Evolution and Western European Music
by Keith Francis
The following essay relates the history of music in the Western European tradition to the evolution of consciousness as described by Rudolf Steiner and makes no claim to be more than a sketch of certain aspects.
Music history as taught in my younger days (the 1940’s) concerned itself largely with composers from Germany, Austria, France, Italy and, sparingly and somewhat grudgingly, England. England got in because Henry Purcell decided to incarnate there and Hӓndel changed his name to Handel. Books like Percy Coles’s The Growth of Music would have been altered very little if Portugal, Spain, Switzerland, Belgium, the Netherlands and the whole of Scandinavia had been left off the map, and the standard texts would have been only a few pages shorter if they had started in the middle of the sixteenth century and ended in 1914.
These were not the only serious omissions. It was customary to speak of a common language existing among musicians for large parts of the sixteenth, seventeenth, eighteenth and nineteenth centuries, but this way of talking is accurate only if we confine our observations to professional musicians writing for the church, the aristocracy and, more recently, the middle class, and leave out the non-European world altogether. What went on among the underprivileged, the farm laborers and the “rude mechanicals” is a story that I should dearly like to know; but to my knowledge it has not been told, and perhaps never will be, for lack of hard copy, at least in its earlier stages. It is true that we have a wealth of folk songs, but most were collected only towards the end of the nineteenth century or later, and what they had been through in order to survive until that point no one really knows.
The traditional way of telling the history of music developed as it did because the people who told it sincerely believed that Western European art music of the Bach to Brahms period was one of the loftiest of all the creations of the human mind and spirit, outstripping by far all that had emerged in earlier times and other places; and because most of them had little knowledge of any other kind of music. Over the past sixty years the situation has changed radically. We have found that mediaeval and Renaissance music can speak to us directly and refreshingly, once we are tuned to it, and Europeans and Americans have become deeply interested in the music of nations all round the world. Jazz and pop cultures have existed long enough to have their own histories and “Bach-to-Brahms” culture is probably almost as foreign to young Europeans and Americans as it is to people from any other part of the world – perhaps more so, since enthusiasm for what is loosely known as “classical” music has sprung up in many Asiatic countries. There are excellent reasons for studying the process that took us from the chants and modalities of the early Middle Ages to the tonal and motivic elaborations of the Bach-to-Brahms period and thence to the comparative chaos of the twentieth century, but it is not a good idea to speak of it as though it were the only show in town. We play, sing and listen to the music because it is wonderful and we study its history because it is fascinating; and if we are students of Rudolf Steiner, we find that the progressive exploration of tonality and structure in European music is intimately connected with the evolution of human consciousness. That is what this essay is about; the fact that some of us still think that the old pedagogues had a point is probably neither here nor there.
Please understand that from this point, when I talk about the history of music, I am referring to the sequence of transitions that can be traced from classical Greek times to mediaeval chant, later mediaeval and Renaissance composition, the European baroque and classical-romantic periods and post-romantic music mostly from Europe and America. I wish to stress again that this selection does not constitute a value judgement or imply that nothing much has been going on elsewhere.
Starlings – a Discussion Not Strictly Necessary
In some respects the history of music seems to resemble more recent versions of the history of our planet, long periods of relatively slow change being punctuated by short periods of energetic upheaval. The great period of polyphonic1 music based on the mediaeval modal system came at the end of more than half a millennium of steady exploration. In the late sixteenth century some of its most famous representatives, such as Palestrina, Byrd and Victoria, were still alive and busy but the Baroque revolution was already in progress and it took only a few years for European musical circles to embrace the new styles and abandon the old. In the 18th century, while Bach was busy with The Art of Fugue and Handel was composing Messiah, the light and pretty music of the galant style was displacing the learned complexities of the late baroque and the Mannheim School2 was in full swing. The dominance of late romantic sentiment and its large-scale musical expression in the works of composers from Bruckner and Brahms to Tchaikovsky and Mahler came to a comparably abrupt end in the early years of the twentieth century, but not because the listening public succumbed to the charms of the new music. Composers whose works seemed to continue the romantic tradition soon came to be regarded by the avant garde and the intellectual establishment as dinosaurs, even if that word wasn’t specifically used. Being something of a dinosaur myself, I cannot forbear to point out that dinosaurs have recently turned out to have been considerably more intelligent than had generally been thought. I have no doubt that a few of them survived the cataclysm that destroyed their race in the geological twinkling of an eye, and that these were the smartest and the most versatile ones.
