Since ancient times music has been understood as number made audible. Music brings to the sense of hearing the numerical order of nature. The mind recognises in the beauty of harmonies this order of nature, which is also a pattern in the soul. In music we hear the qualities of the numbers, not simply their quantities, and it is these qualities that move the heart. There is a correlation between the nature of the soul and the nature of the world, and the harmonies of music derive from this correlation, and when we hear music that springs from this nature it tempers the mind and brings it to its natural order and rest. This is why music can restore the mind and heart.
Since harmonies are relationships of numbers, and since beauty shines most clearly in what is unified and whole, the most simple, unified and whole numbers produce harmonies, while complex numbers produce discords. Discords have a place in music, but only when they are resolved to harmonies. The telos or pull of a discord is the harmony it naturally resolves to. Music therefore moves from simplicity and elaborates in complexity, and then returns to simplicity. This is the natural motion of music. It moves in a circle and returns to where is began. This is reflected in another way. Music begins in silence, manifests in sound, and finally returns to silence.

The Scale
The basis of music is the scale. The musical scale is produced through simple ratios. For example, if we begin with a single note and call that note 1, and if we add to that note other sounds of the same pitch, also 1, we have a unison. This is expressed as a ratio of 1/1 - that is 1 to 1. If we have this same 1 and add to it another note, 2, this brings the simplest harmony ratio of 2/1, which is an octave. What this means is that for every time the first note (1) vibrates once, the second note (2) vibrates twice. It is twice the frequency. This shows us something interesting about numbers. The smallest numerical step, as here from 1 to 2, produces the largest interval, the octave. All the other notes of the scale fall between these two notes or this interval. They are in fact simple divisions of the interval of the octave, dividing the octave only by 2 or by 3.

For example, if we divide the octave by half we arrive at the fifth note of the scale. To put this in numerical terms, half way between 1 and 2 is one and a half (1½). This ratio of 1/1½ may be expressed as whole numbers, which makes a ratio of 3/2. This means that for every time the lower note vibrates twice, the higher note vibrates three times. This interval is called the perfect fifth - it is the notes C and G in C major.

This interval when divided produces the ratio 5/4, which is the major third, the notes C and E in C major. We may halve that interval again, and this produces an interval of 9/8, which is a major second, or the notes C and D in C major.

Notice that we have derived from this simple initial doubling of 1 to 2, and then the division of that by halves, the notes C D E G C. Notice also that these notes contain among themselves other intervals. The interval between D and G, and between E and C' (the higher C). The ratio between D and G is 4/3. The ratio between E and C' is 8/5.

Suppose we divide the octave by one third, instead of one half. This gives us the note F in C major, an interval of 4/3 again - a perfect 4th. If we divide the interval between F and C' we have a major 3rd again, an interval of 5/4, giving us the note A in C major. If we halve the interval between A and C' we obtain B, which completes all the notes of the scale, giving us a ratio of 9/8 once again.

So that we can see all the intervals in a very simple way, we may make a map of all the notes of the scale. This map can be based on the number 24 since this number allows us to express all the ratios in whole numbers related to one another.

We pointed out earlier that all these ratios could be expressed in their smallest whole numbers. For example, if we look at the ratio of 48/24 we see 48 is twice 24, and therefore it is a smallest whole number ratio of 2/1. Similarly with 36/24. 36 is half as much again as 24, so is a simple number ratio of 3/2. See how this works: 12 goes twice into 24 and three times into 36. That is 3/2. One more example: 27/24. If we divide these numbers by 3 we see that 3 goes 8 times into 24 and 9 times into 27, thus giving us the smallest whole number ratio of 9/8. So to reduce any of these intervals to their smallest whole numbers we simply find the greatest common divisor. The larger that greatest common divisor is, the smaller the numbers in the ratio expression. For example, 24 and 48 are divisible by 12 as the greatest number, and this produces a ratio of 2/1 - the smallest ratio. Again, 24/27 cannot be divided by a greater number than 3, and this produces a ratio of 9/8 - a large ratio.

Take the interval 45/48. Which is the greatest number both these numbers are divisible by? It is 3. 3 goes 15 times into 45 and 16 times into 48. This produces a ratio of 16/15. Notice that there is no common number that will divide 15 and 16. Therefore 16/15 is the smallest expression of this ratio between SI and DO.

Again, take 27 and 40, the interval RE and LA. This is not divisible by any common number at all, therefore its smallest expression is 40/27.

Those who know a little about harmony may be surprised by this ratio because it is normally regarded as a perfect 5th, like the interval between DO and SOL. It is not, however, a perfect 5th in the natural tuning, which is what these numbers give us. It is in fact a discord, and a very curious one if you listen to it. This interval cannot be heard on the piano or any other "tempered" instrument, where the tunings between notes are all slightly compromised, save for octaves, so that one can play in any key without retuning the instrument.

The best way to explore these ratios is to reduce each of them to their lowest common ratio expressions. If this is done it will be noticed that the number 7 never occurs in any ratio. This includes 27/24 because that is 9/8. One finds that the numbers involved in all the different ratios are 1, 2, 3, 4, 5, 6, 8, 9, 15, 16, 27, 40. One will also notice that all the harmonious ratios employ the numbers 1 to 6, and that the discords employ all the higher numbers. The number 6 is said by the Pythagoreans to be the number of full manifestation, the limit number. In music this is evident in that it is the limit of the harmonious sounds. Also there are only 6 harmonies in music.

This number 6 may be seen to be a limit number in music in another interesting way. Suppose we add octave upon octave, starting from our original number 1. We saw that octaves are doubling. This gives us a sequence of 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, and so on. Now if we add up the digits in these numbers we find a recurring sequence of 1, 2, 4, 8, 7, 5. This recurs every six octaves, no matter how far it is extended. If we add up that recurring sequence another interesting fact about number occurs. The sequence added together makes 27, and 2 and 7 added together makes 9. The number 9 is the "last" or unbreakable number. All multiples of 9 add up to 9, and every number that adds up to 9 is divisible by 9. This law of number holds even if we change the starting number. Suppose we start from 3 instead of 1. This will give us the sequence 3, 6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6144 etc. This sequence gives us the series 3, 6 recurring, which also always adds up to 9, and each series of 2 octave and 4 octaves and 6 octaves adds up to 9.

If we had started with 5 instead of 3, we would produce the first sequence again. Thus we see that the law of octave sequences expresses principles about number. This "doubling" of the octave is seen in nature as the process of the division of cells in living organisms.

So far we have considered only the ratios of two notes together. What of three? Those who know a little of harmony will realise that no more than 3 notes can be put together to make consonances. Those notes may of course be repeated in higher or lower octaves, but this does not give us more than three notes in any consonance. According to Pythagoras, three is the number of manifestation - not the limit of manifestation, which is 6 as we have seen. This is evident in music in several ways. We saw earlier that if we take 1 and join another 1 with it we have a unison. Nothing "new" has been born. Again, if we double 1 and have the octave, we only have the same note again, only an octavehigher. Again nothing new has been created. But when we halve the octave and make the three notes DO, SOL and DO' sound together we have the "first" real harmony, and the first triad of sounds, and these are produced with the numbers 1, 2, and 3. Pythagoras also says that numbers are male and female, and that to create something there must be a "marriage" of male and female numbers. This is the case here. The number 1 is neither male nor female, but "prior" to gender. Number 2 is female and 3 is male. All even numbers are female and all odd numbers are male. So it is only when we introduce the first female and the first male numbers that we get the first harmony. We notice also that all the consonances in the octaves are combinations of female and male numbers, or even and odd numbers. It may seem strange to us that numbers have the qualities of gender, yet the harmonies confirm this is so.

It may also seem strange to us that numbers express qualities, yet music shows that this is so. We might say that music specifically expresses numbers as qualities. And to this we may add that our response to harmony springs from an innate knowledge of these mysterious yet precise qualities. Music, however, is not explained by number. No composer composed music according to a numeric formula. Rather it might be more true to say that music explains number, because it is the qualities in the sounds that bare the numbers forth meaningfully and according to their nature.

We have looked here at the mathematical proportions of the musical scale. If these are considered further a great deal more can be seen in them than we have elaborated here. For example the numbers will show how the harmonic series arises, and also how these ratios can be applied to geometry. For example, the triangle with line proportions of 3, 4 and 5 which, if made into strings, produces the minor chord. There is ample material here to experiment and explore with that will lead to all kinds of insights into both number and music.

In music theory, a perfect fifth is the musical interval corresponding to a pair of pitches with a frequency ratio of 3:2, or very nearly so.

In classical music from Western culture, a fifth is the interval from the first to the last of five consecutive notes in a diatonic scale. The perfect fifth (often abbreviated P5) spans seven semitones, while the diminished fifth spans six and the augmented fifth spans eight semitones. For example, the interval from C to G is a perfect fifth, as the note G lies seven semitones above C.^[1]  Play (help·info)

The perfect fifth may be derived from the harmonic series as the interval between the second and third harmonics. In a diatonic scale, the dominant note is a perfect fifth above the tonic note.

The perfect fifth is more consonant, or stable, than any other interval except the unison and the octave. It occurs above the root of all major and minor chords (triads) and their extensions. Until the late 19th century, it was often referred to by one of its Greek names, diapente.^[2] Its inversion is the perfect fourth. The octave of the fifth is the twelfth.

A helpful way to recognize a perfect fifth is to hum the starting of Twinkle, Twinkle, Little Star; the pitch of the first "twinkle" is the root note and pitch of the second "twinkle" is a perfect fifth above it.

