Cold irons bound: Dylan’s mathematical songs

In this review of Dylan’s music, song by song, I am finally going to tackle Dylan’s comments about the “mathematical thing”.

Dylan has mentioned the mathematics of music as something he learned from Lonnie Johnson in 1965.  I may have missed it but I can’t find what song Dylan is referring to, but if you want to get an idea, try Another Night to Cry.

And meanwhile I’ll try and explain what I think this is all about.

The link between music, maths and physics is a fundamental of the way music is produced, and the way in the west we like to hear music.  It is a combination of science and preference.

Dylan, when speaking of maths and music, seems mostly to be talking about rhythm in music, and is not interested in the physics (which relates to pitch – that is how high or low the note sounds).

So, to focus on this issue, to make most music work you need a pulse, a regular beat.  You can create this by clapping your hands together with the same amount of time between each clap.

But that is boring in the end, so to make it interesting you might clap at twice the speed, or three times the speed, or four times the speed.  Or you might clap the first of every two notes slightly louder, as in

One two one two one two

Or maybe the first of every three

One two three one two three one two three

Or the first of every four, first of every five, or whatever you want.  If you have never done this, try it and see.  You are now making music.

In Western music we tend to count our music in four much of the time simply because we can halve that (count in two) and quarter it (emphasise each and every beat) without getting into half beats.  If we started in threes and tried to halve the beats we are emphasising every one and a half beats.

So music is mathematical – do you choose to work in twos, threes, fours or anything else.  Listen to Like a Rolling Stone and you hear the beats

ONCE upon a time you dressed so fine THREW the bums a dime in their prime DIDN’T you.

The words in CAPITALs are the start of each bar of four beats, the words in bold are the beats of each bar – four beats to a bar.

Four beats to a bar is the mathematical norm, but there is nothing wrong with counting in threes, or anything else, or indeed in messing with the number system and having extra beats here and there.

You can also have someone playing in fours, and then someone else putting three beats within each one of the fours – and this is what Lonnie Johnson does.  He plays groups of three among the four beats in a bar.  It’s good music, but not revolutionary.

From here you can make melodic lines out of the fours or the threes, and that has been done too.

And you can play with the chords.  A chord is three or more notes played at once, and certain chords are very, very common in pop music, others quite rare.  So you can take the chord of three notes (for example C, E and G to make the chord of C major) and change it to C, E flat and G.  That simple change makes all the difference.  If you can get to a piano and get someone to show you and play you those chords, you’ll hear at once that one tiny change makes a huge impact on what we hear.

Dylan also cites Link Wray’s Rumble which has multiple uses of three notes per beat in a song with four beats in a bar.  In classical music it is called “triplets”.

Dylan said on one occasion, “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.”

Dylan also said, “I don’t know why the number three is more metaphysically powerful than the number two, but it is.”  I’m not sure about the metaphysics, but the simple fact is different numbers do different things.  Three is a prime number, you can’t divide it up more.

I’m not sure Dylan is really serious about taking any of this further other than with playing with rhythms in his songs.  But he knows his Bible – or at least bits of it, and he’ll probably know The Wisdom of Solomon 11:21 “You have ordered all things in number, measure, and weight” which when (as a music student I was obliged to do) I took a look at medieval writing on music.   They got quite hung up on this notion.

The idea is profound – if you understand how numbers work, and how they influence whether music sounds harmonic (ie good) or discordant (bad) we can know how to affect the spirit and take a peek at the Almighty.   From this comes the notion of some numbers being good and some being evil.

And, rather worryingly, I think Dylan got himself a bit hooked on the mumbo-jumbo that comes out of this.

Chronicles for example is really, well, odd.

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.


But I think something else was going on when Bob Dylan mentioned his mathematical notion.  My guess, listening to lots of Dylan and trying to analyse it, I think that in the early days the melodies and the chord sequences just came to him.  He was bursting with creativity, discovering new music all the time, and just writing.  It just came pouring out of him.

However he then hit the various periods of writer’s block that virtually everyone who is involved in the creative arts gets.  And slowly he moved over to thinking about chords, melodies and the like, and looking at the way they were formed.  Instead of just letting the music emerge, he sat at the piano and started looking at what happened when one used this note and that, together or apart.  What happened when patterns repeated, or moved together and apart.

