, so that the >> mapping>>> of the 5-limit is not surjective. >>>> Yes, exactly! But this is not coming from commas, it's coming from a >> val!! >> And I got the val from the commas.But if you go directly from the commas, it's unequivocally torsion and not contorsion. Remember, soon after your joining, that Fokker periodicity block, that you initially said represented 24-equal, but then you retracted that and said it was really 12-equal with torsion?
Message: 11053 - Contents - Hide Contents Date: Sat, 12 Jun 2004 05:45:27 Subject: 41 "Hermanic" 7-limit linear temperaments (was: Re: 114 7-limit temperaments) From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:>>>>> Number 10 Tripletone >>>>> >>>>> [3, 0, -6, -7, -18, -14] [[3, 5, 7, 8], [0, -1, 0, 2]] >>>>> TOP tuning [1197.060039, 1902.640406, 2793.140092, > 3377.079420]>>>>> TOP generators [399.0200131, 92.45965769] >>>>> bad: 8.4214 comp: 4.045351 err: 2.939961 >>>> I'm suggesting calling this "augmented", since the TOP generators > are>> close to 5-limit augmented. >> Makes some sense, but somewhere out there there's something even > closer -- an infinite number of somethings, I think.Only at the cost of ever-increasing complexity. If we cap badness to something reasonable, we get only a few possibilities, or sometimes only one. However, here both "augie" and "tripletone" are live possibilities. It can be even worse than you might think in a sense, since more than one temperament can have the same TOP generators. Consider the following three versions of meantone: <<1 4 10 4 13 12|| [<1 2 4 7|, <0 -1 -4 -10|] <<1 4 41 4 62 84|| [<1 2 4 20|, <0 -1 -4 -41|] <<1 4 -164 4 -262 -292|| [<1 2 4 -66|, <0 -1 -4 164|] All have the same TOP tuning, but it is clear which one we prefer.> >>>> IN >>>>> Number 16 >>>>>>>>>> [6, 10, 10, 2, -1, -5] [[2, 4, 6, 7], [0, -3, -5, -5]] >>>>> TOP tuning [1196.893422, 1906.838962, 2779.100462, > 3377.547174]>>>>> TOP generators [598.4467109, 162.3159606] >>>>> bad: 8.9422 comp: 4.306766 err: 3.106578 >>>> This one needs a name. The TM basis is {50/49, 245/243}. > Erethezontic? >> Where does that come from? We were calling this "Biporky", but of > course we'd like something better.It's from the name for the porcupine family, Erethizontidae. Don't know if it is better.>>>> IN >>>>> Number 29 >>>>>>>>>> [8, 6, 6, -9, -13, -3] [[2, 5, 6, 7], [0, -4, -3, -3]] >>>>> TOP tuning [1198.553882, 1907.135354, 2778.724633, > 3378.001574]>>>>> TOP generators [599.2769413, 272.3123381] >>>>> bad: 10.1077 comp: 5.047438 err: 3.268439 >> >> Doublewide. >> Sure -- but why? Wide what?The generator is a rather sharp (over 7.5 cents) 7/6.
Message: 11054 - Contents - Hide Contents Date: Sat, 12 Jun 2004 05:48:52 Subject: Re: The diaschismic family From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:>> It's h46/\h22 =<<4 -8 14 -2 -22 11 -17 55 23 -54||, and 896/891 and >> 2048/2025 do indeed vanish, though the TM basis is actually >> {121/120, 176/175, 245/243}. >> Oh, so it's not considered part of the diaschismic family because its > generator is only half the diaschismic one (yes?) . . .In the strict sense I was using for "family", but there is a broader sense based on the 5-limit--7-limit--11-limit etc comma family tree structure. It still has 2048/2025 as its 5-limit comma.