In music theory, an interval is the difference between two pitches.^[1] An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, andvertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord.^[2][3]

In Western music, intervals are most commonly differences between notes of a diatonic scale. The smallest of these intervals is a semitone. Intervals smaller than a semitone are called microtones. They can be formed using the notes of various kinds of non-diatonic scales. Some of the very smallest ones are called commas, and describe small discrepancies, observed in some tuning systems, between enharmonically equivalent notes such as C♯ and D♭. Intervals can be arbitrarily small, and even imperceptible to the human ear.

In physical terms, an interval is the ratio between two sonic frequencies. For example, any two notes an octave apart have a frequency ratio of 2:1. This means that successive increments of pitch by the same interval result in an exponential increase of frequency, even though the human ear perceives this as a linear increase in pitch. For this reason, intervals are often measured in cents, a unit derived from the logarithm of the frequency ratio.

In Western music theory, the most common naming scheme for intervals describes two properties of the interval: the quality (perfect, major, minor, augmented, diminished) and number (unison, second, third, etc.).Examples include the minor third or perfect fifth. These names describe not only the difference in semitones between the upper and lower notes, but also how the interval is spelled. The importance of spelling stems from the historical practice of differentiating the frequency ratios of enharmonic intervals such as G-G♯ and G-A♭.^[4]

In music, quartal harmony is the building of harmonic structures with a distinct preference for the intervals of theperfect fourth, the augmented fourth and the diminished fourth. Quintal harmony is harmonic structure preferring theperfect fifth, the augmented fifth and the diminished fifth

Quintal harmony (the harmonic layering of fifths specifically) is a lesser-used term, and since the fifth is the inversion orcomplement of the fourth, it is usually considered indistinct from quartal harmony. Indeed, a circle of fifths can be arranged in fourths (G→C→F→B♭ etc. are fifths when played downwards and fourths when played upwards); this is the reason that modern theoreticians may speak of a "circle of fourths".

Use of the terms quartal and quintal arises from a contrast, compositional or perceptual, with traditional tertianharmonic constructions. Listeners familiar with music of the (European) common practice period perceive tonal music as that which uses major and minor chords and scales, wherein both the major third and minor third constitute the basic structural elements of the harmony.

In music theory, the circle of fifths (or circle of fourths) is a visual representation of the relationships among the 12 tones of the chromatic scale, their corresponding key signatures, and the associatedmajor and minor keys. More specifically, it is a geometrical representation of relationships among the 12 pitch classes of the chromatic scale in pitch class space.

Circle of fifths showing major and minor keys and their signatures

Underlying perceived musical tuning of intervals is the frequency relationship expressed as a fraction. Simple fractions can sound more harmonious than complex fractions; for instance an octave is a simple 2:1 ratio and a fifth, also concordant is the relatively simple 3:2 ratio. The table below gives approximations of a scale to ratios that are rounded towards being as simple as possible.

C	D	E	F	G	A	B	C
1	9/8	5/4	4/3	3/2	5/3	15/8	2

In music theory, a diatonic scale (or heptatonia prima) is an eight-note musical scale composed of seven pitches and a repeated octave. The diatonic scale includes five whole steps and two half steps for each octave, in which the two half steps are separated from each other by either two or three whole steps, depending on their position in the scale. This pattern ensures that, in a diatonic scale spanning more than one octave, all the half steps are maximally separated from each other (i.e. separated by at least two whole steps). The word "diatonic" comes from the Greek διατονικός, meaning progressing through tones.^[1]

The seven pitches of any diatonic scale can be obtained using a chain of six perfect fifths. For instance, the seven natural pitches which form the C-major scale can be obtained from a stack of perfect fifths starting from F:

F—C—G—D—A—E—B

This property of the diatonic scales was historically relevant and possibly contributed to their worldwide diffusion because for centuries it allowed musicians to tune musical instruments easily by ear (see Pythagorean tuning).

Any sequence of seven successive natural notes, such as C-D-E-F-G-A-B, and any transposition thereof, is a diatonic scale. Piano keyboards are designed to play natural notes, and hence diatonic scales, with their white keys. A diatonic scale can be also described as two tetrachords separated by a whole tone.

The term diatonic originally referred to the diatonic genus, one of the three genera of the ancient Greeks. In musical set theory, Allen Forte classifies diatonic scales as set form 7–35.

This article does not include alternative seven-note diatonic scales such as the harmonic minor or the melodic minor.

In music theory, a scale degree is the name given to a particular note of a scale^[3] to specify its position relative to the tonic (the main note of the scale). The tonic is considered to be the first degree of the scale, from which each octave is assumed to begin.

Any musical scale may be thought to have degrees. However, the notion of scale degree is most commonly applied to scales in which a tonic is specified by definition, such as the 7-tone diatonic scales (e.g. theC-major scale C–D–E–F–G–A–B, in which C is the tonic). As for the 12-tone chromatic scale, the selection of a first degree is possible in theory, but arbitrary and not meaningful, because typically all the notes of a chromatic scale have the same importance.

The expression scale step is sometimes used as a synonym of scale degree, but it may also refer, perhaps more properly and less ambiguously, to the distance, or interval, between two successive scale degrees (see Steps and skips). Indeed, the terms whole step and half step are commonly used as interval names. The number of scale degrees and the distance between them together define a scale.

The circle of fifths drawn within the chromatic circle as a stardodecagram.^[7]

In music theory, the circle of fifths (or circle of fourths) is a visual representation of the relationships among the 12 tones of the chromatic scale, their corresponding key signatures, and the associatedmajor and minor keys. More specifically, it is a geometrical representation of relationships among the 12 pitch classes of the chromatic scale in pitch class space. A simple way to see the musical interval known as a fifth is by looking at a piano keyboard, and, starting at any key, counting seven keys to the right (both black and white) to get to the next note on the circle shown above. Seven half steps, the distance from the 1st to the 8th key on a piano is a "perfect fifth", called 'perfect' because it is neither major nor minor, but applies to both major and minor scales and chords, and a 'fifth' because though it is a distance of seven semitones on a keyboard, it is a distance of five steps within a major or minor scale.

A simple way to hear the relationship between these notes is by playing them on a piano keyboard. If you traverse the circle of fifths backwards, the notes will feel as though they fall into each other. This aural relationship is what the mathematics describe.^{[citation needed]}

Perfect fifths may be justly tuned or tempered. Two notes whose frequencies differ by a ratio of 3:2 make the interval known as a justly tuned perfect fifth. Cascading twelve such fifths does not return to the original pitch class after going round the circle, so the 3:2 ratio may be slightly detuned, or tempered. Temperament allows perfect fifths to cycle, and allows pieces to be transposed, or played in any key on a piano or other fixed-pitch instrument without distorting their harmony. The primary tuning system used for Western (especiallykeyboard and fretted) instruments today, twelve-tone equal temperament, uses an irrational multiplier, 2^1/12, to calculate the frequency difference of a semitone. An equal-tempered fifth, at a frequency ratio of 2^7/12:1 (or about 1.498307077:1) is approximately two cents narrower than a justly tuned fifth at a ratio of 3:2.

Circle of fifths showing major and minor keys

Nikolay Diletsky's circle of fifths inIdea grammatiki musikiyskoy (Moscow, 1679)

In music theory, the circle of fifths (or circle of fourths) is a visual representation of the relationships among the 12 tones of the chromatic scale, their corresponding key signatures, and the associatedmajor and minor keys. More specifically, it is a geometrical representation of relationships among the 12 pitch classes of the chromatic scale in pitch class space.

The term 'fifth' defines an interval or mathematical ratio which is the closest and most consonant non-octave interval. The circle of fifths is a sequence of pitches or key tonalities, represented as a circle, in which the next pitch is found seven semitones higher than the last. Musicians and composers use the circle of fifths to understand and describe the musical relationships among some selection of those pitches. The circle's design is helpful in composingand harmonizing melodies, building chords, and modulating to different keys within a composition.^[1]

At the top of the circle, the key of C Major has no sharps or flats. Starting from the apex and proceeding clockwise by ascending fifths, the key of G has one sharp, the key of D has 2 sharps, and so on. Similarly, proceeding counterclockwise from the apex by descending fifths, the key of F has one flat, the key of B♭ has 2 flats, and so on. At the bottom of the circle, the sharp and flat keys overlap, showing pairs of enharmonic key signatures.

Starting at any pitch, ascending by the interval of an equal tempered fifth, one passes all twelve tones clockwise, to return to the beginning pitch class. To pass the twelve tones counterclockwise, it is necessary to ascend by perfect fourths, rather than fifths. (To the ear, the sequence of fourths gives an impression of settling, or resolution. (see cadence))

The circle of 5ths is a fascinating construct in Western music. It is a unifying principle, an underlying comprehensive structure, a guiding force of musical coherence. It is central to a general technical understanding and appreciation of the dynamics of Western music, whether classical or popular. You don't need it to hear music meaning, but it provides powerful insights into explaining music meaning from a technical standpoint.

Out of the potentially continuous infinity of pitch available from slide whistles and fretless strings, Western practice has fixed upon a finite set of discreet values as the set of notes available for crafting musical expression. They are known as semi-tones, of which there are exactly 12. Because of the basic phenomenon of the octave where a note value recurs at a higher or lower pitch with the same fundamental musical identity (e.g. high C, middle C, low C, etc.), the full spectrum of pitch from low to high is reducible to these 12 semi-tones. The circle of fifths is divided into 12 sections, each one rooted on one of these 12 tones.

Out of a complete universe of 12 semi-tones, Western music generally builds most of its melodies and harmonies from a working subset of 7 notes at any one time. (Remember, the 8th note is the octave, a repeat, a return to the beginning again). Such a subset is known as a key or a scale. Out of 12 semi-tones, there are many possible subsets of 7. But Western music has largely concentrated on only 12 of these, a sequence of 7 tones rooted at each of the 12 semi-tones yielding exactly 12 major scales. These are given symbolic names and are shown as labels around the outer circle of 5ths using the letters A through G and symbols for sharp and flat.

