It was commonly held that Pythagoras had investigated sounds made by different hammers striking an anvil, in the 6th century BC. As a result, he became the first to fix music with immutable mathematical laws. This legend can be traced back to the musical writings of Nichomachus in the first century, and the Roman Boethius was to include the legend in his "Fundamentals of Music", some 400 years later. Followers of Pythagoras refined music's principals with the aid of a monochord, a single-stringed musical instrument. An harmonic series of notes was arrived at, that could be replicated by dividing the string into proportions of its length (similar to the way the neck of a guitar is divided by frets). The octave interval, basic to most tuning methods, was established by dividing a string length exactly in two. The full string and the half-string make sounds that uncannily resemble each other, though they are of markedly different pitches (like a bass and a soprano singing the same note). When sounded together, the different notes should not interfere with each other; if they were even slightly out of tune, interference could be heard as fluctuations called beats. Dividing the string by three or other odd numbers produced different notes, also considered harmonious. Using ratios between the numbers one, two, three and four, Pythagoreans divided the monochord into related pitches. From these, musical modes were elaborated that had moral as well as aesthetic force in Greek society.
Of course, little of this is true - the bit about Pythagoras, I mean. By the end of the 16th century, the Galilei father and son had proven one main tenet of the tradition was false in fact - the note struck by a hammer would depend more on the weight and shape of the anvil than on the hammer itself. All manner of knowledge was ascribed to Pythagoras, and his name still adheres to fundamental music intervals. Those who invoke him are claiming, by proxy, to be fellow initiates in the universal mysteries available to the Pythagorean cult. Newton, for one, cited their authority in support of his own axioms; he speculated that the celebrated philosopher of antiquity had uncovered the secret to measuring the heavens, by experimenting with proportions of weights and string lengths.
In contradistinction, Marin Mersenne published the first systematic study of harmonics, as "Harmonie Universelle" in 1634. Here he established that the pitch of a bowed note was determined by the frequency at which the string vibrated. In turn, frequency depended on the properties of an individual string - its length and diameter as well as the tension applied to it. This could be expressed as an algebraic formula that we can recognise today: in the mid-17th century, harmonics offered a true mathematico-experimental framework that might be applied to light and gravity, as much as to strings and pendulums.
Mersenne understood the vibration of a string to be even more complex; as well as the pure tone produced by a wave the length of the string, there are a number of partials that sound less clearly but contribute to the quality of the note. It was later confirmed that any string will allow for multiple waves to occur, chiefly those that fit neatly along its length. Their wavelengths are determined by dividing the length by whole numbers: as well as the octaves that result from repeated divisions by two, other important partials result from an odd number of waves fitting along the length of the string (notably the dominant, or fifth note of the scale, produced by division into thirds). The quality and quantity of partials contribute to the overall sound produced. A patient listener may be able to detect some of these overtones (piano tuners find they have to), though quieter partials are hard to hear and, generally, the ear cannot detect pitch differences towards either end of the auditory range.
To some extent, these (and many other) quicker movements are present in the note produced by XY. Each harmonic can be heard by lightly touching the string at a node - those still-points of oscillation, at A or B. In musical practice, the string is pressed hard, to effectively shorten its length and produce an entirely new note with its own characteristic harmonics. It was important to Pythagoreans (as well as many later theorists) that any new note should be mathematically related to the harmonics of the original string.
The manner in which a note is played, along with the sympathetic vibrations of surrounding strings and from the body of the musical instrument, result in a characteristic timbre. An instrument such as the violin will produce its richest sound when played in keys, such as A or D, which are aligned to the fixed tuning of its strings. A 'remote' key, such as F# major, produces less resonance; Paul Robertson of the Medici Quartet and the psychiatrist Peter Fenwick have noted that the combination of unfamiliar vibrations and difficult hand positions involved in the key of F# can put the violinist into a strange state, making a piece of music in that key feel strange. Different emotional states may also be associated with particular musical keys for historic reasons. Some keyless wind instruments of the Baroque period could only play in fixed keys and we have inherited that tradition of musical pitch to some degree, in spite of the greater flexibility of modern instruments. The bright edge of the brass was heard to best advantage in the keys of C or D, while keys of E or B flats were the natural provenance for the soft plaintiveness of the woodwinds.
