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

Attached Thumbnails

     

And what would this be used for apart from making sounds?

__________________
All Moderation in Purple
To report a post (even this one) to the moderation team, click the reporting icon in the upper-right corner of the post:
─────────────────────────────────────────────
◄Rules For Posting To This Board ► ◄Forum FAQs ► ◄ Conspiracy Theory Advice ► ◄ Alternate Theory Advice ►

Not that I've read the whole note, but I don't think this belongs in ATM. Q&A sounds better, or babbling maybe.

__________________
As above, so below

Babbling...
This isn't really a question, it's more of an opinion of an artistic method of generating a musical composition.

How about trying a few of the ideas and see how they work out?

__________________
Numbers are not case sensitive. (me)

You might consider running this one by the M.I.T. orchestra. They are world class science and tech students who also are avid musicians, and I have heard that they enjoy trying out unorthodox composition.

Close encounters of an otherworldly kind.

The sounds produced by these methods are ordered representations of the solar system. They complement existing visual and numeric representations, opening a new astronomical way of perceiving our cosmic neighbourhood. At first blush, the products may sound like random noise, but the underlying order that provides their structure means they provide an ambient model of the time from which the notes were derived. The opening post gave an example from July 2008. This could be played in about three minutes at a rate of one note per second. The use of midi electronic music technology means the data for any time period for which planetary positions is known can readily be entered, giving a sonic representation drawn from a function of the empirical data. For example a year of planetary data could be represented in two minutes of music. Experimenting with different options by varying speed, rhythm and tone will result in a range of creative options for musical depictions of the harmony of the spheres.

Or perhaps the cacaphony of the spheroids, depending on the ears of the beholder.

Perhaps you or someone in this forum can generate such a sound track and post it accordingly, so we can try it out.

I agree, Off Topic Babbling would be the place for this one.

How?
Sure; it's obviously a different way to represent this. But; no matter what the process or methodology of that sound is, it's still something that really doesn't appear to be all that useful except for the experience and the thoughts that it might invoke.
In other words, other than artistic interpretations, what can this do?

__________________
Numbers are not case sensitive. (me)

Who knows, this exercise might give similar results to one I heard of years ago, when an orchestra played numerous different "tunes" simultaneously, each of which was a series of notes based on the individual member's telephone number. This may have been at MIT, but I am not certain. They might even have been seeking some sort of order in the resulting clash of tones.

Thanks NEOWatcher. In pondering how to respond to your good question I have realised it gives me the opportunity to make good on a recent promise to Hornblower in a Q&A thread on gravity and the barycentre to discuss the theme of planetary resonance. Here are three practical examples of the astronomical scientific use of this method.

1. Using a heliocentric model, at speed one year per second, with Earth and Venus at high volume and all other planets at low volume, will produce a near-totally regular five note pattern. This is an illuminating way to illustrate the orbital relation between earth and Venus. The corresponding geocentric model would turn up the volumes of the Sun and Venus to produce a very similar result, although with the interesting added complexity of the retrograde motion of Venus. Given that this method 'sheds sound' rather than light on the planetary patterns under review, it makes sense to call it 'ilauralating', to coin a neologism, although it is also illuminating in the conceptual sense.

2. A larger 'ilauralating' example, showing the rhythm of the solar system barycentre, is to set the speed at 19.8 years per second, and turn up the volumes of Jupiter, Saturn and Neptune against the rest. Their orbital conjunctions produce a near-exact 14:9:5 ratio every 179 years. This piece will result in a unison every 9 seconds rising chromatically by one semitone using method 1, with overlapping sets of chromatic unison points at 9 second intervals. I have previously documented this visually in a general science thread, and expect that producing an aural representation will make the patterns much more obvious.

3. A third more general example is that comparing geocentric and heliocentric compositions for the same period would be an interesting 'ilauralation' of how the terrestrial orbit produces apparent direct and retrograde motion.

