New file uploaded to tuning-math

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File : /Borasky's Derive Code/Basics.pdf
Uploaded by : znmeb@aracnet.com
Description : Derive code for Partch and Sethares calculations

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File : /Borasky's Derive Code/ScaledVsUnitAmplitudes.pdf
Uploaded by : znmeb@aracnet.com
Description : Plot of Sethares dissonance curves for unit-amplitude and scaled-amplitude spectra, with Partch scale points plotted

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File : /Gene/sevn
Uploaded by : genewardsmith@juno.com
Description : Notations in the 7-limit

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genewardsmith@juno.com

If you take the fifteen 7-limit intervals 25/24, 28/27, 36/35, 49/48,
50/49, 64/63, 81/80, 126/125, 245/243, 1029/1024, 1728/1715,
2401/2400, 3136/3125, 4375/4374, 6144/6125 from the list
http://www.kees.cc/tuning/s2357.html which Paul used, and take the
15 choose 4 = 1365 four-element subsets, you will find that 642 of
them give unimodular matricies, and hence give us notations. I
uploaded all of these. The first list is a list of the four intervals
used, and the second a list of the columns of the inverse matrix. If
a number +-n appears on the list, then +-hn, the column vector
consisting of n, round(n log_2(3)), round(n log_2(5)),
round(n log_2(7)), is meant. If there is just a "v", it means it is
not rounded off in this way, and the entire matrix is given in a
compact form as a list of lists; the lists are horizontal but
represent column vectors.

There are vast numbers of blocks and tempered blocks which could be
extracted from all of this, so it would be helpful to know what sort
of thing people are looking for.

--- In tuning-math@y..., genewardsmith@j... wrote:

> There are vast numbers of blocks and tempered blocks which could be
> extracted from all of this, so it would be helpful to know what
sort
> of thing people are looking for.

The sort of thing described in my 22-tET paper <http://www-
math.cudenver.edu/~jstarret/22ALL.pdf>, things like blackjack, and
everything in-between. Is there an 11-limit analogue to the decatonic
system of my paper? What if we relax one or two of the rules in my
paper?

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File : /Paul/gene3.gif
Uploaded by : paulerlich <paul@stretch-music.com>
Description : Power spectrum of 1/badness

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File : /Dave/SaggitalSingle217C2DK.bmp
Uploaded by : dkeenanuqnetau <d.keenan@uq.net.au>
Description : My first attempt at single-symbol sagittal notation for 217-ET using plan C2

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File : /Dave/SaggitalMulti217C2DK.bmp
Uploaded by : dkeenanuqnetau <d.keenan@uq.net.au>
Description : My attempt at multi-symbol sagittal notation for 217-ET

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File : /Dave/SaggitalSingle217C2DK.bmp
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Description : My attempt at single-symbol sagittal notation for 217-ET

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dkeenanuqnetau <d.keenan@uq.net.au>

--- In tuning-math@y..., tuning-math@y... wrote:
>
> /tuning-math/files/Gene/GWS.tif

This is an old paper (my rejection letter is dated 1984, which means I completed it in 1983) which David Feldman scanned for me.

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File : /DJVU/22all.djvu
Uploaded by : genewardsmith <genewardsmith@juno.com>
Description : Paul Erlich 22 tones

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File : /Paul/bingo0.zip
Uploaded by : wallyesterpaulrus <wallyesterpaulrus@yahoo.com>
Description : how ETs work in the 5-limit -- hexagonal bingo cards

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Hello,

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File : /Paul/xoomcont.gif
Uploaded by : wallyesterpaulrus <wallyesterpaulrus@yahoo.com>
Description : 5-limit rms error contours on "xoomer" ET graph

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> /tuning-math/files/Paul/xoomcont.gif

This .gif is golden.

But I forget the coloring scheme...

