Yahoo Tuning Groups Ultimate Backup tuning-math monzoblock37

thanks, Gene! awesome!
as they say in my neighborhood: "you da man!"

i took a screenshot of the Lattice in Tonescape and
wanted to upload it to the Files section here, but got
a message that the moderator has disallowed uploads. (?)

so i started making a webpage about 37-edo, but it's
taking a long time. so for now, here is a link to the
screenshot graphic:

http://tonalsoft.com/enc/number/37-edo/images/37edo_2,3,5,7,11,13-space_gws-basis_triangular-lattice.jpg

(delete line-breaks in that URL if there are any)

note that i called it "gws-basis", because i didn't know
what else to call it.

-monz
http://tonalsoft.com/tonescape.aspx
Tonescape microtonal music software

--- In tuning-math@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> Here we go:
>
>
> ! monzoblock37.scl
> !
> Symmetrical 13-limit Fokker block containing all of the primes as scale degrees
> ! Commas: 512/507, 121/120, 91/90, 385/384, 64/63; all generators -18 to 18
> 37
> !
> 1024/1001
> 33/32
> 16/15
> 13/12
> 12/11
> 44/39
> 8/7
> 7/6
> 13/11
> 77/64
> 16/13
> 5/4
> 33/26
> 13/10
> 4/3
> 192/143
> 11/8
> 128/91
> 91/64
> 16/11
> 143/96
> 3/2
> 20/13
> 52/33
> 8/5
> 13/8
> 128/77
> 22/13
> 12/7
> 7/4
> 39/22
> 11/6
> 24/13
> 15/8
> 64/33
> 1001/512
> 2/1
>

🔗genewardsmith <genewardsmith@sbcglobal.net>

🔗monz <joemonz@yahoo.com>

yeah ... you are looking at a 3-D shadow of a 5-D structure,
so i'm not sure how much the adjective "squarish" even applies,
but i know what you mean.

of course, it would be a lot easier for you to grasp the
entire shape if you were rotating your view of it in Tonescape!

;-)

-monz
http://tonalsoft.com/tonescape.aspx
Tonescape microtonal music software

--- In tuning-math@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning-math@yahoogroups.com, "monz" <joemonz@> wrote:
>
> > so i started making a webpage about 37-edo, but it's
> > taking a long time. so for now, here is a link to the
> > screenshot graphic:
> >
> > http://tonalsoft.com/enc/number/37-edo/images/37edo_2,3,5,7,11,13-space_gws-basis_triangular-lattice.jpg
>
> Cool! So far as I can tell by looking at this, it's decently squarish.
>

🔗monz <joemonz@yahoo.com>

Would someone please post the ASCII version of
the sagittal notation for this Fokker block?
I would like to add it to my upcoming Encyclopedia page.

Thanks.

-monz
http://

🔗monz <joemonz@yahoo.com>

Here is my new Tonalsoft Encyclopedia page about 37-edo:

http://tonalsoft.com/enc/number/37-edo/37edo.aspx

It is not yet included in the index menu, but in case anyone
here wants to see it and use it, there's the URL.

This is really quite a promising EDO tuning!

I'm still hoping to get the ASCII sagittal notation for
this periodicity-block.

-monz
http://tonalsoft.com/tonescape.aspx
Tonescape microtonal music software

🔗genewardsmith <genewardsmith@sbcglobal.net>

I can't do that for you, but here is an alternative plan you could also try: make use of the fact that 37 is half of 74. The two map the same through the 19-limit no-threes, with 74 mapping 3/2 to a meantone fifth. You could therefore use meantone notation for all of the no-threes 19-limit intervals of 37, but instead of C-G being a fifth, it would be C-E####.

It may be screwball, but it would work.

🔗genewardsmith <genewardsmith@sbcglobal.net>

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

> I can't do that for you, but here is an alternative plan you could also try: make use of the fact that 37 is half of 74. The two map the same through the 19-limit no-threes, with 74 mapping 3/2 to a meantone fifth.

