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Message: 10900 - Contents - Hide Contents Date: Tue, 27 Apr 2004 20:55:36 Subject: Re: Vanishing tratios From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> > wrote: >>> 5-limit 12-equal -- 625:640:648? >> >> I'm going tratio-wild, but I have to go! :( >> Let's define the function > > weird(a,b,c) = a*b*c/gcd(a,b)/gcd(a,c)/gcd(a,b)What's wrong with lcm(a,b,c) = abc/gcd(ab,ac,bc)?
Message: 10901 - Contents - Hide Contents Date: Tue, 27 Apr 2004 20:59:09 Subject: Re: Vanishing tratios From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote:> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote: > > Speaking of vanishing, I was going to respond to a post of yours about > tratios and yantras, and it seems to have vanished!I figured out what you meant.
Message: 10902 - Contents - Hide Contents Date: Tue, 27 Apr 2004 21:04:16 Subject: Re: Vanishing tratios From: Carl Lumma>> >peaking of vanishing, I was going to respond to a post >> of yours about tratios and yantras, and it seems to have >> vanished! >>I figured out what you meant.I appreciate the desire to focus the discussion, but thought I'd mention that your readers might not have figured it out... -Carl
Message: 10903 - Contents - Hide Contents Date: Tue, 27 Apr 2004 21:05:56 Subject: Re: Vanishing tratios 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 "Paul Erlich" <perlich@a...> >> wrote: >>>>> 5-limit 12-equal -- 625:640:648? >>> >>> I'm going tratio-wild, but I have to go! :( >>>> Let's define the function >> >> weird(a,b,c) = a*b*c/gcd(a,b)/gcd(a,c)/gcd(a,b) >> What's wrong with lcm(a,b,c) = abc/gcd(ab,ac,bc)?You're right -- all these formulae seem to produce the same result (that's what you meant, right?) . . .
Message: 10904 - Contents - Hide Contents Date: Tue, 27 Apr 2004 21:19:04 Subject: Re: Vanishing tratios 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:>>> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> >>> wrote: >>>>>>> 5-limit 12-equal -- 625:640:648? >>>> >>>> I'm going tratio-wild, but I have to go! :( >>>>>> Let's define the function >>> >>> weird(a,b,c) = a*b*c/gcd(a,b)/gcd(a,c)/gcd(a,b) >>>> What's wrong with lcm(a,b,c) = abc/gcd(ab,ac,bc)? >> You're right -- all these formulae seem to produce the same result > (that's what you meant, right?) . . .What I actually meant was that I thought what you probably wanted is the least common multiple, and that abc/gcd(ab,ac,bc) is a formula for it in terms of the gcd. Weird(a,b,c) is a different arthmetic function, unknown to me. weird(2,4,6) = 2*4*6/gcd(2,4)/gcd(2,6)/gcd(4,6) = 48/8 = 6 lcm(2,4,6) = 2*4*6/gcd(8,12,24) = 48/4 = 12
Message: 10905 - Contents - Hide Contents Date: Tue, 27 Apr 2004 21:22:08 Subject: Re: Vanishing tratios 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:>>>> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> >>>> wrote: >>>>>>>>> 5-limit 12-equal -- 625:640:648? >>>>> >>>>> I'm going tratio-wild, but I have to go! :( >>>>>>>> Let's define the function >>>> >>>> weird(a,b,c) = a*b*c/gcd(a,b)/gcd(a,c)/gcd(a,b) >>>>>> What's wrong with lcm(a,b,c) = abc/gcd(ab,ac,bc)? >>>> You're right -- all these formulae seem to produce the same result >> (that's what you meant, right?) . . . >> What I actually meant was that I thought what you probably wanted is > the least common multiple, and that abc/gcd(ab,ac,bc) is a formula for > it in terms of the gcd. Weird(a,b,c) is a different arthmetic > function, unknown to me. > > weird(2,4,6) = 2*4*6/gcd(2,4)/gcd(2,6)/gcd(4,6) = 48/8 = 6 > lcm(2,4,6) = 2*4*6/gcd(8,12,24) = 48/4 = 12Hmm . . . the two formulae seem to give the same result as long as gcd (a,b,c) = 1, which was the case for all the tratios in question. Right?