Gradual change has occurred too, and it would be only a minor simplification to say that when it has occurred, at least since the early seventeenth century, it has been at the hands of individual composers, most obviously so in the cases of Haydn and Beethoven. Haydn’s early works seem primitive to us only in relation to his later ones, which are incomparably more complex and sophisticated, and carry a far stronger punch. In the course of a long life he effected what Sir Donald Tovey called “a Copernican revolution in musical form.” 3 Beethoven, far from being a revolutionary, adopted the techniques already brilliantly employed by Haydn and Mozart and, after a slow start, spent the rest of his life evolving them to fulfill his own needs. There’s a big difference between “evolve” (verb intransitive) and “evolve” (verb transitive). The classical4 style didn’t evolve; Haydn, Mozart and Beethoven evolved it.
This is enough to put any analogy to Darwinian evolution out of court. One side of the Darwinian coin is, in Webster’s words, “the theory that all species of plants and animals developed from earlier forms by hereditary transmission of slight variations in successive generations.” These slight variations occur by chance but they may have “survival value.” The essence of Darwinism is that the process goes on involuntarily – no one makes intelligent decisions for it – “evolve” is a purely intransitive verb – but variations that occur in artistic work are usually known as innovations, and they don’t happen by chance. Later artists choose to adopt them, to ignore them or to do something entirely different.
The other side of the coin is the expectation that a species that enjoys favorable circumstances will happily go on reproducing itself, if not for ever, at least for very many generations. The starling is a very successful bird. In my lifetime there have been 76 new generations of starlings and no one has reported the slightest change in their taxonomy or instinctive behavior. It is true that they have shown some versatility in exploiting changing conditions, but a starling is still a starling is still a starling, and whoever is in charge of their reproduction seems to be very satisfied with the product. Unless there are significant changes in the environment or some stray high-energy particle causes a profitable mutation, we may expect the murmuration to continue unabated.5 “Starlings”, however, do not exist in the world of music even when the music is designed for mass consumption and the composers are falling over themselves and each other in the effort to repeat a success. The listening public is fickle and soon gets tired of the same old thing, and some kind of change is commercially essential. Composers, moreover, evolve along with their music, and if they repeat themselves too much they are no longer artists. Haydn produced twelve glorious and amazingly varied symphonies for the citizens of London; when he went home his powers of invention and innovation took new turns and he composed string quartets, masses and two great oratorios, but no more symphonies.
New music comes from the creative activity of composers or improvisers, not from the reproductive activities of older pieces of music; every composition is a new adventure.
And then there’s Aristotle
If, following Rudolf Steiner, we believe that the human race has been around since before the beginning of time and has progressed under the guidance of higher beings, and if, further, we would like to paint an analogous picture of musical evolution, we may be tempted to suppose either that the hierarchies are using the composers as instruments to produce a set of evolving musical forms or that the composers are to music as the hierarchies are to people. What has actually happened to music over the last couple of thousand years doesn’t fit either of these scenarios. The symphony and the sonata do not resemble creatures on upward paths of evolution – there is no analogy to the successive development of the characteristic features of the human organism and nothing parallel to the functioning of reincarnation and karma. It may be tempting to suppose that Schoenberg’s Orchestral Variations is a reincarnation of Machaut’s Mon fin est mon commencement but we must acknowledge that whatever is whimsical or fanciful does have a tendency to be tempting.
You can transform a square into a rhombus simply by pushing a corner in the right direction, but you can’t turn an old symphony into a new one by any method whatsoever. Each new piece of music starts with a blank page. You may feel that although the new symphony doesn’t exist yet, the form does, and the form can be pushed around in various ways, so I should mention that in a previous essay I have done my best to justify the proposition that musical forms do not exist apart from actual pieces of music. This view of musical form is Aristotelian, not nominalistic. There is no archetypal symphony, but musical thought is immanent in the music and the form of the individual piece is the result of the thought.
It is the substance of music that is archetypal, not the outward form, and what has happened to music is an outgrowth of the whole process of human evolution. Sensibility, style and technique have changed over the centuries; these are expressions of consciousness, and consciousness is what evolves.
