The speculations which I shall recount briefly here were closely related to my speculations, reported earlier, on dogmatic and critical thinking. I believe they were among my earliest attempts to apply those psychological ideas to another field; later they led me to an interpretation of the rise of Greek science. The ideas on Greek science I found to be historically fruitful; those on the rise of polyphony may well be historically mistaken. I later chose the history of music as a second subject for my Ph. D. examination, in the hope that this would give me an opprotunity to investigate whether there was anything in them, but I did not get anywhere and my attention soon turned to other problems. In fact, I have now forgotten almost everything I ever knew in this field. Yet these ideas later greatly influenced my reinterpretation of Kant and my change of interest from the psychology of discovery to an objectivist epistemology—that is, to the logic of discovery.
My problem was this. Polyphony, like science, is peculiar to our Western civilization. (I am using the term “polyphony” to denote not only counterpoint but also Western harmony.) Unlike science it does not seem to be of Greek origin but to have arisen between the ninth and fifteenth centuries A.D. If so, it is possibly the most unprecedented, original, indeed miraculous achievement of our Western civilization, not excluding science.
The facts seem to be these. There was much melodic singing—dance-song, folk music, and above all Church music. The melodies—especially slow ones, as sung in Church—were, of course, sometimes sung in parallel octaves. There are reports that they were also sung in parallel fifths (which, taken with the octave, also make fourths, though not if reckoned from the bass). This way of singing (“organum”) is reported from the tenth century, and probably existed earlier. Plainsong was also sung in parallel thirds, and/or in parallel sixths (reckoned from the bass: “fauxbourdon”, “faburden”).58 It seems that this was felt to be a real innovation, something like an accompaniment, or even an embellishment.
What might have been the next step (though its origins are said to go back even to the ninth century) seems to have been that, while the plainsong melody remained unaltered, the accompanying voices no longer proceeded only in parallel thirds and sixths. Antiparallel movement of note against note (punctus contra punctum, point counter point) was now also permitted, and could lead not only to thirds and sixths but to fifths, reckoned from the bass, and therefore to fourths between these and some of the other voices.
In my speculations I regarded this last step, the invention of counterpoint, as the decisive one. Although it does not seem to be quite certain that it was temporarily the last step, it was the one that led to polyphony.
The “organum” may not at the time have been felt to be an addition to the one-voice melody, except perhaps by those responsible for Church music. It is quite possible that it arose simply from the different voice levels of a congregation which was trying to sing the melody. Thus it may have been an unintended result of a religious practice, namely the intoning of responses by the congregation. Mistakes of this kind in the singing of congregations are bound to occur. It is well known, for example, that in the Anglican festal responses, with the cantus firmus in the tenor, congregations are liable to make the mistake of following (in octaves) the highest voice, the treble, instead of the tenor. At all events as long as the singing is in strict parallels there is no polyphony. There may be more than one voice but there is only one melody.
It is perfectly conceivable that the origin also of counterpoint singing lay in mistakes made by the congregation. For when singing in parallels would lead a voice to a note higher than it could sing it may have dropped down to the note sung by the next voice below, thus moving contra punctum rather than in parallel cum puncto. This may have happened in either organum or fauxbourdon singing. At any rate, it would explain the first basic rule of simple one-to-one note counterpoint: that the result of the countermovement must be only an octave or fifth or third or sixth (always reckoned from the bass). But though this may be the way the counterpoint originated, the invention of it must have been due to the musician who first realized that here was a possibility for a more or less independent second melody, to be sung together with the original or fundamental melody, the cantus firmus, without disturbing it or interfering with it any more than did organum or fauxbourdon singing. And this leads to the second basic rule of counterpoint: parallel octaves and fifths are to be avoided because these would destroy the intended effect of an independent second melody. Indeed they would lead to an unintended (though temporary) organum effect, and thus to the disappearance of the second melody as such, for the second voice would (as in organum singing) merely enforce the cantus firmus. Parallel thirds and sixths (as in fauxbourdon) are permitted steps provided they are preceded or followed fairly soon by a real countermovement (with respect to some of the parts).
Thus the basic idea is this. The fundamental or given melody, the cantus firmus, puts limitations on any second melody (or counterpoint), but in spite of these limitations the counterpoint should appear as if it were a freely invented independent melody—a melody melodious in itself and yet almost miraculously fitting the cantus firmus though, unlike both organum and fauxbourdon, in no way dependent on it. Once this basic idea is grasped, we are on the way to polyphony.