Message: 10906 - Contents - Hide Contents Date: Tue, 27 Apr 2004 06:21:07 Subject: Re: Vanishing tratios From: monz hi paul, --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:> Before I finalize my paper, I'd like to explore the > following idea. > > What if I take a 3-term ratio ("tratio"?) and have it vanish? > > Let's say 125:126:128. > > So 128:125 vanishes, 128:126 = 64:63 vanishes, and >126:125 vanishes.traditionally, "ratio" has been used for 2-term comparisons, and for >2-term, "proportion". just nit-picking on terminology. but that's a cool idea you posted about. -monz
Message: 10907 - Contents - Hide Contents Date: Tue, 27 Apr 2004 21:51:37 Subject: 13-limit non-p equal temperaments From: Gene Ward Smith Here are some badness figures for 13-limit non-3, non-5, non-7 and non-11 systems for n from 10 to 1000. Has anyone tried 37-et no-threes? No 3 11 .933415 13 .993093 16 .866454 20 .927445 21 .753388 26 .959486 28 .938646 29 .959085 37 .315364 43 1.031076 46 1.071756 50 1.053462 58 1.033486 66 .919175 74 .750066 87 .921179 103 1.024075 124 .859227 161 .816454 167 .988291 187 1.060722 196 1.070804 224 1.022841 233 .790980 270 .803173 307 .894024 457 .743887 494 .938872 581 .704227 618 .639472 655 1.072421 851 .612436 888 .697934 No 5 10 .852210 17 .558331 26 1.067693 41 .970483 46 1.051292 58 1.033486 94 1.074982 104 1.046808 113 1.028110 166 .979893 207 .695855 224 .834464 253 1.075904 270 .968703 311 1.052496 477 .695780 494 .866938 701 .831650 971 1.034586 No 7 15 .971014 24 .778940 26 1.067693 29 .947011 34 .915970 46 1.071756 53 .944024 58 1.033486 87 .684935 111 .863341 183 .984334 190 1.084133 224 .825561 270 .968703 277 1.071139 407 .767192 494 .422077 901 .846676 988 1.003874 No 11 10 .924760 19 .709316 26 .963807 27 .939214 46 1.071756 53 .899823 58 1.033486 130 .809038 140 .964631 171 1.021568 224 1.022841 270 .968703 441 .685576 494 .938872 571 1.008134 711 1.098197 935 .696284
Message: 10908 - Contents - Hide Contents Date: Tue, 27 Apr 2004 08:17:38 Subject: tratios and yantras From: Gene Ward Smith I took all the 7-limit integers less than 2^20 (recall this is a yantra when reduced to an octave) and found the smallest instance of three successive 7-limit integers which were mapped to the same val when wedged with an 7-limit wedgie, in order to get tratios for some of the most important 7-limit linear temperaments. Here's the results: meantone 1120:1125:1134 miracle 7168:7200:7203 ennealimmal 419904:420000:420175 magic 6048:6075:6125 pajara 441:448:450 (septimal) schismic 27783:28000:28125 orwell 12005:12096:12150
Message: 10909 - Contents - Hide Contents Date: Tue, 27 Apr 2004 21:57:07 Subject: Re: Vanishing tratios From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:> Hmm . . . the two formulae seem to give the same result as long as gcd > (a,b,c) = 1, which was the case for all the tratios in question. > Right? Right.