-Carl

--- In tuning-math@y..., "Carl Lumma" <clumma@y...> wrote:
> > /tuning-math/files/Paul/xoomcont.gif
>
> This .gif is golden.
>
> But I forget the coloring scheme...
>
> -Carl

bluish = consistent

reddish = inconsistent

is that what you meant?

>>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), and real
purple (24)?

-Carl

--- 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?)

>>>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?)

Got it. It's whatever you want to call it.

Did you do this just for visibility?

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

> Did you do this just for visibility?

yes.

>>Did you do this just for visibility?
>
>yes.

It worked!

-C.

--- 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!

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File : /planar plots/p1728.jpg
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File : /planar plots/p64.jpg
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Description : 64/63 (Septimus) planar lattice

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File : /planar plots/p245.jpg
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Description : 245/243 (Beep) planar lattice

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recently, manuel mentioned that the dude with the cule lattices had
settled on a basic structure where one axis was 3/2 while the other
was 27/20. what temperament would this lattice correspond to?

--- In tuning-math@yahoogroups.com, tuning-math@yahoogroups.com wrote:
>
> Hello,
>
> This email message is a notification to let you know that
> a file has been uploaded to the Files area of the tuning-math
> group.
>
> File : /planar plots/p1728.jpg
> Uploaded by : genewardsmith <genewardsmith@j...>
> Description : 1728/1715 (George) planar lattice
>
> You can access this file at the URL
>
> /tuning-math/files/planar%
20plots/p1728.jpg
>
> To learn more about file sharing for your group, please visit
>
> http://help.yahoo.com/help/us/groups/files
>
> Regards,
>
> genewardsmith <genewardsmith@j...>

this one looks "monzian". by which i mean his lattice angles,
not "monzismic". uh-oh -- now i've really asked for it!

--- In tuning-math@yahoogroups.com, tuning-math@yahoogroups.com wrote:
>
> Hello,
>
> This email message is a notification to let you know that
> a file has been uploaded to the Files area of the tuning-math
> group.
>
> File : /planar plots/p64.jpg
> Uploaded by : genewardsmith <genewardsmith@j...>
> Description : 64/63 (Septimus) planar lattice
>
> You can access this file at the URL
>
> /tuning-math/files/planar%
20plots/p64.jpg
>
> To learn more about file sharing for your group, please visit
>
> http://help.yahoo.com/help/us/groups/files
>
> Regards,
>
> genewardsmith <genewardsmith@j...>

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

> recently, manuel mentioned that the dude with the cule lattices had
> settled on a basic structure where one axis was 3/2 while the other
> was 27/20. what temperament would this lattice correspond to?

(1) What in the world is a cule lattice? Did you mean cute, but with a stuffed-up nose?

(2) I imagine it's just 5-limit JI, though it is possible to cook up goofy temperaments such as 4782969/4480000 to go with it.

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Description : <225/224, 385/384> (Marvel) planar lattice

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Description : extreme close-up of 5-limit ETs and linear temperaments; gridlines spaced at 0.004 cent increments

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Paul,

These are tha bomb!

-Carl

--- In tuning-math@yahoogroups.com, "Carl Lumma
<clumma@y...>" <clumma@y...> wrote:
> Paul,
>
> These are tha bomb!
>
> -Carl

just one more to do . . . q, r, s, t, and u are each a factor of 10
zoom of the previous one, and i haven't done s yet (i'm away from
the office).

then i'm hoping we can get gene to produce an ultimate {2,3,7}
list and an ultimate {2,5,7} list . . .

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> /tuning-math/files/Paul/zooms.gif

Awesome. -C.

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--- In tuning-math@yahoogroups.com, tuning-math@yahoogroups.com wrote:
>
> Hello,
>
> This email message is a notification to let you know that
> a file has been uploaded to the Files area of the tuning-math
> group.

