This is an Opt In Archive . We would like to hear from you if you want your posts included. For the contact address see About this archive. All posts are copyright (c).

- Contents - Hide Contents - Home - Section 6

Previous Next

5000 5050 5100 5150 5200 5250 5300 5350 5400 5450 5500 5550 5600 5650 5700 5750 5800 5850 5900 5950

5450 - 5475 -



top of page bottom of page up down


Message: 5475 - Contents - Hide Contents

Date: Thu, 31 Oct 2002 22:29:38

Subject: Re: New file uploaded to tuning-math

From: Carl Lumma

>> >his .gif is golden. >> >> But I forget the coloring scheme... >> >> -Carl >
>bluish = consistent > >reddish = inconsistent > >is that what you meant?
Yes, but what's hot purple (14, 20), and real purple (24)? -Carl
top of page bottom of page up down


Message: 5476 - Contents - Hide Contents

Date: Fri, 01 Nov 2002 19:59:47

Subject: Re: New file uploaded to tuning-math

From: wallyesterpaulrus

--- In tuning-math@y..., "Carl Lumma" <clumma@y...> wrote:
>>> This .gif is golden. >>> >>> But I forget the coloring scheme... >>> >>> -Carl >>
>> bluish = consistent >> >> reddish = inconsistent >> >> is that what you meant? >
> Yes, but what's hot purple (14, 20), reddish > and real > purple (24)?
bluish (isn't that violet, not purple?)
top of page bottom of page up down


Message: 5477 - Contents - Hide Contents

Date: Fri, 01 Nov 2002 21:52:23

Subject: Re: New file uploaded to tuning-math

From: Carl Lumma

>>> >luish = consistent >>> >>> reddish = inconsistent >>> >>> is that what you meant? >>
>> Yes, but what's hot purple (14, 20), > >reddish > >> and real >> purple (24)? >
>bluish (isn't that violet, not purple?)
Got it. It's whatever you want to call it. Did you do this just for visibility?
top of page bottom of page up down


Message: 5478 - Contents - Hide Contents

Date: Fri, 01 Nov 2002 21:54:06

Subject: Re: New file uploaded to tuning-math

From: wallyesterpaulrus

--- In tuning-math@y..., "Carl Lumma" <clumma@y...> wrote:

> Did you do this just for visibility? yes.
top of page bottom of page up down


Message: 5479 - Contents - Hide Contents

Date: Fri, 01 Nov 2002 23:09:59

Subject: Re: New file uploaded to tuning-math

From: Carl Lumma

>> >id you do this just for visibility? > >yes. It worked! -C.
top of page bottom of page up down


Message: 5480 - Contents - Hide Contents

Date: Fri, 01 Nov 2002 23:11:27

Subject: Re: New file uploaded to tuning-math

From: wallyesterpaulrus

--- In tuning-math@y..., "Carl Lumma" <clumma@y...> wrote:
>>> Did you do this just for visibility? >> >> yes. > > It worked! > > -C.
notice how even 76 is visible in one of the zooms i posted. this wasn't easy to arrange, with all the numbers lying on top of one another!
top of page bottom of page up down


Message: 5481 - Contents - Hide Contents

Date: Sat, 02 Nov 2002 23:57:49

Subject: Re: Miracle and 72-et

From: wallyesterpaulrus

--- In tuning-math@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:
> The 72-et version of miracle really only dominates in the 11-limit.
If we look at the convergents to the rms optimal secor, we find that
> 175 is the next convergent beyond 72 for the 5 and 7 limits, and 113 > (and beyond that 298) are the next convergents in the primary 13-
limit version of miracle. For the alternative 13-limit miracle, 72 is not even a convergent! We have however 113 and beyond that, 267. It would seem 175 and 113 have a place at the table. if i recall correctly, graham's program originally spat out the denominator 113 for the miracle generator.
top of page bottom of page up down


Message: 5482 - Contents - Hide Contents

Date: Sat, 02 Nov 2002 03:17:05

Subject: A look at 13-limit linear temperaments

From: Gene Ward Smith

I did this admissions-committee style, with two different ways to make
the cut--either unweighted badness less than 250, or graham badness
less than 660. Limits are graham complexity less than or equal to 50,
and rms error below 20. Note the two different versions of miracle!