I will not enlarge on this. Instead I will explain the historical conjecture I made in this connection—a conjecture which, though it may in fact be false, was nevertheless of great significance for all my futher ideas. It was this.
Given the heritage of the Greeks, and the development (and canonization) of the Church modes in the time of Ambrose and Gregory the Great, there would hardly have been any need for, or any incitement to, the invention of polyphony if Church musicians had had the same freedom as, let us say, the originators of folk song. My conjecture was that it was the canonization of Church melodies, the dogmatic restrictions on them, which produced the cantus firmus against which the counterpoint could develop. It was the established cantus firmus which provided the framework, the order, the regularity that made possible inventive freedom without chaos.
In some non-European music we find that established melodies give rise to melodic variations: this I regarded as a similar development. Yet the combination of a tradition of melodies sung in parallels with the security of a cantus firmus which remains undisturbed even by a countermovement opened to us, according to this conjecture, a whole new ordered world, a new cosmos.
Once the possibilities of this cosmos had been to some extent explored—by bold trials and by error elimination—the original authentic melodies, accepted by the Church, could be done without. New melodies could be invented to serve in place of the original cantus firmus, some to become traditional for a time, while others might be used in only one musical composition; for example as the subject of a fugue.
According to this perhaps untenable historical conjecture it was thus the canonization of the Gregorian melodies, a piece of dogmatism, that provided the necessary framework or rather the necessary scaffolding for us to build a new world. I also formulated it like this: the dogma provides us with the frame of coordinates needed for exploring the order of this new unknown and possibly in itself even somewhat chaotic world, and also for creating order where order is missing. Thus musical and scientific creation seem to have this much in common: the use of dogma, or myth, as a man-made path along which we move into the unknown, exploring the world, both creating regularities or rules and probing for existing regularities. And once we have found, or erected, some landmarks, we proceed by trying new ways of ordering the world, new coordinates, new modes of exploration and creation, new ways of building a new world, undreamt of in antiquity unless in the myth of the music of the spheres.
Indeed, a great work of music (like a great scientific theory) is a cosmos imposed upon chaos—in its tensions and harmonies inexhaustible even for its creator. This was described with marvellous insight by Kepler in a passage devoted to the music of the heavens:59
Thus the heavenly motions are nothing but a kind of perennial concert, rational rather than audible or vocal. They move through the tension of dissonances which are like syncopations or suspensions with their resolutions (by which men imitate the corresponding dissonances of nature), reaching secure and predetermined closures, each containing six terms like a chord consisting of six voices. And by these marks they distinguish and articulate the immensity of time. Thus there is no marvel greater or more sublime than the rules of singing in harmony together in several parts, unknown to the ancients but at last discovered by man, the ape of his Creator; so that, through the skilful symphony of many voices, he should actually conjure up in a short part of an hour the vision of the world’s total perpetuity in time; and that, in the sweetest sense of bliss enjoyed through Music, the echo of God, he should almost reach the contentment which God the Maker has in His Own works.
Here were some more ideas which distracted me and which interfered with my work on those writing desks during my apprenticeship as a cabinetmaker.60 It was during a time when I was reading Kant’s first Critique again and again. I soon decided that his central idea was that scientific theories are man-made, and that we try to impose them upon the world: “Our intellect does not derive its laws from nature, but imposes its laws upon nature.” Combining this with my own ideas, I arrived at something like the following.
Our theories, beginning with primitive myths and evolving into the theories of science, are indeed man-made, as Kant said. We do try to impose them on the world, and we can always stick to them dogmatically if we so wish, even if they are false (as are not only most religious myths, it seems, but also Newton’s theory, which is the one Kant had in mind).61 But although at first we have to stick to our theories—without theories we cannot even begin, for we have nothing else to go by—we can, in the course of time, adopt a more critical attitude towards them. We can try to replace them by something better if we have learned, with their help, where they let us down. Thus there may arise a scientific or critical phase of thinking, which is necessarily preceded by an uncritical phase.
Kant, I felt, had been right when he said that it was impossible that knowledge was, as it were, a copy or impression of reality. He was right to believe that knowledge was genetically or psychologically a priori, but quite wrong to suppose that any knowledge could be a priori valid.62 Our theories are our inventions; but they may be merely ill-reasoned guesses, bold conjectures, hypotheses. Out of these we create a world: not the real world, but our own nets in which we try to catch the real world.
If this was so, then what I originally regarded as the psychology of discovery had a basis in logic: there was no other way into the unknown, for logical reasons.