graduated circles
Jack Campin - bogus address
be a bunch of concentric graduated circles with a transparent cursor
on top. Size, as big as I can get out a single sheet of A4 paper.
So I need to make graduated circles with the divisions in various
ratios: 120 (for 10-cent intervals in 12-ET), 22 (Indian srutis),
53 (Pythagorean commas for the Turkish system), 19 and 31. Given
those I can add more as needed, like just intonation ratios, by
reading off the 120-division circle. (I can't go readably to 1200
divisions at that scale).
I don't have any graphics software that can easily do that and it
would be a bit of a pain to construct those by hand. Is there
anything I can download, or construct remotely using some sort of
graph-and-diagram-constructing server?
==== j a c k at c a m p i n . m e . u k === <http://www.campin.me.uk> ====
Jack Campin, 11 Third St, Newtongrange EH22 4PU, Scotland == mob 07800 739 557
CD-ROMs and free stuff: Scottish music, food intolerance, and Mac logic fonts
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Hans Aberg
> I would like to make myself a circular tunings calculator. It would
> be a bunch of concentric graduated circles with a transparent cursor
> on top. Size, as big as I can get out a single sheet of A4 paper.
>
> So I need to make graduated circles with the divisions in various
> ratios: 120 (for 10-cent intervals in 12-ET), 22 (Indian srutis),
> 53 (Pythagorean commas for the Turkish system), 19 and 31. Given
> those I can add more as needed, like just intonation ratios, by
> reading off the 120-division circle. (I can't go readably to 1200
> divisions at that scale).
What do you need it for, specifically, must it be graphical?
Hans
Jack Campin - bogus address
Yes - I want to visualize the interrelationships between different
scale patterns and tuning systems. Numbers are nowhere near as
intuitive. (I have a whole lot of different analog calculators, and
they can all do things a digital one can't).
Thinking about it, I believe I can do what I want by some sort of
geometric interpolation method, like the way you find the midpoint
of two identical lengths of wood without a ruler.
There's a slide rule to do the sort of thing I'm after in a glass
case in the Reid Musical Instrument Museum in Edinburgh. I might
see if I can persuade them to let me try it out. Circular is better,
though.
Hans Aberg
>>> be a bunch of concentric graduated circles with a transparent cursor
>>> on top. Size, as big as I can get out a single sheet of A4 paper.
>> What do you need it for, specifically, must it be graphical?
>
> Yes - I want to visualize the interrelationships between different
> scale patterns and tuning systems. Numbers are nowhere near as
> intuitive.
OK. By circular tuning, I gather you meant ETs. Hindemith, "Elementary
Training" displays a non-circular spiral of fifths, that is, it does not
close. Going fifths up one turn ends up slightly further out. Then he
says that for 12 ET it closes. Though this is not made for calculation,
just illustration.
> (I have a whole lot of different analog calculators, and
> they can all do things a digital one can't).
What are these?
I found the Haskell interpreter Hugs very useful as a calculator. If
calculations start becoming repetitive, one can write a function.
> Thinking about it, I believe I can do what I want by some sort of
> geometric interpolation method, like the way you find the midpoint
> of two identical lengths of wood without a ruler.
One can have three parallel lines, and mark off values on two of them
using a ruler, reading off the result on the ruler intersection on the
third one.
> There's a slide rule to do the sort of thing I'm after in a glass
> case in the Reid Musical Instrument Museum in Edinburgh. I might
> see if I can persuade them to let me try it out. Circular is better,
> though.
If you want to add intervals, then a classical slide ruler or the
corresponding circular one might be in place. Here is a whole site:
http://sliderulemuseum.com/
Perhaps they can help out. :-)
I found it passing over this link, which mentions a temperamental slide rule
http://www.music.ed.ac.uk/euchmi/udeda.html
Hans
J. B. Wood
> using a ruler, reading off the result on the ruler intersection on the
> third one.
>
engineering handbooks containing them. Sincerely,
John Wood (Code 5550) e-mail: wo...@itd.nrl.navy.mil
Naval Research Laboratory
4555 Overlook Avenue, SW
Washington, DC 20375-5337
Hans Aberg
>> One can have three parallel lines, and mark off values on two of them
>> using a ruler, reading off the result on the ruler intersection on the
>> third one.
> Hello, and its known as a nomogram or nomograph. I have a number of old
> engineering handbooks containing them. Sincerely,
OK. Thanks. MW defines it as a graph of a function of two or more
independent variables. The Wikipedia also has an article.
Hans
LJS
I don't fully understand what you are trying to do, but if I am
anywhere close it sounds like you are trying to create some "overlays"
that will allow you to compare the 12 tones (or maybe 24) in scales
and be able to rotate them for comparison to transpose them to
different keys. this is something that I would be interested in seeing
when you have it done.
BUT to the software.
IF I am on the right track, can this be done with Pie Charts? I am
thinking of a circular pie chart that could be divided into as many
radii as needed (12 for our chromatic system) and the values of the
distances between the tones would then produce a visual representation
so that you could set up 12tet as the even standard and then easily
see how far each one deviates from this as they are overlaid with each
other.