Musical systems had been evolving for two millennia since Pythagoras, but they still contained potential discords. In medieval modal systems, whose main pillars were the octave, fourth and fifth, discrepancies were unavoidable: a cycle of perfect fifths or fourths never quite matches a corresponding cycle of octaves, differing by a small amount called the Pythagorean comma. (The ancient Greeks knew this, and Boethius gave calculations for the comma's value as well as that of other subtleties, such as the schisma.) In the 1500s, the Aeolian mode (based on A) and the Ionian (based on C) were introduced for liturgical use. These permitted greater flexibility in harmony singing and foreshadowed the A minor and C major keys comprising the white notes on keyboards. Still, to make pleasant music, singers had to adjust notes by small amounts as they went along - a process known as musica ficta. Clever composers, such as Adrian Willaert in the 16th century, could shift the tonal centre of a piece through many modes.
On instruments with fixed tuning, one answer to the dilemma was to make small adjustments to some pitches. A more homogeneous gamut of notes could be achieved by sacrificing their theoretical purity. As early as the 14th century, some organs had been built with multiple manuals and split keys to accommodate the vagaries of tuning. Clavichords and harpsichords, virginals and spinets, became popular with the growing bourgeoisie in the 15th century, providing fully-fleshed music to the homes of those with leisure enough to practice and enjoy music. But these instruments also had limitations: because each string's tension remained fixed throughout a performance, certain notes would require adjustment if the performer wished to change into another mode. Retuning the instrument was a tricky chore, and the ability to modulate within any piece of music was restricted.
Gradually, the ancient modes gave way to the key structure that dominates modern music. While the octave interval remained mathematically exact, only traces of musical modes remained in the internal structures of major and minor scales. In exchange, the musician gained the ability to play in any key, without retuning the instrument, and to thus modulate from key to key within the one piece. By the end of the 17th century, theorists like Andreas Werckmeister had devised methods to iron out the niceties of Pythagorean music, and Baroque composers commonly employed types of 'meantone' tuning. Johann Kuhnau's "Keyboard Practice", of 1689, contained seven partitas in ascending major keys (C, D, E, F, G, A, and B flat); a second volume of 1692 consisted of a similar sequence, in minor keys (c, d, e, f, g, a, and b). Using a meantone tuning, it was possible to play Kuhnau's major partitas in B flat, C, D, F, G, and A, and minor partitas in g, d, and a. Even so, the remaining works (E, b, c, e, and f) would have required retuning of the instrument.
The publication of J. S. Bach's "Well Tempered Clavier" of 1722, heralded the triumph of a tempered scale, in which all notes were more nicely spaced. Like his predecessor Kuhnau, Bach began his cyclic work at C. Moving up the scale semitone by semitone, he provided four pieces (preludes and fugues in both major and minor keys) for each of the notes - 48 works in all. As if this were not enough, Bach repeated the exercise with Book II in 1744. Each piece modulated from its native key to related ones and back again, while retaining a distinct flavour of its own (due to slight, residual unevenness in the tempering). Middle C and the white-note scale of C major gained pre-eminence, as the basis on which all other keys depend.
At its theoretical extremes, harmonic science had little to do with real music practice, and scientists had to play catch-up. Isaac Newton attacked the problems of musical tuning like a mathematical puzzle. Arithmetic, geometrical and logarithmic methods, as well as a customised units of 'microtones', were applied to diatonic and chromatic scales, to tuning systems including just intonation and varying temperaments. Ultimately all such attempts produce compromises, so Newton finally separated the octave's notes with an array of just ratios arranged in a palindrome - a series that reads the same way backwards as forwards - to provide a pleasing mathematical symmetry. In this form, an antiquated Dorian mode was likened to the array of pure colours in Newton's "Opticks" of 1704. His analogy satisfied only the most general notions of harmonic science. The colour music wheel was somewhat contrived, with sizes of notes generalized and colour areas approximated (though Newton misleadingly presented his results as a genuine discovery, made from objective measurement). Accepted musical practice was already far in advance of the approach he took in dividing colour into ROYGBIV. Many other existing formats, of scales and modes, could have loosely matched the distribution of prominent colours in the spectrum.
