The importance of the number seven was intimated by the title of "Sevenness: Sublunar"; the first of its events was introduced by a quote attributed to Hippocrates in the 5th. century BC, to reveal something of the origins of seven's significance:
"The number seven, because of its occult virtues, tends to bring all things into being. It is the dispenser of life and the source of all change. For the moon itself changes its phases every seven days. This number influences all sublunar things."
The Roman author Marcus Varro later noted that the numbers one to seven, added together, amount to 28 - lo and behold! - the number of days the moon takes to complete its journey. In reality, new moons occur 29 to 30 days apart, so seven days gives but a rough measure for quarters of the moon, which each average several hours more. The sun, appearing to regulate the lengths of days and years, provides a different time framework, and ancient astronomers were at pains to synchronize it with the moon. An Armenian bronze belt, dated around 1000 BC, bears markings for a lunar-solar calendar of seven-day weeks, twelve months, and New Year at the vernal equinox. The week itself is a somewhat arbitrary division: Babylonians, Celts, Germans, Hebrews and Romans preferred seven days, though ancient Egypt ran on a ten-day week. In keeping track of time, the lower number may be easier to remember. Seven has been suggested as an approximate limit on our capacity to process information; the numbers in small samples can be apprehended immediately, while above the seven threshold we tend to estimate, and not always very accurately.
Besides the moon's quarters, other natural phenomena could be grouped in sevens. The bright planetes - the sun, the moon and the five planets visible with the naked eye - are seven unique heavenly bodies that travel independent paths. They gave seven-fold arrangements an apparent cosmic validity, until Uranus was spotted by telescope, as late as 1781, and Neptune in 1846 (and you can add Pluto, if you like, for a total of ten). Another example of sevenness was located in the seven orifices to the human body (count them silently to yourself). Seven openings could be found in the head alone, if the eyes were included with nostrils, ears and mouth, though this increased the body's hole count to nine. Corresponding sets were sought in nature - seven metals, seven ages of man, seven continents and seas - though their classifications were less certain and absolute. Works of the imagination were also aligned to the cosmic order; each of the planets was assigned gods, daemons and angels, and given musical and colour attributes.
The planets were coloured in many early civilizations, from ancient China [column 1] to Babylon  and Ptolemaic Egypt . Planetary colour schemes were listed in texts on natural philosophy and astrology, and found a use in alchemy, medicine, magic and art. Mars retained its natural red, and Saturn was just as often characterized as black: otherwise, colours were many and varied. Some publications listed musical notes for planets, as well as colours, but usually dealt with them in different chapters, as unrelated attributes.
Leonello d'Este, the Renaissance Duke of Ferrara, chose his clothes astrologically. While those around him wore black, he was bedecked in different colours each day, to draw down favoUrable celestial influences. A century later, the court of Mogul India sat on the 'Carpet of Felicity', woven in coloured rings to represent the planets. The emperor Humayun presided at the centre, on the gold of the sun. On Monday, he wore green robes, aligned to the ruling planet of the day. His Indian officials occupied the black ring of Saturn, the planet of their race and region. Another century on, and Athanasias Kircher coordinated planetary colours and notes, in "Musurgia Universalis" of 1650 [far right column, above table]. He gathered together planets, their colours and musical notes - along with metals, stones, various animals and plants - in one great table of correspondences. The scale of notes up the planetary chain, from A to b, was mathematically defined. Its musical ratios gave sure measurements, more certain than colour relationships, or even the distances to planets, whose very orbits were under dispute.
The music of the planets was an ancient theme. In "Timaeus", Plato had written a breathtaking creation myth, of the soul of the universe being created according to musical principles. Future generations were captivated: the harmony of the spheres of the planets became a subject of learned discourse, into the 17th century and beyond. Scales of seven notes, ascending or descending - or even the succession of musical modes - were applied from the moon to Saturn. The scheme spread as far as India, throughout the Islamic world, and into Western Europe, despite Aristotle having scoffed at it as Pythagorean nonsense. He declared ("On the Heavens", II.9) that no such cosmic music could be heard. Moreover, vibrations of sound from the planetary spheres would be so great as to shatter all the rocks on earth. Humankind delighted, nevertheless, in drawing such parallels, and where sets of seven were deemed useful, they entered common parlance.
