things twice

[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.)

[This post belongs to a series about Dylan’s idea of “mathematical music” in Chronicles]
In the discussion of the Lonnie Johnson technique in Chronicles, Dylan refers to Link Wray’s “Rumble” as one of the pieces that uses this method.
He says:

Once I understood what I was doing, I realized that I wasn’t the first one to do it, that Link Wray had done the same thing in his classic song “Rumble” many years earlier. Link’s song had no lyrics, but he had played with the same numerical system. It would never have occurred to me where the song’s power had come from because I had been hypnotized by the tone of the piece.

He then compares this to a performance by Martha Reeves where she “beat a tambourine in triplet form […] and she phrased the song as if the tambourine were her entire band”.
This is all very interesting, but it hardly sheds any light on the “Lonnie” system as he presents it. Well, let’s see.
“Rumble” is an instrumental, played by a combo of two guitars, bass and drums. It is easy to see how the raw intensity may have caught Dylan’s interest. The introduction goes something like this:

   D     D       E                                     D     D 
   .     .       :     .     .     .       :     .     .     .     
---0-----0-----|-0-----------------------|-------------0-----0-----|
---3-----3-----|-0-----------------------|-------------3-----3-----|
---2-----2-----|-1-----------------------|-------------2-----2-----|
---0-----0-----|-2-----------------------|-------------0-----0-----|
---0-----0-----|-2-----------------------|-------------------------|
---------------|-0-----------------------|-------------------------|
               |                         |                         |
               | :     .     .     .     | :     .     .     .     |
               |-------------------------|-------------------------|
               |-------------------------|-------------------------|
Bass           |-------------------------|-------------------------|
               |-------------------------|-------------------------|
               |-------------------------|-------------------------|
               |-0-----1-----2-----3-----|-0-----1-----2-----3-----|
               |                         |                         |   
               |                         |                         |   
               | :     .     .     .     | :     .     .     .     |
Cymbal         |-x-x-x-x-x-x-x-x-x-x-x-x-|-x-x-x-x-x-x-x-x-x-x-x-x-|
               |                         |                         |   
Bass drum      |-x-----x-----x-----x-x-x-|-x-----x-----x-----x-x-x-|

This is really all there is to the song, with the exception of a “solo” verse, which consists of violent tremolo strumming, and a turnaround figure after each verse, which adds two beats to the general four beats per measure, giving it all a limp that is certain to wake one up, should one against all likelihood have fallen asleep.

   D     D       B7
   :     .       :     .     .     .      
---0-----0-----|-------2-----------------|
---3-----3-----|------0------------------|
---2-----2-----|-----2-------------------|
---0-----0-----|----1--------------------|
---------------|-2-----------------------|
---------------|-------------------------|

                                        E           D     D       E
  :     .     .     .     .     .       :     .     .     .       :     
|-------------3-0---------------------|-------------2-----2-----|-0-----
|-----------------3-0-----------------|-------------3-----3-----|-0-----
|---------------------2-0-------------|-------------2-----2-----|-1-----
|-------------------------2-0---------|-------------0-----0-----|-2-----
|-----------------------------2-0-----|-------------------------|-2-----
|---------------------------------3---|-0-----------------------|-0-----

It makes perfect sense that Dylan has liked this. There is the unpolished character of the whole thing, which reminds one of the best moments of Highway 61. There is the soundscape of sharply differentiated parts, each with its own distinctive rhythmic pattern:

• a raw electric guitar, slightly out of tune, pounding three-chord patterns and a simple run at the end;
• a muffled bass playing simple, chromatic ascending figures over and over again;
• two widely different percussion sounds — the cymbals with their insistent triplets and the bass drums with their dump “tam, tam, tam, ta-ta-ta”;
• and the rhythm guitar, which only plays the strong beats and nothing else.

Both guitars, in different ways, take the part of the drummer, as Dylan has described his own solo guitar playing on several occasions, whereas the drums do just as much “motivic” or “thematic” work as any of the others.
But what does it have to do with Lonnie Johnson and mathematical music?
At first sight: nothing.
At second sight: well, the number three is all over the place: the main line of the guitar is three chords — silence — three chords — etc, ended by a measure which is extended from 2×2 to 3×2 beats. The cymbals play different kinds of triplets all the time, and the bass drum plays three long and three short.
Hey, perhaps we’re on to something here? Triplets, what is it about triplets? He says earlier:

I don’t know why the number 3 is more metaphysically powerful than the number 2, but it is.

