Music 220a, Homework #3, Matt Wright

## Pd “engine”: The Music of the Spheres

music of the spheres
n.

A perfectly harmonious music, inaudible on the earth, thought by Pythagoras and later classical and medieval philosophers to be produced by the movement of celestial bodies.

(source)

Pythagoras wrongly believed that the motions of the objects in the solar system were related to the simple integer ratios of just intonation, and that consonant pitch relationships represented some kind of cosmic harmony. Medieval music theorists used these ideas to give grandiose metaphysical and theological significance to their use of counterpoint.

(David Plant has a nice web page with more information on this idea.)

## What we know today about our solar system:

Here are some web sites with various information about the true frequencies that are present in our solar system:

http://seds.lpl.arizona.edu/nineplanets/nineplanets/data1.html

http://seds.lpl.arizona.edu/nineplanets/nineplanets/data.html

http://solarsystem.nasa.gov/features/planets/profiles.html

## Mapping real astronomical data to human-perceivable sound:

First I looked at the frequencies of the orbits of the planets (i.e., the reciprocal of the length of each planet's “year”). These range from about 88 Earth days for Mercury's year to about 90550 Earth days for Pluto's year. The ratio between these two extremes is 1029.3, which is almost exactly 10 octaves, which is pretty much exactly the range of human hearing. Maybe God's hand really is at work here. ;-)

I scaled these frequencies by a factor of 1.768 billion to get into the range of human hearing, namely about 22 Hertz to 22000 Hertz. (You could think of this as transposing the frequencies upwards by about 37 octaves.) So the Earth, whose orbital frequency is one cycle per year, was scaled to 5475.55166182993 Hertz.

Next I decided to map each planet's mass to amplitude. Pluto is the lighest and Jupiter the heaviest of the planets; the ratio of their masses is about 149610 to 1, or just over 100 dB, which again is surprisingly close to the limits of human perception. But it's not quite close enough, so I put in a little cheat factor to make the smaller planets more audible.

Using one sinusoid for each planet in our solar system, with amplitude and frequency from (scaled) planetary mass and orbital frequency, I produced this sound. Any collection of sinusoids with fixed frequencies and amplitudes is pretty boring, and this one is no exception.

So I made it slightly less boring by using the frequency of each planet's rotation (i.e., the reciprocal of the length of each planet's sidereal day) to control amplitude modulation. Jupiter is the fastest-rotating planet (0.41354 Earth days per Jupiter's sidereal day) and Venus the slowest (243.0187 Earth days). I scaled these to the range of human hearing (or more precisely, to the range of the human attention span) by mapping Earth days to seconds, so that the sinusoid corresponding to Venus would fade in and out every 243.0187 seconds while the sinusoid corresponding to Jupiter would fade in and out every 0.41354 seconds.

Here is the final result.

Here is the Pd patch I used to make these sounds.

## How to interpret what I have done:

Please do not think (or tell anyone, or write an article in the New York Times claiming) that I have “discovered” or “revealed” the sounds of the solar system or anything of the sort. I took some true numbers from the physical world and made some completely arbitrary (and rather poor) aesthetic decisions about how to interpret them as musical parameters.

The chord that I produced really does correspond to the ratios of the lengths of the years of each planet, and there wasn't a lot of choice about how much to transpose these frequencies to get into the range of human hearing, but everything else about my process was subjective and non-empirical, just like whenever anybody reinterprets any kind of data from the natural world (seismic, DNA sequences, etc.) as music.