The fundamental fact behind this history is the decision of the hierarchies to allow the cosmic intelligence, of which they had the stewardship, to descend into minds of human beings, so that we might become responsible for our thinking and all that results from it, rather than experiencing our consciousness as something inseparable from its divine origin. The stage of this process that concerns us began three centuries before the birth of Plato (427 BC) and its effects can be seen in the sudden and otherwise unexplainable appearance, in the sixth century BC, of a small army of Greek philosophers all trying to understand the workings of mind and nature in rational ways rather than in terms of myth.6 This movement spread through Arabia, North Africa and Europe, but any tendency to regard the European races as a sort of historical elite, chosen by destiny to be in the forefront of developing consciousness, is deeply misplaced. There is no cause for rejoicing in being a member of a society which changed rapidly, incessantly and violently while others maintained many of their ancient ways – at least until the arrival of the Europeans. The thousands upon thousands of people uprooted by the agricultural revolution and enslaved by the industrial revolution certainly wouldn’t think so. The children who worked twelve hours a day and slept by their machines were not aware that they were part of the culture that had produced Bach and Beethoven, and would shortly produce Bruckner and Brahms. Neither were their parents. The proposal to become a laboratory for a large-scale experiment in changing consciousness might well have been defeated in a referendum held among Europeans some time in the early Middle Ages if they had known what it would lead to. It may have transformed the souls of all the men and women in the area of its operation, but the artistic manifestations that seem so important to us were matters only for the church and the upper classes.
This is not, however, to romanticize other ancient cultures. Wars for food, territory, wealth and power have taken place all over the world7 and the consciousness soul era8, which we entered at the end of the Middle Ages, is not merely a matter for Europe. We must remember that although, as Rudolf Steiner said, the descent of the divine intelligence was complete by the twelfth, thirteenth and fourteenth centuries, we are still struggling to understand our new capacities and find the best ways of using them. The process still has a long way to go and it involves all of humanity, but Rudolf Steiner’s ideas about the evolution of consciousness make sense of European and Eastern Mediterranean history in a way that no other concepts that I have encountered do, and understanding how events played out in Europe may be important far beyond the boundaries of that continent. To say that the story is deeply tragic is not to give in to pessimism. When the future is in the balance many people suffer beyond their deserts and die before their time. The appearance of historical inevitability does not make the suffering less real or that which induced it less evil, and we can make sense of brutal history only in terms of reincarnation and karma. And then there are the people whose job it is to pick up the pieces and carry on when the remains of all the heroes and villains have been carried away. Shakespeare’s tragedies have a tendency to end on a note of anticlimax – funeral arrangements for Brutus, coronation plans for Malcolm, a twenty-one gun salute for Hamlet and political plans for Fortinbras. The strong element of tragedy in the history of Europe is not absent from the history of its art. I sense that something in music has died, that history has moved on and that there may be no more musical giants of the kind who dominate our perceptions of the whole period from the Middle Ages to the twentieth century. My feeling is that to be a composer now is to be a lost child. But lost children have to cope somehow and they do eventually grow up, perhaps to be the stewards of a diminished kingdom.
The Narrowing Interval
The epoch in which we live, called by Steiner the Post-Atlantean, began in the eighth millennium BC. Steiner tells us that at the start of this epoch the smallest interval that human beings could experience was the fifth. In the preceding epochs, the Lemurian and the Atlantean, the smallest perceptible intervals were the ninth and seventh respectively.9 In the course of the Post-Atlantean Epoch smaller intervals appeared and the classical Greek theorists described many forms of complete scale, but the notion of harmony as we know it had not yet appeared. During the Middle Ages people often sang their melodies in parallel octaves, fifths and fourths. We may think of this practice as the beginning of harmony but in those days singing in parallel fifths or fourths probably didn’t feel much different from singing in octaves or unison – you were simply singing the same melody at your most comfortable pitch. In the later Middle Ages major and minor thirds began to appear frequently as harmonic intervals and by the early Renaissance major and minor triads were very much in evidence. From the Renaissance until the twentieth century harmonies were given their most characteristic flavors by the presence of major and minor thirds.
Knowledge of the Lemurian and Atlantean Epochs is esoteric, but what happened from Classical Greek times onwards is increasingly common knowledge – or would be if people were interested in it. The over-all picture given by Steiner is that the interval of primary interest to the human being has decreased in the sequence ninth, seventh, fifth, third and that eventually we shall come to the prime and the true experience of the octave. Steiner gave only the briefest indications about Lemurian and Atlantean music and although we have reams and reams of confusing and contradictory Greek music theory, our ideas about the actual sound of Greek music are fragmentary and speculative. Our knowledge of actual music starts roughly halfway through the fourth Post-Atlantean epoch.