Message: 11055 - Contents - Hide Contents Date: Sat, 12 Jun 2004 05:53:19 Subject: Re: Family commas From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:> But if you go directly from the commas, it's unequivocally torsion > and not contorsion. Remember, soon after your joining, that Fokker > periodicity block, that you initially said represented 24-equal, but > then you retracted that and said it was really 12-equal with torsion?Which is why I picked this example. If we are thinking Fokker blocks, it is torsion; however why do we have to be thinking Fokker blocks? Admittedly, the contorsion interpretation may be a little articifical, but there's nothing else for it to be, basically. ________________________________________________________________________ ________________________________________________________________________ ------------------------------------------------------------------------ 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: 11056 - Contents - Hide Contents
Date: Sun, 13 Jun 2004 07:34:10
Subject: The unison family
From: Gene Ward Smith
The null or unison temperament is the "temperament" which maps
everything to 1; in the 7-limit, it has wedgie <<0 0 0 0 0 0||. If we
take nexial adjustemnts to it, we get temperaments of the DoubleO type:
null+5 <<0 0 5 0 8 12|| DoubleO 5 {16/15, 27/25}
null+7 <<0 0 7 0 11 16|| Jamesbond = DoubleO 7 {25/24, 81/80}
null+12 <<0 0 12 0 19 28|| DoubleO 12 {81/80, 128/125}
null+19 <<0 0 19 0 30 44|| DoubleO 19 {81/80, 3125/3072}
Like other families, if we enforce a badness limit we get only a
finite number of members of the family. The complexity is O(n) and the
error O(n^(-3/2)), so logflat badness is O(sqrt(n)), and we get
finiteness. Nothing beyond DoubleO 19 seems very interesting from a
badness viewpont, despite the steady decrease of error to zero, which
doesn't happen with other families.
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Message: 11057 - Contents - Hide Contents Date: Mon, 14 Jun 2004 00:36:38 Subject: Paul's nifty fifty From: Gene Ward Smith 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. [1, 4, 10, 4, 13, 12] meantone [5, 1, 12, -10, 5, 25] magic [2, -4, -4, -11, -12, 2] pajara [7, 9, 13, -2, 1, 5] semisixths [1, 4, -2, 4, -6, -16] dominant sevenths [2, 8, 8, 8, 7, -4] injera [6, 5, 3, -6, -12, -7] kleismic [2, 8, 1, 8, -4, -20] hemifourths [4, -3, 2, -14, -8, 13] negri [3, 0, -6, -7, -18, -14] augmented [1, -8, -14, -15, -25, -10] septischismic? [1, 9, -2, 12, -6, -30] superpythagorean [7, -3, 8, -21, -7, 27] orwell [3, 0, 6, -7, 1, 14] augie [3, 5, -6, 1, -18, -28] porcupine [6, 10, 10, 2, -1, -5] erethezontic? [3, 12, -1, 12, -10, -36] supermajor seconds [1, 4, -9, 4, -17, -32] flattone [4, 4, 4, -3, -5, -2] diminished [6, 10, 3, 2, -12, -21] minorsemi? [0, 0, 12, 0, 19, 28] duodecal? [3, 12, 11, 12, 9, -8] gawel [10, 9, 7, -9, -17, -9] nonkleismic [6, -7, -2, -25, -20, 15] miracle [2, -9, -4, -19, -12, 16] beatles [6, -2, -2, -17, -20, 1] lemba [8, 6, 6, -9, -13, -3] doublewide [0, 5, 0, 8, 0, -14] blackwood [18, 27, 18, 1, -22, -34] ennealimmal 25/24 dicot 81/80 meantone 128/125 augmented 135/128 pelogic 250/243 porcupine 256/243 blackwood 648/625 diminished 2048/2025 diaschismic 3125/3072 magic 6561/6250 ragisemi 15625/15552 hanson 16875/16384 negri 20000/19683 tetracot 20480/19683 superpythagorean 32805/32768 schismic 78732/78125 semisixths 262144/253125 tertiatonic 393216/390625 wuerschmidt 531441/524288 aristoxenan 1600000/1594323 amity 2109375/2097152 orwell
Message: 11058 - Contents - Hide Contents Date: Mon, 14 Jun 2004 18:55:59 Subject: 41 "Hermanic" 7-limit linear temperaments (was: Re: 114 7-limit temperaments) From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:>> It's from the name for the porcupine family, Erethizontidae. Don't >> know if it is better. >> How about something related to a porcupine, like say "hedgehog"?My name was related to a porcupine, but there's no reason to stick to New World porcupines. Old World porcupines like hedgehogs are *not* related, but I like "hedgehog"; like "porcupine" the name itself is fun. Porcupines have a good reputation as intelligent and friendly, and would make good pets if they did not have quills. I haven't heard that hedgehogs are so interesting personality-wise, and they have no good reputation for intelligence, but they do roll up into a ball, which is cute. Hedgehog it is?
