Music for Pleasure: 'unnatural' musical intervals and the fate of the hexachordal modes.

Thirty years ago there issued forth from an office somewhere off Soho Square a series of recordings under the all-embracing title of 'Music for Pleasure'. I was always struck by this title. Did the executives of the record company who dreamt this up imagine there was music other than 'for pleasure'? What kind of music could that possibly be? Music for dental drilling perhaps? Or imprisonment? Music for a wet weekend? The inference of this seemingly innocuous title was obvious, the implication serious: those recording executives had hit upon an unspoken reality. There did indeed exist in the world a type of music which might be called 'Music for Displeasure' – music so unpalatable that it was unpleasurable. It exists with us still and many composers who desire street credibility are still writing it.

'Music for Pleasure' was thirty years ago, remember, when the juggernaut of post-Webernian composition was at full steam. No-one – especially a timorous undergraduate like myself – could question the veracity of that system of composition called 'serial technique' which was put before us. The whole panoply of arguments was succinctly laid out in front of us: Wagner's Tristan and Isolde was the sunset and the dawn; Schoenberg, then Webern were the way to a brighter future. Their tree of serial knowledge was groaning with fruitful possibilities. (Alban Berg was too pleasurable to count amongst the pantheon.) Their dodecaphonic system of composition, said the futuristic pundits, was the only real future we had. If we failed to catch hold of the torch, art music of the western world was doomed to die. Boulez carried the brand ever onward; Stockhausen followed hard on his heels. Having no computers to make their great leap forward easier, everyone from Elizabeth Lutyens to Justin Connolly brandished their slide rules with ever increasing fervour to light up the sky. Yet one immutable fact could not be erased from the minds of us undergraduates. The music was unpleasurable. It was so disliked the overwhelming majority of musically literate people gave it a wide berth.

The argument put forward in defence of atonal music – that Beethoven's music was horrible to his contemporaries, that Wagner was considered a madman when he produced Tristan, that there was a riot at the first performance of The Rite of Spring, that it was only a matter of time before the concert going public would grow to love this new music – this argument was so specious no-one with any knowledge of history seriously paid any attention to it. Beethoven, within twenty years of his writing the last quartets, was the composer to whom every other composer aspired. Wagner's music dramas became standard repertoire throughout the opera houses of Europe and the United States almost as soon as they were written; and as for The Rite of Spring: it was conveniently forgotten that the first performance took place at a charity gala night at the Théatre Des Champs Elysées, full to the rafters with Parisian High Society – not a collection of people renowned for their open minds. Had Sir Harrison Birtwistle first shown his world of The Second Mrs. Kong to the corporate members of Country Life, he would very likely have got the same response. Nor must it be forgotten that at the second performance of The Rite of Spring, Stravinsky was chaired shoulder-high through the streets. But it has been eighty years since Schoenberg's first experiments with atonality, and still this method of composition is given the cold shoulder by most of the concert-going public.

There were, it is true, even thirty years ago some still, small voices in the wilderness: Ligeti quietly looking at his clocks and clouds, Tippett occasionally pulling out from his rag-bag of a mind an adventitious nugget of pleasure, and from the East Coast of the United States even fainter voices were beamed across the ether to show us there was indeed at least one other way forward, if only we could take it seriously.

I knew intuitively that there was something wrong with the intellectual argument for atonal serial technique, but I couldn't put my finger on it. I even wrote music using that technique, fearing I must be missing out on something. But there was circumstantial evidence that this music was going nowhere. At no time in the history of world music was a movement, a school of thought so intensely disliked by so many people for so long. This was not some trivial rejection of music because it was 'modern'; there was something much more fundamental about audiences' antipathy, an abhorrence which was not be seen towards the works of other 'modern' composers. For those composers who dallied with atonal serial technique during one phase in their creative lives (Stravinsky, for instance, and Messiaen) it was noticeable that their atonal, serial works were the ones least likely to be performed. One only had to glance at the concert notices to see just how rarely anyone bothered with them There was a flaw somewhere in the argument; the edifice of atonal serial technique was built on sand.

Thirty years later I think I have the answer. It is not an answer that everyone will agree with. But I put it forward as a counterpoint to the relentless propaganda which has beset the music student too aggressively and for too long.