This is a significant date – about 400 AD – since Steiner gives it as the approximate mid-point of the process whereby the stewardship of the cosmic intelligence was brought within the reach of human beings. Just as in more ancient times people experienced their thoughts as the work of angelic beings, so they experienced music as the songs of the higher beings. The early Post-Atlanteans felt the presence of the Hierarchies in the interval of the fifth but, as the higher angelic beings withdrew, the fifth became empty and had to be filled from the human inner experience of feeling, expressed through the major and minor thirds. By the close of the fourteenth century AD the descent of thinking was more or less complete, although it would still take a long time for people to come to terms with their new potentialities; and by that time the transition to something akin to major and minor harmony had gone some way, although it would take another couple of centuries for what we now recognize as the mainstream of harmony and counterpoint to develop.
Back to Ancient Greece and Forth to Modern Europe –
Intervals, Scales and Harmonies
Having been given the opportunity to take control of our thought processes, we have the impression that if only we could get rid of all the anxieties and irrational desires that plague us, we would be able to do whatever we like with our thinking. What we like may not always reflect much credit on us, but we feel that our freedom to make the choice is one of the greatest privileges of modern civilization. Like our thoughts, our musical substance has become divorced from its spiritual origin. We are free to generate and combine sounds however we wish, but whereas Rudolf Steiner described a clear path that we could follow in order to bring life and meaning to our thinking, we have no such guidance in music. Steiner considered that if we want to figure out where we are going with our thinking we need to understand where we have come from and the same must surely be true about music.
At one time musical experiences, perceptions and insights came to us, without our permission, from the spiritual world. For many of us they still do, but we are not aware of it since it happens while we are asleep. This is an unconscious process and, as with our thinking, we feel that we make up our own tunes, harmonies and rhythms. The musical substance is archetypal but what we do with it is individual. Steiner relates the steps of the scales that we have traditionally worked with, and the intervals found in those scales, to the nature of the human organism of body, soul and spirit and to the ways in which we experience ourselves and the spiritual world. Melody, he says, is akin to thinking, and most of our earliest knowledge of it comes from the same source as our earliest knowledge of philosophical thinking – classical Greece. In other words, it comes from a time when the descent of the cosmic intelligence had recently begun and people were in the earliest stages of figuring out how to use it, so it’s not surprising that early Greek musical theory is as confusing and contradictory as early Greek philosophy, especially since the musical tones provided by nature are an ample source of contradictions.
These days we talk blithely about thirds, fourths and fifths as if there were no ambiguities involved in tuning these intervals – the modern system of equal temperament10 has absolved us of all that; and we have a highly influential school of composition – the twelve tone movement – which lasted for eighty years or so, and is not quite dead yet, that took equal temperament as its first axiom. I have no intention of knocking equal temperament – it has its problems but so does every other system of tuning that has ever been invented. This is a very complex subject so I’ll give only a summary of a few of the problems and show how some of the solutions relate to the evolving human condition. If you suffer from math- or music-anxiety you’ll still be able to get the general idea.
Since I’m going to talk about musical intervals I’ll remind the reader that the interval between two tones is designated by starting on the lower tone and counting upwards until we arrive at the upper tone. For example, the interval between the D and the G in our scale is a fourth. We start on D and say, “One” and count until we reach G, when we say, “Four.” I put it in this hyper-careful way so that you realize that these numbers are just for the purpose of stating the difference in pitch between two tones – they are not labels that belong to these particular tones.
If you raise the lid of a piano, play a low note loudly, and listen carefully as the sound dies away, you find that several higher tones become clearly audible. If the low note is a C, the higher tones that you can hear include the C an octave higher, the G above that, the C two octaves higher than the original and the E above this C. These tones must all be coming from the C-string that you played, since all the other strings are damped. Similar effects can be observed using air columns instead of strings. It is impossible to play a note on any of the traditional string or wind instruments without producing a whole chord, although under most conditions the overtones are not consciously heard.
There has been a lot of debate over the extent to which the systems of scales and chords used in Western European music are based on these overtones, but it would be very difficult to deny that there is a strong connection. The overtones of C include not only the notes of the major chord, C, E and G, but also a D, giving us four of the notes of the major scale. Between these tones we find successively narrowing intervals – the octave, fifth and fourth, which were the perfect intervals of mediaeval music, and then the major third and the minor third. The mediaeval modal scales and the major and minor scales and common chords can be derived from these overtones but there are many different ways of proceeding.