In addition to the 12 major scales, Western music uses 12 additional scales which are named "minor". But it turns out that the minor scales are just the major scales starting at a different root. They are have the same selection of notes as one of the major keys but they use a different ordering. Well, the same ordering, but starting from a different note, a root note that has a different character than its major counterpart. In summary, this doubles the set of available keys to 24, with two different scales rooted on each of the 12 semi-tones, one major and one minor. For each major key labeled on the outer circle of 5ths, there is a cooresponding minor key labeled on the inner circle of 5ths. Two keys or scales share the same wedge of the circle: the major and its relative minor, the minor and its relative major. For example, A minor is closely related to C major.

The general tonal universe of Western music comprises 24 keys, 12 major and 12 minor, built on this set of 12 semi-tones. In order to create a comprehensive catalog of music compositions, Bach chose, in his Well-Tempered Clavier, to create one piece in each of these keys, hence, the 24 preludes and fugues of Book 1. Bach published a second set, known as Book 2 of the Well-Tempered Clavier, itself, another complete universe of pieces, one for each of the 24 available keys. And so did Chopin compose 24 preludes, Shostakovich, his own set of 24 preludes and fugues.

Besides encompassing the full set of available keys, the circle of 5ths also governs (or describes) the way an individual composition moves. Within each scale, rooted at a particular semi-tone, the 5th note has a powerful role to play. Taking the key of C major as an example, its 7 tones are named C, D, E, F, G, A and B. The fifth tone is named G. G is the fifth tone in the key of C. Starting from any key in the circle (major or minor, outer or inner), you will see that the next key moving in a clockwise direction is in fact the 5th. So C moves clockwise to G, A minor to E, and so on. This circular movement has everything to do with the underlying dynamic of musical movement, the coherence of melody and harmony within a given key. It also turns out that a counterclockwise movement has a similar significance. As movement from C to G has a crucial musical meaning, so does the opposite movement from C to F (from A minor to D).

While most compositions of Western classic music are firmly based in a single ruling key (exactly one of the nodes on the circle of 5ths) most compositions shift to one or more alternate keys for contrast within a single dramatic narrative. Thus, a musical selection in the key of C major will migrate temporarily into another key such as G major. Or perhaps A minor. This is known as modulation. Curiously, the choice of a new key as the target of modulation is also well represented by the circle of 5ths. Most instances of modulation occur in simple movements around the circle of 5ths, often a single step clockwise, counterclockwise or, a shift to a relative key within the same wedge, moving from the outer circle to the inner, or, from the inner to the outer (e.g. C to A minor or A minor to C).

This is a brief, high-level summary. It is both logical and somehow mystical. It is a beginning of understanding, as well as a contemplation to return to again and again. The circle of 5ths encapsulates the full universe of Western tonality and provides a map for how music moves both within a key and how it modulates to different, related keys. It is a core unifying force, recurrent at many levels.

Philosophical influences and influence of colour[edit]

Scriabin was interested in Friedrich Nietzsche's Übermensch theory, and later became interested in theosophy. Both would influence his music and musical thought. During 1909–10 he lived in Brussels, becoming interested in Jean Delville's Theosophist philosophy and continuing his reading of Helena Blavatsky.^[18]

Theosophist and composer Dane Rudhyar wrote that Scriabin was "the one great pioneer of the new music of a reborn Western civilization, the father of the future musician", and an antidote to "the Latin reactionaries and their apostle, Stravinsky" and the "rule-ordained" music of "Schoenberg's group."^{[citation needed]} Scriabin developed his own very personal and abstract mysticism based on the role of the artist in relation to perception and life affirmation. His ideas on reality seem similar to Platonic and Aristotelian theory though much less coherent. The main sources of his philosophy can be found in his numerous unpublished notebooks, one in which he famously wrote "I am God". As well as jottings there are complex and technical diagrams explaining his metaphysics. Scriabin also used poetry as a means in which to express his philosophical notions, though arguably much of his philosophical thought was translated into music, the most recognizable example being the Ninth Sonata ("the Black Mass").

Keys arranged in a circle of fifths in order to show the spectral relationship^{[clarification needed]}

Though Scriabin's late works are often considered to be influenced by synesthesia, a condition wherein one experiences sensation in one sense in response to stimulus in another, it is doubted that Scriabin actually experienced this.^[31][32] His colour system, unlike most synesthetic experience, accords with the circle of fifths: it was a thought-out system based on SirIsaac Newton's Opticks.^{[clarification needed]} Note that Scriabin did not, for his theory, recognize a difference between a major and a minor tonality of the same name (for example: c-minor and C-Major).^{[clarification needed]} Indeed, influenced also by the doctrines of theosophy, he developed his system of synesthesia toward what would have been a pioneering multimedia performance: his unrealized magnum opus Mysterium was to have been a grand week-long performance including music, scent, dance, and light in the foothills of the Himalayas Mountains that was somehow to bring about the dissolution of the world in bliss.

In his autobiographical Recollections, Sergei Rachmaninoff recorded a conversation he had had with Scriabin and Nikolai Rimsky-Korsakov about Scriabin's association of colour and music. Rachmaninoff was surprised to find that Rimsky-Korsakov agreed with Scriabin on associations of musical keys with colors; himself skeptical, Rachmaninoff made the obvious objection that the two composers did not always agree on the colours involved. Both maintained that the key of D major was golden-brown; but Scriabin linked E-flat major with red-purple, while Rimsky-Korsakov favored blue. However, Rimsky-Korsakov protested that a passage in Rachmaninoff's opera The Miserly Knight accorded with their claim: the scene in which the Old Baron opens treasure chests to reveal gold and jewels glittering in torchlight is written in D major. Scriabin told Rachmaninoff that "your intuition has unconsciously followed the laws whose very existence you have tried to deny."

While Scriabin wrote only a small number of orchestral works, they are among his most famous, and some are performed frequently. They include a piano concerto(1896), and five symphonic works, including three numbered symphonies as well as The Poem of Ecstasy (1908) and Prometheus: The Poem of Fire (1910), which includes a part for a machine known as a "clavier à lumières", known also as a Luce (Italian for "Light"), which was a colour organ designed specifically for the performance of Scriabin's tone poem. It was played like a piano, but projected coloured light on a screen in the concert hall rather than sound. Most performances of the piece (including the premiere) have not included this light element, although a performance in New York City in 1915 projected colours onto a screen. It has been claimed erroneously that this performance used the colour-organ invented by English painter A. Wallace Rimington when in fact it was a novel construction supervised personally and built in New York specifically for the performance by Preston S. Miller, the president of the Illuminating Engineering Society. It was also performed at Yale University’s Woolsey Hall, New Haven, Connecticut, both in 1969 and again in 2010 (as conceived by Anna M. Gawboy on YouTube, who, with Justin Townsend, has published ‘Scriabin and the Possible’).^[33]

Scriabin's original colour keyboard, with its associated turntable of coloured lamps, is preserved in his apartment near the Arbat in Moscow, which is now a museum dedicated to his life and works.

Sacred Geometry and the Structure of Music

Legend recounts how Orpheus was given a lyre by Apollo. By playing his lyre, Orpheus produced harmonies that joined all of Nature together in peace and joy.

Inspired by this Orphic tradition of music and science, Pythagoras of Samos conducted perhaps the world's first physics experiment. By plucking strings of different lengths, Pythagoras discovered that sound vibrations naturally occurred in a sequence of whole tones or notes that repeat in a pattern of seven.

Like the seven naturally occurring colors of the rainbow, the octave of seven tones — indeed, all of Creation — is a singing matrix of frequencies that can be experienced as color, sound, matter, and states of consciousness.

This correlation of sound, matter, and consciousness is important. For as Stanford physicist William Tiller has proved, human consciousness imprints the space and matter of the universe. It is our intent that gives the direction and quality to Creation.

I believe that this matrix of Creation is waiting for us to sound the most harmonious vibrating chord — to sound the universe itself into a perfect, idealized form.

The Music of Atomic ShapesThe Platonic solids, basic shapes of Sacred Geometry, are five three-dimensional geometric forms of which all faces are alike. And each platonic solid represent one of the five elements of creation, as follows:

1. Tetrahedron — Fire
2. Cube — Earth
3. Octahedron — Air
4. Dodecahedron — Ether
5. Icosahedron — Water

These five Platonic solids comprise the alchemical dance of the elements and of Creation itself. My introduction to the spiritual power of sound began with an experience of this truth.

This happened many years ago, when I was studying with Michael Helios — who is for me a reincarnated Atlantean wizard. Helios discovered the musical proportions and corresponding tone scales for each of the Platonic shapes. He even tuned his keyboard to specific frequencies in order to achieve exact proportions.

During his presentations, he would play the scales and geometries of each shape, without disclosing to his listeners which geometric shape he was playing. Participants meditated on each piece as he was playing it, and then described which of the shapes they had experienced.

The results were extraordinary. Every Platonic solid was correctly perceived, felt, and "seen" during each of the five musical meditations. As a participant myself, this was my first experience of realizing the power of musical transmission and its potential to specifically re-order creation.

This is exactly what the ancient mystics and scientists had always been telling us!

The Dodecahedron, the Universe, and the Human FormWhen Michael Helios played his five compositions, I was most profoundly affected by the Dodecahedron. This shape can be seen to represent the order of the heavens and also the perfect mediation between the infinite and the finite — the sphere and the cube.

So let us look more closely at this as one example of the sacred geometric forms that permeate Creation. Through seeing the simplicity and complexity of the Dodecahedron in its relationship of shape and sound, perhaps we can intuit the rest. And through understanding our relationship to the Dodecahedron, perhaps we can begin to sense our own place within the Divine Song that is Creation.