By the way, here is another factiod for you: take a basis for the commas of no-threes 37 through the 19-limit, for example 170/169, 176/175, 209/208, 247/245, 476/475, 608/605. Add 81/80 to this and you get <74 117 172 208 256 274 302 314|. If you add 250/243 instead you get <37 59 86 104 128 137 151 157|.

🔗gdsecor <gdsecor@yahoo.com>

Hi Monz,

The simplest way to get the sagittal notation for a tuning is to load your .scl file into Scala. For a JI set you have to choose a precision level:
Athenian level (medium precision): set nota saji1
Promethian level (high precision, no accents): set nota saji2
Herculean level (high precision, right accents): set nota saji3
Olympian level (extreme precision, left & right accents): set nota saji4

Promethean level is closest to the 37-equal notation I'm proposing below.

To get saji3 & saji4 you'll need to download the very latest version of Scala, which Manuel released within the past week. (Note to Mike B.: native-fifth notations for 16-equal and 23-equal are now supported by Scala: set nota sa16n; set nota sa23n)

For 37-equal, if you enter "set nota sa37" you'll see it notated as a subset of 111-equal.

If you want a native-fifth notation for 37-equal, you'll need to edit (and save) the (text) file sag_et.par, inserting the following two lines immediately before the line consisting of "d 38 22":

n 37 22
)~| /| )/|\ N\ ~N\ /N\

Then enter "set nota sa37n" on the command line to use this 37-equal native-fifth notation. (If you get an error message stating that this notation was not found, then exit Scala and rerun it to load the modified sag_et.par file.

One possible substitution for the )/|\ symbol (3deg37) is /|), but I didn't choose it for two reasons:
1) it's valid for 13M (1024:1053), but not 35M (35:36, its primary role, which is 2deg37);
2) since the apotome is 6deg37, this symbol represents 1/2 apotome, in which case it would be preferable to use a symbol representing a JI interval closer in size to 1/2 apotome; )/|\ is defined as 5:49M (392:405), which is as close as you can get;

/|\ (11M, 32:33) might have been a good candidate for 3deg37, except that it's 2deg37, for which instead I chose /| (5C, 80:81), because the latter is a lower prime limit, and its symbol is easier to distinguish from )/|\ .

For 1deg37, the )~| symbol is defined as 143C (143:144, its primary role). There are other valid symbols, but this one appears to have the least amount of baggage (I'll spare you the details).

--George

--- In tuning-math@yahoogroups.com, "monz" <joemonz@...> wrote:
>
> Would someone please post the ASCII version of
> the sagittal notation for this Fokker block?
> I would like to add it to my upcoming Encyclopedia page.
>
> Thanks.
>
> -monz
> http://
>
> --- In tuning-math@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> >
> > Here we go:
> >
> >
> > ! monzoblock37.scl
> > !
> > Symmetrical 13-limit Fokker block containing all of the primes as scale degrees
> > ! Commas: 512/507, 121/120, 91/90, 385/384, 64/63; all generators -18 to 18
> > 37
> > !
> > 1024/1001
> > 33/32
> > 16/15
> > 13/12
> > 12/11
> > 44/39
> > 8/7
> > 7/6
> > 13/11
> > 77/64
> > 16/13
> > 5/4
> > 33/26
> > 13/10
> > 4/3
> > 192/143
> > 11/8
> > 128/91
> > 91/64
> > 16/11
> > 143/96
> > 3/2
> > 20/13
> > 52/33
> > 8/5
> > 13/8
> > 128/77
> > 22/13
> > 12/7
> > 7/4
> > 39/22
> > 11/6
> > 24/13
> > 15/8
> > 64/33
> > 1001/512
> > 2/1

monzoblock37

🔗genewardsmith <genewardsmith@sbcglobal.net>

🔗monz <joemonz@yahoo.com>

🔗genewardsmith <genewardsmith@sbcglobal.net>

🔗monz <joemonz@yahoo.com>

🔗monz <joemonz@yahoo.com>

🔗monz <joemonz@yahoo.com>

🔗genewardsmith <genewardsmith@sbcglobal.net>

🔗genewardsmith <genewardsmith@sbcglobal.net>

🔗gdsecor <gdsecor@yahoo.com>

🔗Wolf Peuker <wolfpeuker@googlemail.com>