According to tradition, the relationships of the tones produced by the vibrations of stretched strings were brought to Greece in the sixth century BC by Pythagoras. Apart from the first few overtones the series is difficult or impossible to hear but the Pythagoreans found that the same tones can be produced one at a time using a monochord, consisting of a wire stretched between two bridges on a long wooden box. A moveable bridge is placed at any point under the wire to change the length of the vibrating segment without perceptibly altering the tension. Taking the tone produced by the vibrations of the whole string as the fundamental, assumed for simplicity to be C, we then listen to the tones produced by 1/2, 1/3, 1/4, 1/5, and so on, of the length of the whole string. We find that 1/2 of the string produces the C an octave higher than the fundamental, 1/3 produces the G in the second octave above the fundamental, 1/4 the C two octaves above the fundamental, and 1/5 the E in the third octave. These are the actual tones and we can go on to specify the intervals between them, namely the octave from the fundamental to the next higher C, the fifth from this C to G and the fourth from G to the next C, which are the traditional perfectly consonant intervals. If we keep going up the series we have the interval from C to E – a major third – and the interval from E to G – a minor third. The first five tones in this series (referred to as the harmonic series) form a complete major chord spread out over three octaves. If we continue the process, we find that the sixth harmonic is another G and the seventh is a very flat B flat that doesn’t correspond to any note in any scale ever used in Western Europe.11 The eighth harmonic is another C and the ninth is a D. Figure 1 shows the harmonics in bold, the remainder of the scale in italics, the intervals between successive harmonics above, and the lengths of the string below.
This all seems very reassuring – our beloved major chord comes naturally from all our wind and stringed instruments. Noting that doubling the length of the string lowers the pitch by one octave, we can get all these overtones into the span of an octave as follows. (I have omitted the awkward B*)
Greek musical theorists engaged in complex and contradictory discussions on the exact way to fill in the whole octave and on the possible scales that could be formed. The great and highly literate musical historian Gustave Reese12 remarked that the historian is sometimes left with the difficult task of reading meaning into what the writers say. “This task has tormented many excellent minds”, he continues, “and is doubtless what a lecturer before the Musical Association of London had in mind when he introduced a paper, ostensibly on Greek music, with the following words:
“The only professor of Greek I have ever known who was also a musician always refused on principle to give me any help with a stiff passage from a Greek author on music. ‘Put that stuff away’, he would say, ‘Nobody has ever made head or tail of Greek music, and nobody ever will. That way madness lies.’”
Reese was not deterred by this piece of advice but, not wishing to disturb my own or anyone else’s sanity, I shall mention only that Greek musical theory was seriously misunderstood by scholars in the Middle Ages, with the result that the ensuing systems of ecclesiastical modes with Greek names bore only a superficial and misleading resemblance to anything current in classical Greece. Perhaps the most important point to bear in mind is that people were singing songs and playing instruments long before the theorists started producing systems of scales. It was only when people began to create music that went beyond the pentatonic or diatonic scales, and particularly when keyboard instruments were involved, that the nature of the overtone series began to cause serious problems, but even the production of a complete seven-note scale, such as appeared in mediaeval music, required some decision-making. We have C, D, E and G, but no acceptable tuning for F appears in the series and we have to go into the stratosphere to find anything plausible for A and B. The following example is intended only as an illustration of the difficulties, not as a historical reconstruction.
Using the acoustically perfect fifth from C to G as a measuring rod, we could make our F a perfect fifth below the top C of the scale and our A and B perfect fifths above the D and E that we already have from the harmonic series.
* With this tuning, the sequence G-A-B-C has the same relative pitches as the sequence C-D-E-F. Tunings corresponding to the A and B can be found as the 27th and 15th harmonics. The A corresponds to the open-string A of a well tuned cello.
It will be helpful to show a second octave, which can be done by halving all the lengths – 8/9 becomes 4/9 and 4/5 becomes 2/5 and so on.
This looks innocent enough but its apparent guilelessness conceals certain “stratagems and spoils” which it would take more than a whole book to elucidate. When you get to the end you will realize that these are not five different problems, but five different expressions of the same inherent properties of the harmonic series.
1. Whole Steps
We hit on the first complication when we find that the “whole step” from D to E is smaller than the one from C to D. (Arithmetically we are talking about the difference between 8/9 and 9/10.) You can imagine the confusion caused by having two different whole-steps when tuning a modern keyboard instrument.