Message: 10910 - Contents - Hide Contents Date: Tue, 27 Apr 2004 14:51:11 Subject: Re: tratios and yantras From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote:> I took all the 7-limit integers less than 2^20 (recall this is a > yantra when reduced to an octave) and found the smallest instance of > three successive 7-limit integers which were mapped to the same val > when wedged with an 7-limit wedgie, in order to get tratios for some > of the most important 7-limit linear temperaments.You lost me. Can you break down this process, step-by-step, with examples? Here's the results:> > meantone 1120:1125:1134 > miracle 7168:7200:7203 > ennealimmal 419904:420000:420175 > magic 6048:6075:6125 > pajara 441:448:450 > (septimal) schismic 27783:28000:28125 > orwell 12005:12096:12150 ________________________________________________________________________ ________________________________________________________________________ ------------------------------------------------------------------------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: 10911 - Contents - Hide Contents Date: Tue, 27 Apr 2004 23:50:14 Subject: Re: notation of monzos From: Dave Keenan --- In tuning-math@xxxxxxxxxxx.xxxx "George D. Secor" <gdsecor@y...> wrote:> I think there was only one person who disliked the idea (I'm pretty > sure it wasn't Dave, because he's a stickler for perceptual > improvements in notation), IIRC on the grounds that the commas are a > convenience rather than a necessity. I responded that commas are > widely accepted as serving a similar purpose as place-markers in > large decimal numbers. However, not enough people expressed any > further opinions one way or another for my suggestion to be either > adopted or rejected. > > Now's the time for others to speak up so the issue can be resolved.Yes. I wholeheartedly support putting a comma after the 3-exponent and then after every third exponent beyond that. Not only because of the improvement in readability (not having to count all the way from the end to figure which exponent you're looking at), but also because it allows one to distinguish octave-equivalent vectors (and even the 2,3-reduced ones George and I sometimes use in describing notational commas relative to a chain of fifths) from complete vectors. [2 3, 5 7 11, 13 17 19> ordinary, complete [3, 5 7 11, 13 17 19> octave-equivalent, 2-reduced [, 5 7 11, 13 17 19> 2,3-reduced And I agree that 11 and 19 are two natural stopping places, for various reasons. I don't remember anyone objecting to these commas, but maybe some wouldn't bother using them that way themselves. I don't like the pipe or vertical bar since it is too easily confused with a digit one. You folks who still have perfect eyesight may not think so, but wait 'til you get a bit older. Even for the inner product I prefer <2 3, 5][2 3, 5> or <2 3, 5].[2 3, 5> ________________________________________________________________________ ________________________________________________________________________ ------------------------------------------------------------------------ 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: 10912 - Contents - Hide Contents Date: Thu, 29 Apr 2004 05:17:26 Subject: lattice definitions and geometries From: Paul Erlich Gene, would you comment on this: Lattice Geometries * [with cont.] (Wayb.) in regard to tuning, and what they have been / might be useful for (see concurrent tuning list thread) . . . ? -p
Message: 10913 - Contents - Hide Contents Date: Thu, 29 Apr 2004 15:26:41 Subject: Re: lattice definitions and geometries From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:> Gene, would you comment on this: > > Lattice Geometries * [with cont.] (Wayb.) > > in regard to tuning, and what they have been / might be useful for > (see concurrent tuning list thread) . . .I don't see the concurrent thread. Mathematicians would normally call what he calls lattices "tessellations" (if the geometry is fixed) or "infinite regular graphs" (if all we are interested in is the graph.) ________________________________________________________________________ ________________________________________________________________________ ------------------------------------------------------------------------ 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: 10914 - Contents - Hide Contents Date: Fri, 30 Apr 2004 00:09:27 Subject: Re: lattice definitions and geometries From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote:> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> > wrote:>> Gene, would you comment on this: >> >> Lattice Geometries * [with cont.] (Wayb.) >> >> in regard to tuning, and what they have been / might be useful for >> (see concurrent tuning list thread) . . . >> I don't see the concurrent thread.On "cubic ice", the diamond form of carbon, etc.