I understand that use of the term 'planetary resonance' to describe these Earth-Venus and Jupiter-Saturn-Neptune patterns is not conventional, but I struggle for a better term for the apparent phenomenon. The point, in answer to your question, is that as well as producing artistic ambient soundscapes (with more cosmic structure than phone numbers!) the method enables us to condense regular periodic structures of the solar system into a very short time period to help perceive their rhythmic cycles.

Sorry, but that doesn't sound like "use" to me.
Those sound more like definitions of the process of creating it.

Fine; but I was asking what this can do? What good is it?

It's a method of representation... I get that.

How do I interpret the meaning? How do I use it to do research or explain something?

In other words, you are describing a way to draw a picture of a fuzzy wuzzy bunny. Now; what can I do with a picture of a fuzzy wuzzy bunny?

__________________
Numbers are not case sensitive. (me)

I disagree. I think some people have an inherently harder time understanding concepts like orbital resonaces and such when just presented with numbers. For some, animations of orbits helps illuminate the concept. This might be a way to use sound, and I can see where it could help a lot of people (students, perhaps) "get" orbital resonances.

Beyond that, I guess maybe you're right, and it serves no deeper value for research or understanding. But it it definitely NOT a fuzzy wuzzy bunny (although even a drawing of a fuzzy wuzzy bunny could be used to illustrate light and shadow, or colors, or drawing techinques).

CJSF

__________________
Two years ago moved from my town
I was looking up past the city lights
But the city lights got in my way

See the constellation ride across the sky
No cigar, no lady on his arm
Just a guy made of dots and lines

-from "See The Constellation"
by They Might Be Giants

Exactly, and that is why I mentioned it as a method of representation.

I once took a course in electronic music, and learned alot (but not near enough by musician standards) about waveforms, harmonics, envelopes, and other things, and it did help me gain some insights into other "wavelike" applications. So, I do agree with that.

Exactly... Maybe the fuzzy, wuzzy was a bit over the top, but I was trying to get my thought processes across.

__________________
Numbers are not case sensitive. (me)

Of course, some people aren’t interested in dynamic understanding of the solar system, but then some are not interested in other topics in astronomy either. The second example, the Jupiter-Saturn-Neptune relation, is the one which to me best shows the power of this method to reveal new findings. It goes well beyond definition of the process. In looking at the solar system as a whole over long periods, the JSN cycle is a significant defining empirical structure. This method illustrates it very clearly. It differs from a rabbit or a phone number in that it is defined by the actual structure of our solar system, so produces sonic shapes which are physically determined rather than arbitrary.
Thanks. In the JSN case, I am arguing that there are secondary orbital resonances between planetary conjunctions, which are a different but real resonant phenomenon from the mean motion and Laplace resonances described at the orbital resonance wiki. These secondary resonances have not to my knowledge been much previously examined, but they emerge clearly from this method of representation. As well, this method quantifies non-resonant relations. For example, a heliocentric sonic model of the four inner planets will illustrate the temporal relations between their orbits.

This is just another excursion into serialism. It may carry information about harmonic relationships (strictly in the musical sense), but will offer no recoverable information about the solar system to the listener. The tonal assignments are "designed" but ultimately arbitrary, since they can be designed according to whatever pattern the composer decides to rationalize. In fact, it offers no way of perceiving our cosmic neighborhood in any direct experiencial sense (because the listener has no way of decoding all the information), but if you combined it with a pitch-keyed decoding system that translated the sound into graphic models as it played, you might have something interesting in multimedia.

__________________
Time is a great teacher, but unfortunately, it kills all its pupils. Hector Berlioz

"To complete the picture all the photons can be seen to be synchronising friction on and off throughout the overall cone which itself is synchronised to the equal and opposite reaction of equilateral triangulation"... by a scientificator in ATM, too priceless to be lost to posterity.

Well, it could be used to encode the configuration of the solar system in a presentation to an ET race. Just don´t ask me about the efficacy of the method.