And I begin with Bach's Wohltemperirte Clavier. It is not clear whether this monumental work is built on the premise – then but recently in the ascendant – that the octave is best divided into twelve parts, and – more significantly – each of those twelve parts should be equidistant to its neighbours. But by writing 24 preludes and fugues in all the keys, major and minor – not once, but twice – Bach opened up a Pandora's box. He showed that any piece of music could have as its fundamental base any note of the chromatic scale of the keyboard. Even he, as we now know, found this awkward, and first composed some of the Preludes and Fugues in more familiar keys and then had to transpose them to the more outlandish ones. Bach was by no means the only composer to write such a work, but its popularity has subsequently given it a seminal influence. Not only did the popularity of Wohltemperirte Clavier confirm to the musicians of Western Europe that it was feasible – nay, desirable – to write music in any key, not only did Bach sow the seeds of the discord which would eventually plague the music of Western Europe ever after, but he sounded the death-knell of the very foundation of music up to that point: the hexachordal mode.

Let us get a few definitions both clearly stated and out of the way. A mode is any invariable sequence of notes which forms the basis of a musical construction. A scale is a mode, but a mode is not necessarily a scale. Play some music using only the black notes on a piano and you are using a mode, but it is obviously not a scale (there are some bits missing). Diatonic ('twice toned') scales are a stepwise ('scala' - steps) sequence of notes using only whole tones and semitones within an octave. There are no bits missing. Our much-hated practice of scales is based on the three commonest versions; the major scale, the minor and the chromatic. A hexachord is the first (or last) six notes culled from any diatonic scale: C to A (or E to C) on the white notes of a piano, put at its simplest. The vast majority of music before the middle of the 18th century was written using the transposable hexachordal mode as its primary building block of notes.

It can be no accident that at the very time atonal music – the ultimate expression of Bach's experiment – reached its zenith in the twentieth century, so began to appear a renewed interest in, even a passion for, music of pre-Bach eras. That is: music based on simple, singular hexachordal relationships. It is as though a Jungian collective unconscious was at work: this psyche was repulsed by the enormity of the aurally chaotic, but stringently logical position music had got itself into, and rebelling, turned back to a Rousseau-like past of sweet airs and inevitability. The proof is in the pudding: for every concert given by the International Society for Contemporary Music or the Park Lane Group, fifty are given by The Academy of Ancient Music and Les Arts Florissants.

Another twist to this tangled web is a simple truth which any fiddle player and any singer can tell you: the hexachordal mode is the product of natural phenomena and the natural inclinations of the ear. The relationship between any note and the note a fifth above it (or a fourth below) is a small part of the universal laws of acoustics. I shall expand on that a little later, but pause briefly to point out that this 'natural' interval of a fifth is not the one you usually hear (if your piano has been tuned recently). Equal-tempered chromaticism - the notion that all the semitones within the octave are the same distance apart from their neighbours - is a fabrication developed by harpsichord and organ tuners of the early eighteenth century. I do not deny its legitimacy; clearly equal temperament had to be concocted to satisfy the needs of composers who were drifting further and further away from the confines of closely related keys. But fabrication or concoction it is nonetheless, and we should bear that in mind. We should also bear in mind that this move to equal temperament – that all the semitones are the same distance apart – was a slow and halting one. When Beethoven in the Waldstein Sonata shifted from his original C major to a new idea in E major, it would not have sounded the same to his audience as to us. The E major passages would have had a different 'feel' because the spacing of the notes was different to the spacing in the original C major. Beethoven was making a virtue out of necessity; but if we hear the Waldstein Sonata as Beethoven would have imagined it, our ears now hear it out of tune - not just 'different' - because we are conditioned only to hear equal-tempered scales.

With a wrench that would leave Sir David Attenborough gasping, I move to Asia. It should be remembered – and stressed – that nowhere on the globe, save Western Europe and its satellites, is the octave divided into twelve equal parts. In Asia, with the notable exception of India, modes are almost always based on a hexachord, and most frequently are pentatonic (using only five notes) within the hexachord. I could take any number of examples from Japan, China, Tibet, Korea, Thailand – even, if I move out of Asia, Ireland, South America and Central Africa – but it is only proper for me to use as examples for my argument the music with which I am most familiar: that of the Indonesian archipelago.

