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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)?
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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.
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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
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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?) . . .
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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
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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 = 12
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?
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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
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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


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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


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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.
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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.)
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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.)
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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


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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.)
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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.
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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.)


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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.)


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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.)
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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 . . .


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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.)
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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]
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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?
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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.)
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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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