The Dodecahedron is comprised of twelve pentagonal faces. It represents the fifth sacred element, the divine potentiality known as "ether."

Considering that the Dodecahedron is made up of five-sided faces, it is fascinating that quantum physics researchers in the US and France have recently concluded that, based upon measurements of cosmic waves left over from the so-called "Big Bang," the universe itself is a Dodecahedron!

Besides the fact that there are five platonic solids and five corresponding basic elements of life, it can be shown that the entire human race is joined in these same basic sacred proportions. For the physical body, with the arms and legs spread, is overlaid by a pentagram, with the fifth point being at the top of the head and the reproductive organs at the exact center.

And each of these points also relates to the number five: five fingers at the terminus of each arm, five toes on each leg, and five openings on the face. Additionally, we each possess five senses of physical perception.

So the Golden Mean proportions of the cosmos and our body temples are closely aligned with the harmony of the musical fifth.

If we can imagine the dodecahedronal-pentagonal shape of this One Song that is the universe, together with the pentagram geometry of the human body, we find inherent in both a divine proportion and a potential for harmonic perfection. The universe and humanity ARE singing geometries. And it is we ourselves who embody the geometry of the cosmos!

Phi and the Musical FifthTo follow this discussion, we first need to know that the Golden Mean and the Pentagram are closely related. For the angles of the five sides of a Pentagram are at a ratio of exactly 1.618 — the Golden Mean ratio, known mathematically as phi.

The fifth is the interval found in most sacred music, and has a powerful harmonizing effect on the human energy system. It is the first harmonic sounded by a plucked string, and is what gives the note its depth and beauty. Its sacred sound is the hallmark of the Gregorian chant. In fact most divinely inspired music, including some New Age music and that of indigenous cultures, is built around the musical interval of the fifth.

This music-geometry connection is well stated by Goethe, who said, "Sacred architecture is frozen music." The same is true of the "architecture" of the human body.

It was Pythagoras who first described the fifth interval that has come to be universally recognized for its beauty. It is "an archetypal expression of harmony that demonstrates the 'fitting together' of microcosm and macrocosm in an inseparable whole. The fifth is a beautiful sound because it demonstrates how the universe works."[1]

And in building the phi proportions, along with those of the other musical intervals, into the designs of cathedrals and temples, the architects also are building in the effects of the musical intervals upon which the sacred proportions are based.

These effects, immediately experienced as harmonious, powerful, and centering, can be experienced first-hand when one enters a Gothic cathedral or an ancient Egyptian temple. Being inside such a space helps us to access other dimensions of consciousness. It is the same experience that is reached through listening to sacred music.

The Circle of Fifths and the ChakrasBy applying the principles of progression to the harmonics of the fifth, we come to the Circle of Fifths: a musical sequence that prefigures the harmonic relationships of the human energy system. For the Circle of Fifths delineates the chakra system in the human body.

As we know, each chakra is a spinning wheel. Here, we will also note that each chakra comprises, in both sound and color, a literal mandala of geometries.

The musical tones and colors traditionally associated with the chakras are: C (root) red, G (throat) turquoise, D (belly) orange, A (brow) indigo, E (solar plexus) yellow, B (crown) magenta, and F# (heart) green.[2]

The interweaving of the chakras that we get by applying to them the Circle of Fifths represents a more complex system than the traditional, linear progression. And it is interesting to note that in sound healing, the connections between these "chakra harmonics" reflect a strong correspondence between our issues.

For example, in the Circle of Fifths progression, the root chakra (sexuality, survival, and money) is directly connected to the throat chakra (our expression; speaking our truth). And by working with these two chakras, we find that we can heal survival issues.

The Circle of Fifths and the Fibonacci Sequence

In the Circle of Fifths we see another way in which the musical scale is related to Sacred Geometry, for the musical progression is an exact parallel to the Fibonacci sequence.

As we know, the Fibonacci sequence starts with the number 1, and proceeds by adding the two previous numbers. So the second number in the sequence also is 1, then 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so on. And a graph of this sequence almost exactly matches the spiral graph of the Golden Mean sequence. One is finite, the other infinite. "As above, so below."

Fibonnaci realized that the natural branching, flowering, and spiraling forms in Nature followed the same uniform laws found in musical scales, for his sequence mathematically predicts all of the intervals that comprise the chords of music.

Note

A

A

D

F

E

C

E

C#

F#

C#

D

F

Interval

root

octave

4th

aug. 5th

5th

minor 3rd

5th

3rd

6th

3rd

4th

aug. 4th

Fibonacci ratio

1/1

2/1

2/3

2/5

3/2

3/5

3/8

5/2

5/3

5/8

8/3

8/5

Sacred Geometry and the Chanting of Our World

Plato, discoverer of the "Platonic" solids, believed that music was the strongest of all life's influences. In his treatise the Temaeus, he describes the numerical (vibrational-musical) creation of the physical universe and the soul that animates it. He called upon his students to activate the ancient shrines and sacred temples of the earth with sacred song, employing "perpetual choirs" in order to echo the harmonies of the Heavenly Choir.

Plato's Republic describes the cosmos as being held together by eight spinning "whorls," like a giant spinning wheel with eight feminine weavers sounding the fabric of Creation. Each of the whorls contains a planet. And on each planet is a siren who sings her particular note and emits her specific color.

The work of German astronomer and mystic Johannes Kepler (1571-1630) focused on the five Platonic solids, their harmonic ratios, and how these shapes correlated with planetary orbits and sound frequencies. He found the musical tones of individual planets, and the musical scales of planetary movements. As Stephen Hawking reports, Kepler was even able to determine that "four kinds of voice are expressed in the planets: soprano, contralto, tenor, and bass."

In finding the music of the cosmos, Kepler showed that life forms on Earth follow the same harmonic principles as those found in the stars.

Temples of SoundSimilar knowledge has come out of the hermetic tradition, which saw its Western resurgence in the beginning of the second millennium. During this time, hundreds of Gothic Cathedrals were constructed across Europe, all inspired by this Eastern hermetic knowledge that had just been rediscovered by the mystical order known as the Knights Templar.

Excavating Solomon's Temple in Jerusalem, the Knights Templar discovered vaults of hidden artifacts and scrolls that described the alchemical sciences of sacred geometry and architecture and their relationship to sound, astronomy, and genetics. Ancient sacred relics also are said to have been found, including the Ark of the Covenant, the Holy Grail, and secrets pertaining to Mary Magdalen and a Holy bloodline.[3]

Inspired by this material, the great Gothic cathedrals, including Chartres, Notre Dame, Salisbury, St.Denis, and Cluny, were designed and built using the principles of sacred geometry and harmonic acoustics.

Chanting and Millennial ShiftsSacred music and chant is always with us. But surges in its popularity occur at the crucial millennial turning points. This was so during the beginning of the first millennium, at the inception of Christianity, and during the era of the Grail Romances, which began around 1000 AD. And now today, as we forge a new paradigm and write our "script" for the next one thousand years, chanting has again come into prominence.

The sacred architecture employed in the medieval cathedrals reflected specific acoustical properties that were conducive to the constant rounds of perpetual choirs maintained by the monks.

Author John Michell, who has researched the tradition of "perpetual choirs" in ancient Britain, reports that these choirs were maintained in at least three sites: Glastonbury, Stonehenge, and Llantwit Major in Wales. Together, the sites form the rim of a circle in the landscape, with the center at an old Druid site called Whiteleafed Oak.

Michel found that these sacred sites were equidistant from each other, and that their individual locations corresponded to sunrise points and sacred proportions.[4]

Similarly, sacred sites in other cultures also were laid out in geometric relationship to each other, and were maintained with sacred music and chant, synchronized with the seasons and cosmic cycles.

Emotion, Sound, and FormScience is only now beginning to discover these interrelationships of sound and matter.

Launching the new science of cymatics, Swiss researcher Hans Jenny (1904-1972) conducted experiments showing that inert powders, pastes, and liquids, when animated by audible, pure tones, would form into flowing patterns that mirrored those found throughout Nature, art, and architecture. He showed that there was a correlation between sound and form — that, in effect, the matter of the universe is a physical manifestation of vibration.

And as several articles in the Spirit of Ma'at have reported, Dr. Masaru Emoto has proven over and over again, through photographing water crystals, that there is a geometrical correspondence between human thoughts and emotions and the very shape of the matter that surrounds us. Water, Emoto has shown, "treated" with love or beautiful music, undergoes molecular change into beautiful, harmonious geometrical forms. And the same happens in reverse: chaotic or "negative" thought and emotion cause the crystals of water to become unformed and unlovely.

These ideas are modern reflections of timeless principles well known to all ancient and indigenous cultures.

As Billy Yellow, a Navajo medicine man, sums it up: "Our task is to chant the world, chant the beauty. The world is a reflection of our chanting."