[[1, 1, -5, -1, 2, 4], [0, 2, 25, 13, 5, -1]]   [1200., 351.6171952]

rms   4.164243901   comp   13.36413110   graham   26

bad   203.4451071   grabad   552.0725839

mos   [10, 17, 24, 41, 58, 99]


[[1, 2, 2, 3, 4, 4], [0, 4, -3, 2, 5, 3]]   [1200., -126.4454893]

rms   19.07231186   comp   5.059644256   graham   11

bad   217.0617566   grabad   695.8127255

mos   [10, 19, 28, 47, 66, 85]


[[1, 1, -1, 3, 6, 8], [0, 3, 17, -1, -13, -22]]   [1200., 234.4801337]

rms   2.768744646   comp   18.44857718   graham   39

bad   219.3952496   grabad   674.3413860

mos   [11, 16, 21, 26, 31, 36, 41, 46, 87]


[[1, 1, 3, 3, 2, 0], [0, 6, -7, -2, 15, 38]]   [1200., 116.7795117]

rms   2.215733090   comp   21.71865558   graham   45

bad   224.2677630   grabad   668.8615243

mos   [10, 11, 21, 31, 41, 72]


[[2, 5, 8, 5, 6, 8], [0, 6, 11, -2, -3, 2]]   [600.0000000,
-183.2252192]

rms   3.167218102   comp   17.40114939   graham   30

bad   229.9031248   grabad   520.4270399

mos   [14, 20, 26, 46, 72]


[[3, 0, 3, 10, 8, 0], [0, 6, 5, -2, 3, 14]]   [400.0000000,
316.9938762]

rms   1.823490161   comp   25.26064132   graham   48

bad   231.5101214   grabad   606.4085004

mos   [12, 15, 27, 42, 57, 72, 87]


[[1, 0, -4, 17, -6, 10], [0, 1, 4, -9, 6, -4]]   [1200., 1892.727763]

rms   12.11708320   comp   7.338255924   graham   15

bad   240.8725835   grabad   703.9389215

mos   [12, 19, 26, 45, 71, 97]


[[1, 0, -31, -21, -14, -9], [0, 1, 21, 15, 11, 8]]   [1200.,
1904.391710]

rms   6.209025908   comp   11.46080276   graham   21

bad   240.9051197   grabad   597.5199555

mos   [12, 17, 29, 46, 63]


[[1, 0, -6, 4, -12, -7], [0, 4, 21, -3, 39, 27]]   [1200.,
475.6946183]

rms   2.245890676   comp   22.61415486   graham   42

bad   241.5233672   grabad   611.3114745

mos   [13, 18, 23, 28, 33, 38, 43, 48, 53, 58]


[[29, 46, 0, 14, 33, 40], [0, 0, 1, 1, 1, 1]]   [41.37931034,
2788.239580]

rms   2.277983567   comp   22.46330341   graham   29

bad   242.5275176   grabad   355.7521911

mos   [58, 87]


[[1, 1, 0, 2, 3, 3], [0, 5, 20, 7, 4, 6]]   [1200., 139.4310901]

rms   8.867498827   comp   9.091204541   graham   20

bad   243.0710758   grabad   793.1332067

mos   [17, 26, 43, 69]


[[3, 0, 7, 6, 8, 4], [0, 2, 0, 1, 1, 3]]   [400.0000000, 950.4747331]

rms   15.05561416   comp   6.434283174   graham   12

bad   245.7246539   grabad   625.8501279

mos   [15, 24, 39, 63, 87]


[[1, 0, 15, 25, -33, -28], [0, 1, -8, -14, 23, 20]]   [1200.,
1902.127698]

rms   2.806870405   comp   19.72435043   graham   37

bad   245.8818240   grabad   631.7204666

mos   [12, 17, 29, 41, 53, 94]


