Electro-magnetic spectrum and Microtonality?

Is there a connection? Is there some sort of octave equivalence going
on? Can points along the frequency range be converted to ratios and
cents (or even scales and sound ranges using say, mod100 or whatever)?
Can Maxwell's equations be used to produce microtonal music (like say,
fractals and cellular automata music software)? These are sincere
questions because I honestly don't know. I don't understand Einstein's
equations but the same for him. Can they be adapted to microtonality?

I remember a while ago I tried to create a "major triad" with colors -
I found colors that were 3/2 and 5/4 the frequency of other colors. I
couldn't tell whether I was supposed to blend all of the colors
together, or put them next to each other, or what I was supposed to
do. Furthermore, on a computer, it isn't like we're getting spectral
light waves out of the monitor anyway. But hey, go get two variable
lasers and set the frequencies in a 3/2 ratio and see if anything
interesting happens.

-Mike

On Sat, Jun 21, 2008 at 5:36 AM, robert thomas martin
<robertthomasmartin@...> wrote:
> Is there a connection? Is there some sort of octave equivalence going
> on? Can points along the frequency range be converted to ratios and
> cents (or even scales and sound ranges using say, mod100 or whatever)?
> Can Maxwell's equations be used to produce microtonal music (like say,
> fractals and cellular automata music software)? These are sincere
> questions because I honestly don't know. I don't understand Einstein's
> equations but the same for him. Can they be adapted to microtonality?
>
>

At 02:36 AM 6/21/2008, you wrote:
>Is there a connection? Is there some sort of octave equivalence going
>on? Can points along the frequency range be converted to ratios and
>cents

The human visual range is narrower than an 'octave' of light.
And there doesn't seem to be an "equivalence color" of any size
in vision.

>(or even scales and sound ranges using say, mod100 or whatever)?
>Can Maxwell's equations be used to produce microtonal music (like say,
>fractals and cellular automata music software)? These are sincere
>questions because I honestly don't know. I don't understand Einstein's
>equations but the same for him. Can they be adapted to microtonality?

Almost any equation can be used to generate music. Whether there's
any rhyme or reason for doing so is another question. In a now
famous column, Martin Gardner showed that common melodies are
statistically closer to some noise functions than others. These
noise functions were subsequently used to produce melodies.
Fractals are another obvious source of nice patterns. The results
are often interesting but these equations don't capture anything
deep about what we listen for in music in my opinion.

-Carl

> On Sat, Jun 21, 2008 at 5:36 AM, robert thomas martin
> <robertthomasmartin@...> wrote:
>> Is there a connection? Is there some sort of octave equivalence going
>> on? Can points along the frequency range be converted to ratios and
>> cents (or even scales and sound ranges using say, mod100 or whatever)?
>> Can Maxwell's equations be used to produce microtonal music (like say,
>> fractals and cellular automata music software)? These are sincere
>> questions because I honestly don't know. I don't understand Einstein's
>> equations but the same for him. Can they be adapted to microtonality?

Good question!

No, rational number ratios are not nearly as important to
electromagnetic waves as they are to acoustic waves, and I'll tell you
exactly why.

Mathematicians and physicists have a concept called a "linear system".
In a linear system, you can put in two different inputs at the same
time and the output is simply the combination of the outputs you would
get from each input alone. The two inputs don't interfere with each
other; they're independent. If f is a linear function, then f(a + b) =
f(a) + f(b).

Most acoustic systems are essentially nonlinear. That is, if I play
two sine waves at one end of a room, and you listen at the other end
of the room, you will hear not only the two original pitches, but also
difference tones (and harmonics) that are generated spontaneously.
This happens because the acoustic response of the room is nonlinear.
This nonlinearity makes most intervals beat, and the only intervals
that don't beat are simple rational numbers.

On the other hand, the propagation of light through a material like
air or glass is extremely close to being perfectly linear. (The
technical reason for this is that air and glass are almost perfectly
linear dielectric media.) If I shine a red laser and a blue laser
through the same space, they come out as the same red and blue
wavelengths, and they don't generate any other wavelengths like green.
(The combination will appear purple, because that's just how your eyes
see a mixture of red and blue.) In particular, there can be no
"beating" or interference patterns generated by different wavelengths.
Therefore rational and irrational ratios of wavelengths don't act any
different in practice.