Geometry, Music and Healing by Ani Williams text and photos ©Ani Williams January 2004		Golden Mean Pentagram
"Legend recounts how Orpheus was given a lyre by Apollo…by playing his lyre, Orpheus produced harmonies that joined all of nature together in peace and joy. Inspired by this Orphic tradition of music and science, Pythagoras of Samos conducted perhaps the world’s first physics experiment. By playing strings of different lengths, Pythagoras discovered that sound vibrations naturally occur in a sequence of whole tones or notes that repeat in a pattern of seven. Like the seven naturally occurring colors of the rainbow, the octave of seven tones". ‘The Harmonic Lyre’ by Stephen Ian McIntosh All of Creation is a singing matrix of frequencies, which can be experienced as color, sound, matter and states of consciousness. Through the research of Stanford University physicist William Tiller PhD, we find that all space, even a so-called vacuum is waiting to receive instruction from us…waiting for us to project our intention so that space or matter can have direction and take on specific qualities. What intentions are we sending to our world? I believe that this matrix of creation is waiting for the most harmonious vibrating chord to sound it into a perfect idealized form. The discoveries of Japanese researcher Dr. Masaru Emoto have shown the glorious snowflake-like mandalas that form in water when a beautiful piece of music is played, or similarly, when a positive feeling or thought is projected into the water, such as appreciation and love. He has even conducted global ‘appreciation meditations’ with the goal of purifying some of Earth’s great rivers that we have polluted. "High-speed photography of crystals formed in frozen water reveals changes in the water after specific, concentrated thoughts were directed toward it… Naturally, since water covers the largest portion of our planet, and comprises the largest percentage of our physical bodies, the impact of our thoughts and feelings will play a large part in the way our environments get created, both globally and personally." (Dr. Masaru Emoto). Water treated with love or beautiful music reflected a molecular change and a harmonious geometry. The following image was photographed by Dr. Emoto after 500 people sent the feeling of love to the water: This is a perfect example of what Swiss researcher Hans Jenny (1904-1972) discovered while projecting pure tones onto fine grains of matter or liquid and observed the forming of distinct geometric shapes. He termed this sound-matter connection Cymatics and his groundbreaking work has become a cornerstone of sound healing. The following quote is from the Hans Jenny website at www.cymaticsource.com: "For 14 years he (Jenny) conducted experiments animating inert powders, pastes, and liquids into life-like, flowing forms, which mirrored patterns found throughout nature, art and architecture. What's more, all of these patterns were created using simple sine wave vibrations (pure tones) within the audible range. So what you see is a physical representation of vibration, or how sound manifests into form through the medium of various materials." The pioneering research of Fabion Mamon in the 1970’s found that when they sounded a specific tuning fork tone onto a cancer cell, that cell would dissolve. Even allopathic medicine has adopted this same principle in new, non-invasive forms of surgery. Scientific American magazine reported one example of an effective method for removing kidney stones by identifying the frequency of the stone, and projecting the ‘reversed’ frequency to dissolve it. This interrelationship of sound and matter is at the core of an exciting new wave of science, which is based on timeless principles well known to all ancient and indigenous cultures. Billy Yellow, a Navajo medicine man summed it all up with this wisdom: "Our task is to chant the world, chant the beauty. The world is a reflection of our chanting." How are we each using sound to affect our state of being, the health of the earth and our children? Ancient Seekers of Universal Harmony Throughout the last few millenniums, dreamers, scientists, philosophers and seekers of the patterns of creation have studied the movements of the cosmos and the mirroring of these cycles and proportions on Earth. The ancient Chinese, Egyptian, Sumerian, Druid, and Mayan cultures including great thinkers and pioneers such as Plato, Pythagoras, Copernicus, and Kepler, all discovered the interconnectedness of the planetary cycles, sacred geometry, and musical scales long before modern science began to confirm these connections. The divine order of the movements of the cosmos and the sacred proportions found in ancient temple design, are the same principles found in music. "According to Plato there are five mathematical sciences: (1) Arithmetic (2) Plane geometry, or the study of numerical proportions (3) 3 dimensional geometry, including the ‘Platonic Solids’ (4) Astronomy and (5) Music, which illustrates the harmonious composition of the universe." ‘The Dimensions of Paradise’ by John Michell Plato believed that the strongest of all life’s influences is music. In his treatise the Temaeus, Plato describes the numerical (vibrational–musical) creation of the physical universe and the soul, which animates it. He called his students to activate the ancient shrines and sacred temples of the earth with sacred song, employing ‘perpetual choirs’ in order to echo the harmonies of the Heavenly Choir. Plato’s ‘Republic’ describes the cosmos as being held together by eight spinning ‘whorls’, like a giant spinning wheel with eight feminine weavers sounding the fabric of creation. Each of the whorls contained a planet, and on each planet was a siren singing her particular note, and emitting a specific color. "The diameters of the planets can be seen as corresponding to the strings of a lyre, in which case the note sung by a siren would be in accordance with the length of diameter of the planet she rode upon." John Michell ‘The Dimensions of Paradise’ The German astronomer and mystic Johannes Kepler lived from 1571-1630 and was possessed his entire life with finding the cosmic proportions and musical harmonies, represented by the distances and orbits of the planets. His writings reveal that in addition to his lifetime of calculations and observations, he was deeply influenced by Egyptian hermetical science. His monumental work ‘Harmonice Mundi’, or Harmonies of the World, contained five books covering his life’s work on the correspondences between music, astrology, geometry and astronomy. According to Stephen Hawking in his book ‘On The Shoulders Of Giants’, Kepler discovered how planets orbited and he paved the way for the later Isaac Newton to discover why. Kepler’s work focused on the five Platonic solids, their harmonic ratios, and how these shapes correlated with planetary orbits and sound frequencies. He found the musical tones of individual planets, and the musical scales of planetary movements. He was even able to determine that "…four kinds of voice are expressed in the planets: soprano, contralto, tenor, and bass." (Stephen Hawking). Basically, Kepler had found the music of the cosmos, and that the same harmonic principles found in the stars, and life forms on earth are musical. Perpetual Heavenly Choirs "God hungers for songs." Marius Schneider Between 1100-1300 AD hundreds of Gothic Cathedrals were constructed across Europe, inspired by the eastern Hermetic knowledge rediscovered by the mystical order of monk-knights, the Knights Templar. During the tenure and excavations of the Tempars at Solomon’s Temple in Jerusalem, they discovered the vaults of hidden artifacts and scrolls concerning the alchemical sciences of sacred geometry and architecture, sound, astronomy, and genetics. Ancient sacred relics are also said to have been in the Templar’s cache of discoveries there, including the Ark of the Covenant, the Holy Grail, and secrets pertaining to Mary Magdalene and a Holy Bloodline. (See: Article about Mary Magdalene. The building of the great Gothic cathedrals such as the ones at Chartres, Notre Dame in Paris, Salisbury, St.Denis, and Cluny was inspired by these transforming discoveries. These edifices were monuments to the rediscovery of ancient mysteries, a new elevated awareness, and were constructed using the principles of sacred geometry, harmonic acoustics for their transforming potential. "The huge number of Gothic cathedrals that were erected, as graceful and sublime as if they were designed in heaven, have yet to be surpassed for their dignity and spiritual potency, almost a thousand years later." ‘Dance of the Dragon’ by Paul Broadhurst and Hamish Miller (The authors discovered many of these cathedrals are located on a major energy grid they call ‘The Apollo- St. Michael axis’, and stretches from Britain’s St. Michael’s Mount to Mt. Carmel) The sacred architecture employed in these majestic structures reflected a new ‘alchemical light and specific acoustical properties’, according to ‘Dance of the Dragon’ authors, that was conducive to the constant rounds of perpetual choirs maintained by the monks. Interestingly, it is precisely at these millennium shifts, when perpetual chanting becomes a device of the collective creative intention. Sacred music and chant is always with us, but surges in its necessary popularity at these crucial turning points, as during the inception of Christianity in the first century AD, during the beginning of the first millennium and time of the Grail Romances, and now as we forge a new paradigm and write our ‘script’ for the next one thousand years. Author John Michell has researched the tradition of ‘perpetual choirs’, in ancient Britain. According to Michell, these choirs were maintained in Britain in at least three sites: Glastonbury, Stonehenge and Llantwit Major in Wales, which together form the rim of a circle in the landscape, with the center at an old Druid site called Whiteleafed Oak. He found the distances between these sacred sites to be equal and corresponding to sunrise points and sacred proportions. Similarly, sacred sites in other cultures were also laid out in geometric relationship, and were maintained with sacred music and chant, which were synchronized with the seasons and cosmic cycles. "Similarly, in Revelations, 24 elders stand before the throne of the Lamb, ‘every one of them having harps, and golden vials full of odours, which are the prayers of saints. And they sung a new song…’ The elders’ new song was their accompaniment to the appearance of the New Jerusalem and a new dispensation on earth." ‘The Dimensions of Paradise’ by John Michell King David and his harp from a Medieval Bible c. 1170 AD The Music of Atomic Shapes Five basic three dimensional geometric forms are found to represent the five elements in creation: The tetrahedron–fire, the cube–earth, the octahedron--air, the dodecahedron–ether, and the icosahedron–water, as shown in order here: These five Platonic solids comprise the constantly changing dance of creation, the alchemical dance of the elements. "In bringing order to the universe the Creator gave geometric forms to the atoms….interacting with human senses to produce appearances and feelings." John Michell I was able to experience the ‘musical proportions’ of Platonic solids many years ago, when I was studying with Michael Heleus, who I consider to be a reincarnated Atlantean wizard. Heleus’ early pioneering research in music, mathematical proportions, astronomy and healing became one of my areas of study in sound healing during the early 1990’s. Heleus had discovered the musical proportions and corresponding tone scales of the each of the Platonic shapes, which included tuning his keyboard to specific frequencies to achieve the exact proportions. During his presentations Michael would play the scales and geometries of each shape and the participants would meditate on the five different musical pieces, without his disclosing which geometric shape he was playing. After each piece, the listeners would describe which of the shapes they experienced. It was quite extraordinary, that every Platonic solid was directly perceived, felt, and ‘seen’ with the inner eye during each of the five musical meditations. This was my first experience of realizing the power of musical transmission and its potential to specifically re-order creation. This is exactly what the ancient mystics and scientists were telling us! I was especially profoundly affected by the Dodecahedron, and while Heleus played the musical proportions, I felt as if I ‘became’ this geometric solid, and this shape and I became the Great Mother matrix of the universe. The dodecahedron can be seen to represent the order of the heavens and also the perfect shape of mediation between the infinite and the finite, the sphere and the cube. The dodecahedron is comprised of twelve pentagonal (five-sided) faces, and represents the fifth sacred element, ether, or divine potentiality. Recently, quantum physics researchers in the US and France have said that based on measurements of cosmic waves left over from the ‘big bang’, it appears that the shape of the universe is a Dodecahedron. This is fascinating, considering there are five platonic solids and the corresponding five basic elements of life. The entire human race is joined in these same basic sacred proportions of the physical body as it is overlaid in a pentagram, with the arms and legs spread to make a five-pointed star, with the reproductive organs at the exact center. And there are five appendages from the human torso, five appendages on each leg and arm, five openings on the face, and five senses of physical perception. If we can imagine the dodecahedral-pentagonal shape of the uni-verse (meaning one song), and see the human body pentagram geometry, we find in both a divine proportion and potential for harmonic perfection, inherent in physical embodiment and the harmony of the spheres. We embody the geometry of the cosmos! And we find that the Golden Mean proportions of the cosmos and our body temples are closely aligned with the harmony of the musical ‘fifth’, or stated another way, the universe and humanity are geometries singing! "One of the properties of the pentagram is that the lines bisect each other according to the Golden Section …the ideal human proportions lie in the canon defined by the Golden Section or PHI." Nicholas Mann’s ‘Sedona Sacred Earth’.          