[[1, 4, 5, 2, 4, 8], [0, 9, 10, -3, 2, 16]]   [1200., -322.1404543]

rms   6.393156943   comp   11.47388339   graham   21

bad   248.4740356   grabad   615.2396380

mos   [11, 15, 26, 41, 67]


[[2, 0, 11, 31, 45, 55], [0, 1, -2, -8, -12, -15]]   [600.0000000,
1903.786589]

rms   2.880707578   comp   19.68247952   graham   34

bad   251.5468524   grabad   571.1070885

mos   [10, 12, 22, 34, 46, 58]


[[1, 1, 3, 3, 2, 4], [0, 6, -7, -2, 15, -3]]   [1200., 116.8457500]

rms   6.194083836   comp   11.81524439   graham   22

bad   251.5597433   grabad   639.1622256

mos   [10, 11, 21, 31, 41, 72]


[[1, 0, -4, -3, 4, 0], [0, 3, 12, 11, -1, 7]]   [1200., 633.5217226]

rms   12.76012488   comp   7.304108433   graham   13

bad   251.8869934   grabad   598.0946990

mos   [11, 13, 15, 17, 19, 36, 53, 89]


[[2, 1, -12, 2, -9, -2], [0, 3, 23, 5, 22, 13]]   [600.0000000,
434.1894677]

rms   2.006172054   comp   26.72452058   graham   46

bad   277.1616007   grabad   625.8999601

mos   [14, 22, 36, 58, 94]


[[2, 1, 0, 5, 6, 4], [0, 7, 15, 2, 3, 11]]   [600.0000000,
185.9945003]

rms   4.007057140   comp   17.17556404   graham   30

bad   285.2279283   grabad   658.4266756

mos   [14, 20, 26, 32, 58, 84]


[[2, 2, 5, 6, 5, 7], [0, 3, -1, -1, 5, 1]]   [600.0000000,
231.2498543]

rms   12.34827552   comp   8.160882306   graham   14

bad   287.8803242   grabad   646.8422283

mos   [10, 16, 26, 36, 62, 88]


top of page bottom of page up down


Message: 5483 - Contents - Hide Contents

Date: Sat, 02 Nov 2002 08:34:24

Subject: Miracle and 72-et

From: Gene Ward Smith

The 72-et version of miracle really only dominates in the 11-limit. If we look at the convergents to the rms optimal secor, we find that
175 is the next convergent beyond 72 for the 5 and 7 limits, and 113
(and
beyond that 298) are the next convergents in the primary 13-limit
version of miracle. For the alternative 13-limit miracle, 72 is not
even a convergent! We have however 113 and beyond that, 267. It would
seem 175 and 113 have a place at the table.


top of page bottom of page up down


Message: 5484 - Contents - Hide Contents

Date: Tue, 5 Nov 2002 01:36:12

Subject: 156edo, articulating septimal kleisma

From: monz

hmmm ... this is interesting:

i was searching for an EDO which would articulate the
"septimal kleisma" [2 2 -1] = 225:224 (~7.711522991 cents).

156edo looked very good, since the "augmented-6th" 225:128 and
the "harmonic-minor-7th" 7:4 are approximated very closely
by is 127 and 126 degrees, respectively.  thus, the
"septimal kleisma" is almost exactly 1 degree.

but then, when i made a bingo-card-lattice of 156edo
("perfect-5th" ~3:2 = 91 degrees, "major-3rd" ~5:4 = 50),
the representation of 225:128 turned out to be 126.

so at least in this mapping (which to me is the one
which makes the most sense ... i think ...), the
"septimal kleisma" is not articulated after all!

help.




-monz


top of page bottom of page up down


Message: 5485 - Contents - Hide Contents

Date: Tue, 05 Nov 2002 19:09:25

Subject: Re: 156edo, articulating septimal kleisma

From: Carl Lumma

> i was searching for an EDO which would articulate the > "septimal kleisma" [2 2 -1] = 225:224 (~7.711522991 cents).
You could really articulate it with ets like 27 and 37, which both represent it as one step, or 26, which shrinks it to -1 steps! If you really want to articulate it accurately, why not use JI? If Gene/Paul would follow through and make the tree zoom duals, you might be able to see this kind of thing at a glance! -Carl
top of page bottom of page up down


Message: 5486 - Contents - Hide Contents

Date: Tue, 5 Nov 2002 10:56:20

Subject: Re: 156edo, articulating septimal kleisma

From: manuel.op.de.coul@xxxxxxxxxxx.xxx

Use DIVIDE/CONSISTENT 225/224
You see the size is zero in 156-ET, 152 is better.

