Encapsulated PostScript for Just Intonation

Dear JI Fans,
I have just added a new section to my website:

Encapsulated PostScript for Just Intonation
http://www.mbay.net/~anne/david/eps4ji/

excerpt:
In the course of my music theoretical explorations, I have found certain
graphical representations helpful in understanding scales and tunings in
just intonation. And after I realized that PostScript was a general
programming language capable of generating high-quality
resolution-independent graphics on a wide variety of platforms, I taught
myself enough to develop these Encapsulated PostScript graphics. Each one
represents a particular graphical idea, and the file can be easily modified
to change the scale and/or many style options (in the "USER SETUP" section;
see the Variations for examples of the ease of editing). The resulting EPS
graphic can not only be printed on any PostScript printer (or other printers
using "Ghostscript"), but can also be imported (and resized if necessary)
into many graphics, page-layout, and word-processing programs, for
incorporation into other documents.

Check it out! Take your favorite JI scale and make an interval matrix, or an
acoustically-spaced slide rule, or a harmonic-melodic diagram, or lay out a
fretboard for your ukelele...

David Canright (831) 656-2782 (or -2206)
Math. Dept., Code MA/Ca (831) 656-2355 (FAX)
Naval Postgraduate School DCanright@NPS.Navy.mil
Monterey, CA 93943 USA http://www.mbay.net/~anne/david/

David Canright wrote,

>Encapsulated PostScript for Just Intonation
>http://www.mbay.net/~anne/david/eps4ji/
>[...]
>Check it out! Take your favorite JI scale and make an interval matrix, or
an
>acoustically-spaced slide rule, or a harmonic-melodic diagram, or lay out a
>fretboard for your ukelele...

Excellent! Would it be possible to include the triangular and
tetrahedral-octahedral representations we've been using here on the list, as
well as Dave Keenan's altered projections thereof?

> -----Original Message-----
> From: tuning@onelist.com [SMTP:tuning@onelist.com]
> Sent: Friday, June 18, 1999 4:20 PM
> To: tuning@onelist.com
> Subject: [tuning] Digest Number 223
> Message: 24
> Date: Fri, 18 Jun 1999 17:54:00 -0400
> From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
> Subject: Re: Encapsulated PostScript for Just Intonation
>
> David Canright wrote,
>
> >Encapsulated PostScript for Just Intonation
> >http://www.mbay.net/~anne/david/eps4ji/
> >[...]
> >Check it out! Take your favorite JI scale and make an interval matrix, or
> an
> >acoustically-spaced slide rule, or a harmonic-melodic diagram, or lay out
> a
> >fretboard for your ukelele...
>
> Excellent! Would it be possible to include the triangular and
> tetrahedral-octahedral representations we've been using here on the list,
> as
> well as Dave Keenan's altered projections thereof?
>
Dear Paul,
In response to your request, I added to my site. I modified the
harmonic-melodic diagram file (harmel.eps) to make the vertical coordinates
arbitrary instead of pitch-based. The result is:
lattice.eps : Harmonic Lattice Diagram -- shows the harmonic structure of
a scale by links for each prime harmony.
(Basically, you enter the scale and what directions each prime harmony goes;
it makes the lattice.)
Also, for links other than prime harmonies I made:
lattica.eps : Harmonic Lattice Diagram, Advanced -- shows the harmonic
structure of a scale by links that you specify (so can handle triangular
lattices, for example), with the option of showing each link in a specified
line style.
(I include examples of tetrahedral and triangular lattices.)

I hope some of you find these useful. I must say, I a very impressed with
the ASCII versions some of you, notably Dave Keenan, have come up with:
wonderful!

David Canright (831) 656-2782 (or -2206)
Math. Dept., Code MA/Ca (831) 656-2355 (FAX)
Naval Postgraduate School DCanright@NPS.Navy.mil
Monterey, CA 93943 USA http://www.mbay.net/~anne/david/

David Canright wrote,

>Dear Paul,
>In response to your request, I added to my site. I modified the
>harmonic-melodic diagram file (harmel.eps) to make the vertical coordinates
>arbitrary instead of pitch-based. The result is:
> lattice.eps : Harmonic Lattice Diagram -- shows the harmonic structure
of
>a scale by links for each prime harmony.
>(Basically, you enter the scale and what directions each prime harmony
goes;
>it makes the lattice.)
>Also, for links other than prime harmonies I made:
> lattica.eps : Harmonic Lattice Diagram, Advanced -- shows the harmonic
>structure of a scale by links that you specify (so can handle triangular
>lattices, for example), with the option of showing each link in a specified
>line style.
>(I include examples of tetrahedral and triangular lattices.)

Excellent! Thank you, David!

I tried downloading Ghostscript by following the link from your page but I
got a "login denied" message. If anyone has run David's software
successfully, how did you download Ghostscript?

David, I think you were on this list shortly before I joined, several years
ago, and it's good to see that you're back. You're a fantastic mathemusician
and it's too bad you weren't contributing to the many interesting
discussions we've had around here. I'm sure there's plenty more ahead!

Further suggestions for your program:

Instead of printing the ratios on the lattice diagram, allow other forms of
notation to be used. For JI, you could use the notation that Manuel just
described; a line in the program could specify, say, that ratio for C is
1/1. Or you could use notation corresponding to tempered tunings. Meantone
is most obvious, as it uses standard Western musical notation, and you can
use the 7- and even 11-limit approximations in 31-tET as a guide to meantone
notation of those ratios (Graham Breed at
http://www.cix.co.uk/~gbreed/meantone.htm#approx and
http://www.cix.co.uk/~gbreed/meantone.htm#11lim and Dave Keenan have
discussed why this is a good idea). Another notational alternative I would
like would be decatonic rather than heptatonic (see my paper
http://www-math.cudenver.edu/~jstarret/22ALL.pdf but ignore the erroneous
page 20). Or one that simply prints the pitch-class numbers for a given ET,
proivded the ET is consistent in the appropriate harmonic limit. . . .

Dan Canright excerpt:
>In the course of my music theoretical explorations, I have found certain
>graphical representations helpful in understanding scales and tunings in
>just intonation. And after I realized that PostScript was a general
>programming language capable of generating high-quality
>resolution-independent graphics on a wide variety of platforms, I taught
>myself enough to develop these Encapsulated PostScript graphics.

Dan,

I enjoyed using the dofrets.ps postscript file and found it very useful for
testing various arrangments of string and scale tunings. Is there anyway of
specifying a scale length such that the graphic will be guitar size, as I
don't plan on refretting any ukelalies. It would then print on two or pages
which could then be printed and tiled together.

Darren Burgess
Gainesville, FL

Woop see daisy. Sorry for the name snafu David.

>From: "Darren Burgess" <dburgess@acceleration.net>
>
>Dan,
>
>I enjoyed using the dofrets.ps postscript file and found it very useful for
>testing various arrangments of string and scale tunings. Is there anyway
of
>specifying a scale length such that the graphic will be guitar size, as I
>don't plan on refretting any ukelalies. It would then print on two or
pages
>which could then be printed and tiled together.
>
>Darren Burgess
>Gainesville, FL
>
>
>
>
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