Message: 10915 - Contents - Hide Contents Date: Fri, 30 Apr 2004 01:25:39 Subject: book: Harmonic Analysis and Hypergroups From: Carl Lumma just something i came across: Harmonic Analysis and Hypergroups * [with cont.] (Wayb.) -Carl ________________________________________________________________________ ________________________________________________________________________ ------------------------------------------------------------------------ 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: 10916 - Contents - Hide Contents Date: Sat, 01 May 2004 20:48:20 Subject: Rational wolves for some temperaments From: Gene Ward Smith Here are some rationalized wolves for three temperaments (meantone, hanson/kleismic, magic) which have consonances as a generator. I give the generator leading to a (13-odd-limit or less) rational wolf, the wolf itself, and a basis obtained by adding to the existing (7-limit in the case of meantone and magic, 5-limit for hanson) basis the condition that the approriate number of generator steps gives us the wolf. Note that one of the Meantone[17] tunings is a version of the Meantone[19] tuning. The two magic wolves lead to two different 11-limit versions of magic, identical in 41-equal, which I give wedgies and mappings for. meantone[12] generator (416/5)^(1/11) wolf 20/13 TM basis 81/80 126/125 105/104 meantone[17] generator (5632/9)^(1/16) wolf 18/11 TM basis 81/80 126/125 99/98 meantone[17] generator (8192/13)^(1/16) wolf 13/8 TM basis 81/80 125/125 640/637 meantone[19] generator (18432/13)^(1/18) wolf 13/9 TM basis 81/80 126/125 640/637 hanson[15] generator 13^(1/14) wolf 16/13 TM basis 325/324 625/624 hanson[19] generator (352/13)^(1/18) wolf 13/11 TM basis 352/351 15625/15552 magic[16] generator (352/13)^(1/15) wolf 13/11 TM basis 225/224 245/243 275/273 magic[19] generator (576/11)^(1/18) wolf 11/9 TM basis 100/99 225/224 245/243 <<5 1 12 -8 -10 5 -30 25 -22 -64|| [<1 0 2 -1 6|, <0 5 1 12 -8| magic[22] generator (707/7)^(1/21) wolf 14/11 TM basis 225/224 245/243 441/440 <<5 1 12 33 -10 5 35 25 73 51|| [<1 0 2 -1 -7|, <0 5 1 12 33|] ________________________________________________________________________ ________________________________________________________________________ ------------------------------------------------------------------------ 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: 10918 - Contents - Hide Contents Date: Mon, 03 May 2004 18:38:51 Subject: Re: book: Harmonic Analysis and Hypergroups From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "hstraub64" <hstraub64@t...> wrote:> --- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:>> just something i came across: >> >> Harmonic Analysis and Hypergroups * [with cont.] (Wayb.) >> >> Interesting math, in any case! > But, hmm, the word "harmonic" seems to be used not in a musical way - > what would the connection to music be?Beats me; "harmonic" here is in the sense of "abstract harmonic analysis", meaning Fourier analysis on groups. ________________________________________________________________________ ________________________________________________________________________ ------------------------------------------------------------------------ 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: 10919 - Contents - Hide Contents Date: Wed, 05 May 2004 22:27:04 Subject: 10+16 (continued from tuning) From: Paul Erlich 7-limit now . . . val for 10: <10 16 23 28] val for 16: <16 25 37 45] wedgie: <<-6 2 2 17 20 -1]] According to Gene's file, this has TOP error of 3.740932 and L1 complexity of 14.626943. Not too bad. It just barely, by a hair, falls outside the bound in my paper. Not too late to change that, though . . .