In the middle of the first century AD, Petronius wrote of the connection between days and planets. His character Trimalchio, in "Satyricon", used an astrological calendar with some kind of colour coding, to ensure his activities fell on propitious dates. At the entrance to his Roman house there were
"...two wooden tablets, one on each doorpost...On the other were painted the phases of the moon and images of the seven planets, and lucky and unlucky days were marked with studs of different colours."
A god was firmly attached to each planet by the 1st century BC, giving his or her name to a corresponding day. What we call Thursday became the day of the chief Roman god, Jove or Jupiter. His Latin name is retained for the week-day, as the Italian giovedi and French jeudi; in English, naming-rights are given to his Germanic counterpart, Thor. (The same planet had previously been assigned to Zeus, the head of the Greek pantheon, while the Babylonians had their main god Marduk rule over this star, which shines brightest in the dark of night.) When the seven-day week became official in AD 321, the Emperor Constantine proclaimed that "all the judges, the city folk and the handicraftsmen shall cease work on the venerable day of the sun". Thus Sunday, the day of rest, commemorates Sol Invictus, Constantine's divinity of choice prior to his conversion to Christianity.
The musical method could be used to generate the names of days, according to the 3rd century historian Dio Cassius. When tracing the diagram above, the musical notes selected by each point of the star occur at regular intervals. They are separated by leaps of fourths and fifths, both ascending and descending. As the chief divisions of the octave, the intervals generate all the notes within it; in this application, they also pick out a sequence of planets to align within the week. Such cycles of fourths and fifths had been used to tune lyres since Mesopotamian times, and the Greeks built a considerable body of music theory on them. Plato expressed his cosmic harmony in the same mathematical ratios, first dividing an octave into a fourth and a fifth. Their difference was defined as a single tone, used to subdivide the larger intervals, and so Plato arrived at five tones and two remainders (or semitones) per octave. His arithmetic reasoning justified a diatonic mode underpinning the fabric of the universe. Aristoxenus, a later theorist and less of a Pythagorean, simply agreed that "the diatonic is the first and oldest; this is the type that the human voice naturally finds".
But cosmic music was fraught with dilemmas - if the lowest sound emerged from the slowest planet, did the moon or Saturn claim the privilege? Pundits invented scales that either climbed in pitch away from the earth, or deepened as they fell away into the heavens. Either way, flaws emerged when applied to the cosmic week. As shown above, irregularities occurred in both ascending (red) and descending (blue) musical scales. In blue notes, an augmented fourth of B flat to E crops up, between Friday and Saturday, rather than the perfect fourth of B flat to E flat. Likewise, between Wednesday and Thursday in the red-note scale, a diminished fifth of B to F appears, rather than the perfect one that an F sharp would give. (These intervals, called tritones, divide the octave in half, a feat considered mathematically impure by the Greeks. Musicians of the Middle Ages called them 'the devil in music', due to their jarring sound.)
In musical tuning, the cycle would normally be repeated a second time - a planetary fortnight, as it were - to touch on the remaining sharps and flats. In doing so, the twelve semitones of the modern scale are generated, ending back at the starting note. (Alexander Scriabin, the noted Russian composer, used the progression to create a colour-music code, early in the 20th century. Starting on F, the red note shown above at Thursday, he gave its key a deep red colour. In leaps of fifths, to C, G, D, A, E, and B, he distributed the colours of Newton's ROY G BIV - though the final violet coincided with an F#, and subsequent accidentals were non-spectral colours.) Even this double tuning cycle leaves a small musical imperfection; a cycle of twelve perfect fifths will overreach the equivalent seven octaves, by an amount called a Pythagorean comma. (Likewise, twelve fourths falls short of five octaves by the same amount.) The attempt to align these physical systems to a unifying mathematical ideal seems impossible: as with the cycles of the sun and the moon, we are obliged to accept irregularities in music. The seven-day week and the seven-note scale are human contrivances, whose uses are justified by convenience and tradition. They approximate a broader reality only by analogy, not by the dogmatic numerology that grew around them. Although ancient peoples were well aware of the limitations, the urge to expand systems of sevens proved irresistible.