While contemporaries could justly criticize the relevance of Newton's musical mathematics, this did not affect the validity of his observations on the nature of light. With marvellous skill he unravelled white light and reconstituted it, mixing coloured lights in unprecedented ways. The colour-music code was almost as relevant to this purpose as the recently discovered sine law of refraction, allowing Newton to deck out Descartes' geometrical rainbow in its colours. "Opticks" started from simple experiments with a prism - "the usefullest Instrument Men have yet imploy'd about the Contemplation of Colours", according to Boyle. Thus, tentative observations begun in the 13th century, with quartz crystals and glass flasks, were brought to fulfilment. Newton couched his findings in a framework of geometrical optics, a tradition dating back to Alhazan in the 11th century, and thence through Ptolemy to Euclid. The exploration of coloured properties of light, only partially explored by others, entered the realm of modern science with Newton's "Opticks". Along with it, for better or worse, came an articulated colour-music code.
Louis-Bertrand Castel explored the practical possibilities of colour music as early as 1725. He discovered the idea of colour music from Newton's "Opticks", which he had reviewed in its French edition. Castel proposed a 'harpsichord for eyes', a keyboard instrument which would displayed a patch of colour whenever a note was struck. At first, he aligned spectral colours with the white-note scale of C major. The usual order of ROY G BIV was reversed (as indeed it was for some prism experiments in Newton's book), so violet coincided with the lowest note, C, and red with the c an octave above. The musical scale of C was orthodox, representing the contemporary standard rather than Newton's old-fashioned Dorian mode on D. While admiring Newton as a mathematician, Castel thought his physics uninspired, feeling "there is no need to borrow ambiguous traits from Descartes or Newton to embellish the work of God". Castel put aside his original Newtonianism, to hail the earlier colour music theories of Athanasias Kircher instead. Encouraged by the composer Jean-Philippe Rameau, Castel also embraced a triadic theory of musical harmony. He emphasized the notes C, E and G, which make up the common chord of C major, by allotting them the painters' primary colours of blue, yellow and red. The primaries began with blue on C, at the bottom of the octave, since Castel considered it potentially the darkest of the three. There, the expressive capabilities of blue could best represent the musical ground-base, so important to the theories of Rameau. By 1734, Castel had begun to build his first 'ocular harpsichord', using twelve hues of colour aligned to a twelve-note chromatic scale. Each hue was varied further, by twelve degrees of tone from light to dark, so Castel could cycle his scheme through many octaves.
Castel's endeavours captured Enlightenment imagination, to provide a talking point throughout Europe. In Germany, the composer Telemann praised his marvellous instrument, saying, "This play of colours will please, for music is nothing but a pleasure". The mathematician Leonard Euler doubted that the fluttering, coloured cloths of Castel's harpsichord could afford enjoyment. He preferred an analogy with artwork, since "painting rather seems to be that to the eye which music is to the ear". Voltaire was skeptical, too: he dubbed Castel "the Don Quixote of mathematics", and suspected his performances would "shock, dazzle and exhaust the sight". In St Petersburg, the Imperial Academy of Sciences held a public meeting in 1742, to discuss the merits of colour music. Whether colour came from vibrations of the aether, as sound was carried by vibrating air, was debate by learned gentlemen. One question on the agenda asked: "Can colours, if arranged in a particular manner, provide a deaf person with the same type of enjoyment as we experience when our ears perceive a harmonious consonance of musical tones?" In the French encyclopaedia, Denis Diderot rendered homage to Castel, and took a special visitor to his workshop in 1751:
"My deaf mute imagined that this inventor of genius was equally deaf and mute; that he used his harpsichord to communicate with other people; that each colour shade on the keyboard had the value of one of the letters of the alphabet; and that by way of the keys and the agility of his fingers, he combined these letters and formed words, phrases..."