Message: 10920 - Contents - Hide Contents Date: Thu, 06 May 2004 21:39:44 Subject: Re: 10+16 (continued from tuning) From: Herman Miller Paul Erlich wrote:> 7-limit now . . . > > val for 10: > > <10 16 23 28] > > val for 16: > > <16 25 37 45] > > wedgie: > > <<-6 2 2 17 20 -1]] > > According to Gene's file, this has TOP error of 3.740932 and L1 > complexity of 14.626943. Not too bad. It just barely, by a hair, > falls outside the bound in my paper. Not too late to change that, > though . . . >This is the "Number 82" temperament that I commented on back in January. I still haven't done anything with it, but I've been kind of busy lately. ________________________________________________________________________ ________________________________________________________________________ ------------------------------------------------------------------------ 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: 10921 - Contents - Hide Contents Date: Thu, 06 May 2004 00:50:48 Subject: Re: Request for Gene From: Paul Erlich Thanks again for this, Gene. Would it be too much trouble to also do [8, 6, 6, -9, -13, -3] and [6, -2, -2, -17, -20, 1] ? Those would be great. Also add these to the tratio request . . . --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote:> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote: >>> Can you (would you) provide a nice list of commas that vanish in each >> of the following 7-limit wedgies? >> Below I give a list in descending size order of the subgroup commas > for each temperament, plus any on a 7-limit comma list which I either > cooked up for you or which you computed, of commas with relative error > less than 0.06 and epimericity less than 0.5. > > > [1, 4, 10, 4, 13, 12] > [59049/57344, 81/80, 126/125, 225/224, 3136/3125, 703125/702464] > > [2, -4, -4, -11, -12, 2] > [50/49, 64/63, 2048/2025, 225/224] > > [5, 1, 12, -10, 5, 25] > [3125/3072, 875/864, 245/243, 225/224, 10976/10935] > > [7, 9, 13, -2, 1, 5] > [686/675, 245/243, 126/125, 78732/78125, 4375/4374] > > [1, 4, -2, 4, -6, -16] > [256/245, 36/35, 64/63, 81/80, 5120/5103] > > [3, 0, -6, -7, -18, -14] > [128/125, 64/63, 126/125, 4000/3969, 250047/250000] > > [4, -3, 2, -14, -8, 13] > [16875/16384, 525/512, 49/48, 686/675, 225/224] > > [2, 8, 1, 8, -4, -20] > [49/48, 81/80, 245/243, 19683/19600] > > [6, 5, 3, -6, -12, -7] > [1029/1000, 49/48, 875/864, 126/125, 15625/15552] > > [1, 9, -2, 12, -6, -30] > [20480/19683, 64/63, 245/243, 1728/1715, 420175/419904] > > [2, 8, 8, 8, 7, -4] > [6561/6272, 405/392, 50/49, 81/80, 4000/3969] > > [6, -7, -2, -25, -20, 15] > [34171875/33554432, 1063125/1048576, 1029/1024, 225/224, 16875/16807, > 2401/2400] > > [6, 10, 10, 2, -1, -5] > [250/243, 50/49, 2430/2401, 245/243] > > [7, -3, 8, -21, -7, 27] > [2430/2401, 1728/1715, 2109375/2097152, 225/224, 6144/6125, 65625/65536] > > [4, 4, 4, -3, -5, -2] > [360/343, 648/625, 36/35, 50/49, 3125/3087, 126/125] > > [1, -8, -14, -15, -25, -10] > [3125/3087, 4000/3969, 225/224, 5120/5103, 33554432/33480783, 32805/32768] > > [3, 0, 6, -7, 1, 14] > [405/392, 36/35, 128/125, 225/224] > > [0, 0, 12, 0, 19, 28] > [648/625, 128/125, 531441/524288, 81/80, 2048/2025, 32805/32768] > > [1, 4, -9, 4, -17, -32] > [137781/131072, 525/512, 875/864, 81/80, 4375/4374] > > [0, 5, 0, 8, 0, -14] > [256/243, 28/27, 49/48, 64/63, 1029/1024] > > [3, 12, -1, 12, -10, -36] > [81/80, 1728/1715, 1029/1024] > > [10, 9, 7, -9, -17, -9] > [10077696/9765625, 559872/546875, 126/125, 1728/1715, 2401/2400] > > [3, 5, -6, 1, -18, -28] > [250/243, 64/63, 875/864, 6144/6125]
Message: 10922 - Contents - Hide Contents Date: Thu, 06 May 2004 06:26:34 Subject: Re: 10+16 (continued from tuning) From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:> 7-limit now . . . > > val for 10: > > <10 16 23 28] > > val for 16: > > <16 25 37 45] > > wedgie: > > <<-6 2 2 17 20 -1]] > > According to Gene's file, this has TOP error of 3.740932 and L1 > complexity of 14.626943. Not too bad. It just barely, by a hair, > falls outside the bound in my paper. Not too late to change that, > though . . .What is the bound of your paper at the moment?