2. Perfect Fifths. 13
The interval from A in the first octave to E in the second, which looks as if it ought to be a perfect fifth, is smaller than the four perfect fifths that we built into the system. (The E has the acoustically correct ratio of 2/5 so the A below it ought to have a ratio of 3/2 times 2/5, which is 3/5, not 16/27.) We could correct this by tuning A to 3/5, which is the tuning usually given in this kind of system, but unfortunately this would have the effect of making the fifth from D to A less than acoustically perfect. Oh dear! Well, perhaps it doesn’t matter if one of the fifths isn’t quite the same as all the others. The Pythagoreans, however, wanted all the fifth intervals in the scale to be the same as the perfect C-G interval, so they simply altered the tuning of the E to make A-E the same as C-G. This tuning worked quite well in the earlier Middle Ages, when harmony, such as it was, was based on octaves, fifths and fourths, all of which are acoustically perfect in the Pythagorean system, and when musicians mostly made do with just the seven notes of the scale – what we call the “white-note scale” in modern times. But the C-E interval is our precious major third and Pythagorean tuning makes the E perceptibly and uncomfortably sharper than the natural major third in the harmonic series. This is not the only problem inherent in Pythagorean tuning. Much of the music of the baroque and the classic-romantic periods requires instruments that will play equally well, or, as some would say, equally badly, in all the major and minor keys and this is impossible with any system that uses the pitches of the harmonic series or is based on the exclusive use of acoustically perfect fifths.
3. Major Thirds.
The major thirds from C to E and from G to B in Figure 4 are the same as the C-E interval in the harmonic series, but the one from F to A is significantly wider. This can be cured by using a 3/5 tuning for A but, as we have seen, the result of this is that the interval from D to A is no longer a perfect fifth.
4. Another Version of 2.
If we start on C and rise by successive intervals of a perfect fifth – C-G-D-A-E – the E we arrive at is significantly higher than the overtone E in the harmonic series. So it seems that in tuning E we have either to generate it from this sequence of perfect fifths or make it agree with the natural harmonic. In the latter case, one of our fifths will be less than acoustically perfect.
5. The Circle of Fifths.
If you look at a piano you have the impression that twelve intervals of a fifth fit exactly into seven octaves. If you start on the bottom C and rise by successive fifths (C – G – D – A – E – B – F# – C# – G# – D# – A# – E# – B# = C) you end on the top C. This is clearer if we recognize that on the piano, E# is the same as F and B# is the same as C. So we have C – G – D – A – E – B – F# – C# – G# – D# – A# – F – C. Actually you may run out of keys before you reach your top C, but, once again, I put the matter in terms of C to keep things simple. The problem here is that twelve acoustically perfect fifths add up to more than seven octaves, so if you want them to fit you can compress them all by the same very small amount, which is what happens in the equal temperament system, or compress them selectively, which is what happens in every other system.
Two oddball characters missing from this discussion are the augmented fourth from F to B, and the diminished fifth from B to the F in the second octave. In the equal temperament system these two intervals are identical but in any system derived from the harmonic series, they are slightly different.14 Together they constitute the so-called diabolus in musica, of which so much has been written, not all of it to the point. The augmented-fourth/diminished-fifth is not just a product of some delicate decision about tuning – it’s a whole half-step greater than a perfect fourth or less than a perfect fifth and it has played a crucial part in the transitions from the modal system to the major/minor harmonic system and from the latter to the freely modulating techniques of the classic-romantic period.
From Fifths to Thirds
The point I’d like to emphasize is that in the Middle Ages people were moving from a period in which the fifth was the musical interval in which there was still some experience of divine beings to one in which the fifth began to feel empty or, as we say now, bare. So, in the absence of divinity, we filled it with human feeling by inserting the major or minor third, and it was natural to move from a tuning system based on fifths to one that gave greater importance to the correct tuning of the third. This was the mean-tone system that appeared in the fifteenth century.
In the Pythagorean system the major thirds are so out of tune that it is not surprising that they were considered dissonant. This was not a problem in the earlier Middle Ages since thirds rarely appeared as harmonic intervals and when they did it was only in passing. In the mean-tone system the fifths – C-G, G-D, D-A and A-E – are each reduced very slightly so that the sequence results in an acoustically pure major third. This produces a very sweet sound in simple keys with not more than one or two sharps or flats, but becomes unworkable in more remote keys. The moral is, “Yer pays yer money and yer takes yer choice.” You could have pure fifths or pure thirds, but you couldn’t have both.
Most modern musicians prefer to have neither and cut their losses by adopting the system of equal temperament, in which the octave is divided into twelve equal half-steps and all the intervening tones are slightly out of tune with their acoustical forerunners. It took a long time for this to happen.
At the beginning of the 17th century a sign of the times emerged in the form of a fantasia by the English composer (I’m not making this up!) John Bull (1562-1628). Bull’s fantasia, which you can find in the Fitzwilliam Virginal Book15, published in 1612, passes though a complete enharmonic cycle, although not in the simple order described below. This may need some explanation.