Other enthusiasts suggested their own colour-music codes, and some even went so far as to design a colour keyboard. In 1743, J G Krüger sketched an ocular harpsichord, "to delight the eye by the alternation and blending of the seven colours just as much as the ear by the seven tones". He took Newton's ROY G BIV for his colours and arranged them along a C scale. Beginning with violet on the lower C, his code was identical to Castel's first attempt (which was later rejected). But Krüger was not satisfied with a display of coloured swatches when notes were played. He designed his keys to move shutters and reveal glass flasks, filled with the appropriately coloured fluids. Light from candles radiated through the liquids, and lenses and mirrors cast each colour onto a screen. They fell as overlapping circles, with lower notes being larger in size: Krüger apparently planned his octave to appear as a circle filled with rainbow-coloured rings, red at the centre and violet round the rim. If he ever built the device, Krüger would have found the colours simply became brighter and whiter towards the centre, where more and more colours fell.
At the end of the 18th century, Karl von Eckartshausen claimed to have built a very similar device to produce colours of indescribable beauty, "for they surpass the most valuable jewels". That his colours might all combine into an insipid white, would worry the Bavarian mystic not one jot. The most enlightened spiritual masters, he proclaimed, were distinguished by auras of white light: they formed a hidden élite, still revered by theosophists today, that became known as the Great White Brotherhood. As for his harpsichord, Eckartshausen credited Castel with the original idea, and filled his flasks with liquids "in keeping with the theory of colours". But, believing colours expressed sentiments of the soul, he would interpret them symbolically, naturalistically, or even synaesthetically. In a poem that accompanied his theory of ocular music, each line of words was given directions for music and colour. A flowery meadow was predictably represented in green, violet, and daisy yellow. A sad maiden was pink and white mixed with olive, and accompanied by a plaintive flute; when she sang as joyfully as a lark, the colours changed to dark blue, scarlet, and yellow-green.
Like Diderot's deaf-mute, Eckartshausen thought the ultimate purpose of colour music was to supplement and support the written or spoken word. Others were more direct, seeking a more worldly pleasure from the combination. And every intellectual of the Enlightenment seemed provoked into an opinion, for or against, by Father Castel's invention. Some were rational and scientific in their support of colour music. In 1789, Erasmus Darwin found a coincidence of proportions between notes of a melody, and the colours of after-images - such as the blue-green tinge that remains with the eye, after staring too long at something red. Darwin suggested an improvement to ocular harpsichords; a newly-invented oil lamp, shining through coloured glass, could throw a stronger light than the feeble candles Krüger and Eckartshausen employed. Colour music was assured a modest place among the worthy subjects of science, after endorsement from such a patriarch (his grandson was Charles, after all). Count Rumford, the noted American physicist, was one that felt its appeal. In 1794, after repeating Newton's experiments with colour discs, and exploring the subjective effects of coloured shadows, he ruminated on the possibility of:
"...instruments for producing that harmony for the entertainment of the eyes, in a manner similar to that in which the ears are entertained by musical sound."
Castel's 'harpsichord for eyes' became a de facto ancestor to the many colour organs that began to appear in 19th century - culminating in Scriabin's tastiera per luce, designed for his 1911 premiere of "Prometheus: a poem of fire". (Unfortunately, the colour component of the performance was dispensed with, due to technical difficulties with primitive electrical equipment.) This work is the only major orchestral piece to include a scored part for colour, but it is rarely performed. Scriabin's colour-music code employed an approximately spectral array of colours, but aligned them to a cycle of fifths rather than the simple note progression of a scale. Like other Theosophists, Scriabin tried to link moods (and even smells) to the colours and notes - C with red and human will; G with orange and creative play; D with yellow and joy; A with green and matter; E with blue and dreams, and so on. Scriabin's arrangement was pompous and obscure, as muddy as Castel's, and it too never caught on as a colour-music code. When "Prometheus" was given its New York debut in 1915, a colour organ (based on A. Wallace Rimington's patented instrument) provided the light component. Unfortunately, light did not flood an auditorium filled with white-clad figures, as Scriabin had envisaged, and who is to know but the colours themselves were not rearranged, in accord with Rimington's own Newtonian code (a fairly straightforward spectral progression up the C scale).