In Genesis, at the start of the Old Testament, God is described as creating the world in seven days. Philo Judaeus wrote a commentary "On Creation", at the start of the Christian era, listing over a hundred examples of sevenness. He included moon phases, heavenly bodies, and musical harmony, though stating, "I doubt whether anyone could adequately celebrate the properties of the number seven, for they are beyond all words". The Gnostics did indeed try, singing hymns with lyrics composed solely of the seven Greek vowels - an early example of speaking in tongues. The imaginative prose in Revelations, that ends the New Testament, is also littered with sevens; its main protagonists are a lamb with seven horns and seven eyes, and a beast with seven heads.
In the third century, St Hippolytus singled out Plato's harmonious universe for approval. He calculated distances to the planets according to musical ratios, and symbolized the melodiously constituted world, as well as the days of creation, by a seven-stringed lyre. But Hippolytus cautioned against Pythagorean approaches to seven, "since almost every heresy (that has sprung up) through the arithmetical art has discovered measures of hebdomads". St Augustine further sanitized the classical inheritance for Christian use in the fourth century, addressing himself "to those who understood the number seven, which signifies the perfection of the universal Church". The Councils of Trent, held from 1545 to 1563, set the official number of Catholic sacraments as necessary steps for salvation at seven (as distinct from the two recommended by Luther and Calvin). And Christians have commonly held there are seven virtues as much as there are seven deadly sins, while superstition still views it as a lucky number.
But the sanctified use of seven is not an exclusively Christian practice: the seven-branched menorah, the sacred candlestick of the Jews, commemorates the seven days in which God created the world; the proscribed pilgrimage routes of Hinduism include seven sacred rivers and seven holy cities; Muslims performing the hadj circle the Kaaba at Mecca seven times; and the ancient Persian mystery cult of Mithras - the most powerful rival to Christianity in 4th-century Rome, and whose god shared Christ's birthday - was entered into by seven stages of initiation. Hierarchies, progressions and groupings of seven have been common in secular society, too: both pages and squires in the 12th century were required to undertake seven year's training. Even the Australian Government has funded a seven-step program as a quick-fix for long-term unemployment - seven easy steps of self-awareness 'awaken the giant within' to achieve 'job readiness' in a final breakthrough.
Many management courses, as well as the self-improvement programs and spiritual panaceas available from New Age bookshops, employ seven-step techniques. Other than their common numerology, most of them aim at a rearrangement of a person's interior architecture - of aspirations, emotions, psyche, and so on - into neat, hierarchical levels. One clear example of a seven-step code, currently used in Australia, is found in "Colour Therapy", by Julie Gunstone. Like De Clario, she saw significance in a parallel arrangement of ROY G BIV, the C scale and the chakras. But even though their two codes share the cornerstone of 'sevenness', commonality diminishes when details are compared. For example, De Clario located desire and emotion at the second chakra, aligned to orange, but Gunstone relegated passion and other basic emotions to red, at the base chakra. Moving up to the second chakra, she assigned wisdom, inspiration and insight to the colour orange. However, they agreed that yellow at the third chakra stood for intelligence and both saw green at the fourth, or heart chakra as representing balance (since it is central in each system). Logically enough, they agreed the throat was the seat of communication and that the brow accounted for second sight and clairvoyance (as held in folk tradition). Here other minor differences began; by omitting indigo, De Clario had to colour this sixth chakra violet, while Gunstone reserved that colour for the crown.
The particular importance De Clario attached to violet's position at the brow helped set the two systems apart, but his main point of departure was with the use of white at the final chakra. White was so clearly intended to surpass violet, as used by Gunstone, that it created the main difference between the two codes. De Clario's white light was the necessary goal of "Sevenness: Sublunar", a symbol of spiritual completion and a journey into the light. It signified the untrammelled nature of a soul, as it passing on to a higher plane. For that purpose, white shrouds are used to wrap corpses of the dead, and it is the common colour of mourning in India. On a more esoteric level, white could indicate everlasting life for early Christians. A parable, in the apocryphal Gospel of Philip, likened white cloth to a soul baptised:
"The Lord went into the dye works of Levi. He took seventy-two different colours and threw them into the vat. He took them out all white. And he said, 'Even so has the Son of Man come as a dyer'" and "so it is with those whom God has dyed. Since his dyes are immortal, they become immortal by means of his colours. Now God dips what he dips in water."