Manuel


top of page bottom of page up down


Message: 5487 - Contents - Hide Contents

Date: Tue, 05 Nov 2002 19:58:14

Subject: Tree zoom duals

From: Gene Ward Smith

--- In tuning-math@y..., "Carl Lumma" <clumma@y...> wrote:

> If Gene/Paul would follow through and make the tree zoom > duals, you might be able to see this kind of thing at a > glance!
Here you go: We can consider 5-limit ets to be vals [a,b,c] with elements positive integers; they define a point in the projective plane. Since "a" is not zero, we can divide by "a" and get the point [b/a,c/a] in the affine plane as a coordinate patch. We now note that the points are all clustered about [log2(3),log2(5)], so we may move the origin to this point. We now have the "tree zoom" picture. Similarly, if q is a comma, then we may consider it to be [a,b,c] where 2^a 3^b 5^c = q. We no longer can always divide by "a", so we cannot take "a=0" to be the line at infinity as we did with ets. Instead, we can take a+log2(3)*b + log2(5)*c=0 to be the line at infinity, since the comma is not 1. This means we can divide through by log2(q) (or cents, etc--which log map we use is not important) and get [a/log2(q),b/log2(q),c/log2(q)]; taking the last two gives us an affine coordinate patch: [b/log2(q), c/log2(q)] which can be used to plot commas as points.
top of page bottom of page up down


Message: 5488 - Contents - Hide Contents

Date: Tue, 5 Nov 2002 02:02:37

Subject: Re: 156edo, articulating septimal kleisma

From: monz

thanks, Manuel.


> From: <manuel.op.de.coul@xxxxxxxxxxx.xxx> > To: <tuning-math@xxxxxxxxxxx.xxx> > Sent: Tuesday, November 05, 2002 1:56 AM > Subject: Re: [tuning-math] 156edo, articulating septimal kleisma > > Use DIVIDE/CONSISTENT 225/224 > You see the size is zero in 156-ET, 152 is better. > > Manuel -monz
top of page bottom of page up down


Message: 5489 - Contents - Hide Contents

Date: Tue, 05 Nov 2002 20:57:54

Subject: Re: Tree zoom duals

From: wallyesterpaulrus

--- In tuning-math@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:

>taking the last two gives us an affine coordinate patch: [b/log2(q), >c/log2(q)] which can be used to plot commas as points.
interesting . . . thanks so much gene!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
top of page bottom of page up down


Message: 5490 - Contents - Hide Contents

Date: Tue, 05 Nov 2002 21:02:37

Subject: Re: 156edo, articulating septimal kleisma

From: wallyesterpaulrus

--- In tuning-math@y..., "monz" <monz@a...> wrote:
> hmmm ... this is interesting: > > i was searching for an EDO which would articulate the > "septimal kleisma" [2 2 -1] = 225:224 (~7.711522991 cents). > > 156edo looked very good, since the "augmented-6th" 225:128 and > the "harmonic-minor-7th" 7:4 are approximated very closely > by is 127 and 126 degrees, respectively. thus, the > "septimal kleisma" is almost exactly 1 degree. > > but then, when i made a bingo-card-lattice of 156edo > ("perfect-5th" ~3:2 = 91 degrees, "major-3rd" ~5:4 = 50), > the representation of 225:128 turned out to be 126. > > so at least in this mapping (which to me is the one > which makes the most sense ... i think ...), the > "septimal kleisma" is not articulated after all! > > help.
monz, this is really no different from 55-equal -- although the *just* 80:81 (syntonic comma) is very nearly one degree of 55-equal, the *native* 80:81 (syntonic comma) of 55-equal vanishes. in that case you just need a much better 5-limit approximation -- 53- equal of course does the trick. in the current case you just need a much better 7-limit approximation -- 152-equal, the universal tuning, will work. :) similarly, one of your webpages claims that the schisma is well- represented by one degree of 614-equal. of course, 612-equal would, functionally, work much better, since it offers a far better 5-limit approximation. maybe we should start using the symbol 81;80 for the native syntonic comma of any temperament?
top of page bottom of page up down