The technical ingenuity of the late 19th century gave rise to a number of colour music instruments, like Rimington's or Bainbridge Bishop's (the latter being displayed by P. T. Barnum). Typically, they took the form of a standard organ console with a screen above it, onto which different colours were projected - usually a standard spectrum was divided into a progression to match the C scale. The musical component of colour music was frequently eclipsed by the novelty of colour music instruments. Thomas Wilfred, sponsored by prominent Theosophists, had devised large spectacles in New York in 1916; he later invented the Clavilux, his light organ, to perform Lumia concerts. By 1930, he had put the Home Clavilux on the market. Before the advent of television, a buyer could install a cabinet in the corner of the living room that silently generated visual imagery for days - without producing the same pattern twice.
Colour musicians often justified their work with references to science, spirituality and the grand order of nature, while the press shared their enthusiasm for a potentially revolutionary new art form. After World War I, some film makers had turned their attention to colour music as an ideal subject for abstract animations. Sometimes, they might collaborate with an artist (Viking Eggerling with Hans Richter) or work with a colour organist (Oskar Fischinger with Alexander Laszlo). Their valuable innovations were often obscured by later advances in mainstream film - the advent of talkies and colour films - and public attention diverted to bowdlerized versions of colour music, such as Disney's "Fantasia".
Not until the rock shows of the 1960s and 70s did colour music regain a large audience, with psychedelic performances synthesizing light and sound. Pioneering work in electronics and computing enabled animators to participate in major films as well - John Whitney's contribution to the Stargate Corridor sequence in "2001: A Space Odyssey" being one example. The effort to co-ordinate colour and music on domestic computers has led to further software advances. In exploring possible interrelationship of colour and music, programmers have been obliged to analyse anew the formal elements, to map flexible links between any arrangements of pitch, colour, shape, movement and so on. Video makers and live performers have been able to take advantage of the broad theories supplied by traditional colour music. Even something of its persistent mysticism has been readily assimilated in the age of multimedia. Modern computing and animation experts can (and often do) claim a lineage that extends back through colour organists and animators of the early 20th century, to Castel's Ocular Harpsichord in the 18th century.
Richard Wagner had put out the call for a Gesamtkunstwerk in 1850, a new kind of theatre that would synthesize music, verse and staging into a unified, total artwork. His Beyreuth playhouse introduced the wedge-shaped amphitheatre, hidden orchestra and darkened auditorium, to which audiences are now accustomed. With the introduction of arc lighting (and incandescent globes soon after), theatrical illusion was near complete. Loïe Fuller, the Parisian dancer, put these effects to good use, timing her movements in response to atmospheric lighting. Wafting diaphanous veils under ever-changing coloured lights, she inspired Toulouse-Lautrec and D. W. Griffith and influenced Isadora Duncan and Martha Graham. The Wagnerian spirit affected others, too. Kandinsky wrote stage pieces from 1909 to exemplify the new values: "The Yellow Sound", "Black and White" and "Violet", employed the colours themselves, in motion to music, as the central characters. Sadly, his works proved too difficult to mount. Around the same time, Schoenberg composed "The Lucky Hand", to be accompanied by a range of colours according to no known theory:
"Tone-colour melodies! How acute the senses that would be able to perceive them! How high the development of spirit that could find pleasure in such subtle things! In such a domain, who dares ask for theory?"
Of course, he did have theories, primarily the twelve-tone system that used the chromatic scale as its fundamental unit. Wagner had introduced greater colour to orchestration and melody by including chromatic variations beyond the scope of orthodox classical forms. Schoenberg, the painter and composer, sought to order the cacophony that could result from excessive chromaticism: in "The Lucky Hand", musical chromatics and visual chroma seemed intended to meet.
A major influence on composers at the time was the introduction of a new kind of musical scale, which we have inherited today. Modern keyboards, both acoustic and electric, employ a basic method of tuning called equal temperament, whereby the octave is evenly divided into twelve semitones by a logarithmic progression. The octave (an interval between two notes of the same name, created by doubling the frequency of the lower note) is the only remaining aspect of Western music that might be said to accord with natural laws. The bottom A on the piano has its frequency doubled seven times over, producing a cycle of seven octaves, from A to A, before the end of the keyboard is reached. This man-made construct gives us a mathematical and homogeneous system for organising sound into music across the audible range.