The same miracle was played in reverse in the Infancy Gospels, where many different colours were drawn from the one vat of dye. That God brought out the many from the one was accounted the supreme mystery, by some Gnostics of the second century. They visualized creation in a single white egg, from which an array of peacock colours emerged. In much of Western metaphysics, light itself was coloured a transcendent white, and served as a metaphor of enlightenment. But few would perceive the truly spiritual light, according to Karl von Eckartshausen in the late 18th century. Most could only guess at it, he wrote in "The Cloud Upon the Sanctuary", "even as the blind imagine colours and the deaf judge tones". The light was visible only to the Elect, who formed a hidden Council of Light. By the 19th century, Theosophists, Rosicrucians and other occultists were scrambling to join the select few. They were marked by white auras - glowing lights visible only to spiritualists - that surround the mental bodies of the most enlightened beings. The Rev Leadbeater wrote of them as the Great White Brotherhood, and many leading theosophists claimed white and glowing masters for their spirit guides. Annie Besant, a president of the Theosophical Society, was among them; she described how other adepts could reach that enlightened state through the practice of yoga. Seen from a higher plane, one's mental body exhibited a constant play of colour, and it was the initial task of yoga to still their vibrations, to render the mental body white and colourless. Though she assigned no colours to chakras, Besant did draw an analogy from science, of prisms and the spectrum, in her "Introduction to Yoga" of 1907 :
"The mind is like a prism. If you put a prism in the path of a ray of white light, it will break it up into its seven constituent rays and seven colours will appear. Put another prism in the path of these seven rays, and as they pass through the prism, the process is reversed and the seven become one white light. The mind is like the second prism. It takes in the five sensations that enter through the senses, and combines them into a single precept", and "Manas, the sixth sense, adds to the sensations its own pure elemental nature. What is that nature that you find thus added? It is the establishment of a relation, that is really what the mind adds."
In the right column, the Newtonian spectral array of ROY G BIV rises from the base chakra to the crown. Julie Gunstone used this sequence to provide "inner direction and healing". When indigo is omitted, the spectrum contracts to the version shown in the left column. As used by De Clario and Eileen Goble, the colour vacancy at the crown chakra is filled by white. Corinne Heline used the same tactic but specified further variations, as in the middle column. Perhaps the lack of green was intended to preserve yellow around the heart, the traditional location of the sun for Eastern and Western mystics alike. The variegated colour at the brow is curious: such was a characteristic of the planet Mercury, the patron of alchemists, until largely replaced by plain purple in the Renaissance. Still, the overall order of rainbow colours provided the basis for this, and all the other codes.
White represented the sum of all the colours that preceded it in De Clario's system: Gunstone's final violet omitted this symbolism. As the 'colour of everything', white produces all the colours of the rainbow when refracted and the same colours can be reconstituted as white light when passed back through a lens. When tacked to the end of his colour code, De Clario cited "Healing and Regeneration through Colour and Music" as his source. Its author, Corinne Heline, was also responsible for "New Age Bible Interpretation", where the chakras were opened by seven sounds, to reveal 'Musical Lights'. No pitches were specified, notes being distinguished by their subtle rhythm and vibrations, encompassed by the seven-stringed harp of David. Quoting Theosophists and Anthroposophists, Heline's journey through the chakras culminated in liberation from the wheel of birth and death, marked by white at the seventh chakra. Along a path of psychic perception, clairvoyance and healing powers were gained, memories of past lives and of the 'Lost Word' were recovered, and a state of transcendent consciousness was reached. Colours marked each step of the way, in an approximate spectral sequence starting from a dark red base. Green was reduced to a transitory light, tingeing the gold of the third chakra and to be replaced by soft yellow at the fourth. However, the main departure from the Newtonian ROY G BIV came at the sixth chakra: neither indigo nor violet was used. Heline designated it as multicoloured - rose, yellow, blue and purple were major components - before all colour was negated, or combined, in the white of the seventh chakra.
De Clario was to quote Heline again in a later exhibition, but to contrary purpose. "The colour of seven is indigo...seven is a perfect number and signifies completion or consummation." Indigo, not white, would seem indicated here for the seventh and final note of the scale, and for the last of the chakras. But indigo, an obsolete dyestuff from Newton's day, is often omitted. Another Australian, Eileen Goble, did so in her "Rainbow Meditation Tape", to arrive at 'the pure white light of enlightenment' on the seventh chakra. The same white caps many New Age spectral sequences with a symbolic finale, their seven-part codes attempting to embody optical and religious symbolism from both East and West.
