Musical Cosmos Theory Methods Diary - Part one - Measurements and Calculations

first release of musical cosmos theory 1.0

I wanted to write an explanation of how I’ve gone about calculating musical properties and ratios between the planets, especially as it is useful to know how I have arrived at my answers at each point and so any one who is curious can have a better idea of what went into making the maps and scales of musical cosmos theory.

The Data

To arrive at an idea of planetary music I have chosen to hone in on the most essential and basic properties I can find that are measured and recorded. For planets, I have considered Mass, Size, Distance to the Sun or Earth, Year Length, Day Length, Spin-Orbit Resonance and Angular Momentum in my calculations. Most of the data that I have could be easily garnered from Nasa’s own planetary fact sheet, which is freely available online here. I gathered further data on Ceres and Eris as they are not on that particular sheet.

Other than that it really helped to use Mathematica, which directly links to Nasa for its data, so that I could check results and calculate all the terms at once where it used to mean days and many hours of calculating now it takes hours or seconds in some cases.

Calculating the Music of the Planets by Day Length

To calculate the scales of the solar day lengths of the planets in relation to the galactic day length of the Sun, I originally simply compared period to period. For instance, Earth and Mars could be compared via day length in hours as

24.7/24

or roughly 1.029, which is nearly a quarter tone interval in music.

This is the mistake I made originally and as late as Musical Cosmos Theory beta. Though there is nothing wrong with using this calculation as food for thought or even as a basis for a musical cosmos scale, it is much more interesting and relevant to cosmic music to use the frequency.

If you compare the chart below with the chart above you will see the strange way in which the scale changes but retains a lot of its form from one case to the next. In 3 cases (Venus, Mercury and the Moon) the note is different but they are related by being the same distance from the root but in opposite directions.

excerpt from the beta release of musical cosmos theory maps

These changes in note occured because pluggin in period to frequency switches the order of terms and in some cases that changes the calculation.

A very standard equation in wave mechanics is that the frequency is equal to 1 divided by the period. The units of the period must be converted to seconds. So to get the frequency in the standard unit of Hertz you divide one second by the period in question to arrive at number of cycles per second, or Hertz.

So one ratio for Venus and the Earth might look like

2802/24= 116.75

Then I would take this and reduce it to a number between 1 and 2 using the law of octaves where diving or timesing by 2 gives you Its equivalent tone in a higher or lower register or pitch. So for the above ratio, I would divide by 64 or 2 x 2 x 2 x 2 x 2 x 2. This gives you roughly 1.8242 as the ratio, which is not near enough to a musical interval for me to mark it as a hit on a scale chart which needs to be within 1 % for a note in the scale or 3% for a chord note. I used the equal tempered octave of 12 intervals in these maps, and those can be easily calculated these days with a calculator or phone., or you can simply look them up.

The other version which uses frequency as the resonance ratio unit of interest would be

1/2802÷1/24 or .008565.

Reduce it to a Musical number and you arrive at 1.0963. This ratio is also too far from a musical interval to be marked as a hit on a scale in the maps I make.

Above you see Mercury in one scale at the Major Sixth interval, 1.681 (or 2^(9÷12) ). In the other, he is at a Minor Third interval, or 2^(3/12)= 1.189. In both cases the same distance is described it just depends on which direction you are traveling from 1 or 2, one of the strange qualities of musical numbers.

Correct Order of Terms

One more rule I have encountered in musical math is that when it comes to calculating scales to any root frequency or length, they have a correct a particular order they go in.

For calculating the stellar scale of day length with the Sun as the root day length, the Sun is always the bottom term as a frequency, or the top term as a distance.

Length> Root tone/any other tone

Frequency> any tone/root tone

When I used the period to calculate the scales the order was switched on all ratios that were below the root (which was another error in some calculations).

AVERAGE DISTANCE MAPS

Also worth noting is that I have realized that the tree of life inspired maps of the 32 average paths to Earth and Sun must also be corrected. Instead of having only 1 average path per pair, it is actually more correct to have 2 paths per pair. The reason is because the interval size depends on which planet or body you start from. The average distance is always the same between them, but in a musical octave it makes a difference in tone and name depending on which direction you go from one interval to the next.

A minor Third interval backward or forward is the same size on a logarithmic curve. But how is a minor Third backwards equal to a major 6 forwards? Such is the strange nature of musical math. But it is this very property which lead me to map out this mirror symmetry between musical notes in what I call Harmonys Mirror. It has been mapped out many times in the past, but it helps a lot in my experience to do the work of mapping things out clearly for future use.

Suffice it to say that the 32 average paths maps need to be edited still before I feel they give a good idea of the “average” music of the Solar system.

So ends part one of my methods diary. I am currently working on an expression of musical cosmos theory 1.0. I also plan on releasing an explanation of the maps which include algorithms for mapping letters of Hebrew and English to the tree paths soon, as part 2.