Mapping of planetary patterns can make ‘music of the spheres’ by assigning notes of different frequencies to each position of the ecliptic and representing the positions of each planet around the ecliptic as a mathematical musical composition. This method offers new ways to depict the dynamic spatial structure of the solar system in sonic form and is not in conflict with scientific consensus. This thread gives three methods of assigning note values to planetary positions to produce cosmic compositions somewhat like the music of Olivier Messiaen. Each composition, as in the example given below, has an analogous character to the time period which provides its ephemeral source.

I would welcome any questions on the methods outlined here, assistance in transferring ephemeral data into midi format or comment on how better to develop the harmonic mathematics in the third method.

Method 1. Each thirty degrees of arc around the ecliptic is represented by one of the twelve semitone notes in the western octave chromatic scale. Each planet’s orbital position is mapped on to the scale. Planetary inferior conjunctions are in octave relations and other angles produce their corresponding intervals. For modeling purpose both the note and the starting point are arbitrary. 30° of the ecliptic is given a note, such as C. The next 30° section is designated as C#, and then each successive chromatic note is similarly assigned to the next section: D, D#, E, F, F#, G, G#, A, A#, B, and the return to the starting note of C completes the orbit. In linking these note values to planetary positions, data can be obtained from heliocentric or geocentric positions, and from sidereal or tropical ephemerides. Using the geocentric tropical ephemeris to produce a music of the spheres in this way as shown here could use the March equinox as the note C. Each semitone above would then correspond to the next tropical sign, giving Aries = C, Taurus = C#, … Pisces = B. With each time period - ranging from one hour to one week - represented by a bar of music, each bar would be made of a chord or arpeggio of the notes corresponding to selected planetary positions at that time to produce a composition for a calendar period. As planets and the sun and moon appear to move directly along the ecliptic they will produce a rising chromatic note series, and when they are retrograde they can produce a falling chromatic series. For the year 2008, (diagram here), the first week of January would produce notes of A for the Sun, Jupiter and Mercury, A# for Neptune, B for Uranus, D for Mars, G# for Pluto and Venus and F#, G and G# for the Moon.

Assignment of qualities to each planet as part of a musical composition depicting a given time period could depict outer planets with low notes and inner planets with high notes, over a frequency range of perhaps four or five octaves, and with each planet assigned a different musical timbre and volume. All planets could either sound continuously as a chord, or each given time period, such as a day, week or longer, could be arpeggiated with each planetary note sounding successively. With time interval of two days planetary movement per bar, and using geocentric tropical positions, the moon would usually rise by one semitone per bar, the sun would remain on the same note for fifteen bars, Venus and Mercury would loop around the sun with periodic rising and falling sequences corresponding to their direct and retrograde motion, and the outer planets would stay on the same note for periods ranging from two months for Mars to up to twenty years for Pluto. By this method, inferior conjunctions would produce octaves, sextiles major seconds (or ninths etc), squares minor thirds, trines major thirds, and superior conjunctions (oppositions) would produce tritones. A Grand Trine of planets would produce an augmented chord, while a Grand Square would produce a diminished chord.

Division of the ecliptic in twelve segments will distort the actual continuous movement of the planets, with near conjunctions in separate signs (eg Jupiter –Pluto) producing semitone dissonance, and near 30 degree separations within a sign producing unison or octaves. As such, this is a crude initial schematic. A more sophisticated version can approach continuous glissandi rather than the twelve tone scale. The use of the twelve tone scale, with equal temper giving each successive note a frequency of the twelfth root of two times the note below, enables direct composition on to the keyboard. Using the 360th root of two will produce notes corresponding to planetary degrees (12 signs x 30), while the 2160th root of two will give exactness to the level of ten minutes of arc (360 degrees x 6).

Method 2. A second method, illustrated in the table below for July 2008, is like the first except that the orbit is stretched over four octaves, producing more rapid and large scale change of note. The notation has C1 as the lowest note and C5 as the highest. C3 = middle C, B3 = B above middle C, C4 = C above Middle C, etc. It is fairly easy to play on the piano, playing each row in turn. Looking at the almanac, the Mars-Saturn-Moon conjunction of 6 July (in between the given two day intervals) would correspond to these planets each producing the note G#2.
3. A third method of assigning note values can adjust the scale so that planets in opposition produce notes separated by multiples of a perfect fifth, rather than the tritone given by the method outlined above. The reason for suggesting this alternative is that in the natural harmonic scale, each note is in integer fraction to the tonic. Hence the major scale consists, at the simplest factor level, of notes in the relation 24:27:30:32:36:40:45:48 = C:E:F:G:A:B:C. It can be seen that the tonic : dominant relation C:G = 24:36 = 2:3. Using the scale of notes from 24 Hz to 48 Hz, the half way point is 36 Hz. An alternative harmony of the spheres can use this fact to create exact harmonic relations of multiples of 2:3 when planets are opposite (superior conjunction). This method appears to require that the scale be broken into two halves, with the lower half (C-F#) assigned to the signs Aries to Virgo, and the upper half (G-B) assigned to Libra to Pisces, with each position in the upper half having frequency 1.5 times its corresponding position in the lower half. A complicating factor, for those who have borne with me through the mathematics so far, is that this method does not map directly on to the twelve tone scale, or on to higher harmonics. For example, when planets are one third of the ecliptic apart (trine), this method suggests their frequencies should be in ratio 4:3. Hence planets in Aries and Leo would produce the notes C and F. However this breaks down, because the notes G:C should also represent a trine (36:48 = 3:4), but they have already been defined by the method of splitting the scale in two parts to produce an opposition. By this method, planets in square position (eg Aries-Cancer) should be in relation 24:30 = 4:5, but the upper square within the lower half (Cancer-Libra) has the relation 30:36 = 5:6. For the upper half of the scale (Libra to Aries), the square point has frequency 42 = 24 x 7/4 = A. These anomalies illustrate that experimentation with a range of harmonic functions, and further consideration of the mathematical relations, is needed to develop a frequency pattern that gives best fit to the natural harmonics of the solar system. This method is intended to produce exact integer harmonic relations corresponding to major planetary alignments, unlike the first method which was based on the equal temper scale devised by Johannes Sebastian Bach in the Well Tempered Clavier, using the twelfth root of two to enable near-harmonic relations in all scales, at the expense of exact harmonic integer resonance. An example of the dissonance produced by equal temper is that in the 24:48 scale frequencies outlined above the relation D:A = 27:40 = 81:120 = 2:3 + 1:120, producing an audible dissonance of almost 0.83%. Error diagram for harmonic and equal tempered scales is here.

Robert Tulip

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