That said, there are certain materials, called nonlinear optical
crystals, that have enough nonlinearity that if you shine very intense
laser beams into them, you can observe nonlinear effects like
difference frequencies and low-order harmonics (see
http://en.wikipedia.org/wiki/Second_harmonic_generation ). But as Carl
Lumma just pointed out, the human visual range is less than an
"octave", so if you can see the fundamental, you can't see the second
harmonic, and vice versa. Similarly, if you use two input lasers, both
in the visible range, then their difference frequency will be
invisible. So even with these exotic nonlinear materials, there's no
practical way to see nonlinear optical effects with your eyes (other
than simple beating, and even that may be impossible in practice).

On Sat, Jun 21, 2008 at 3:48 AM, Mike Battaglia <battaglia01@...> wrote:
> I remember a while ago I tried to create a "major triad" with colors -
> I found colors that were 3/2 and 5/4 the frequency of other colors. I
> couldn't tell whether I was supposed to blend all of the colors
> together, or put them next to each other, or what I was supposed to
> do. Furthermore, on a computer, it isn't like we're getting spectral
> light waves out of the monitor anyway. But hey, go get two variable
> lasers and set the frequencies in a 3/2 ratio and see if anything
> interesting happens.

"Putting them next to each other" won't do a thing. In order to have
any hope of seeing nonlinear effects, the light waves must propagate
through the same region of space. Also, as I said, you need a
nonlinear optical crystal to observe anything. Plus, if you want to
actually see any beating with that 3/2 ratio, you need to tune your
lasers extremely carefully. The frequency of visible light is on the
order of 10^14 Hz, so if you want to see the beating your lasers have
to be tuned to one part in 10^13 or so. That's about 10^-10 cents, or
less than a billionth of a cent!

Keenan

Yes.....

math levels it all as long as it doesn't depend on the properties of
photons.

On Sat, Jun 21, 2008 at 5:36 AM, robert thomas martin <
robertthomasmartin@...> wrote:

> Is there a connection? Is there some sort of octave equivalence going
> on? Can points along the frequency range be converted to ratios and
> cents (or even scales and sound ranges using say, mod100 or whatever)?
> Can Maxwell's equations be used to produce microtonal music (like say,
> fractals and cellular automata music software)? These are sincere
> questions because I honestly don't know. I don't understand Einstein's
> equations but the same for him. Can they be adapted to microtonality?
>
>
>

[Non-text portions of this message have been removed]

Visual perception is so different from auditory perception that I doubt
frequency ratios of light mean anything to our eyes. And we only see a bit
less than an octave of light frequencies, so octave equivalence doesn't
mean anything in a visual context.

We only see three colors (red, green, and blue), so most colors are
already "chords" with varying amounts of those three. It's too crude a
system for perception of a scale in any meaningful way.

> I remember a while ago I tried to create a "major triad" with colors -
> I found colors that were 3/2 and 5/4 the frequency of other colors. I
> couldn't tell whether I was supposed to blend all of the colors
> together, or put them next to each other, or what I was supposed to
> do. Furthermore, on a computer, it isn't like we're getting spectral
> light waves out of the monitor anyway. But hey, go get two variable
> lasers and set the frequencies in a 3/2 ratio and see if anything
> interesting happens.
>
> -Mike
>
> On Sat, Jun 21, 2008 at 5:36 AM, robert thomas martin
> <robertthomasmartin@...> wrote:
>> Is there a connection? Is there some sort of octave equivalence going
>> on? Can points along the frequency range be converted to ratios and
>> cents (or even scales and sound ranges using say, mod100 or whatever)?
>> Can Maxwell's equations be used to produce microtonal music (like say,
>> fractals and cellular automata music software)? These are sincere
>> questions because I honestly don't know. I don't understand Einstein's
>> equations but the same for him. Can they be adapted to microtonality?
>>
>>
>

--
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~ Shroud for the Dead ~ available at http://cdbaby.com/cd/droakroot7