Message: 11060 - Contents - Hide Contents Date: Mon, 14 Jun 2004 19:06:32 Subject: Re: Paul's nifty fifty From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:> If a porcupine is a member of the erethezontic family, wouldn't that > falsely suggest that one temperament is more general than the other?"Hedgehog" seems good.>> Minorsemi from the approximate 21/20 generator, and >> duodecal because like waage it's got 12 on the brain. >> What happened to "catler"?I forgot about it. Is the attribution of this to Catler securely based?>> [2, 8, 1, 8, -4, -20] hemifourths> semifourths, I think. OK. >> 135/128 pelogic > mavila.Is that one "l" or two?>> 6561/6250 ragisemi> A little too wild."Ragisemitonic" seems worse; what about "ragitonic"? See message 8331 for this comma.>> 262144/253125 tertiatonic > meaning?It's another 12-et comma, which I couldn't find a name for when I was considering 12-note Fokker blocks. The name comes from the fact that it is a third of a tone--see Yahoo groups: /tuning-math/message/8338 * [with cont.]>> 393216/390625 wuerschmidt >> 531441/524288 aristoxenan > compton.This is the second time you've wanted to change this one. :)
Message: 11061 - Contents - Hide Contents Date: Mon, 14 Jun 2004 18:00:24 Subject: 41 "Hermanic" 7-limit linear temperaments (was: Re: 114 7-limit temperaments) From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote:> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote: > >>>>>>> Number 10 Tripletone >>>>>> >>>>>> [3, 0, -6, -7, -18, -14] [[3, 5, 7, 8], [0, -1, 0, 2]] >>>>>> TOP tuning [1197.060039, 1902.640406, 2793.140092, >> 3377.079420]>>>>>> TOP generators [399.0200131, 92.45965769] >>>>>> bad: 8.4214 comp: 4.045351 err: 2.939961 >>>>>> I'm suggesting calling this "augmented", since the TOP generators >> are>>> close to 5-limit augmented. >>>> Makes some sense, but somewhere out there there's something even >> closer -- an infinite number of somethings, I think. >> Only at the cost of ever-increasing complexity. If we cap badness to > something reasonable, we get only a few possibilities, or sometimes > only one. However, here both "augie" and "tripletone" are live > possibilities. It can be even worse than you might think in a sense, > since more than one temperament can have the same TOP generators. > Consider the following three versions of meantone: > > <<1 4 10 4 13 12|| [<1 2 4 7|, <0 -1 -4 -10|] > > <<1 4 41 4 62 84|| [<1 2 4 20|, <0 -1 -4 -41|] > > <<1 4 -164 4 -262 -292|| [<1 2 4 -66|, <0 -1 -4 164|] > > All have the same TOP tuning, but it is clear which one we prefer.In some cases the choice might not be so clear.> >> >>>>> IN >>>>>> Number 16 >>>>>>>>>>>> [6, 10, 10, 2, -1, -5] [[2, 4, 6, 7], [0, -3, -5, -5]] >>>>>> TOP tuning [1196.893422, 1906.838962, 2779.100462, >> 3377.547174]>>>>>> TOP generators [598.4467109, 162.3159606] >>>>>> bad: 8.9422 comp: 4.306766 err: 3.106578 >>>>>> This one needs a name. The TM basis is {50/49, 245/243}. >> Erethezontic? >>>> Where does that come from? We were calling this "Biporky", but of >> course we'd like something better. >> It's from the name for the porcupine family, Erethizontidae. Don't > know if it is better.How about something related to a porcupine, like say "hedgehog"?
Message: 11063 - Contents - Hide Contents Date: Mon, 14 Jun 2004 18:02:52 Subject: Re: Family commas From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote:> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote: >>> But if you go directly from the commas, it's unequivocally torsion >> and not contorsion. Remember, soon after your joining, that Fokker >> periodicity block, that you initially said represented 24-equal, but >> then you retracted that and said it was really 12-equal with torsion? >> Which is why I picked this example. If we are thinking Fokker blocks, > it is torsion; however why do we have to be thinking Fokker blocks?Who said anything about Fokker blocks? If you start with JI (as true temperaments do), and then temper out the two commas in question, you end up with 12-equal, not 24-equal. It's that simple.> Admittedly, the contorsion interpretation may be a little articifical, > but there's nothing else for it to be, basically. ??