I uploaded plots of the major thirds of some well-temperaments, going
around the circle of fifths. The three "Smith Wells", decribed in the
file, are the ones with squirrel index 8 and seven pure fifths. These
are, of course, far closer to 12-equal than Werckmeister III, which I
also give a plot for. I was going to put my version of this
temperament on the same plot, but they are so close this is
impossible, as one covers the other.

Does Robert read this list? I'd be interested in comments from well
temperament mavens about these plots, which strike me as a useful way
of looking at wells.

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--- In tuning-math@yahoogroups.com, tuning-math@yahoogroups.com wrote:

> File : /hex2.gif
> Uploaded by : paulerlich <perlich@a...>
> Description : Projective 5-limit tuning space?

Vals are points, so I guess this is provo space. :)

Is there going to be a promo space diagram too?

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hi Paul,

> File : /promo/promo0.gif
> Uploaded by : paulerlich <perlich@a...>
> Description : A projective look at the 5-limit lattice
>
> /tuning-math/files/promo/promo0.gif

please explain.

-monz

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As an attempt to organize the microtonal links on the WEB,
I have started a microtonal community page for us to place
our links.

For 2 months I am happy to place the link for you if you mail me
your website:

tony@tonysalinas.com

Also feel free to place a link or arrange the site by yourself if necessary:

www.microtonality.wikispaces.com

I placed a section on mathematical mappings of tunings under the Theory sections,
so feel free to suggest here or change the page so all the tuning mathematics matters
are covered.

Sincerely,

Tony Salinas

See my delicious profile

http://del.icio.us/clumma

-Carl

At 08:39 PM 8/26/2007, you wrote:
>As an attempt to organize the microtonal links on the WEB,
>I have started a microtonal community page for us to place
>our links.
>
>For 2 months I am happy to place the link for you if you mail me
>your website:
>
>tony@tonysalinas.com
>
>Also feel free to place a link or arrange the site by yourself if
>necessary:
>
>www.microtonality.wikispaces.com
>
>I placed a section on mathematical mappings of tunings under the
>Theory sections,
>so feel free to suggest here or change the page so all the tuning
>mathematics matters
>are covered.
>
>Sincerely,
>
>Tony Salinas

Thanks Carl for your delicious links!

Cheers,

Tony Salinas

On 2007/08/27, at 14:15, Carl Lumma wrote:

> See my delicious profile
>
> http://del.icio.us/clumma
>
> -Carl
>
> At 08:39 PM 8/26/2007, you wrote:
> >As an attempt to organize the microtonal links on the WEB,
> >I have started a microtonal community page for us to place
> >our links.
> >
> >For 2 months I am happy to place the link for you if you mail me
> >your website:
> >
> >tony@tonysalinas.com
> >
> >Also feel free to place a link or arrange the site by yourself if
> >necessary:
> >
> >www.microtonality.wikispaces.com
> >
> >I placed a section on mathematical mappings of tunings under the
> >Theory sections,
> >so feel free to suggest here or change the page so all the tuning
> >mathematics matters
> >are covered.
> >
> >Sincerely,
> >
> >Tony Salinas
>
>
>

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Thanks for documenting your work so beautifully, Graham!

In the Conclusion, this sentence reads bit awkwardly:
"A good, simple to calculate error to calculate is the RMS..."

-C.

At 05:00 AM 2/6/2008, you wrote:
>
>Hello,
>
>This email message is a notification to let you know that
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> Description : Prime errors and complexities, final version
>
>You can access this file at the URL:
>/tuning-math/files/primerr.pdf
>
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>
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Carl Lumma wrote:
> Thanks for documenting your work so beautifully, Graham!
> > In the Conclusion, this sentence reads bit awkwardly:
> "A good, simple to calculate error to calculate is the RMS..."

There we go, one for the errata.

Graham

Graham wrote:
>Carl Lumma wrote:
>> Thanks for documenting your work so beautifully, Graham!
>>
>> In the Conclusion, this sentence reads bit awkwardly:
>> "A good, simple to calculate error to calculate is the RMS..."
>
>There we go, one for the errata.