It says something for their durability and infinite subtlety that, from Northern Sumatra to Papua New Guinea (a distance greater by far than from Dublin to Athens and enjoying 250 different languages), there are only two significant modes on these 13,000 occupied islands. They are slendro, a pentatonic mode extracted from the hexachord C - A (CDEGA), and pelog, a pentatonic mode extracted from the hexachord E - C (EFGBC). The significance of my discovery, which I have not seen written in any musicological treatise, is that if you superimpose these two modes within one octave, you get our common diatonic scale of C major, though of course not in equal temperament. The tuning of slendro and pelog is much more subtle than that.

Now: musicians in the Indonesian archipelago are not stupid. They have stringed instruments and bamboo flutes overblowing at the octave and fifth; and they can sing. Blow across the top of a bottle to get a note; blow it harder and the note changes to either an octave or a fifth above. This is a natural phenomenon. Slendro is quite clearly a redistribution of the first five notes of this natural cycle of rising fifths (CGdae' becomes cdega). Professor Gurney has shown that the ancient Babylonians knew of this, so did the Chinese in the first millennium BC, as Dr. Picken has demonstrated in his recreation of the Zhou dynasty melody 'Longevities without boundaries' which uses the first four notes of the cycle of fifths (gaCD) – eschewing the last E, which redistributed becomes the 'third' of the mode, in the first five notes of a diatonic scale. And slendro is, by other names, perhaps the most common hexachordal pentatonic mode to be found throughout the world. It is our black notes on the piano. The Scots and the Irish have it, the Indians have it, the Chinese and Koreans have it, the Aztecs have it and so do the Malays. Even Debussy gives it prominence in many of his works. I am still recovering from the shock of hearing an old Balinese suling player piping out 'Auld Lang Syne' to attract tourists to buy his bamboo flutes. Any day now a slendro gamelan group will discover they can play 'Amazing Grace', and then we are all doomed.

Slendro - or its other names - is common throughout the world because it is derived from natural laws: the overblowing of flutes and the halving of string lengths follow the same acoustic precepts. It is not, then, a confection of man. Man has learned of it, much as he learned of the hybridisation of plants or the breeding of livestock. The first bowmen plucking bow-strings learnt empirically about the position of acoustic nodes along a stretched string. We have ancient mouth-bows and tromps (what used to be called 'Jews' harps' - the genggong still in use in Bali); they all made their contribution to the empirical understanding of harmonics and therefore pitch-relations. This understanding was achieved in relative isolation. Can it be possible that an Aztec flute player had an ancient, common point of reference with a Javanese gamelan? Certainly we can imagine the Greeks learning from the Egyptians who learnt from the ancient Babylonians of the 3rd Millennium BC. But the Aztecs? And the Polynesians? It is surely much more likely they discovered the properties of the hexachord through their own empirical knowledge of the cycle of fifths.

Pelog (efgbc') is a harder nut to crack. It is a pentatonic mode but formed, as I demonstrated before, out of the hexachord at the upper end of the diatonic scale. But how was it formed? It has no direct link with the natural harmonic series. There is a simple explanation which involves its relationship with slendro, but this simple relationship with its more common cousin has ramifications which will make every protagonist of atonal music blanch. If you transpose slendro up a third within a notional diatonic scale you get pelog. It is as simple and as complicated as that. Moreover, if you extract from that notional diatonic scale the notes which are common to both slendro and pelog, they form that sweetest of chords - the major triad. If you reverse the process and transpose pelog up a third within a notional diatonic scale, you get slendro. And this diatonic scale is the Phrygian mode, or - to put it more pointedly - an early version of the modern minor scale. And again, the notes common to both modes form a minor triad. This is quite startling. It means in the Malay archipelago there must have been previous knowledge of the diatonic major and minor scales which preceded the abstractions of these two modes. It is too much of a coincidence to suppose the superimposition of these two modes on each other 'accidentally' creates the very same diatonic scales we have in the West. Western Europe is always considered to be the birthplace of the major and minor scales - and latecomers to them at that. But I am convinced that the properties of these comparatively 'modern' scales were known by peoples much older, much more scattered than has previously been thought. Pelog and slendro are not the confections of man. The diatonic scales, major and minor, are not the confections of man. I would go so far as to say all indigenous modes throughout the world, with the singular exception of the equal tempered chromatic scale of Western Europe, are products of a slow, sometimes cautious discovery of what are reasonably called 'natural phenomena'. All over the world, men have for millennia discovered sections of, or entire diatonic major and minor scales and their triads without the benefits of communication, or even without the aid of notation – let alone the blessing of the Grade V Theory paper of the Associated Board.

