Music of the Spheres

Scientists demand empirical proof in all fields of enquiry. But the fact is that the scientific method is not suitable to all fields of study.

Empirical proof is as one sided as is, say, reductionism. Scientific method involves formulating a hypothesis and testing it empirically, i.e. if it can not be measured by external instruments, it is not a fit subject for Science. What the empiricists did not take into account was the fact that the human body itself is a measuring device of remarkable complexity. According to the Oxford Reference Dictionary, empirical proof relies on observation and experiment, and not on theory; but at the same time defines empiricism as the theory that regards sense-experiences as the only source of knowledge. How, we may well ask, can scientific proof be based on an empiricism which is only a theory?

One way I believe we can demonstrate this dilemma brought about by a reliance on a so-called empirical knowledge, is by considering music and our ‘empirical’ sense-experience of hearing in regard to the phenomenon known as the Pythagorean comma. I first came across this strange creature when I was asked by Macmillan to write a book about the steelpan of Trinidad and Tobago. They wanted a simple, large format picture book to tell the story about the evolution of pan, as the instrument is called. From the very start of my research I realised that I was dealing with something very special and quite magical, the alchemical story of the only acoustic instrument to be invented in the 20th century. It was the story of the transmutation of industrial waste material into a musical instrument.  Ring of Steel, pan sound & symbol

“In the last century, the British attempted to control Carnival in Trinidad by banning the drum. This act was as cruel as destroying their language of the slaves had been. This led, however, to the evolution of the tambour bamboo bands in which bamboo 'reeds' were cut to varying lengths and the music made by striking them on the ground or with sticks. In the present century, during World War two, when Carnival itself was banned, the steel band evolved - appropriately from the tambour bamboo bands.” [Ring of Steel]

At the end of the 1939-45 war, American forces had left discarded oil canisters on the islands and in a remarkably short period of time, these had been transformed into finely tuned melodic and harmonic instruments. These were to become a symbol of the unity in the diversity so characteristic of the Caribbean territories.

“The development of pan has paralleled the development of calypso and carnival in which the right to play mas is deeply rooted in the archetypal human and Dionysian need for a sense of meaning and validation. Dionysus, was not the god of drunkenness but the god of 'ecstatic vision' and we each need our ecstasy. If we do not get it legitimately, we will get it in an illegitimate way. Carnival, or Mas, is not only an ongoing re-enactment of historical reality but a psychic process, integrating the dark and the light, the masculine and the feminine, leading to individuation” [ibid] The development of pan was pure alchemy.

In the final chapter of my book I proposed that the universal appeal of steelpan music may be due to its special harmonic structure, although I make it clear that research still had to be done into the acoustics of the instrument. The study of harmonics in the West can be traced back to Pythagoras, the 6th Century BC Greek philosopher and if pursued, will take us to that mysterious comma which was named after him. His theory of the harmony of the spheres was itself most likely derived from the Egyptian sidereal musical scale. He had, after all, studied for 21 years in Egypt and the school which he later set up in Crotone, Southern Italy, was based on Egyptian mathematical and religious (pan theistic) principles.

In his book on the life of Pythagoras, the historian Iamblichus, describes how the Greek philosopher, was walking past a brazier’s shop, when he heard ‘hammers beating out a piece of iron’. The hammers were producing sounds that ‘accorded’ with each other. Going into the shop he found that those that sounded well together had weights that were related - twice, three times or half the weight of one another. He applied what he had discovered to various instruments, to pipes, reeds, monochords, triangles and to instruments known as patellae or pans He had in fact discovered the overtone series. The sounds he heard - ‘hammers beating out a piece of iron’, have resonated down the centuries. Today Trinidadians refer to playing pan as beating iron!