Symbolic use of colour came totally unstuck when transferred to the musical scale. The use of white disrupted the even flow of spectral colour when the music spanned more than one octave. Positioned at the note B in the scale of C major, white fell between violet at A and red at C, causing a visual hiatus on the leading note just before the full octave was complete. Another Australian artist, Roy De Maistre, had tackled this problem in 1919, using red-violet instead of white to bridge the gap between the violet and red ends of the spectrum. He had created a graduated colour disc divided into twelve sections, one for each semitone of the octave. Travelling round and round the disc, continual colour change mimicked the smooth movement of music through cycles of octaves.
Attending to other niceties, De Maistre had begun his code at the note A and assigned it to red. Allocating Newton's ROY G BIV colours to the white notes, ending with violet on G, he could 'conceal' the non-spectral red-violet on a black note, A flat. An interesting coincidence emerged as a result: the frequency increase from starting note A to end note G encompasses some 78% of an equally-tempered octave. The colours allotted to them, from low red to high violet, are separated by a 75% frequency difference. (So it is commonly held, though a wider range of colours might be detected under test conditions.) De Maistre could claim some mathematical serendipity for his code.
By similar reasoning, Goble, Heline and De Clario could reach B flat, with the same 78% jump from their starting points at C. Only six of the seven white notes would be coloured, this time leaving the final note B exposed as a blank and open for interpretation. It could be that originators of modern codes planned it this way, though many, like Gunstone, stretch ROY G BIV across the total octave regardless. Any colour and symbolism could be inserted at B: however, many codes seem preoccupied with white, as a sort of spiritual coda to fashionable meditation techniques. Otherwise, there is little concern for the niceties of colour music: the notional value of colour-music codes, like De Clario's, becomes apparent when the musical scale is laid out side by side with the spectrum.
Division of the spectrum into six provides a check on De Clario's code. In a best-fit situation, most notes and colours match up only approximately, given that notes are in fact point frequencies rather than broad ranges as shown. The spectrum could be considered as a 'colour octave', accommodating about three-quarters of a musical octave within it. To make up the size difference, De Clario added white. Colours, on their own, fall short of any musical equivalent - a fact known to science ever since the spectrum was first measured. All the same, a comparison of octaves persisted: even Max Planck, the founding father of quantum physics, would refer to visible light as "a small spectral range of hardly an octave".
De Clario's system does not account for black notes, and the variation of intervals between white notes, of either tone or semitone, is ignored. But most strange of all is the colouristic scope of the note B - it could be construed as another whole spectrum, compressing the colours back into the original white light from whence they came. Seen this way, B is given the same colour weight as the entire three-quarters of an octave before it. There is, in fact, no white light among the colours, let alone past B at the end of the spectrum. But that region is not empty: beyond the spectral colours lies a realm of powerful radiation, of high energy and frequency. Johann Ritter detected the ultraviolet rays, at the start of the 19th century. They turned silver salts black (a property essential to the development of photography), though the light itself was normally invisible.
W H Wollaston noticed, around the same time, that a faint lavender-grey could be seen in this region, provided that the brighter colours of the spectrum were masked out. In mid-century, Hermann von Helmholtz was to measure the elusive UV light. He found the ultraviolet rays present in sunlight surpassed the octave by a musical third or fourth - in De Clario's code, beyond high C to the E or F above. When the artificial light from an arc lamp was analysed, yet another octave of ultraviolet appeared. The more intense the light, the bluer it became; Helmholtz surmised that a greenish fluorescence of the retina was added to the normal sensation of lavender grey. In effect, the eye begins to see itself.
All the above - the colours of the spectrum, the lavender grey of ultraviolet, the fluorescence of the eye - are encompassed by De Clario's white on B. This one note, of least musical importance, is treated inconsistently. There is nothing in De Clario's notes to justify an undue emphasis on B, or white, other than their coinciding at the summit of a hierarchy of enlightenment. The spiritual truth they purport to represent would be of dubious utility. According to Helholtz, writing in 1856, the concepts we form of things from our sensations and understandings, are valid only so far as they are useful:
"In my opinion, therefore, there can be no possible sense in speaking of any other truth of our ideas except of a practical truth. Our ideas of things cannot be anything but symbols, natural signs for things which we learn how to use in order to regulate our movements and actions...To ask whether the idea I have of a table, its form, strength, colour, weight, etc., is true per se, apart from any practical use I can make of this idea, and whether it corresponds with the real thing, or is false and due to an illusion, has just as much sense as to ask whether a certain musical note is red, yellow, or blue. Idea and the thing conceived evidently belong to two entirely different worlds, which no more admit of being compared with each other than colours and musical tones or than the letters of a book and the sound of the word they denote."