Equal temperament became available with improvements in piano manufacture in the late 19th century, though it is a much older idea. The ancient Greeks had developed a close arrangement of semitones - called the chromatic genus - to supply nuances, or musical colouring, unavailable with the diatonic. (Boethius had likened their difference to surfaces that changed colour when turned, possibly having peacocks' tails or turtledoves' necks in mind.) Derived from chroma, the Greek word for colour, the musical term 'chromatic' had crossed back over into painting in the 17th century, along with 'harmony'. Scientists of the era calculated the position of each note in a chromatic scale of equal temperament, though it was primarily a theoretical exercise. And Isaac Newton used the scale, in his first description of some important experiments; the colours of thin plates, similar to those on oil slicks, were separated into spectral arrays of equally-tempered proportions.
Though Newton's "Opticks" went some way to provide a consensual model of the spectrum, his colour-music analogy of ROYGBIV was no more than a pretty conceit. In a sense, it is the prolongation of a medieval tradition, which joined music theory with other mathematical arts - specifically arithmetic, geometry and astronomy - in the quadrivium studied at universities. Since optics was essentially a geometric discipline, the inclusion of a musical component gave Newton's conclusions an extra stamp of academic authority. Descartes, Huygens, and many others of Newton's peers wrote on the subject, as would Euler and d'Alembert among the scientists that followed them. The association of music with colour was also acceptable, following a philosophical tradition that ranked sight and hearing at the top of a hierarchy of the five senses. Since Plato and Aristotle, colour and light, along with form, were considered the sole means by which we detect objects visually, while music was considered the most refined form (and the most readily analyzed) of auditory stimulus. While Castel might question the ROYGBIV colour-music code that Newton stipulated, he did not doubt that such a correspondence existed. Nor did Euler: though he felt his own theory of light superior, he adopted the code with little alteration. It suited Euler's wave theory of light (an hypothesis popular in some circles, as distinct from Newton's corpuscular theory), comparing sound travelling through air to movement of light through an aether. The belief in an overarching unity of colour and music continued, and even today parallels are being drawn, between sound and pure, spectral light.
Music has evolved over millennia, through many compromises, to a relatively 'impure' state, and its contrived formulae are not echoed in the natural phenomena of the spectrum. The idea of a colour-music code lost much of its importance for scientists in the 19th century. Many, like Thomas Young and Hermann von Helmholtz, wrote separate works on both music and colour. While denying any link between the two phenomena, they still felt the need to address the claims of colour music. The spectrum of light was found to contain no equivalent of the musical octave, let alone the intervals within it. A comparable light octave might be envisaged by doubling the lowest red frequency, but doing so takes one immediately beyond the range of visible light. The spectrum, from red to violet, can barely span three-quarters of one such 'colour octave', let alone encompass the cycles of octaves used in music. Nor can any unifying principle be meaningfully divined from the separate vibrations of light and sound: disparities between them are clear and fundamental. To connect pitch and colour by a relationship of frequencies would require a formula so convoluted as to be ridiculous - not that this has stopped many from trying.
The ROYGBIV sequence retained its appeal for more general audiences; the classic status of Newton's "Opticks" inspired many variants, with spectral colours assigned to notes of a scale. The idea was adapted to specific purposes - as an aid in teaching music, as a theosophical demonstration of an occult system, and so on. But oft-times it was invented anew, in the search for a relation between the realms of the ear and the eye. Variations in colours and in notes will almost automatically invite comparison; seekers can arrive at a colour-music code they genuinely believe to be new, but may in fact be known of old. There are still those that marvel to discover that frequencies of certain notes, when doubled forty times over, can fall within the measurable range of visible light (a factor Young had noted, but discounted as meaningless). In some quarters, the size of the spectrum has been exaggerated beyond the range of average vision, to create a colour octave. Some have claimed to see extra colour, faintly, particularly at the red end of the spectrum. Others have consciously squeezed the musical octave to fit the spectrum, though Helmholtz rightly pointed out that such a process made arithmetic nonsense of the original musical proportions. Naive or cynical, such conjuring tricks with dimensions have taken hold in New Age movements, bolstered up by references to popular and exotic mystical beliefs. With all the variations, the most pervasive influence on colour-music codes today remains the prototype Newton supplied in his "Opticks" of 1704.