The science of harmonics has revealed a phenomenon of sound that has application not only it seems in the field of mathematics, physics and many other natural sciences (to our body structures and sense organs) but also to sound and music therapy. The overtone scale is also known as the harmonic series where the notes rise in exact numerical relationships to the fundamental. Taking the fundamental as the first note, the second note is twice its frequency (an octave); the third note is three times the fundamental (a fifth in musical terms),; the 4th - four times the frequency (the next octave) and so on. As we move further away from the fundamental the intervals between the octaves become progressively smaller [i.e. the ratios between the numbers become smaller and smaller the greater their number]

The harmonic series is to sound what the rays of the colour spectrum are to light. Overtones are always present although not always filtered out by our hearing. But the rainbow of sound, the overtone series, can be heard, for instance, in the magical art of overtone singing. This kind of singing was first introduced to the West through the recent interest in world religious practices and music - the chanting of Tibetan monks and the many toned singing (known as throat singing) of the Tuvan people from Mongolia. It has led to a revival of interest into the nature of sound.

Overtones are in pure mathematical proportions, or whole number ratios, and the most consonant of these are the octave(2/1) and the fifth(3/2). But no matter how many times you put a fifth on top of a fifth you will never reach an octave. A succession of twelve musical fifths is almost the same as seven octaves, but not exactly. This discrepancy in pitch is known as the Pythagorean comma, because Pythagoras was thought to be the first to discover it. To bridge this discrepancy, Western music, since the Seventeenth century, adopted what is called equal temperament in which the interval between each of the twelve semitones of the octave is exactly equal; but apart from the octave, all the notes are to some extent out of tune!

What we simply refer to as music, according to the great Sufi master Hazrat Inayat Khan, “is only a miniature from the music or harmony of the whole universe which is working behind everything, and which is the source and origin of nature. It is because of this that the wise of all ages have considered music to be a sacred art. For in music the seer can see the picture of the whole universe…”

The ancient Greeks were also deeply aware of this cosmic relationship of music to science and culture. They knew that the mathematical laws of music were the same as the laws that regulated harmony in all matters, from the spiral growth patterns we see in nature** to geometry and good government. This magical connection between sound and all aspects of manifestation, including form, was integral to many cultures and a way of restoring harmony at all levels of society. They used various modes for calming, stimulating and creating desired moods. These modes resonate with the endocrine system of the body.

Music was also integral to every aspect of ancient Chinese culture and government. According to the Yue ji, “under the effect of music, the five social duties are without admixture, the eyes and the ears are clear, the blood and the vital spirits are balanced, habits are reformed, customs are improved, the empire is in complete peace”. [qtd. Danielou]

This was to a lesser extent true of the music of Arabia. Iran, Turkey, Tibet and Africa. African Music was “divine expression., is medicine. Its intensity, its pitch, its timbre all translate the power of the gods into action among human beings and the physical world. Thus music can charm a person, send her/him into an altered state of consciousness: it can heal someone..” Dr. Anthony Ekemezie Mereni The British Journal of Music Therapy Vol.10 No 1

Indian classical music is modal (each piece being based on a single scale or mode [raga] and not on chords which are constantly changing), with a fixed ground tone, but finding its true expression in improvisation, tone colour, embellishments and intervals that are not found in Western tempered scale.. Improvisation is at the very heart of this music as it is in jazz which is also modal in character. Music is communication linking both he performer and the audience to the cosmic forces. The art of improvisation, which is no longer found in the Western classical musical tradition, connects the musician to the subtle bodies or auras (the higher harmonics of his physical body) by activating the psychic centres, or chakras, of his body. Indian classical music has a history which goes back three millennia.

According to Joachim-Ernst Berendt, knowing this “might make Western music lovers become more humble about their generation-old pretension of having a monopoly on musical culture and on ‘classical music’ in particular” Except for the atonality of Schoenberg, Berg, Webern, etc., Western music came to incorporate key signatures related to scales and with a tonal centre and the tension and resolution away or towards that centre. Early Western music employed modes which did not have a tonal centre, but produced music with that timeless quality found in plainsong and Gregorian chant. These intervals have a universal consonance and appeal as in early Christian music and are still to be found in Eastern Church music. Modal music has a spiritual feel-good quality connecting us to something greater than ourselves, the cosmic order and tranquillity.