The colour-music code of Sir Isaac Newton indeed partook of the 'sevenness' extolled by De Clario. But colours and notes were given no moral or spiritual attributes, only numerical values. Each was merely an increment in a geometrical progression, and that Newton likened them at all gave an insight into physical similarities. Though a grand, metaphysical scheme might be inferred, Newton's ordered system pertained to the realm of natural phenomena. Since much of his data was first composed as lecture notes, a pedagogic intent is just as likely: "Opticks" may reflect the quadrivium - arithmetic, music theory, geometry and astronomy - that formed the traditional basis of higher learning. (In medieval times, these combined with the trivium of grammar, rhetoric and dialectic, for a total of seven subjects.) Number itself was represented by arithmetic data obtained from experiments; music combined number in relations as a colour-music code; and Euclidean geometry traced the path of light through prisms and lenses. Even astronomy may be included, since the main subject of enquiry was light from the distant sun. His white light was not the ne plus ultra of philosophy, theology or spiritualism, but the very origin of all the colours. Due to its heterogeneous nature, Newton would never have considered aligning it to any one note.
Whereas De Clario's B was white, Newton had made B a marker between blue and indigo - the fifth and sixth colours of ROY G BIV. It was the sixth note of the Dorian mode, a traditional church mode equivalent to a white note scale beginning on D. Modern colour-music codes that employ white note scales (and most of them do) revive the essence of modal music. The key of C major is commonest and paraphrases the Ionian mode - described as late as 1600 as 'the wanton mode'. None has its final on B (except the entirely theoretical, highly unstable Locrian). The note had some importance in the Phrygian mode (starting on E), where it was the fifth, or dominant. But it was usually avoided wherever possible, as it created difficulties in melody and harmony. According to the Oxford Companion to Music, B was "a note which the spiritual advisers of our ancestors considered barely respectable".
It is paradoxical to find B has become extolled where it was once anathema to modal musicians, and glorified in spite of its low rank in the musical hierarchy. Extra notes were invented so as to avoid it (the black note we call B flat was the first). The legacy of this discrimination can still be seen on any keyboard today. B is the only white note that does not have another white note a perfect fifth above it. While other fifths (C to G, D to A, etc.) sound clear and stable, B to F is unresolved. In fact, it is a diminished fifth (or augmented fourth), a tritone made up of three whole tones. To avoid it, B could be lowered to B flat, forming a perfect fourth with the F below. Otherwise, a perfect fifth above B was provided by an F sharp, the second 'black' note added to the musical gamut.
Use of the tritone has increased since the 19th century, to create melodic tension. For example, the song "Maria" from West Side Story begins with a tritone leap, resolving immediately to a perfect fifth. Wowsers can take alarm at more recent use of 'the devil's interval' in rock music, such as Black Sabbath's title song about Satan. That band denied knowing its connotations, though an album by metal act Slayer, "Diabolus in Musica", paid conscious tribute to the interval medieval musicians abjured. Around the year 1000, Guido D'Arezzo had avoided it by excluding the troublesome seventh note; he used six notes only in the first sol-fa system, devised to teach choir boys to sing. According to Guido, no chant used any other intervals, though the reasons were aesthetic rather than religious. Admitting that more consonants could be found on the monochord, he thought it better to let "art restrain us by its authority".
Six notes took precedence in music, at least in the system of Guido. But a B flat was generally accepted, to provide seven convenient steps within the octave, and other notes were also used in practice. To turn the modes of theory into good music, medieval musicians used unscripted notes. These were not written on the manuscript but interpreted by the performers - a style known as musica ficta, as distinct from the Pythagorean rules of musica recta. What notes were written down were hung on rudimentary staves, three horizontal guidelines which were often colour-coded. The bottom line was usually red, to signify F, while black and yellow lines above it located A and C, to complete the triad of F major. By the 14th century, the lines had increased to five, making the stave we are familiar with today.