Composing in short became more structured, more experimental, more thought about.  And there’s nothing wrong with that.  It is a way of finding new patterns – exactly what every other artist ever has done.  Sit at the piano and play three notes over and over, and a song starts to emerge.  Take a set of words from a movie or a book you’ve read, and a song begins to emerge.  Take the notion of playing three notes inside each beat in a piece with four beats in a bar, and a song begins to emerge.

Above all it stops you getting stuck in the same system.

Cold Iron Bound starts with sounds, with a bass riff, with a long-short rhythm (in music we call it a dotted rhythm) as the vocal line is more regular.  The drums against this are playing

1 2 3 1 2 3 1 2

in each bar – ie eight beats in a bar of four beats but broken up into a mix of two groups of three and a group of two at the end.  So drums and bass are playing different rhythms, and the melody is working in more straightforward four beats in a bar.

It is the mathematical system.

The chords are unusual for Dylan too.  The song is in B flat, with the band playing the chord of B flat major and Dylan often using the notes of B flat minor in the vocal.  The chorus line changes, and for once I am flummoxed.  Maybe my ears are decline (well, yes I know they are) and maybe I am just getting old, but those last three chords I can only express as D flat major, E flat ?????, B flat major.

I turned to – usually helpful in such matters, but there the song is transposed to another key, and quite honestly I can’t make their version of the chorus chords work at all when I play the piano along with the piece. Eyolf Østrem on the site admits though his chords are “only a faint approximation to the wealth of notes sounding at this point (and never twice the same, it seems)”.

Maybe it is that mathematical thing!

Index to all the songs on this site


  1. I think this is my favorite Dylan blog, I have been reading your blog for some time now, but never commented. Dylan’s “mathematical music” section of Chronicles has long intrigued me, and I have asked many friends for their ideas and opinions about just what in the world he is talking about – I have no idea, nor do any of those I have questioned! And that you have chosen to approach that subject with this song, which is one of my favorite songs, and is an intriguing song *musically* is perfect. I have always described this song as “tightly controlled chaos” – the music is just about to spin out of control but never does, something is pulling it back in. It is one of Dylan’s most unfathomable songs to me musically. I have absolutely no idea what he is doing musically and I love it. So I listen again and again and again…

  2. And a bit of John Keats as well:

    Where but to think is to be full of sorrow/
    …Where beauty cannot keep her lustrous eyes”
    (Ode To A Nightingale)

    “It’s such a sad thing to see beauty decay”
    (Cold Irons Bound)

  3. Lyric wise, the sentiments expressed draw from Keats’ well of poetry:

    “Well, I’m all used up and the fields have turned brown/
    …..It’s such a sad thing to see beauty decay/
    ……Well the road is rocky and the hillside’s mud/
    Up over my head nothing but clouds of blood”
    (Cold Irons Bound)

    Now Keats:

    “And sure in language strange she said/
    I love thee true/
    …..And I awoke on the cold hillside/
    …..Though the sedge is withered from the lake/
    And no birds sing”
    (La Belle Dame Sans Merci)

  4. “Were but to think is to be full of sorrow/
    And leaden eyed despairs/
    Where beauty cannot keep her lustrous eyes”
    (OdeTo A Nighingale)

  5. I found this blog ( and another on the same subject ) quite helpful in understanding what Bob was talking about . But something you didn’t mention was that Bob was also talking about applying this method to songs he’d already written, which he had grown tired of performing. He seems to be referring MAINLY to performance as I read it.

  6. Dylans reference to “mathematical music” goes well beyond just patterns of rhythm, timing, meter, pitch, etc. It’s also in the lyrics, in the words. He maps words, phrases, lyrics to create patterns and sets of pattern much the way the mathematician maps numbers, objects, and sets of objects to create different geometries and relations revealing abstract patterns that would otherwise lie hidden in plain view. Long before I ever heard any reference to “mathematical music” when listening to his music I would often say to myself, “this guy uses words the way mathematicians use symbols, numbers, objects and sets of such objects. And in a remarkable way.

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