Equal temperament has virtually eliminated that connection - our musical intervals no longer accord with the laws of physics. If physical laws can be ignored there can be no such thing as empirical proof. We have lost that sense of magic the ancient Greeks once embraced. So today we have something in music called the Pythagorean comma, which is considered irrational, and therefore, of no import, because we need to be in control, not only in the sacred realm of music and the beat of the drum, but of time itself. At the very time equal temperament was introduced in Enlightenment Europe, clocks were becoming commonplace, The first Astronomer Royal, John Flamsteed, [1646-1720] claimed that "The clocks have proved rational conjecture to be a very truth”.

The switch to equal temperament at the end of the 18th century began in earnest with the Industrial Revolution and the standardisation of pianos and organs. Today, the New Oxford Companion to Music (1983) actually defines Just Intonation, a system of tuning instruments derived from the natural Harmonic Series1, as a system of tuning in which the notes furthest from the fundamental “are severely out of tune, hence the introduction of Equal Temperament as a substitute for the ‘natural’ non-tempered scale” One can safely speculate that. Equal temperament is part of the foundation of modern Western civilisation, based on technology and has contributed to our separation from nature and inappropriate science.

Equal temperament was once considered inharmonious, producing ‘a harmony extremely coarse and disagreeable’ (Robert Smith 1759) Hermann von Helmholtz (1821-1894), the father of scientific acoustics and who proposed the first scientific theory of consonance and dissonance, claimed that equal temperament ‘had a deplorable effect on music practice’ But Sir James Jeans “The indisputable dissonance's of equal temperament no longer distress us in the way that they seem to have distressed our more fastidious predecessors” [ibid] Today anyone whose ear is attuned to the western tempered musical scale does not hear any dissonance.

Since its introduction much of early music by the great composers is no longer heard as it was written e.g. J.S. Bach’s vocal and organ music and Handel’s works for clavichord and harpsichord which were written in the mean-tone 2 system. All this was to change when in 1723, Bach himself adopted the system. His Wohl-temperiertes Klavier (Well Tempered Clavier) covers all twenty four major and minor keys and ‘enabled compositions in all keys to be played without disagreeable discords’. [Science & Music] It also facilitated modulation and transposition. Resisted at first, equal temperament gradually caught on and spread dramatically, swamping the music of all other cultures. It should be noted that the tempered scale was in fact been proposed as early as 1492 by the Spanish musician, Bartolo Rames, and by the French mathematician Marin Mersenne in 1636. [Jeans] It was also proposed by Chu Tsai-Yu, a Chinese Prince, over a hundred years before Bach adopted it. The Chinese, however, have stayed with the natural intervals as sacrosanct to the relationship between man and the Cosmos.

In the West, we learned to hear the inexact intervals of equal temperament as true. The mathematical pure overtone series is no longer the empirical tuning. The dissonant tempered scale now the more ‘appealing’. As I mentioned in Chapter 1, I was brought in a musical family. My mother taught the piano and I myself could play Fur Elise by Beethoven, and some of the relatively easy pieces for students of the piano. My ears were entrained to equal temperament as my mind had been to Western versions of history and, more importantly, to the dualism that underpins the Western paradigm, a subject dealt with in Chapter 12. In tempering the musical intervals we have tampered with nature, claiming the product as the real thing - reality. . Perhaps that is why the world is in the state that it is in today According to Hazrat Inayat Khan , “The cosmic system (works) by the law of music, the law of harmony; and whenever that harmony in the cosmic system is lacking in any way, then in proportion disaster comes to the world, and its influence is seen in the many destructive forces which are manifest there”.

Herman Hesse in his book Musique, seems to be saying the same thing: “The music of a harmonious epoch will be calm and serene and the government will be moderate. The music of an agitated epoch will be shouting and loud and the government will be wrong. The music of a State on the decline is sentimental and sad and the government will be in danger”. [qt. Fabien Mamam: The Role of Music in the Twenty-First Century] This corresponds with the view of the ethno-musicologist, Alain Danielou, who stated that “For the world to be in a state of equilibrium, its different elements need to be harmonized. Since music expresses the relations between human and cosmic orders, it must respect the exact intervals on which these relations are based…Disregard for such an obvious law necessarily leads to a breakdown of equilibrium and social disorder…” He went as far as to say that “By allowing such aberrations as equal temperament, the lack of a proper theoretical foundation will in all probability drive the European classical system to complete decadence. The success of African American music, with its ‘blue’ notes so alien to equal temperament and therefore so expressive, is not due merely to fashion. It shows the need for an understandable musical system, for logical and true intervals that can remove the veil of inexpressive insipidity which temperament spreads over even the most impassioned movements of the greatest symphonies”. Music & The Power of Sound.