Message: 10923 - Contents - Hide Contents Date: Thu, 06 May 2004 06:51:27 Subject: Re: Request for Gene From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:> Thanks again for this, Gene. > > > Would it be too much trouble to also do > > [8, 6, 6, -9, -13, -3]390625/373248, 5971968/5764801, 50/49, 875/864, 1728/1715> and > > [6, -2, -2, -17, -20, 1]140625/131072, 525/512, 50/49, 1029/1024> Also add these to the tratio request . . .You'd better give me the whole request, because doing it piecemeal adds to the work. Are you giving names to all the temperaments you plan on tabulating, and if so, which names? ________________________________________________________________________ ________________________________________________________________________ ------------------------------------------------------------------------ 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: 10924 - Contents - Hide Contents Date: Sat, 08 May 2004 00:16:34 Subject: Re: Request for Gene From: Paul Erlich The tratio request I referred to would involve finding the smallest tratios, and/or the tratios with smallest LCM, for the 23 (now 25) wedgies listed below. --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:> Thanks again for this, Gene. > > > Would it be too much trouble to also do > > [8, 6, 6, -9, -13, -3] > > and > > [6, -2, -2, -17, -20, 1] > > ? > > Those would be great. > > > Also add these to the tratio request . . . > > > > --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> > wrote:>> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> > wrote: >>>>> Can you (would you) provide a nice list of commas that vanish in > each>>> of the following 7-limit wedgies? >>>> Below I give a list in descending size order of the subgroup commas >> for each temperament, plus any on a 7-limit comma list which I > either>> cooked up for you or which you computed, of commas with relative > error>> less than 0.06 and epimericity less than 0.5. >> >> >> [1, 4, 10, 4, 13, 12] >> [59049/57344, 81/80, 126/125, 225/224, 3136/3125, 703125/702464] >> >> [2, -4, -4, -11, -12, 2] >> [50/49, 64/63, 2048/2025, 225/224] >> >> [5, 1, 12, -10, 5, 25] >> [3125/3072, 875/864, 245/243, 225/224, 10976/10935] >> >> [7, 9, 13, -2, 1, 5] >> [686/675, 245/243, 126/125, 78732/78125, 4375/4374] >> >> [1, 4, -2, 4, -6, -16] >> [256/245, 36/35, 64/63, 81/80, 5120/5103] >> >> [3, 0, -6, -7, -18, -14] >> [128/125, 64/63, 126/125, 4000/3969, 250047/250000] >> >> [4, -3, 2, -14, -8, 13] >> [16875/16384, 525/512, 49/48, 686/675, 225/224] >> >> [2, 8, 1, 8, -4, -20] >> [49/48, 81/80, 245/243, 19683/19600] >> >> [6, 5, 3, -6, -12, -7] >> [1029/1000, 49/48, 875/864, 126/125, 15625/15552] >> >> [1, 9, -2, 12, -6, -30] >> [20480/19683, 64/63, 245/243, 1728/1715, 420175/419904] >> >> [2, 8, 8, 8, 7, -4] >> [6561/6272, 405/392, 50/49, 81/80, 4000/3969] >> >> [6, -7, -2, -25, -20, 15] >> [34171875/33554432, 1063125/1048576, 1029/1024, 225/224, > 16875/16807, >> 2401/2400] >> >> [6, 10, 10, 2, -1, -5] >> [250/243, 50/49, 2430/2401, 245/243] >> >> [7, -3, 8, -21, -7, 27] >> [2430/2401, 1728/1715, 2109375/2097152, 225/224, 6144/6125, > 65625/65536] >>>> [4, 4, 4, -3, -5, -2] >> [360/343, 648/625, 36/35, 50/49, 3125/3087, 126/125] >> >> [1, -8, -14, -15, -25, -10] >> [3125/3087, 4000/3969, 225/224, 5120/5103, 33554432/33480783, > 32805/32768] >>>> [3, 0, 6, -7, 1, 14] >> [405/392, 36/35, 128/125, 225/224] >> >> [0, 0, 12, 0, 19, 28] >> [648/625, 128/125, 531441/524288, 81/80, 2048/2025, 32805/32768] >> >> [1, 4, -9, 4, -17, -32] >> [137781/131072, 525/512, 875/864, 81/80, 4375/4374] >> >> [0, 5, 0, 8, 0, -14] >> [256/243, 28/27, 49/48, 64/63, 1029/1024] >> >> [3, 12, -1, 12, -10, -36] >> [81/80, 1728/1715, 1029/1024] >> >> [10, 9, 7, -9, -17, -9] >> [10077696/9765625, 559872/546875, 126/125, 1728/1715, 2401/2400] >> >> [3, 5, -6, 1, -18, -28] >> [250/243, 64/63, 875/864, 6144/6125]
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