The overlaying might be a problem with software, (could be done in
something like Adobe Photoshop) but if you have a printer and you get
some transparent stock (like used in overhead projectors in school)
You could then make a separate sheet for each and overlay them by hand
as needed for your studies.
If you need different size circles to make something that can pivot,
you can resize the circles so that when overlaid, they can be
manipulated as you like with them all connected at the center as if on
a "card" that has multiple layers with each being able to
independently spun to adjust for keys and such.
The other approach might be something like a compass type of program
that could do the same thing.
Just some thoughts, I hope that they can be of use to you.
LJS
J R Laredo
http://www.sphere.bc.ca/test/circular.html#catalog
"Jack Campin - bogus address" <bo...@purr.demon.co.uk> wrote in message
news:bogus-199038....@news.albasani.net...
Jack Campin - bogus address
>> be a bunch of concentric graduated circles with a transparent cursor
>> on top. Size, as big as I can get out a single sheet of A4 paper.
>> So I need to make graduated circles with the divisions in various
>> ratios: 120 (for 10-cent intervals in 12-ET), 22 (Indian srutis),
>> 53 (Pythagorean commas for the Turkish system), 19 and 31. Given
>> those I can add more as needed, like just intonation ratios, by
>> reading off the 120-division circle. (I can't go readably to 1200
>> divisions at that scale).
> http://www.sphere.bc.ca/test/circular.html#catalog
I've got a few calculators like that (a big old Fowler like the one
my father used to use in his architectural work, a small ex-Soviet
one, and simpler specialist ones for heating engineering calculations
and for working out body mass index). The issue is not the basic
package, but marking the graduations in the right places - there is
no Euclidean ruler and compass construction to divide a circle into
19 sectors, for example.
I think I've worked out a procedure, but it won't lead to anything
computer-readable so I won't be able to share the result.
I was hoping there might be some option in a program like Photoshop
that worked like "divide this arc into n equal parts". It seems
there isn't.
-----------------------------------------------------------------------------
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Jack Campin * 11 Third Street, Newtongrange, Midlothian EH22 4PU, Scotland
mob 07800 739 557 <http://www.campin.me.uk> Twitter: JackCampin
LJS
Well, there are those pie charts you can make in Microsoft Office!
Even if it comes from me, it will still make an equal division of the
pie for how ever many subjects you have and it you put in the
distances between the tones, you can creat a chart with the notes at
any ratio to each other. Then print to a transparency and stick a pin
through the middle to see them in real time.
If you then want to you can scan or print them to a jpg format and
layer them in Photoshop if you want to use them in the electronic
form. With that in place you can superimpose them all or any
combination you like by showing or hiding the layers. Make sure that
you set the background to transparent.
Of course if a solution is no good because you don't like the one
giving it to you, well that is your choice.
LJS
DublinKevin
whith their task --then, again, might not...
Most printers today have PostScript or one of its clones. It is not
generally known that a PS printer runs an interpreted postfix
interpreter inside its guts which renders the page. It can accept
statements in plain ASCII. Over two decades ago I wrote a program in
BASIC which sent the printer PS code to print a page of text formatted
(this was before the heavy duty page layout programs and modern
computers were affordable by our not-for-profit organisation).
This is not as irrelevant as it sounds to your problem.
You can write PostScript code into a text file that gets the printer's
onboard processor to do all the work
--draw a circle any size, any thickness, etc;
--divide the circle into any number of division by simple calculations
(like 2*PI / x);
--draw ticks at these points (getting them tangental to the circle
will take a bit of trig perhaps);
--label these ticks (Helvetica is nearly always built into any PS
printer);
In principle, if you are prepared to get your hands dirty with some
coding, you have far more flexibility that most off-the-shelf
software.
But, and it's a big but....
You need to understand PostScript language, syntax, etc--Adobe used to
publish cookbooks which explained all and there is probably
explanations and tutorial around the internet somewhere;
You also need a way to fire the code you create directly to the
printer (not printing it via the usual print command as all you would
get would be your code--not its interpretation)
Years since I've done anything like this on 64k CP/M computers and PS
printers and a program like BASIC might help, being a sort of shell to
create the code and fire it as ASCII to the printer. Windows (and I
imagine Mac OS) don't make this trivial as they don't expect people
these days to get under the hood as we used to.
Maybe you know someone who might be computer nerdy enough to help you
with this?
Intrinsically, the task is not so difficult, but that's what Brecht
said about socialism :o
OK end of techie diversion.
BTW I've learnt a lot about music, theory etc here. Thank you all for
that. I only lurk, I have nothing to offer, but do please--all of you--
keep up the discussions. There are probably lots of lurkers like me,
expanding our understanding a little, invisible to the regulars. So
please remember that when you're tempted into flame wars. Music is too
important for that sort of thing.
Best wishes, Kevin