I believe that steelpan music by virtue of its unusual and complex acoustics and tuning (the harmonics or partials are tuned in), produces healing natural harmonics [unstruck \vibrations 3], an infinite spiral of fifths beyond the circle of fifths 4 which is the basis of equal temperament Pan music accentuates the 5th interval, the most consonant interval, used throughout the ages to invoke the divine. As I noted in my book Ring of Steelpan sound & symbol (Macmillan 1999).

“In countries like Indonesia and Tibet, gongs, bells, musical bowls and the gamelan form part of the spiritual life of these areas. Whenever, they sound they invoke the transcendental, the higher dimensions of reality. Perhaps the prevalence of bells in Switzerland accounts for their love of steelpan music!

“The steelpan is an acoustically multi-toned bell/gong which I suspect may also have apotropaic, therapeutic resonances. Nowadays most pans are tuned to the harmonics. Coupled with the invocatory African drumming patterns, as in the calypso arrangements at Panorama, the music has an ecstatic transcendental power”.

Acoustic instruments, including those of metal, harmonize the physical body to the five elements of Chinese cosmology (fire, water, earth, metal, and wood) reconnecting us to nature What is certain is that the sound the instrument makes follows the rules of Physics, which are universal. The overtone series is pure sound and not the product of Western tempered tuning. It may well be that steelpan music bridges both. and that an exploration into the world of pan will not only be about steel drums, but also about the true meaning and significance of the word pan (‘all’ in Greek) -It has certainly led me to an understanding that everything in creation has a harmonic base, that metaphysics is part of reality.

In his book, Temperament, Stuart Isacoff, a prominent music critic, sets out to show ‘How Music became a battleground for the great minds of Western civilization’. Although the book documents the controversy the raged through the centuries, the conclusion is simply an attempt to justify equal temperament, documenting in detail its importance to western science. The case however is not proven as the Coda makes quite clear. After conceding that equal temperament is impossible to attain on a modern piano ‘because of the permanent out-of-tuneness of the strings (due to the variations in materials, temperature changes etc.,etc.,etc.). He then recounts his experience at a private recital by the composer and pianist Michael Harrison on his ‘microtonal’ harmonic piano, which left the invited audience completely spaced out.

“It sounded like a jumble at first - a drone, or a room full of drones. Then, from within the din, high-pitched sounds seemed to rise and float towards the ceiling……he seemed to free an angelic choir above…..musical concords seemed to emerge and shake hands above the fray…. I though of Huai Nan Tzu, his temperament theories and his ascent to heaven….. And I thought: Perhaps Pythagoras was right after all”

He seemed to be conceding that non tempered music may reflect the ‘great cosmic dance’ of string theory (which holds that everything in the universe is composed of infinitely vibrating strings) “ What were once described as different elementary particles are ….. really just different notes in an enormous celestial symphony.”.

For Max Planck, one of the founders of modern Physics, “the term matter implied a bundle of energy which is given form by an intelligent spirit” Planck, who was interested in music supposedly worked out his quantum theory on the basis of the overtone series of natural harmonics - the notes on the scale jump from whole number to whole number; the point being that “‘particle energy’ in the atom changes not gradually but in ‘jumps’ ” [Nada Brahma J. Berendt]

According to a recent computer generated hypothesis, the primordial matter of the Universe arranges itself, because of gravity, in thin filaments into a Cosmic Spider’s web. This reminds me that an early version of the steelpan which had spawned the modern tenor pan, was known as a spider web pan [in which the notes were tuned in a cycle of fourths and fifths]. What is it that connects the evolution of the steel pan to Pythagoras’ Music of the Spheres and a vision of the Universe as a Cosmic Spider’s web?