__________________
What brings us together is stronger than what pulls us apart

I can understand why it would superficially appear as 'just serialism' but this is a misunderstanding. The serialism wiki page states that serialismMy method shares the absence of conventional melody and the equal use of all notes in the scale, but it does not repeat sets, and its structure is externally given by the planets, so it lacks a key serialist dimension in that the notes are not 'related only to one another' but are related only to the planetary positions. The wiki quotes serialist composer Karlheinz Stockhausen:I don't know if anyone has taken Stockhausen up on this suggestion of finding serial patterns in constellations, but that is a very different project from my effort to depict the dynamics of the solar system.
It is frustrating that I do not have the resources to put the theory into practice, except at the rudimentary level outlined in the OP. Putting the long term Earth-Venus and Jupiter-Saturn-Neptune cycles into this method will most definitely provide recoverable information about the solar system. By programming volumes so that planetary conjunctions are loud, the Earth Venus composition will produce a five note pattern reflecting the 8:13 E:V relation every eight years, which will very slowly precess according to the model here. Similarly, the 5:9:14 JSN patterns will produce overlapping ascending semitone compositions which directly correlate to the major long term structure of the gas giant orbits which produces the basic pattern of the solar system barycentre shown here. These are far from arbitrary. It is not about 'rationalizing' but choosing a time period, empirical inputs and parameters with which to depict them.

Wiki quote excerpt: "The basis for serial composition is Schoenberg's twelve-tone technique, where the 12 notes of the basic chromatic scale are organized into a row. This "basic" row is then used to create permutations, that is, rows derived from the basic set by reordering its elements. "

The Wikipedia description is much too narrow. Serialism originated with 12-tone rows, but has evolved and encompasses much more. The bold print above says it more accurately. You have established a basic set and are building musical structures from it according to a set of rules. That's serialism.

Stockhausen's suggestion obviously goes beyond Schoenberg's rule-bound 12-tone technique. Serialism is no more limited to Shoenberg's original set of rules than modern composition is limited by Bach's rules of counterpoint.

I could not have stated a better definition of "rationalizing."

I'm wondering how you intend for a listener to derive information without some up-front knowledge of your musical encoding system. The tonal, dynamic, and rhythmic changes are meaningless unless the listener is provided some context: the composer's "basic set" and the rules by which it is ordered and reordered--and probably perfect pitch as well. The problem I see in the concept (if I'm understanding it correctly) is that your are trying to express empirical data through a medium that is ultimately (and almost exclusively) a medium for evoking emotion. You'll get some emotional response to the sound--for better or worse, but it will evoke no understanding of the solar system without a guidebook. I suggested the graphic accompanyment as one possible way to make the sound meaningful to the observer in the context you've set. But without some context to put it in (more than just titling it Music of the Spheres), it's just sound (that is not to say it won't be interesting sound).

__________________
Time is a great teacher, but unfortunately, it kills all its pupils. Hector Berlioz

"To complete the picture all the photons can be seen to be synchronising friction on and off throughout the overall cone which itself is synchronised to the equal and opposite reaction of equilateral triangulation"... by a scientificator in ATM, too priceless to be lost to posterity.

Readers may have been following the beautiful interplay of Venus, Mars and Mercury in the evening sky over the last weeks. Looking again at the 2008 almanac from the OP, this musical technique could depict this planetary interplay by taking a 90 degree band of arc covering tropical Leo, Virgo and Libra for the months of August, September and October, and also including Sun, Moon and Saturn in the picture. This band could be spread over four octaves so that each semitone movement represented about 2 degrees of planetary movement, and rendering it in musical format with six instruments, one for each of these celestial bodies.

The following responds to the discussion point raised by Thorkil about serialism.
No, you are wrong. The planetary music I describe does not involve "re-ordering of elements" in the serialist sense, because each element is solely a function of the moving position of a planet, and so is solely determined in relation to the corresponding element in the previous row, and is never 're-ordered' in the serialist sense.