Message: 11064 - Contents - Hide Contents Date: Mon, 14 Jun 2004 22:02:55 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: >>> If a porcupine is a member of the erethezontic family, wouldn't that >> falsely suggest that one temperament is more general than the other? >> "Hedgehog" seems good. >>>> Minorsemi from the approximate 21/20 generator, and >>> duodecal because like waage it's got 12 on the brain. >>>> What happened to "catler"? >> I forgot about it. Is the attribution of this to Catler securely >based?Well, his tuning is very different from TOP, but the addition of 7- limit notes at a fixed offset from a basic 12-equal 5-limit system is clearly the basis behind the FreeNote 12-tone-plus guitars.>>> [2, 8, 1, 8, -4, -20] hemifourths>> semifourths, I think. > > OK. > > >>> 135/128 pelogic >> mavila. >> Is that one "l" or two? One. >>> 6561/6250 ragisemi>> A little too wild. >> "Ragisemitonic" seems worse; what about "ragitonic"? See message 8331 > for this comma.I remember you mentioned it was a ragisma off from 21/20. That's what I see as a little too wild -- bringing in all these 7-limit intervals when we're still in 5-limit land.>>> 262144/253125 tertiatonic >> meaning? >> It's another 12-et comma, which I couldn't find a name for when I was > considering 12-note Fokker blocks. The name comes from the fact that > it is a third of a tone--see > > Yahoo groups: /tuning-math/message/8338 * [with cont.]This seems to go against the grain -- if the comma vanishes, it's not a third of any nonzero interval.>>> 393216/390625 wuerschmidt >>> 531441/524288 aristoxenan >> compton. >> This is the second time you've wanted to change this one. :)As I've mentioned before, Carl pointed out the Compton reference for this, and it seems the earliest we have.
Message: 11065 - Contents - Hide Contents Date: Mon, 14 Jun 2004 18:09:58 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. Thanks. > Septischismic in place of schismic, augie in the place > of augmented, and erethezontic in the place of biporky have been > discussed.If a porcupine is a member of the erethezontic family, wouldn't that falsely suggest that one temperament is more general than the other?> Minorsemi from the approximate 21/20 generator, and > duodecal because like waage it's got 12 on the brain.What happened to "catler"?> > 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. > > [1, 4, 10, 4, 13, 12] meantone > [5, 1, 12, -10, 5, 25] magic > [2, -4, -4, -11, -12, 2] pajara > [7, 9, 13, -2, 1, 5] semisixths > [1, 4, -2, 4, -6, -16] dominant sevenths > [2, 8, 8, 8, 7, -4] injera > [6, 5, 3, -6, -12, -7] kleismic > [2, 8, 1, 8, -4, -20] hemifourthssemifourths, I think.> [4, -3, 2, -14, -8, 13] negri > [3, 0, -6, -7, -18, -14] augmented > [1, -8, -14, -15, -25, -10] septischismic? > [1, 9, -2, 12, -6, -30] superpythagorean > [7, -3, 8, -21, -7, 27] orwell > [3, 0, 6, -7, 1, 14] augie > [3, 5, -6, 1, -18, -28] porcupine > [6, 10, 10, 2, -1, -5] erethezontic? > [3, 12, -1, 12, -10, -36] supermajor secondsAnyone have another suggestion?> [1, 4, -9, 4, -17, -32] flattone > [4, 4, 4, -3, -5, -2] diminished > [6, 10, 3, 2, -12, -21] minorsemi? > [0, 0, 12, 0, 19, 28] duodecal? > [3, 12, 11, 12, 9, -8] gawel > [10, 9, 7, -9, -17, -9] nonkleismic > [6, -7, -2, -25, -20, 15] miracle > [2, -9, -4, -19, -12, 16] beatles > [6, -2, -2, -17, -20, 1] lemba > [8, 6, 6, -9, -13, -3] doublewide > [0, 5, 0, 8, 0, -14] blackwood > [18, 27, 18, 1, -22, -34] ennealimmal > > > 25/24 dicot > 81/80 meantone > 128/125 augmented > 135/128 pelogic mavila. > 250/243 porcupine > 256/243 blackwood > 648/625 diminished > 2048/2025 diaschismic > 3125/3072 magic > 6561/6250 ragisemiA little too wild.> 15625/15552 hanson > 16875/16384 negri > 20000/19683 tetracot > 20480/19683 superpythagorean > 32805/32768 schismic > 78732/78125 semisixths > 262144/253125 tertiatonic meaning? > 393216/390625 wuerschmidt > 531441/524288 aristoxenan compton. > 1600000/1594323 amity > 2109375/2097152 orwell
Message: 11066 - Contents - Hide Contents Date: Mon, 14 Jun 2004 18:44:23 Subject: Re: Nexials From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Paul G Hjelmstad" <paul.hjelmstad@m...> wrote:>>> So the anwser is no, right? >>>> OK, no. :) >> So how is that single value (like 53:) generated?It isn't. The no meant no, it isn't a single value. ________________________________________________________________________ ________________________________________________________________________ ------------------------------------------------------------------------ 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: 11067 - Contents - Hide Contents Date: Mon, 14 Jun 2004 21:55:13 Subject: Re: Paul's nifty fifty From: Herman Miller Paul Erlich wrote:> --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> > wrote:>> Septischismic in place of schismic, augie in the place >> of augmented, and erethezontic in the place of biporky have been >> discussed. > >> If a porcupine is a member of the erethezontic family, wouldn't that > falsely suggest that one temperament is more general than the other?Actually, "porcupine" is more general; there are New World porcupines (Erethizontidae) (note the "i": not "Erethezontidae") and Old World porcupines (Hystricidae). So if <<3, 5, 1, 1, -7, -12]] is tentatively "Hystrix", maybe <<6, 10, 10, 2, -1, -5]] could be "Erethizon".>> [3, 12, -1, 12, -10, -36] supermajor seconds >> Anyone have another suggestion?Trimeantone? (3 generators = a meantone fifth) Or just plain supermajor?