The answer is surely the process of transmutation or transformation. The prima materia of the Alchemists, is the same as the primordial matter of the Universe, from which all things evolve. Alchemy involves a base metallic material, the outward form of which has to be first destroyed, the energy released and reunited. Then heat is applied, blackening the substance, something known as nigredo. This is precisely what is involved in making steel drums - sinking, marking and grooving disturbs the molecular and crystalline balance of the steel which tempering corrects. They are then heated for a specific time over intense heat to make the metal stronger and more ductile - the soul of the material lingering on, induced into liquid iridescent sound colours or overtones.

In Trinidad, in the middle of the last century, the transmutation of industrial waste material, i.e. discarded oil drums, into a highly tuned percussion instrument took place without its innovators being aware that they were alchemists. The goal of Alchemists was not just the materialist transmutation of base metal into gold, but for a deeper understanding of the processes of transformation and creation. Hated at first, the steelpan is now the national instrument of Trinidad. It has healed a divided society and all races play it .Today the music of pan resonates around the world.

What we need is a quantum leap in consciousness if we are to transcend the limitations of the prevailing paradigm that the West seeks to impose on the rest of the world. According to Itzhak Bentov; “Knowledge moves in an ever-expanding upward spiral, which allows us to see from the higher turns of the spiral our previous knowledge in a broader perspective. Thus, Newton’s mechanics have become a ‘special case’ within Einstein’s theory of relativity” [Stalking the Wild Pendulum]; in the same way as Einstein’s theory of relativity had become a ‘special case’ in an endless spiral of cosmological theories purporting to be the final grand unified theory of everything. Another ‘special case’ that strikes a cosmic chord is String Theory - that the Universe is composed of myriad vibrating strings and not the elementary particles of a previous model - the world is sound, Nada Brahma.

Just as the Pythagorean cycle of musical fifths reach upwards in an infinite spiral, so it seems does consciousness. Harmonic conscious emptiness, symbolised by zero and the infinite spiral of harmonic energy ratios (the .octave and the natural fifth) transport the listener to a deep level of consciousness; The harmonic ratios model the emptiness of the Absolute void circle, the Wu Chi containing the yin/yang of the Tai Chi (the Supreme Ultimate) symbol.


1 Just Intonation is limited to one key. Its aim is to make the intervals as concordant as possible with both one another and with the harmonics of the key note and of closely related notes. Most of the frequency ratios can be expressed in terns of comparatively small numbers, indicating consonant harmonies - Science & Music Sir James Jeans ]

2 mean-tone scale an earlier attempt to solve the problem caused by the Pythagorean comma ]

3 In Hindu musical theory there are two kinds of sound, ahata nada, struck sound, and anahata nada, unstruck sound. The former corresponds with our scientific understanding of sound vibration, the latter with what Pythagoreans called the music of the spheres. In Shabad Yoga,, the Sound Current (also referred to as the Audible Life Stream) equates to the concept of limitless sound, the WORD, or Divine Creative power, or LOGOS. This yoga of the Divine Word utilizes Anahad Shabd or unstruck sound as an aid to spiritual development and liberation from the bonds of mind and matter while living here and now on earth. In the teachings of the Saints (Sant Nat), the soul (Surat) merges with the Word (Shabd) and is carried to the Source, the Godhead. It is a system of meditation that takes its followers to the highest attainable states of spiritual development and consciousness by developing the Audible Life Stream or Sound Current.

In Healing Sounds, Jonathan Goldman speculates that the fundamental may be the struck sound, whilst the harmonics which are created the unstruck. "Perhaps they are the bridge between the physical and the metaphysical". He quotes Pir Vilayat Khan "The overtones can be followed with the conscious mind and used as a 'Jacobs' ladder' to climb to other planes of consciousness": In other words, listening can be used as a tool for enhanced consciousness. "There is acknowledged an understanding of the Shabda, the 'Sound Current', which can be ridden like a flying horse to other planes of existence. This is accomplished through meditation on sound".

4 The circle of fifths is no more than a graphic representation of keynotes with their signatures in the shape of a circle; the notes progress clockwise in ascending fifths (C_G_D etc)

© Cy Grant

Share This