[This post belongs to a series about Dylan's idea of "mathematical music" in Chronicles]
“I’m not a numerologist”, Dylan says (Chronicles, p. 159). But before and after this statement, he builds up such a metaphysical web around the force of numbers, that the only definition of a numerologist that he does not fit into, is the kind who calculate a lucky number from the letters of their name. Alright, this is after all not a Rod Stewart blog.
In the Rolling Stone interview from November 2001, where he first mentioned the Lonnie Jonhson method explicitly, he says:
Lonnie Johnson, the blues-jazz player, showed me a technique on the guitar in maybe 1964. I hadn’t really understood it when he first showed it to me. It had to do with the mathematical order of the scale on a guitar, and how to make things happen, where it gets under somebody’s skin and there’s really nothing they can do about it, because it’s mathematical.
In Chronicles, he continues:
I had the idea that he was showing me something secretive, though it didn’t make sense to me at the time…
So we have an esoteric system, communicated to him in the secrecy of the back room or wherever he was taken aside, which works, regardless of what the player or listener know, understands, or thinks of it, solely on the force of the mathematical structure of the system — “because it’s mathematical.”
The Pythagorean Tradition of numbers
The belief that something can work simply “because it’s mathematical”, depends in some way or another on the idea that numbers have certain metaphysical qualities with a real influence on things in reality.
This is the foundation of the Pythagorean theory of numbers, which I’ve alluded to before in this series. Most people know the Pythagorean Theorem, about the relations between the sides in a right-angled triangle: a2 + b2 = c2 (Dylan knows it too, even though he got the formula wrong in the Rome interview, where he presented it as “a square equals b square equals c square”, which may reveal a truth on a more profound level, but which would do you no good in your calculus 101 class).
But the classic didactical myth, handed down in numerous treatises throughout Antiquity and the Middle Ages, tells of how Pythagoras walked by a blacksmith who was pounding away on his anvils, and Pythagoras discovered that some of the anvils produced harmonious sounds together, while others did not. He investigated this closer, and found that the mass of the harmonious anvils were in simple proportions to each other — 1:2, 2:3, or 3:4 — while those in more complex relations produced unpleasing sounds. An anvil twice as big as another, would sound an octave lower, whereas one 1.3658 times the size, would sound like… dunno, the Shaggs or something.
The physical facts of this legend have been proven wrong, but what matters is the belief (1) that harmoniousness depends on proportions that can be expressed in simple ratios, (2) that these proportions, which can be described in a purely mathematical form, not only govern harmony in music, but also in the universe as a whole, and (3) that there is some kind of connection between the different kinds and areas of harmony. Thus, playing a tune in a mode which emphasises certain intervals, will influence the balance between the body fluids, and can thus alter the mood of the listeners.
This discovery and the theoretical/religious system that was built around it, became essential to all ideas of harmony and beauty from Antiquity up until the eighteenth century. Plato considered this kind of mathematical harmony to be the fundamental property of the world. In his creation myth Timaios, the creator-god shapes the world beginning with unity, then extending it with ‘the other’ and ‘the intermediary’, and along the corresponding number series 1, 2, 4, 8 and 1, 3, 9, 27, the whole world is created.
In the Middle Ages, this idea was adapted to the Christian frame of thought. In the apocryphical Wisdom of Solomon in the Bible, it says, “You have ordered all things in number, measure, and weight” (Wisdom of Solomon 11: 21), and this verse was quoted time and again in medieval treatises on music.
Thus, what at first sight may look like a dry and slightly tedious exercise in simple arithmetics, is of vast importance because behind the dry façade lies the notion that numbers and numerical relations are reflections of the divine principles governing the universe; that we find the same relations in the universe as a whole, in human beings, in musical sounds, and in visible beauty, and that by knowing the numbers, we can affect humans and glimpse God.
This is why the slight irregularities in the purely mathematical definition of the scale became such a heated topic. The theorists spent gallons of ink on discussing the problem with the division of a tone in two equal halves, which according to the Pythagorean system is impossible, because it is founded on ratios between natural numbers (the equal division of a tone requires the square root of 2, which was unknown to ancient and medieval thinkers).
The Christian heritage from antiquity was largely Platonic. One of the consequences of the humanistic re-appraisal of the classical traditions during the Renaissance, was that other voices from antiquity were added to the stew. Aristotle, with his less mystical and more rationalistic approach, was revived from the twelfth century, and in the field of music theory, Aristoxenos, whose theories were based on geometrical rather than arithmetical considerations, was more palatable to the practically oriented writers of the Renaissance, who were more concerned with actual sound and preferred the pure harmonies of just intonation to the theoretically “correct” but ugly-sounding harmonies.
Approaching Dylan again
If you object that this doesn’t seem to have much to do with Dylan and Lonnie, you’re absolutely right. I’m partly exerting my right to write whatever I want to do — this is my blog — but partly I’m also trying to demonstrate how important the concept of mathematical music has been, way back in history, and how widely the implications it carries reach.
In order to gradually work our way back to Dylan again, one might point to yet another element that entered the picture in the Florentine academies in the fifteenth century: an extension of the notion of the special mystical character of certain numbers. The mainstream medieval tradition had mainly been concerned with twos and threes, but — partly owing to influence from the cabbalistic tradition — a more extended array of meaningful numbers was established and systematized. The Fibonacci sequences and other similar number sequences, and all the sacred numbers of the Bible — just about every number seemed to have a secret meaning, a value beyond the numerical one.
This is the background for Dylan’s perception of the system he learned back in ‘64. In the following quotation from Chronicles (p. 158), I have emphasised some words which highlights the strong dichotomy that Dylan sees between the world of 2 and the world of 3:
The system works in a cyclical way. Because you’re thinking in odd numbers instead of even numbers, you’re playing with a different value system. Popular music is usually based on the number 2 and then filled with fabrics, colors, effects and technical wizardry to make a point. But the total effect is usually depressing and oppressive and a dead end which at the most can only last in a nostalgic way. If you’re using an odd numerical system, things that strengthen a performance automatically begin to happen and make it memorable for the ages. You don’t have to plan or think ahead.
What is most striking, I think (apart from the description of popular music as based on the number 2, which quite bluntly disregards the blues/jazz tradition, where a triple feel is predominant), is the statement that these are different worlds, different value systems, which have an automatic effect on the performance: it is not something the performer does, but something that is done through the performer.
Does Dylan believe all this? Yes, I would think so. He is after all a poet, a sponge, a mystic, a sage; he takes what he can gather from coincidence, mixes it all together, and out comes… well, sometimes Knocked out Loaded, but we can forgive him that, since he also produces Blood on the Tracks and Chronicles, which is a fascinating read, even though what he writes is less clear than what an academic might have wanted.
More to come…
(Those of you who have access to Judas! may want to look up my article “Beauty may only turn to Rust” in the 8th issue, where I go into these things in more detail, and relate them to Dylan’s liner notes to Joan Baez in Concert, vol. 2, his aesthetical manifesto.)