There is a long line of thinking behind this, which of course goes back to the pythagoreans, again. I will write more about this in a forthcoming post, but as a teaser, the numerical system in Plato’s account is based on each number having its own metaphysical character, one being unity (and not really a number at all), two representing “the other” and three “the intermediary”. The difference between two and three has been central to all numerological systems throughout the history of ideas.
I’m not saying Dylan is a Platonist (and he says himself that he’s not a numerologist, so we better believe him, right?)(Right!), but it is not either unlikely that he has picked up some sort of idea along these lines, and why not from Lonnie Johnson? And if he believes the beauty of the system is that it works, regardless of artifice: the audience will go wild, no matter — if it works, then why not use it?
Be that as it may, the beauty of this explanation is that it works whether Dylan is right or not, whether there is a firm basis for the system or not. What Link Wray does, through his use of various permutations of threes, is to create a polyphonic structure with different layers of rhythmic activity in different instrument parts, all going on at the same time, and creating a remarkable complexity with very limited means. Whether it works because of the number three or because of the raw sound, the hypnotic repetitivity, and the underground Rumble of ominous ta-ta-ta in the drums and weird chromatics in the bass, barely audible as such, but mostly very disturbing — who am I to tell why it works?
And these elements: pared down resources, insistent repetition, sometimes weird “chromatics” (which one might — O horrible thought! — have mistaken for mistakes, but now we know better…), guitars playing drums and vice versa — these are precisely what characterizes Dylan’s band and his playing from 1988 and in the following years.
Now it remains to take a closer look at some of his own music making during those years, to see where the triplets went.

[This post belongs to a series about Dylan’s idea of “mathematical music” in Chronicles]

I agree with the comment in the first post on this subject, that rhythm and a deliberately ambiguity between 3/4 and 4/4 time may be part of what Dylan is talking about. Some of the problem is that he seems to glide — at least in the way he talks about it — between pitch and rhythm as the topic. Some of it, which is the part that I emphasised in my previous post, makes sense as a descripion of a formulaic system of composition, where a set of generic rules can be applied in a variety of situations and produce the goods.
This has been described in the field of literature by Albert Lord and Milman Perry, who studied the formulaic composition of epic poetry in the Balkans, and compared it, as a (then, at least) living tradition, with the Homeric epics, and found the same fundamental traits. The conclusion that the Iliad and the Odyssey are written-out versions of improvised poetry, while upsetting some notions about the Genius who laid the foundation for Western Literature, is hardly surprising, since Homeros was supposed to have lived before the development of writing.
But apart from that, the Lord/Perry studies have been important for the development of a framework for studies of formulaicism in general. This has been taken up by the musicologist Leo Treitler who has applied some of it (but with major qualifications) to the medieval repertory of plainchant.
Anyway, I’m rambling; stop me. [Stop!][Ok, thanks].
The other side would be the rhythmic aspect, which is also clearly part of what he’s talking about. It makes sense, judging from his singing style in the late 80s and early 90s, that he has had considerations about various ways to circle around the various rhythmical strata in a song.
It reminds me of Levon Helm’s comment in the video about the making of “The Brown Album”, about people thinking that it must be difficult to sing lead and play drums at the same time. But for him, he says, it’s the other way around, because he can sing ‘around’ what he plays (or vice versa).
But in either case, there is no easy connection between what Dylan says he does, and what one can hear him doing. Especially when he gets concrete. When he says:

It’s a highly controlled system of playing and relates to the notes of a scale, how they combine numerically, how they form melodies out of triplets and are axiomatic to the rhythm and the chord changes.

–there are a number of possible interpretations, but also a quagmire of possible mistakes, on Dylan’s part and on the reader’s. One is fairly easily taken care of:

• “triplets” is a rhythmical term, denoting the subdivision of a beat in three instead of two units. What he probably has in mind, is triads, the units of three tones separated by major and minor thirds, which have been the foundation of Western harmony since the fifteenth century, and which is usually called “chords”.