Pentagram image courtesy Bruce Rawls at www.intent.com PHI Ratio and the Musical Fifth In the book ‘The Power of Limits’, architect Gyorgy Doczi surveys the similarity between the sacred geometry proportions in ancient temple construction of the Golden Mean ratio (1.618) and the interval of the fifth in music (1.667). The fifth is the interval found in most sacred music and has a powerful harmonizing effect on the human energy system. The fifth is the first harmonic sounded by a plucked string and gives the note its depth and beauty. This music–geometry connection is well stated in the poet-mystic Goethe’s phrase that ‘sacred architecture (or human body proportion!) is frozen music.’ "Since its discovery by Pythagoras, the fifth has come to be universally recognized for its beauty…the fifth is an archetypal expression of harmony that demonstrates the ‘fitting together’ of microcosm and macrocosm in an inseparable whole. The fifth is a beautiful sound because it demonstrates how the universe works." ‘The Harmonic Lyre’ Stephen Ian McIntosh All of creation expresses itself through number and number is frequency, manifest as color, sound and form, and even as emotion and states of consciousness. The effects of harmonious design based on sacred proportions can be experienced first hand when one enters an ancient temple in Egypt or a Gothic cathedral, such as Chartres. The effect can be immediately sensed as harmonious, powerful and centering, and being inside a space designed with sacred proportions helps us to access other dimensions of consciousness. "The most common proportions found in ancient Egyptian temple architecture correspond to the most harmonious intervals found in music: the octaves, fifths, fourths, thirds and sixths. In the temple of Horus at Edfu, the dimensions of one chamber's measurements of width to height equaled 2:3, which defines an interval of a fifth in music. ‘Rediscovering Music in the Architecture of Egyptian Temples’ by Antoine Seronde. This expansion and transformation experienced by being inside a sacred space, can also be reached directly through listening to sacred music, or ‘aural geometry’. Most divinely inspired music, such as Gregorian chant, some ‘new age’ music, and the music of indigenous cultures, features the musical interval of the fifth. An easy way to understand a musical ‘fifth’, would be to use the white keys of a piano, and play middle C and counting C as the first note, play the fifth key up, which is G. ... the Egyptians utilized musical scales analogous to our own. The positions of the harpists' hands on the strings clearly indicate ratios such as the fourth, fifth and octave, revealing an unquestionable knowledge of the laws governing musical harmony. Lucy Lamy, Egyptian Mysteries (Thames and Hudson 1981) The basic chords of most western music are made of a combination of a fundamental tone, a fifth with a third, or in the case of a C chord, the notes C-E-G, the first, third and fifth notes. However, when we leave out the third (E), the chord sounds distinctly ancient or sacred. I can remember that when I first began teaching myself to play the harp, I tended to play mostly in fifths, just because I liked the sound and the feeling effect of being centered and expanded when playing them. At that time I was not consciously aware of the harmonious principles at work. During those early days of my ‘harping’, I had a music colleague who played in symphony orchestras, who commented: ‘didn’t I play anything other than temple music?’ The Circle of Fifths and Chakras The circle of fifths is a musical sequence in which we can find the harmonic progression of musical scales and also the harmonic relationship of the human energy system. Each human energy center, or chakra, is a spinning wheel or mandala of geometries, sound and color. The musical tones and colors traditionally associated with the chakras are: C (root) red, G (throat) turquoise, D (belly) orange, A (brow) indigo, E (solar plexus) yellow, B (crown) magenta, and F# (heart) green. Beginning this harmonic cycle at the root or first chakra with the tone of C, we progress in the sequence of fifths, and end at the heart chakra and a tone of F#. Many have wondered why the heart chakra would be represented by the tone F#, rather than F, and the circle of fifths answers that question. This interweaving of the charkas is more complex than the traditional linear progression and it is interesting to note the connections between these ‘chakra harmonics’. For instance, in energy and sound healing, there is a strong correspondence between issues in the root chakra--sexuality, survival and money and the throat chakra–our expression, speaking our truth. Working with the fifth harmonic of the root chakra and the throat chakra of authentic communication, these survival issues can heal. The harmonic relationship of the other chakras invites further explorations. To the find all the notes in the western chromatic twelve-tone scale, we continue creating musical fifths beyond the first seven tones of the chakras. If we begin at the note ‘C’ and sound each consecutive fifth, we have all twelve tones, and arrive at the thirteenth tone, ‘C’ on a higher octave: C–G–D–A–E–B–F#--C#--G#--D#--A#--F–C. In the circle of fifths we can see how a musical scale is geometry! Circle of Fifths (E to A) from ‘The Harmonic Lyre’ by Stephen Ian McIntosh Fibonacci Ratios and Musical Intervals Leonardo de Pisa (circa 1180-1240 AD), better known as Fibonacci, discovered the uniformity of ancient harmonic wisdom. He realized that the natural branching, flowering, and spiraling forms in nature follow the same uniform laws found in musical scales. He found this harmonic in nature is equal to a number sequence of 1--1–2–3–5–8–13–21–34–55–89--144 and so on, found by adding each number to the previous one to get the next number. The Fibonacci series relates to all of the musical intervals, which comprise beautiful chords. The following table shows some Fibonacci ratio musical chords using the fundamental tone ‘A’: Note A A D F E C E C# F# C# D F Interval root octave 4th aug. 5th 5th minor 3rd 5th 3rd 6th 3rd 4th aug. 4th Fibonacci ratio 1/1 2/1 2/3 2/5 3/2 3/5 3/8 5/2 5/3 5/8 8/3 8/5 The Fibonacci ratios were also utilized in sacred temple architecture, including the towering Gothic Cathedrals. Guillaume Dufay (c. 1400-1474) from the Netherlands composed music for the dedication of Florence’s cathedral of Santa Maria del Fiore in 1436. His musical piece was based on the Fibonacci series of tones, which corresponded to the dimensions of the cathedral’s dome. These ‘musical temples’ were part of the medieval renaissance of sacred geometry, Hermetic mysteries and the flowering of art and music. The Geometry of Sound Healing "The sky and its stars make music in you." Denderah Temple wall inscription, Egypt The healing potential of the magical fifth and the natural harmonics of our beautiful earth hold a powerful key for bringing us back to a state of well being. Songaia (song of the earth) Sound Medicine was founded in 1992, a system of sound therapy based upon ancient knowledge of the harmonious arrangement of heaven and earth. The ancients understood that if we live harmony with the heavenly and earthly cycles, and use those harmonic principles in our physical environment, we can be whole, healthy and truly connected. Just spending time in nature puts us back in touch with the primordial harmonies that heal. The basic purpose of Songaia Sound is to reintroduce the harmonic fields found in nature into our lives using a musical formula in twelve sound recordings. The twelve musical meditations are based on the twelve tones of the chromatic music scale, and incorporate the pure healing harmonics of harp, Australian didjeridu, voice overtones, and Tibetan bowls, all instruments used by ancient cultures in healing. Each of these twelve tones correlate with specific physical conditions, organs of the body, emotional states, and even vitamins and minerals. The Songaia Sound Wheel illustrated below, shows sound, color and zodiacal associations. According to the findings of Johannes Kepler, Pythagoras, and many ancient cultures, the planetary frequency patterns are mirrored in life on earth, in music, geometry, and in our bodies. This was called ’musica speculativa’, or music as a mirror of the cosmos, by many researchers in Kepler’s era of the 16th century. (In the GONG project, modern science has been monitoring the tone emissions from the sun, and observing those effects on earth.) One of the most exciting aspects of our work at Songaia Sound is in observing thousands of clients demonstrating the truth stated on the Egyptian temple wall at Denderah: "The sky and its stars do make music in you." The pattern of sounds emitted from the planets at the time of birth, based on the positions of those planets, is mirrored in the human energy system. This pattern is like a blueprint of influences and tendencies, and each one of us has this unique ‘song-print’. The amazing thing about an individual ‘song-print’ is that the same planetary sound pattern is detected in the frequency pattern of the speaking voice. (Voice frequency patterns are also mirrored in each person’s ability to hear specific frequencies. Dr. Alfred Tomatis, a French ear and eye specialist, developed the Tomatis Method, with diagnostic and therapy centers around the world.) "The body is held together by sound–the presence of disease indicates that some sounds have gone out of tune." Dr. Deepak Chopra ‘Songaia Sound Wheel’ © Ani Williams Each of us is a living symphony of frequencies…some of our notes singing in harmony, and some singing ‘off key’. Because of stress, trauma, and negative mental and emotional patterns, the instruments of our symphony need tuning up. Some notes in our body-mind symphony have become so stressed that they are missing, which makes it more difficult for our orchestra, or whole energy system to play. These missing tones can be identified by listening to the notes in our speaking voice with a digital tuner. (These frequency patterns are also mirrored in the individual’s planetary tone frequencies.) By knowing the frequency of something, we can alter or change it, and when the missing frequencies are played back, we can return to wholeness, health and harmony. (See Voice Spectrum Analysis) Playing the full spectrum of tones of our living symphony, and especially audibly sounding these tones (called toning), has been found to have the following effects:  Releases ‘feel good’ endorphins and supports healthy immune system function Nourishes and feeds the physical and emotional bodies, harmonizing the system Assists in releasing limiting belief systems, stress and general dis-ease Alters brain state, inducing alpha-theta states associated with healing Synchronizes mind-heart-body rhythms and a sense of being centered and balanced Expands creativity, vision, and clarity, opening a gateway for soul freedom In our modern high-tech digital world, we have lost much of these healing harmonies in our daily lives. Hours spent at computers, on cell phones, traveling in cars and planes at high speeds, and living in structures that are most likely not designed with sacred architectural principles, we are removed from the natural harmonic environments that heal. In the ideal whole and healthy state, our bodies and minds are ‘singing’ with the harmonic ‘fifths’ and Fibonacci ratios of the stars and with all of the natural world. "We are the stars which sing–we sing with your light." Algonquian traditional song The Musical Geometry of Crop Circles Gerald Hawkins, astronomer at the Smithsonian Astrophysical Observatory, author of ‘Stonehenge Decoded’ and crop circle researcher, has found that the proportional dimensions of the extraordinarily complex geometries of the crop circles are also in direct correspondence with musical intervals of the white keys of a piano. Does this indicate a musical intention from the ‘circle makers’? Given the divine harmonics within these amazing formations, they appear to be mandalas for awakening, or visual ‘alarm clocks’ with a language calling us to return to the essential harmony of creation before we destroy our beloved planet. They call us to return to the healing potential within divine proportions and sacred music, as in the writer Dostoyevsky’s prophecy that ‘beauty will save the world’. Most creation myths maintain that the world grows by way of song and music, and ’God hungers for songs’. (Marius Schneider) After visiting many of these amazing crop circles in Britain over the last decade, I have found the energetic intensity and consciousness expanding effects to be immediate and potent, even greater than those experienced in ancient temples. Perhaps, that is because these ‘geometric temples’ are freshly constructed, and hence still alive and active in their energetic effects. Upon entering a formation, I have often heard the sound currents like a ringing in the air, and have seen increased light particles within and above the formation. In others, it has felt as if my very cells were being realigned and harmonized with a higher design or template. It is quite exciting that crop circles are now forming not just in England, but more frequently in the US and Canada, and Europe, including Poland. While discussing the mathematics and geometry of crop circles with Michael Glickman in 2000, he said that the language of the circles appears to intentionally increase in complexity in a progression that correlates with expanding knowledge and consciousness. And these progressions of geometry often mirror the current planetary alignments and eclipses, a mirroring of the cosmos on the earth. Regarding the claims that many of these phenomena are ‘hoaxes’, I would like to see someone work out the mathematical precision required to manifest one of these forms in the short time that lapses between a farmer seeing his field of growing grain and looking again, sometimes only minutes later, to see a huge design imprinted in the field. Often these formations are accompanied by observations of unusual lights and sounds. The following crop circle images are from the 2003 season. The 13-pointed star geometry of the top image appeared at West Stowell, near Huish in Wiltshire, England. It was first reported on July 20th, and the photo was taken by Nick Nicholson. The second formation shown here is the fantastic pentagram within the rays and pentagon, which appeared on June 29 at Sharpenhoe, near Barton Le Chay, Bedfordshire, England. The photograph was taken by Russell Stanard.