Modern seven-note scales, with their different keys according to pitch, are little related to the church modes of medieval times. The prevailing theory differed yet again; they relied on a partial Greek legacy, promulgated through manuscript copies of Boethius's "De Musica". He had outlined a Pythagorean music with the number four as its foundation, rather than six or seven. Four notes spanning the interval of a fourth (4:3) made up the basic unit of a tetrachord. Two of these could overlap, or be conjunct, so the highest note of one served as the starting point for the tetrachord above it. An array of seven notes was formed this way, while eight notes and a complete octave were created when the tetrachords were disjunct, separated by a gap of one tone. All ratios between notes were compiled of the numbers 1, 2, 3 and 4, or their multiples.
In 1558, Gioseffo Zarlino revolutionized music theory with the publication of "Institutioni Harmoniche", and six emerged as the pre-eminent musical number. Intervals between notes could be made of ratios including five and six (in addition to the Pythagorean four), to sweeten the major and minor thirds with the ratios 5:4 and 6:5. Zarlino also stipulate six consonances, six species of harmony, and six species of voices, calling his numero Senario (number six) the 'harmonious number'. Like those who praised the number seven, he saw six everywhere - six planets (excluding the sun), six directions (including up and down), six surfaces of the cube, and so on. Others began to write paeans to six, as Zarlino's system of just intonation took hold. By the 18th century, composers such as Bach, Vivaldi, and Handel followed the custom of publishing instrumental music in collections of six pieces, and we find Rameau using six as the basis for his harmonic theory. Even Newton used the just ratios promoted by Zarlino to measure the spectrum: in initial observations of the colours of thin plates he noted their similarity to a musical major sixth. Placing five colours - red, yellow, green, blue, and violet - between the six notes, he devised an alternative colour-music code to the usual ROY G BIV spanning an octave.
Even today, six is a factor in the way we divide hours into sixty minutes of sixty seconds, and circles into 360 degrees. Both are legacies of ancient Mesopotamia, where a sexagesimal system (based on sixty) was employed for complex calculations in mathematics, astronomy, and commerce. Legend has it that Pythagorus absorbed both the practical and the symbolic sophistication of Eastern mathematics, during a stay in Egypt and especially from his stopover in Babylon at the time of the Captivity. Certainly, his famed theorem - used to calculate the size of the sides of a triangle - was derived from that source. On returning to the Greek world, clad in oriental trousers, Pythagorus gathered a cult following around him. To them, he imparted his expertise in music, and the belief that all numbers were sacred and significant. Theirs was an ascetic lifestyle, adopting the Egyptian esoteric practice of not eating beans. (Perhaps their beans were reserved for use as mathematical counters, and the Pythagoreans would surely wish to avoid flatulence in the close quarters of their commune.)
The Pythagoreans acquired a special reverence for the number six, as an important prime factor at the base of the sexagesimal system. The significance of six - equal if not greater to that of seven - was due to it being a perfect number. That is, its factors of one and two and three not only multiply together to form six, but also add up to six. When it is cubed (or multiplied by itself three times), the product is 216, the span in years that Pythagoreans believed the soul must wait in the heavenly spheres before being reincarnated on earth. It is an odd coincidence that this pagan significance given to 6x6x6 was later reversed, and that Christians were prompted to anathematize 666 as the number of the Beast.
In traditional Judeo-Christian cosmogony, six stood for the days of creation listed in Genesis - excluding the day of rest - while seven represented the full week of that creation. Not until Revelation, at the end of the New Testament, do we find that 666 is not only a wild beast's number but that of a man. Following the clue that the wise can calculate it, bible scholars concluded John the Evangelist intended to signify the emperor Nero. By assigning sequential numbers to letters of the Greek alphabet, the name Nero Caesar gave the required sum. But another fragment of parchment, discovered at the end of the twentieth century, gave the number as 616. Scholars were forced to an alternate conclusion; using the same method of numerology, the name Gaius Caesar, or Caligula, was put forward as the culprit.
Needless to say, the number six is dogged by bad press, and eclipsed by the positive connotations of seven. It is true that, on superficial examination of an orthodox musical scale, the note count is seven - but only if the eighth octave note is omitted - and that there are seven intervals within an eighth. While six, or four, or even eight, may be considered the real generators of musical structure in the West, it is seven that has captured popular imagination. Consequentially, many colour-music codes comport themselves in a seven-note sequence, resulting in more or less arbitrary selections of an equal number of colours.