Message: 5491 - Contents - Hide Contents

Date: Tue, 05 Nov 2002 23:54:38

Subject: Re: 156edo, articulating septimal kleisma

From: wallyesterpaulrus

--- In tuning-math@y..., "Carl Lumma" <clumma@y...> wrote:

> If Gene/Paul would follow through and make the tree zoom > duals, you might be able to see this kind of thing at a > glance! >
unfortunately, 225:224 has components in all three directions (3, 5, and 7), so it might be hard without a nice VRML implementation of this . . .
top of page bottom of page up down


Message: 5492 - Contents - Hide Contents

Date: Tue, 5 Nov 2002 22:34:24

Subject: Re: Tree zoom duals

From: monz

> From: "Gene Ward Smith" <genewardsmith@xxxx.xxx> > To: <tuning-math@xxxxxxxxxxx.xxx> > Sent: Tuesday, November 05, 2002 6:58 PM > Subject: [tuning-math] Re: Tree zoom duals > > > --- In tuning-math@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote:
>> --- In tuning-math@y..., "Gene Ward Smith" <genewardsmith@j...> wrote: >>
>>> taking the last two gives us an affine coordinate patch: [b/log2(q), >>> c/log2(q)] which can be used to plot commas as points. >>
>> interesting . . . thanks so much gene!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! >
> Yer welcome--of course now you need to zoom out rather than > in if you want to fool with this. > > What would be really cool is a 3D applet, which let you look at > a 7-limit picture from various directions. We could have either > ets as points, linear temperaments as lines, and commas as planes, > or a dual picture with commas as points, linear temperaments > again as lines, and ets as planes.
this is all stuff that i've always intended from the beginning to have available in my JustMusic software. JustMusic software, (c) 1999 by Joseph L. Monzo * [with cont.] (Wayb.) unfortunately, both the project and the Yahoo group have been slumbering for quite some time. any chance we can wake them up? -monz (still looking for a Microsoft Visual C++ programmer to help out)
top of page bottom of page up down


Message: 5493 - Contents - Hide Contents

Date: Wed, 06 Nov 2002 20:07:58

Subject: Re: Tree zoom duals

From: wallyesterpaulrus

--- In tuning-math@y..., "monz" <monz@a...> wrote:
> > ----- Original Message ----- > From: "wallyesterpaulrus" <wallyesterpaulrus@y...> > To: <tuning-math@y...> > Sent: Tuesday, November 05, 2002 11:55 PM > Subject: [tuning-math] Re: Tree zoom duals > >
>> --- In tuning-math@y..., "monz" <monz@a...> wrote: >> >>>>
>>>> What would be really cool is a 3D applet, which let you look at >>>> a 7-limit picture from various directions. We could have either >>>> ets as points, linear temperaments as lines, and commas as planes, >>>> or a dual picture with commas as points, linear temperaments >>>> again as lines, and ets as planes. >>> >>> >>>
>>> this is all stuff that i've always intended from the beginning >>> to have available in my JustMusic software. >>> >>> JustMusic software, (c) 1999 by Joseph L. Monzo * [with cont.] (Wayb.) >>
>> is that really true? do you have any of the ideas above referenced >> anywhere? > > >
> what's on the webpage and in the archives of the Yahoo JustMusic group > is all i've ever made public about it. the rest of my ideas are in > folders and folders of notes and old BASIC code ... stuff that i > haven't even looked at in over 5 years.
monz, if you dig up notes in your folders that mention even one of these ideas, let alone all of them, i'll be absolutely stunned.
top of page bottom of page up down