usic of the Spheres -- The Story

Music of the Spheres consists of twelve pieces inspired by the ancient Pythagorean conception of the Universe. It includes a wealth of musical symbolism based on almost a year of William's research into ancient through modern cosmology—mostly reading the ancient writers directly.

William writes:

The "Music of the Spheres" was an understanding of the Cosmos that held sway for about 2000 years. According to this view, each of the planets rode on giant crystal spheres, and each of these planetary crystal spheres emitted a musical sound as they moved. The combined sound of all the planets was "the Music of the Spheres".

The Music of the Spheres in Plato

William Zeitler Playing the Glass Armonica at Stonehenge

The original concept of the "Music of the Spheres" is credited to Pythagoras (c.569–475 BC), a musical-mathematical-mystic, but its first surviving written account appears in Plato (c.427–347 BC). At the end of his Republic, the spirits are giving Socrates a tour of the afterlife and a view of the planetary spheres. But for Plato they aren't true spheres, they are hemispheres, nested inside of each other with just the rims exposed, all rotating on a giant spindle of light, with a Siren assigned to each rim singing a note. (See the album cover above.) Here is the passage:

Now when the spirits which were in the meadow had tarried seven days, on the eighth they were obliged to proceed on their journey, and, on the fourth day after, he said that they came to a place where they could see from above a line of light, straight as a column, extending right through the whole heaven and through the earth, in colour resembling the rainbow, only brighter and purer; another day's journey brought them to the place, and there, in the midst of the light, they saw the ends of the chains of heaven let down from above: for this light is the belt of heaven, and holds together the circle of the universe, like the under-girders of a trireme. From these ends is extended the spindle of Necessity, on which all the revolutions turn. The shaft and hook of this spindle are made of steel, and the whorl is made partly of steel and also partly of other materials. Now the whorl is in form like the whorl used on earth; and the description of it implied that there is one large hollow whorl which is quite scooped out, and into this is fitted another lesser one, and another, and another, and four others, making eight in all, like vessels which fit into one another; the whorls show their edges on the upper side, and on their lower side all together form one continuous whorl. This is pierced by the spindle, which is driven home through the centre of the eighth. The first and outermost whorl has the rim broadest, and the seven inner whorls are narrower, in the following proportions --the sixth is next to the first in size, the fourth next to the sixth; then comes the eighth; the seventh is fifth, the fifth is sixth, the third is seventh, last and eighth comes the second. The largest (of fixed stars) is spangled, and the seventh (or sun) is brightest; the eighth (or moon) coloured by the reflected light of the seventh; the second and fifth (Saturn and Mercury) are in colour like one another, and yellower than the preceding; the third (Venus) has the whitest light; the fourth (Mars) is reddish; the sixth (Jupiter) is in whiteness second. Now the whole spindle has the same motion; but, as the whole revolves in one direction, the seven inner circles move slowly in the other, and of these the swiftest is the eighth; next in swiftness are the seventh, sixth, and fifth, which move together; third in swiftness appeared to move according to the law of this reversed motion the fourth; the third appeared fourth and the second fifth. The spindle turns on the knees of Necessity; and on the upper surface of each circle is a siren, who goes round with them, hymning a single tone or note.(Republic, 10)

The word here translated 'whorl' (SPHONDOLOS) is quite complex: it can mean 'vertebra', 'the circular whorl which balances and twirls a spindle', and the head of an artichoke. (See A Greek-English Lexicon (unabridged), Liddell-Scott).

In short, in Plato's view, the Cosmos is an enormous GLASS ARMONICA in the sky! If Plato's Sirens merely touched their rims with moistened fingers instead of singing, we'd be crediting Plato with the invention of the glass armonica instead of Benjamin Franklin (1706–1790).

The Music of the Spheres in Kepler

The concept of the Music of the Spheres probably found its greatest literal expression in the works of Johannes Kepler (1571–1630), who is now considered one of the founders of modern astrophysics. Kepler constructed a musical/mathematical theory of the solar system from which he derived his famous Kepler's Laws —one of the major foundations of Newton's physics and still taught in physics courses today.

The Celestial Spheres were making Music all the way from Pythagoras until Isaac Newton (1642–1727)—over 2000 years. Then, Newton founded modern science, and the Music stopped. Before Newton the Cosmos was full of Music; with Newton and modern science the Cosmos fell silent.

The Music of the Spheres and the Afterlife

In the Greek Gnostic imagination, when You were born you descended from the heavens, passing through the Spheres on your way to life on Earth, pausing at each sphere to acquire the quality associated with that Sphere. When you died, you ascended through the Spheres on your way to the afterlife, pausing at each Sphere once again to address the aspect of your life associated with that sphere—your "warrior" at Mars, your "lover" at Venus, etc. And since each of these is a musical sphere, it was of course the Muses who escorted you on your final journey.

The MUSICAL SYMBOLISM of the Individual Tracks

In the history of Western civilization until relatively recent times the line between "science" and "magic" has been rather fuzzy. This would certainly be true of Pythagoras, to whom is ascribed both the idea of "mathematical proof" and the invention of mystic "numerology". This blurring between "science" and "magic" was still true through Newton: recent research suggests that Newton himself may have gotten some of his important ideas for modern physics from his extensive alchemical experiments. Newton was also heavily involved in esoteric Bible research.

Consequently I felt that the Music of the Spheres ought to have both "mathematical" and "mystical" elements drawn from the history and lore of the Music of the Spheres.

Ptolemy

In the ancient Music of the Spheres model, the Earth is at the center of the Cosmos. Ancient thinkers developed a mathematical model based on this assumption that allowed them to predict the positions of the planets in the night sky. These efforts reached their culmination in Ptolemy (c. 87–150 AD). His most famous work, the Almagest, was a mathematical treatise on practical astronomy that worked within the accuracy of the astronomical instruments then available, and was the standard work on mathematical astronomy until the 16th century. As technology improved, so did astronomical measurements, and discrepancies between Ptolemy's system and the new improved measurements ultimately resulted in Ptolemy's system being replaced by the model developed by Copernicus, Galileo, Kepler and Newton. (As the accuracy of measurements continued to improve, Newton's model was itself replaced by Einstein's for exactly the same reason.)

