Music – more supernatural than mathematical

One for you music-lovers. Back in 2014 I did a couple of pieces on the musical concept of “swing,” to demonstrate how central human subjectivity is to important things, and in this instance, to the beauty of music. The links are here and here, though unfortunately most of the YouTube links are broken now. Great music is something generated by the human spirit, and is not simply tapping into mathematical concepts of rhythm, harmony and so on (though it builds on those).

I was put in mind of this last week by a couple of YouTube clips about the far-from-metronomic timing of great musicians, as a part of what makes them great. I’m not so much thinking of the rubato playing of, say, romantic pianists stretching and pulling the timing of a piece for emotional effect, but rather what musicians do with the basic beat of a piece, largely unconsciously. In particular, the following two clips contrast their respective players’ sense of “feel” with the mechanically precise rhythm of much modern music, which is produced to a strict electronic click track and, since the advent of computerisation, has any inconsistencies dragged on to the beat by a process called “quantisation.”

A disclaimer up front. If you’ve heard any of my own clips posted here, they were produced to a click track, simply because multi-tracking solo work can’t be easily done any other way. A group of musicians playing live has an indefinable chemistry, which is why all the lockdown videos produced by internet collaboration are no substitute for that endangered species, the live musician. “Keep Music Live” was the motto of the Musicians Union when I was briefly a member, and it is more than simply a sales pitch.

The first clip is about Jimi Hendrix, and uses perhaps my two favourite Hendrix tracks as examples (Little Wing and Bold as Love):

Using the wonders of technology, the YouTuber measures the time of each bar of music to show how, in mathematical terms, Hendrix and the Experience are all over the place. And yet what the human ear, and heart, hears is near-perfection. Worth a watch if you have 12 minutes spare.

The second clip is about Led Zeppelin drummer, John Bonham.

I was never a big Zep fan (I always saw them as Cream without the finesse), but Bonham was undoubtedly one of the great rock drummers. In this case Rick Beato not only once more takes a classic segment of his playing to show how inexact, metronomically, it is, but he goes further and quantises the segment to “correct” the rhythm, as would usually happen in a recording studio in 2020. The surprising result is to drain the life out of the thing: it was the irreducibly human manipulation of the rhythm that made the drumming great, rather than merely competent, in the first place.


Another example of this human greatness in making music somehow transcendant over nature – which I would suggest is something to do with the spiritual aspect of man – is in intonation, the tuning of notes. Back in 2013 I did a piece on the “tempered scale,” that is the way modern musical scales are a compromise to make complex chords and key changes possible, at the price of constant imperfection in the harmony. Older music was produced using “just intonation,” which roughly speaking maximises the harmony of overtones by a closer match to the mathematics of the physical wave-forms. Pythagoras meets physics to make mediaeval and other non-standard music somehow deeply satisfying to the ear.

I had always used this idea to explain the apparently odd intonation of the great blues-gospel guitarist Rev Gary Davis. Here’s an example:

Depressingly often in YouTube comments on his work, modern folks frequently say “great guitar playing – no sense of tuning.” But in fact his tuning is careful, and consistent throughout his long career.

I started experimenting with my own guitar and a tuner, to see what Davis was actually doing. One early finding was that the rather flat low E (which is prominent in the clip because the tune is in E minor) has the effect of making G and C chords sound much better, and in Davis’s playing those keys are the most frequent. I found that tuning my low E a little below what the electronic tuner dictates makes stuff sound “right” compared to using the “correct” tuning.

But to my surprise, when I analysed the actual frequencies of my “improved” tuning, expecting their relationships to come out closer to the mathematics of the “natural harmonies” predicted by the physics, they didn’t. “Correct” tuning didn’t match the physics either, of course, but that was to be expected since guitars use the tempered scale and so are always a bit out of tune. But what sounded “just right” to my ears was no closer to theoretical perfection. And what sounded “just right” to Gary Davis matched physics even less.

And yet the guitar playing of Gary Davis moves my soul more than most other players I’ve heard, and has done so since I first heard him play in 1972.

You may or may not have taken the time to hear the clips I’ve included here, and may or may not have kept up with what was going on if you did. I remember Merv Bitkofer, because musically untrained, being unable to hear the distinctions of some of my examples on “swing” back in 2014. But if you have ever been moved by music – which is a near universal experience – you will have appreciated the phenomena I’m describing at the level it matters. That Hendrix, Bonham or Davis are “great” is public knowledge, even though most of us, and probably they themselves, could not analyse why.

On the original “swing” blog, we had a discussion with an atheist, who equated “public knowledge” with “truth” and “scientific objectivity.” But my point now, as then, is that being subjectively human is a real and more wonderful truth than what we can reduce to scientific objectivity. To take it a step further, I suspect that when we eventually see true spiritual perfection, in the age to come, it will be more asymetrical and “untidy” than the neat patterns of mathematics, and not less. There will be more Gary Davis gravel, and less autotune; more groove and less digital quantization.

Jon Garvey

About Jon Garvey

Training in medicine (which was my career), social psychology and theology. Interests in most things, but especially the science-faith interface. The rest of my time, though, is spent writing, playing and recording music.
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2 Responses to Music – more supernatural than mathematical

  1. Robert Byers says:

    I agree, even surprised you said, that music is about spirit and thought. In fact I think Adam speech was just thought with spirit. No nothing to do with math/straight lines.
    I only see music as tones/sounds which people agree to meaning. Since its universal it must be simply tones with spirit.Not a agreement from when we were one tribe.
    Music is just speech. We are all day long doing usic because our speech is using so many tones around our words which are theselves fixed tones fro the past.
    Singing is just stretching our words in order to get more tones in because the words are packed tones.
    so there is no such thing as usic. its just in a spectrum of tones recognized for eeaning.
    I don’t agree there is any great music people but simply they tapped into some tones in combination people like.A ccident they hang on to.
    In the bible its only said usic is to expree sounds of this thought/spirit. Its just that.
    By the way this is why typing on the internet leads tp problems because tones of voice don’t get through with our sentences.

    • Jon Garvey Jon Garvey says:

      Robert

      I wouldn’t wish to give the impression that music has nothing to do with maths. Its beauty is partly in the order that maths gives, just as it’s partly in the physicality of matching human biological rhythms.

      So basic harmony is related to the mathematical relationships Pythagoras noted, which turn out to correspond to physical frequencies and how they reinforce or clash with each other. Cross rhythms depend, essentially, on arithmetic.

      And biologically swing matches the way our bodies move in dance, the 120BPM of disco music matches heartbeats, etc.

      And you’re right when you raise the language of shared meaning, too. That’s why we have to develop “ears” for any new kind of music we hear.

      But beyond all that, yet encompassing it in a human unity, the spiritual (and indefinable) takes its place. That’s probably true in all the arts, but I’m a musician and not a sculptor!

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