The circle of fifths that we’ve already discussed lands on a B#, which we then call C:
C – G – D – A – E – B – F# – C# – A-flat – E-flat – B-flat – F – C.
This is called an enharmonic cycle because at some point it assumes the identity of a pair of enharmonic tones – in this case, G-sharp and A-flat. If you start a piece of music in the key of C and repeatedly change to a key with one more sharp in the key signature you will pass through all the keys named in the cycle of fifths. When you get to G-sharp you will find that you have to start using double sharps in the key signature and will simplify things by writing the key as A-flat, with a more manageable signature of four flats. If you then continue your modulations until you arrive at the key of C again, you will have completed an enharmonic cycle.
John Bull’s Fantasia visits all twelve keys and the reason for mentioning it is that a composition like this requires an instrument capable of playing tolerably in tune in all these keys. Unfortunately this requirement can only be met by using an instrument that plays somewhat out of tune in some or all of them. If we take the overtone series as our standard, the Pythagorean system is out of tune in its thirds and the mean-tone system is out of tune in its fifths. If the Pythagorean system is extended to the whole twelve-tone chromatic scale it must include, as well as its out of tune thirds, at least one fifth that is not acoustically pure. If the mean-tone system is similarly extended we have to use instruments with extra keys. This is the situation we are in as long as we try to keep the connection with nature as strong as possible, and we must recognize that in trying to extend our system beyond the four notes that are easily obtained from the overtone series we are already venturing beyond what the natural world provides.16
This, however, is exactly what composers wanted to do. Bull’s Fantasia might be considered an oddity, but J. S. Bach’s Well-Tempered Clavier17 certainly wasn’t. His preludes and fugues stick to one key at a time but they cover all twenty-four major and minor keys – all, that is, that you can discover on an ordinary keyboard, where G-sharp and A-flat are the same thing. By the 1770’s, however, Haydn was feeling free to start a symphony with five sharps in the key signature and modulate to any key he liked within a single movement.18 None of this automatically meant the adoption of equal temperament but it did go hand in hand with determined efforts to make all the keys tolerably accessible.
The idea that the chromatic scale should consist of twelve notes comes from the near-equality of twelve fifths and seven octaves. It is part of the evolutionary plan for humanity that at some point that which was provided out of the spiritual world is taken over and recreated by human beings. For a long time musicians continued to root their compositions in the experience of the chords derived from the overtone series even though they could not use acoustically pure tunings. The impulse that arose early in the twentieth century to abolish all distinctions between the twelve tones meant that the only remnants of acoustical respectability were the retention of the octave as a musical unit and its division into twelve steps and not some other number. The other arts have traveled in somewhat similar directions. The vanishing point introduced in Renaissance painting does not correspond exactly to anything in nature. Natural pigments have been supplemented or replaced by artificial ones. We use poured concrete, pulverized rock, plastic and glass so that our sculptors, architects and builders are neither limited nor inspired by the characteristics of natural materials. The twelve tone system of composition, which does its best to eliminate natural tonal relationships, is the musical equivalent of poured concrete and I have no objection in principle to either. These things are results of the freedom granted to us from the spiritual world to think our own thoughts, make our own music, paint our own pictures, form our own sculptures and construct our own buildings. The real crunch comes when we apply such ideas to the workings of human society. The tendency for rulers to treat the multitude of the ruled like a mass of substance that can be forced or persuaded to take any desired form has existed as long as anyone can remember, but in our technological society it takes particularly vicious forms. But that’s another story.
Efforts to restore some form of Pythagorean tuning have failed because we are in the age of the third and we can’t tolerate Pythagorean thirds. As far as that goes equal temperament is just a little better, as the following little bit of arithmetic shows.
In specifying the actual pitches produced by tuning according to equal temperament the system of cents was introduced. A half step in this system is divided into 100 cents,19 so an interval of 1 cent is 1/100 of a half step. If you count in half-steps from C to G you find that the interval of a fifth contains 7 half-steps. As each half-step is worth 100 cents this means that an equal temperament fifth is equivalent to 700 cents. A slightly more complicated calculation shows that the acoustically perfect fifth is equivalent to 702 cents, so the equal temperament fifth is off by 2 cents, or 1/50 of a half-step. This difference is well below that which can be consciously detected by human ears. It’s a different matter with the major thirds. A major third contains 4 half-steps, so in equal temperament it’s equivalent to 400 cents, whereas the acoustically pure major third is 386 cents, a difference that is plainly audible. In this respect the Pythagorean system is a greater sinner still, most of its major thirds being equivalent to 408 cents, a discrepancy of more than 1/5 of a half-step.