Message: 5494 - Contents - Hide Contents

Date: Wed, 06 Nov 2002 20:09:45

Subject: Re: Tree zoom duals

From: wallyesterpaulrus

--- In tuning-math@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:
> --- In tuning-math@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote: >
>>> Yer welcome--of course now you need to zoom out rather than in if >>> you want to fool with this. >>
>> what do you mean? >
> The high-octane ets crowd in towards the origin, so you zoom in to >find them. The high-octane commas expand out to infinity, so you >would need to zoom out to include them.
right -- i realized this as soon as i signed off last night. i also realized that each et line will intersect each axis at a distance from the origin inversely proportional to that consonance's error in that et. this will spare me the effort of having to construct a list of commas.
top of page bottom of page up down


Message: 5495 - Contents - Hide Contents

Date: Wed, 06 Nov 2002 21:51:43

Subject: Re: Tree zoom duals

From: Gene Ward Smith

--- In tuning-math@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote:

> i also realized that each et line will intersect each axis at a > distance from the origin inversely proportional to that consonance's > error in that et. this will spare me the effort of having to > construct a list of commas. Slick!
top of page bottom of page up down


Message: 5496 - Contents - Hide Contents

Date: Wed, 06 Nov 2002 00:33:10

Subject: Re: 156edo, articulating septimal kleisma

From: Carl Lumma

>> >f Gene/Paul would follow through and make the tree zoom >> duals, you might be able to see this kind of thing at a >> glance! >> >
>unfortunately, 225:224 has components in all three directions (3, >5, and 7), so it might be hard without a nice VRML implementation >of this . . .
Maybe Robert Walker can help us there... For now, the 5-limit would still be cool. I suspect even cooler than the et-centric versions... -Carl
top of page bottom of page up down


Message: 5497 - Contents - Hide Contents

Date: Wed, 06 Nov 2002 02:58:54

Subject: Re: Tree zoom duals

From: Gene Ward Smith

--- In tuning-math@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote:
> --- In tuning-math@y..., "Gene Ward Smith" <genewardsmith@j...> wrote: >
>> taking the last two gives us an affine coordinate patch: [b/log2(q), >> c/log2(q)] which can be used to plot commas as points. >
> interesting . . . thanks so much gene!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Yer welcome--of course now you need to zoom out rather than in if you want to fool with this. What would be really cool is a 3D applet, which let you look at a 7-limit picture from various directions. We could have either ets as points, linear temperaments as lines, and commas as planes, or a dual picture with commas as points, linear temperaments again as lines, and ets as planes.
top of page bottom of page up down


Message: 5498 - Contents - Hide Contents

Date: Wed, 06 Nov 2002 03:09:37

Subject: Re: 156edo, articulating septimal kleisma

From: Gene Ward Smith

--- In tuning-math@y..., "Carl Lumma" <clumma@y...> wrote:

> Maybe Robert Walker can help us there... For now, the 5-limit > would still be cool. I suspect even cooler than the et-centric > versions...
Plus you can always use inversive geometry, turn either version inside-out, and replace the lines with circles.
top of page bottom of page up down


Message: 5499 - Contents - Hide Contents

Date: Wed, 06 Nov 2002 07:53:52

Subject: Re: Tree zoom duals

From: wallyesterpaulrus

--- In tuning-math@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:
> --- In tuning-math@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote:
>> --- In tuning-math@y..., "Gene Ward Smith" <genewardsmith@j...> wrote: >>
>>> taking the last two gives us an affine coordinate patch: [b/log2 (q), >>> c/log2(q)] which can be used to plot commas as points. >>
>> interesting . . . thanks so much gene!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! >
> Yer welcome--of course now you need to zoom out rather than in if >you want to fool with this.
what do you mean?
> What would be really cool is a 3D applet, which let you look at a 7- >limit picture from various directions. We could have either ets as >points, linear temperaments as lines, and commas as planes, or a >dual picture with commas as points, linear temperaments again as >lines, and ets as planes.
yup yup yup yup yup!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!
top of page bottom of page up

Previous Next

5000 5050 5100 5150 5200 5250 5300 5350 5400 5450 5500 5550 5600 5650 5700 5750 5800 5850 5900 5950

5450 - 5475 -

top of page