Ptolemy's Epicycles

If you follow the positions of the planets in the night sky, it quickly becomes apparent that they move in complicated ways. The Ptolemaic theory accounted for these complications by assuming that the planets move in circles within circles, called "Epicycles".

Tracks of the Music of the Spheres album use the actual Ptolemaic ratios of the planets in musical ways (discussed below in the section about the tracks themselves).

Ptolemy's model—that the planets moved in "circles within circles"—was later replaced by Kepler's model—that planets move in ellipses with the sun at one of the foci. (But it can be shown mathematically that Kepler's model is a special case of Ptolemy's more general model).

The Ptolemaic ratios would be a "mathematical" dimension of the Music of the Spheres.

Gematria

Pythagoras taught that everything is arranged and defined by Number — which is still an axiom of modern science. The Pythagoreans went further, however, and asserted that "Number represents a celestial power working in the divine sphere, a veritable blueprint of creation. Consequently Number is itself divine and associated with the divinities." [JCSG p.25]

Numerology is the study of the mystical significance of numbers. In numerology, a number is assigned to each letter of the alphabet, so if you add up all the numbers that correspond to the letters in, for example, your name, you will arrive at a unique number that has mystical significance for you. An ancient form of numerology called "gematria" (geh-MAY-tree-uh) goes back to Babylonian times, around 700 BCE. [JCSG p.27]. By the time of Pythagoras, two centuries later, gematria was probably well known to the Pythagorean School. [JCSG p. 75]

In modern times we have a separate set of characters for our numbers ('0' through '9') as opposed to our alphabet ('A' through 'Z'). But the ancient Greeks used their alphabet for both numbers and letters:

The Greek Alphabet & Numbers (for Gematria)

Thus, in ancient Greece, you would write "123" as "Rho-Kappa-Gamma." For numbers greater than 1000 they'd add an accent mark ('), so "123,123" would be rho', kappa', gamma', rho, kappa, gamma. Thus they could express numbers up to one million—more than adequate for most accounting purposes. The ancient Greek reader would have to distinguish between words and numbers by context.

Because, for the ancient Greeks, the letters of their alphabet were already assigned to numbers, their cognitive leap to gematria would be much smaller than ours today.

Gematria was used heavily in early Christianity, and even occurs in the New Testament itself:

"Here is wisdom. The one having understanding, let him count the number of the wild-beast, for it is the number of a man. And his number is six hundred sixty six." (Rev.13:18)

Interestingly, the gematria value of 'Jesus' is '888'.

For "musical gematria" in the same spirit, here is an example of a simple mapping of rhythms to the ancient Greek alphabet that was used on one of the tracks:

An Example of Musical Gematria Using the Greek Alphabet

Naturally, when doing Greek gematria like this, you would want to use the ancient Greek names of the planets.

Gematria would be a "mystical" dimension of the Music of the Spheres.

The Circle of Fifths

Circles play a central role in the Music of the Spheres, and the most famous circle in music is the "Circle of Fifths". Here's how it works:

If you sing to yourself the "Do-Re-Mi-Fa-So…" song, the two notes Do and So are a fifth apart.

An Example of Musical Gematria Using the Greek Alphabet

Pythagoras discovered that the fifth, or the "perfect fifth" as it is also known, is governed by a simple mathematical property: if you have two strings at the same tension and identical in every way except that the lengths are in a ratio of 2 to 3 (for example, the first string is 2 feet long and the second is 3 feet long), the two strings will always sound a perfect fifth from each other.

If you start at Middle C, and move to the note a fifth above that (G), and then the note a fifth above that (D), after 12 of these steps you'll be back to C again—hence it's a "circle".

Consequently a sojourn through the circular Spheres would naturally have to use the Circle of Fifths. And, in fact, starting with Earth, the ascent through the planets on the Music of the Spheres album ascends through the circle of fifths.

The Musical Symbolism of the Individual Tracks:

The fundamental concept of Music of the Spheres is to portray the soul's final journey from life on Earth ascending through the planetary spheres to the Afterlife.

On the soul's journey to the afterlife, I imagined that "understanding" would be the priority of the first half, but "acceptance" would be the priority of the second.

Consequently, both the Ptolemaic ratios and Musical Gematria are only used in the "first half" planets (since they fall in the "understanding" portion of the soul's journey), but not in the second half (since they are concerned with the "acceptance" portion of the soul's journey).

NOTE: there are only seven planets on Music of the Spheres because only seven "planets" (including the sun and moon) are visible with the naked eye. Seven was the total number of known planets until 1781, when Neptune was discovered by William Herschel.)

1. Earth

This is, musically speaking, the simplest piece on the album. I'm reminded of that saying: "Now we see in a mirror dimly, but then face to face." The imagination for this track is that we know nothing now, but after death all will be made clear. Given how little we are able to understand in this life, there is a certain logic to "Eat, drink, and be merry!" I used no Musical Gematria or Ptolemaic ratios on this track. I imagined this as my "Mr. Roger's Neighborhood" track—appropriate for children, which metaphysically speaking is what we are in Life on Earth.

2. Moon - the Sphere of Intuition

The music for all of the other planetary spheres is very structured; that for the Moon is not at all—it's "constructed"entirely intuitively. It's also the first sphere you'd visit after leaving your life on earth, so there would be shock and confusion, and wonder.

Both Musical Gematria and Ptolemaic ratios were used on this track.

3. Mercury - the Sphere of the Mind

The Sphere of the Mind is boundlessly optimistic: everything is ultimately understandable by the mind. At least that's the assumption of the mind in general—and modern science.

Both Musical Gematria and Ptolemaic ratios were used on this track.

4. Venus - the Sphere of Love

At the Sphere of Venus the soul pauses to reflect on all of the ways that Love manifested itself during life. Love is a two edged sword: sometimes it is bliss, and sometimes it is sorrow.

Both Musical Gematria and Ptolemaic ratios were used on this track.

5. The Sun- the Sphere of the Will

This is the halfway point of the soul's journey to the afterlife. Up to this point the soul has largely been concerned with "understanding". The focus now shifts to "acceptance".

Musical Gematria and Ptolemaic ratios were not used on this track, nor on any subsequent tracks, as the soul finishes the second half of its journey.

6. Mars, the Sphere of the Warrior

At the Sphere of Mars the soul pauses to reflect on all of the ways that it had to be a Warrior during earthly Life.

7. Jupiter, the Sphere of Aspirations

At the Sphere of Jupiter the soul pauses to reflect on all of its aspirations during life; how they gave life so much meaning; how they must all be left behind now for the greatest aspiration of all—God—which is now its destination.

8. Saturn, the Sphere of Wisdom

At the Sphere of Saturn the soul pauses at the last sphere in the ordinary Cosmos to experience true wisdom for the first time (because all other earthly concerns have been left behind). It is now time to cross over into the next realm.

9. The Fixed Stars, the Frontier to the Beyond

You'll notice that there's a fixed note that plays on the wine glass chorus all the way through this piece, and the armonica does its musical thing against that fixed note. The fixed note gently fades in and out, "twinkling" in slow motion, but it's present all the way through the piece. And, the wine glass chorus, which plays this fixed note, has its own kind of shimmer—like the stars do.

10. Primum Mobile ("PREE-mum MOH-bee-lay"), the Prime Mover of the Spheres

Below is a diagram of the circle of fifths with the 12 notes indicated around the circle. The three chords are indicated which are used in a huge amount of harmonically simple music (which may, of course, be quite sophisticated in other ways) - the blues, "Happy Birthday To You", and "Twinkle Twinkle", for example. Having a piece in different keys would just rotate the triangle around the circle, but it would still have the same shape:

Chord Diagram of a Simple Song (Like 'Twinkle Twinkle')

This diagram shows the chords used in "Venus", just to choose one more or less at random:

Chord Diagram of 'Venus' from Music of the Spheres

But Primum Mobile and Empyrean are the two spheres that are outside of normal reality. Here are the chords that are used on Primum Mobile:

Chord Diagram of 'Primum Mobile' from Music of the Spheres

It's a perfect square.

11. Empyrean ("em-PEER-ee-en"), the Sphere of God

See the discussion for Primum Mobile just above, and observe the chord diagram for Empyrean:

Chord Diagram of 'Empyrean' from Music of the Spheres

Naturally it's an equilateral triangle (three equal sides).

12. Centrum, the Still Point at the Center of the Spheres

If you could stand at the center of all the spheres, you would see what would almost look like a giant cosmic clock, each of the spheres moving in its own rhythm. This piece is built on several independent melodies, each moving at their own speed, each taking a different amount of time to complete — just like the planets.

Now that we're at the center of all the spheres, if we were to start moving outward again, the first sphere we would encounter would be Earth. Thus the Music of the Spheres album itself has closed its own circle.

Degree	Name	Meaning	Note (in C)
1st	Tonic	Tonal center, note of final resolution	C
2nd	Supertonic	One whole step above the tonic	D
3rd	Mediant	Midway between tonic and dominant	E/E♭
4th	Subdominant	Lower dominant, same interval below tonic as dominant is above tonic	F
5th	Dominant	2nd in importance to the tonic	G
6th	Submediant	Lower mediant, midway between tonic and subdominant	A/A♭
7th	Leading tone/Subtonic	Melodically strong affinity for and leads to tonic/One whole step below tonic	B/B♭
1st (8th)	Tonic	Tonal center, note of final resolution	C'