The fact is that in any system that makes all twelve major and minor keys equally available, twelve fifths have to add up to seven octaves and three major thirds have to add up to one octave, and the discrepancy is much greater for the thirds than it is for the fifths. Although there have been more sophisticated versions of the mean-tone system and other ways of minimizing the damage, at some time in the nineteenth century the tide turned in favor of equal temperament. Nothing on this earth is permanent, however, and nobody knows what will emerge when the system of key relationships that made a necessity of equal temperament has become as much a thing of the past as the mediaeval modal system is now.
That ends this brief survey of the relationships of tuning systems to the evolution of consciousness from the Fourth to the Fifth Post-Atlantean Age. Part II deals with some musical signs of the transition.
PART II »
1 Polyphony is a style of composition in which all the voice or instrumental parts are melodic and in which harmony arises from combinations of melody. This can be contrasted with homophony, in which a single melody is supported by an accompaniment essentially consisting of chords.
2 Mannheim is a city in Western Germany, famous in the mid-eighteenth century for the skill, discipline and flamboyant style of its great orchestra. Compared to the composers who wrote for the Mannheim Orchestra, Bach and Handel seemed very old-fashioned. Some of the elements of the classical style, including bold dynamic and textural contrasts and the use of crescendo and diminuendo, were developed there. Footnote to footnote: Some historians assert that there was no such thing as the Mannheim School and that all these techniques had already been developed in Italy.
3 Tovey; The Mainstream of Music, OUP, 1949
4 As a technical term, “classical” refers to the music of Haydn, Mozart and Beethoven.
5 Webster seems to be unfamiliar with the use of murmuration as the collective noun for starlings.
6 See Rudolf Steiner, The Driving Force of Spiritual Powers in World History, (1923) Steiner Book Centre, North Vancouver, 1972. A key lecture from this cycle was reprinted in The Inner Nature of Music and the Experience of Tone, Spring Valley, NY, 1983. An excellent account of the pre-Socratics can be found in Early Greek Philosophy, Penguin 1987, translated, edited and introduced by Jonathan Barnes.
7 See Jared Diamond, Guns, Germs and Steel, Norton, New York, 1997.
8 The consciousness soul is the expression of the human psyche that has developed since the beginning of the Fifth Post-Atlantean Age around 1400 AD. It is characterized by a feeling of isolation from both the spiritual and the physical world but it also carries the potentiality for working back into full and conscious communion.
9 This is a very bald statement of a complex issue – you should at least read the whole of Lecture 3 of The Driving Force. Taken at face value, these observations suggest that music as we know it did not exist until a considerable time after the beginning of the Post-Atlantean epoch. Bone flutes (oboe-related really, since they have reeds) have been found dating back at least to 30,000 B. C., which can play complete scales, so probably the best thing we can do about the music of these really ancient times is to keep an open mind.
10 Equal temperament is a system of tuning in which the octave is divided into twelve equal half-steps. These half-steps are slightly different from those found in the scales derived from the overtone series, having a ratio of 1/21/12 instead of 15/16.
11 This very flat B-flat is part of the scale produced by a natural, valveless trumpet and appears to great effect in the second movement of Vaughan Williams’s Pastoral Symphony.
12 Gustave Reese, Music in the Middle Ages, Norton, New York, 1940
13 In what follows I use the phrase “perfect fifth” to mean the acoustically perfect fifth, derived from the overtone series and corresponding to the 2/3 ratio. In general music theory “perfect fifth” means any fifth that contains three whole-steps and one half-step, regardless of the tuning.
14 This must be so, since the length of the string producing the lower F is 2 times the length for the upper F. The product of the B-F ratio and the F-B ratio is therefore 2 and the two ratios can be the same only if they are each the square root of two – an irrational number. This is exactly what happens with equal temperament but there are no irrationals in anything connected with the harmonic series.
15 The book itself is not virginal – the music is to be played on the virginals, a form of harpsichord dating back at least to the early sixteenth century. A modern edition is available from Dover Publications
16 I omit discussion of the putative series of tones that extends below the fundamental on the ground that it seems to me to be more a convenient but unnecessary fiction than a spiritual reality.
17 It is now generally thought that J. S. Bach’s Well-Tempered Clavier, compiled in the 1740’s, was not intended as a boost for equal temperament. Neither, of course, was Bull’s Fantasia.
18 Symphony No. 46 in B major contains a passage in G-sharp minor. Violinists were shocked at the sight of an F-double-sharp (the leading tone) apparently below the G string. They had never seen anything like that before.