But other points are less clear-cut:

• “How [the notes of a scale] combine numerically” — is this a reference to the esoteric tradition of harmony-of-the-spheres which goes back to the Pythagoreans, or simply a way of saying that there are certain patterns in the scale?
• “How [the notes of the scale] form melodies out of triplets” (i.e. triads). Is this a reference to the triadic nature of melody in the western tradition, where certain melodic tones get a particular emphasis because of their structural importance in the triads? In functional harmony, a certain sounding chord is described according to which function it fulfills, which means that the same chord can mean different things depending on the context (see the “D” in different versions of Girl of the North Country), or a chord can be called a G chord without even containing the tone G. (I know I have an example of that in one of the tabs, but I can’t remember where). As I’ve argued in some of my articles in the “Self-Ordained Professors” section, the skillful handling of these features can be observed in Dylan’s music, but I still doubt that that is what Lonnie told him.
• “axiomatic to rhythm and chord changes”. Yes, again: the relationship between rhythm and harmony is close, even though they are different phenomena. The pivot is “structural importance”, which is decided in the interrelations between triad and rhythm: a structural tone is one which is placed on a strong beat, but in some situations, a weak beat may become strong because it is inhabited by a structural tone.
  This is fairly straightforward, but Dylan actually makes a much wider claim when he says that the notes of the scale are “axomatic to rhythm and chord changes”. “Axiomatic” would imply that the notes of the scale are the fundamental building blocks upon which the system is defined, without themselves needing any definition within the system. This would mean that rhythm is inconceivable without a structured pitch hierarchy, which — as a general statement — is pure bullshit. He may be thinking only of his own system, but for an artist working in a tradition based so heavily on rhythm, this becomes a strange statement, to say the least.
  Is this what Dylan means, then, or does he actually mean “triplets” when he says “triplets”, and hints at some direct, mystical connection between harmony and triple rhythm? If that’s what Lonnie told him, he lied…

[This post belongs to a series about Dylan’s idea of “mathematical music” in Chronicles]

Well, what is it — the musical style that Dylan talks about in Chronicles?
I’ll be writing some more on this on the main site, but here are some less processed ideas about it, in preparation for the longer study. I welcome comments.

He’s been talking about this before. The first time was already in 1966, in the interview with Klas Burling in Sweden:

Well you know my songs are all mathematical songs. You know what that means so I’m not gonna have to go into that specifically here. [yeah, sure] It happens to be a protest song … and it borders on the mathematical, you know, idea of things, and this one specifically happens to deal with a minority of, you know, cripples and orientals, and, uh, you know, and the world in which they live, you realize, you know, you understand, you know. It’s sort of a North Mexican kind of a thing, uh, very protesty. Very very protesty. And, uh, one of the protestiest of all things I ever protested against in my protest years. But uh…

Not necessarily very clear, but he certainly had the idea about mathematical music already back then. It might perfectly well be true, that he learned about this from Lonnie Johnson in 1965.
But what was it that he learned? If one wanted, one could go as deeply into this as one wished. There is a long tradition, going back to the Pythagoreans in pre-ancient times, of a connection between music and numbers. It is my contention, however, that

1. what Dylan talks about in Chronicles has nothing whatsoever to do with the Pythagorean tradition,
2. Dylan’s method is less clear-cut and conistent than what he presents it as,
3. it probably has nothing to do with whatever Johnson may have told him in the 60s,
4. but that doesn’t matter, as long as it has worked for him.

All this stuff about even and odd numbers — well, I don’t think it makes sense. What does seem clear, judging from what he actually says and comparing it with what he does on stage, is that he’s talking about the peculiar guitar style that he has developed during the Never Ending Tour years: the little two-three-note figure solos that he has kept churning out and that at times has driven most of us crazy, but which also — in a strange way and to a surprisingly high degree — work, musically. Outgrowths of this is probably also the sing-song/”up-singing” style of the recent years: it all fits his description fairly well, of a system of infinite permutations of very simple formulas, nothing to do with improvisation or inspiration, but a schematical approach to the basic chords and melodic shapes, which can be applied to just about any song — which is what he does.
That said, I don’t think it is a system that someone else can learn to use — it is hardly insignificant that there are twenty years of touring and music making between the time he first learned it and when he understood how to put it to use. It has taken him those years to gain the musicianship (and perhaps also the need for routine which persistent touring must bring with it) which he then could cross-fertilize with what Lonnie Johnson had told him, to produce his new method. In other words: I think Dylan should receive more of the credit for it than Lonnie.