Does this new version include the stuff you were working on
in October

/tuning-math/message/16815
/tuning-math/message/16816
/tuning-math/message/16817
/tuning-math/message/16819

?

-Carl

Carl Lumma wrote:

> Does this new version include the stuff you were working on
> in October
> > /tuning-math/message/16815
> /tuning-math/message/16816
> /tuning-math/message/16817
> /tuning-math/message/16819
> > ?

I took out some of the rank 2 details. The formula I have for scalar badness in the paper has the geometric properties I was looking for then.

Equation 79 shows the badness in terms of "badness vectors". Maybe the custom notation obscures that, but each vector is the original mapping minus the weighted mean. So it's a weighted generalization of the covariance matrix -- which I do mention. The parameterized badness has the same properties because it's a linear combination of scalar complexity and badness (give or take some squaring).

Under "Wedgie Complexity" I give the reference for the volume of a matrix. I don't go into the geometric details but you can extrapolate them from that observation.

Under "Wedgie Error" I explain that it isn't as easy to calculate the error from unison vectors as I originally claimed :(

Singular value decompositions are certainly interesting, and I originally used them in my first TOP-RMS error proof, but I ended up not needing them. One of the matrices you get from an SVD seems to uniquely identify the temperament class.

The connection between scalar complexity and the number of notes in a periodicity block is the main thing I forgot to add when I declared the paper near-enough finished. I toyed with adding it anyway but decided not to.

Graham

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On 5/1/2011 12:48 AM, tuning-math@yahoogroups.com wrote:
>
> Hello,
>
> This email message is a notification to let you know that
> a file has been uploaded to the Files area of the tuning-math
> group.
>
> File : /x31eq/catalog2.html
> Uploaded by : x31eq<gbreed@gmail.com>
> Description : All my temperament names

Thanks for this useful list! I notice right away though that you've got 270 and 764-ET mappings for abigail. Is there any special reason for picking those over 46 and 132? You can't even use more than 128 notes for MIDI.

On 1 May 2011 23:48, Herman Miller <hmiller@io.com> wrote:

> Thanks for this useful list! I notice right away though that you've got
> 270 and 764-ET mappings for abigail. Is there any special reason for
> picking those over 46 and 132? You can't even use more than 128 notes
> for MIDI.

They're all picked automatically. They should be the best pair given
the badness parameter that was used for the list the temperament was
discovered in. I check small errors first, so you're likely to see
over-complex ETs. That much is arbitrary. At least they're less
likely to be ambiguous.

Graham

On 1 May 2011 23:48, Herman Miller <hmiller@io.com> wrote:
> On 5/1/2011 12:48 AM, tuning-math@yahoogroups.com wrote:
>>
>> Hello,
>>
>> This email message is a notification to let you know that
>> a file has been uploaded to the Files area of the tuning-math
>> group.
>>
>>    File        : /x31eq/catalog2.html
>>    Uploaded by : x31eq<gbreed@gmail.com>
>>    Description : All my temperament names
>
> Thanks for this useful list! I notice right away though that you've got
> 270 and 764-ET mappings for abigail. Is there any special reason for
> picking those over 46 and 132? You can't even use more than 128 notes
> for MIDI.

I've got special reasons for choosing the ETs now. I took the best
linearly independent set where "best" is determined by Cangwu badness
with the error parameter set to the actual TE error of the optimized
temperament. Except for very accurate temperaments where I used 0.01
cents/octave to stop the ETs getting stupidly complex (and also to
suppress rounding errors).

The result is that there are still some very large ETs. Abigail is now 270&494.

Graham

--- In tuning-math@yahoogroups.com, Graham Breed <gbreed@...> wrote:

> The result is that there are still some very large ETs. Abigail is now 270&494.

I think 270&494 is a very sensible way to describe abagail, so I suspect this method is a success. Congratulations!

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