Had Bach arranged his two books of 24 preludes and fugues in the more natural way – as a cycle of rising or falling fifths – he would have done us a great service. He would have shown the marvellous and magical phenomenon of the unending circle of relationships of fifths which is unique to the dodecaphonic, equal-tempered scale. At the same time, he never allowed individual preludes and fugues to fluctuate from intrinsic hexachordal key relationships. Instead, perhaps deliberately or perhaps without thinking, he arranged them chromatically; and by doing so set off a train of events from which we in Western Europe have yet to recover.

Nevertheless, progress – if that is what it is – towards full chromaticism, which propounds that all twelve semitones have an equal intervalic relationship with every other semitone, was very slow. I need not lay out the history of the rise of chromaticism here; whole libraries are devoted to it. But all through the nineteenth century and even as late as Richard Strauss there is an intrinsic acknowledgment that hexachordal relationships, discovered and elaborated upon long before equal-tempered scales were theorised sufficiently to become the standard, are the fundamental building block of music. Consider the waltz from Der Rosenkavalier: it lurches wittily from one 'unrelated key' to another, but within each phrase the melody and the harmony remain firmly within the hexachord, – indeed, the waltz-tune itself blossoms into a series of hexachords. Richard Strauss – like every other composer before him – instinctively holds to all hexachordal truths: they are, after all, incontrovertible natural phenomena.

Schoenberg, blinded by the possibilities of unconfined chromaticism, forgot where this chromaticism had come from. He assumed, wrongly in my view, that because all the 12 semitones were now tuned equidistantly, they possessed intrinsically an equal relationship with every other semitone. However much apologists for his theories protest to the contrary, he confused 'note' with 'interval'. But the ear of the listener intuitively knows otherwise. The natural affinity of the diatonic intervals within a hexachord outweighs by far the theoretical notion of an affinity between any or all semitones which are tuned equidistantly. Thus the perfect fifth or even the augmented fourth (notwithstanding that old medieval law) have 'natural characteristics' which the minor ninth or the major seventh – or any other non-hexachordal interval – cannot possibly possess. Moreover, our ears tend to grasp hold of these 'natural characteristics' as they flash by. We cannot help doing this because we, ourselves, are as natural a product of the universe as are the laws of acoustics. In any random cluster of notes, the ear will still pick out from the aurally chaotic mess those intervals which adhere to the principles discovered by our bow-plucking ancestors. As we receive cluster after cluster into our brains we cannot help but force their seeming atonality into a personal kind of tonality. And if these clusters are too difficult or too fast for the brain to accommodate, or to sort out into their component, hexachordal parts, we become confused. The aural experience – the music – is no longer 'for pleasure'. This repulsive reaction is nothing to do with our subjective responses to 'new' music; it is not a qualitative judgment borne out of ignorance, as the protagonists for atonal serialism would like to believe, which we can correct by education. Sad to say: all those years of striving for a 'new music' have been for nothing. We are children of the universe, and the universe stays loyal to its hexachord. There is, even now, research abroad which seems to show there is a mathematical relationship between the diatonic scales and the formations in the cochlea.

Equal temperament and the consequent aural acceptance of complete atonality are, if you like, 'genetic engineering' of music. This genetic engineering of sound may produce something wonderful, just as biochemical genetic engineering might produce the perfect potato; but equally it may produce a monster. My contention is that Schoenberg and his followers did not think carefully enough about what they were doing when they ignored so much of, and tinkered with, the natural characteristics of the hexachord. Their genetically engineered baby, serial atonality, is a Frankenstein's monster: 'Music for Displeasure'.

(Bali 1998)