Message: 11068 - Contents - Hide Contents Date: Tue, 15 Jun 2004 23:30:49 Subject: Re: Paul's nifty fifty From: Herman Miller 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).
Message: 11069 - Contents - Hide Contents Date: Tue, 15 Jun 2004 00:46:09 Subject: Re: Paul's nifty fifty From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:>>> What happened to "catler"? >>>> I forgot about it. Is the attribution of this to Catler securely >> based? >> Well, his tuning is very different from TOP, but the addition of 7- > limit notes at a fixed offset from a basic 12-equal 5-limit system is > clearly the basis behind the FreeNote 12-tone-plus guitars.Catler it is, I guess.> I remember you mentioned it was a ragisma off from 21/20. That's what > I see as a little too wild -- bringing in all these 7-limit intervals > when we're still in 5-limit land.However you slice it, it's nearly the same size as 21/20. The generator is slightly sharper--less than a schisma sharper--than 100 cents, and represents either 27/25 or 250/243, but of course these are not very close in size to 100 cents.>>>> 262144/253125 tertiatonic >>> meaning? >>>> It's another 12-et comma, which I couldn't find a name for when I > was>> considering 12-note Fokker blocks. The name comes from the fact that >> it is a third of a tone--see >> >> Yahoo groups: /tuning-math/message/8338 * [with cont.] >> This seems to go against the grain -- if the comma vanishes, it's not > a third of any nonzero interval.You could describe the relationship differently. The point is that (10/9)/(262144/253125)^3 = kwazy comma. Kwazytone?
Message: 11072 - Contents - Hide Contents Date: Tue, 15 Jun 2004 05:33:27 Subject: Re: Nexials From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Paul G Hjelmstad" <paul.hjelmstad@m...> wrote:> What I meant is, how is 9: below arrived at. You call it the nexus... > > 9: <<3 0 3 -7 -4 7|| {15/14, 128/125} > [392.25, 96.15]The 9 is shorthand for the 9 standard val. <<3 0 3 -7 -4 7|| = <<3 0 -6 -7 -18 -14|| + <<0 0 9 0 14 21|| In other words, the temperament is augmented plus doubleO 9.
Message: 11073 - Contents - Hide Contents Date: Tue, 15 Jun 2004 19:38:15 Subject: Re: Paul's nifty fifty From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx Herman Miller <hmiller@I...> wrote:> Paul Erlich wrote:>> --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> >> wrote:>>> Septischismic in place of schismic, augie in the place >>> of augmented, and erethezontic in the place of biporky have been >>> discussed. >> >>>> If a porcupine is a member of the erethezontic family, wouldn't that >> falsely suggest that one temperament is more general than the other? >> Actually, "porcupine" is more general; there are New World porcupines > (Erethizontidae) (note the "i": not "Erethezontidae") and Old World > porcupines (Hystricidae). So if <<3, 5, 1, 1, -7, -12]] is tentatively > "Hystrix", maybe <<6, 10, 10, 2, -1, -5]] could be "Erethizon". >>>> [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? ________________________________________________________________________ ________________________________________________________________________ ------------------------------------------------------------------------ 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: 11074 - Contents - Hide Contents Date: Wed, 16 Jun 2004 19:34:58 Subject: Re: Paul's nifty fifty From: Gene Ward Smith --- 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. "Wonder" adds 245/243 to 1029/1024 linear to extend to the 7-limit and "slendric" 81/80 if we adopt this naming system. "Slendric" would then be closely associated to 31-et; "wonder" would be 41&46. Both extend nicely to the 11-limit.
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