You said previously "The tonal assignments are "designed" but ultimately arbitrary, since they can be designed according to whatever pattern the composer decides to rationalize." This again is a basic misunderstanding, or at least a non sequitur, in that the tonal assignments are determined by nature, ie planetary physics. Choosing the time period and tonal scale etc is arbitrary, but once these functions are chosen the composition writes itself. Your comment could be taken to imply you could make a star map and "arbitrarily" choose to move a star. It is arbitrary what part of the sky an astronomer chooses to point a telescope at, but this does not mean the photo produced is arbitrary. Serialism is arbitrary, this method is not.

Yes of course a guidebook is needed, if the intention is scientific rather than artistic. Writing a musical composition called, say, 2008, would require explanation if the listener is to understand that the music correlates to planets. For example, we could have Sun = french horn; Mercury = piccolo; Venus = bassoon; Moon = glockenspiel; Mars = violin; Jupiter = cello; Saturn = moog synthesiser; Uranus = trombone; Neptune = pipe organ; Pluto = electric guitar, or any other chosen orchestration. Because the music is determined by the planets this needs explanation if the listener is to understand the conceptual basis. Given that the chromatic lines might be rather dull in their unadorned state, musicians might even use them as a basis for improvisation.

My next step is to compose a piece summarising the solar system for the Age of Pisces from year 0 to year 2148. Setting the Jupiter-Saturn cycle in six eight time with one beat per 9.9 years will produce a strong rhythmic harmonic result. An ascending sequence every three bars will result from the Jupiter-Saturn-Neptune cycle. With range of two octaves, the JSN sequence will produce a whole tone scale. All other bodies will be left out. This is purely empirical. Any help appreciated.

Guess what! That makes me the Sun.

Watch out. Depending on the playback speed, the whole thing might sound like a Bronx cheer.

You might want to see a doctor about those spots.

__________________
Numbers are not case sensitive. (me)

What spots?

__________________
Microsoft is over if you want it.

The bar has been lowered for the promotion of ATM ideas; the bar for the acceptance of ATM ideas must remain high.

Solar zits, aka sunspots.

I believe he is referring to the fact that the problem is currently in remission. (Or maybe one heck of a vanishing cream)

__________________
Numbers are not case sensitive. (me)

Okay, here is a piece describing the basic temporal structure of the solar system. It assigns notes to the positions of Jupiter, Saturn and Neptune over a 179 year period, as this cycle provides the basic rhythm of the centre of mass. This cycle repeats, with the final note as tonic, exactly twelve times each zodiacal age, which is why I call it the House of the Age. I have divided the house into twelve bars, each lasting 14.9 years. Each bar has three beats lasting 4.97 years. The range is two octaves.

This version is suitable for playing on guitar. It presents the ratios between Jupiter Saturn and Neptune orbits. Jupiter moves by a minor seventh per five year beat, Saturn moves by just over a major third and Neptune moves by just under a semitone.

So Robert Tulip,
This is just a different way of finding mathematical analogies (in the nature of planets & movements) converted to a musical score.

Record it and play it to us.

Then we can decide if it "sounds good" and make our decisions based on how the sounds resonate with us....just like American Idol, but with an ATM twist.

__________________
*Those that can, do, those that can't, ask.
*Those that need proof, none is suitable, & those that don't need proof, everything is possible.
*If you need to ask, then you haven't listened.
*If you need to question then you haven't learned.
*You can only see as far as your blinkers allow.
*All the world is crazy, except the two of us, and sometimes i have doubts about thee.

Why you look so small in there my friend, :-)

Thanks GGC. I have today recorded this piece electronically for french horn (Jupiter), cello (Saturn) and tubular bells (Neptune). It is interesting, if rather weird at first listen! There is a descending whole tone scale motif, and octaves every second note. I am happy to share, but BAUT does not support midi files. Can some one suggest a best way to put this on the internet? (btw I can't imagine Anton Webern or Alban Berg going too well on TV trash dancing shows.)