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Isaac Newton, it is said,
Was sitting after lunch
Under an apple tree.

You know what happened next.

An apple, ripe, ready
To be picked, left the branch
Where it had grown, ripened,
Swelled to its juiciest.

Falling on Newton’s head.

That’s why we have gravity.

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A Mathematician

First of all, on the fundamental relationship between mathematics and music: yes, the chromatic scale is based on simple geometric ratios, but beyond this (and a few other things perhaps), I think saying “Music comes from mathematics” or “Music is founded upon mathematics,” or anything similar, are more subtle statements than one might let on. It’s very philosophically grounded in whether one thinks mathematics can exist to be touched upon without having defined it first, or whether one sees mathematics as a lens through which physical and theoretical phenomena can be analyzed. Certainly mathematics has played an important part in serialism, which utilizes set theory and algebra, but can we say it has played a similar role in either the creation or musical essence of a Beethoven piano sonata? Certainly we can analyze the music in a mathematical fashion, but does this make it fundamentally an object of mathematics?

There are two unsupportable (because nothing is so black and white, right?) positions on this topic:

a) you are a quantophiliac, who looks for deterministic mathematical relationships to aesthetics, forgetting that music is art and therefore cannot be fully defined by the sum of any set of empirical observations.

b) you are a quantophobe, for whom mystical inspiration is all and you simply ignore the fact that mathematics is often a useful tool in achieving and describing aesthetic objectives.

Certainly, composers have taken direct inspiration from mathematics. Bartók used golden mean proportions, Ligeti used strange attractors and other fractal phenomena, etc. Music is not mathematics any more than architecture is mathematics, but as Thelonious Monk said, all musicians are subconsciously mathematicians.

I have also wondered if there is not a musical connection to playing chess via a (subconscious?) mathematical ability: e.g. Prokofiev apparently was a very good player.

Certain mathematicians have remarked upon proofs, etc., with the words “elegant” and “beautiful,” with some openly suspicious of any series of equations that shows too much sweat and not enough grace as being on the wrong path.

I have, however, been bored to tears by articles in scholarly musical journals going through “permutations of sets” blah blah fucking blah! For an elite who might claim they can actually hear such things in a work and follow them, fine.

You can interpret anything mathematically (with probably mixed results) but what is the point? You can interpret things however you want, and call it a world view. But that would be ignoring the world, and the various ways that people experience existence, let alone art.

There are composers who probably use a mathematical-like mindset for composition. But there are plenty of composers who probably couldn’t give a flying fuck about such methods (Birtwistle springs to mind, and man have you seen one of his scores?).

I am always humbled when I think that every single note of every single composer who is in our current pantheon was set on paper by himself. Though there are rare recorded exceptions (Bach to his son on his deathbed with Vor deinen Thron tret’ ich hiermit), it is in general impossible to dictate music. It has been estimated that it would take 40 years of 40-hour work weeks just to transcribe Bach, let alone think about the composition while you were going along.

I’ve always found lots of visual satisfaction of looking at certain scores from Lully first editions to Gregorian chant to Berlioz operas to Tom Adès’ Asyla. Regardless of the music, some scores seem a lot more beautiful to me visually. Composers such as Dutilleux and Berg have always been interested in the visual aspect of the music on the page, and Dutilleux even composes sometimes in “shapes” that are visible in the page to an interesting effect musically (or sonically).

At the moment I’ve been lost in a study of Harrison Birtwistle’s Earth Dances which is an absolutely gargantuan work that is as fun to listen to as it is to look at on the page to see his “shifting geological strata” of sound.

One composer who makes particularly striking looking scores (and of course striking sounding as well) is Pierre Boulez. His Pli selon pli, besides being one of the most sublime and wonderful compositions of the last century, is also one of the most gorgeous looking scores I’ve seen.

Of course, in the dim and distant past, music was about much more than just “the sound it makes” (Beecham) – it was about the play of proportion, the interaction of pattern and motive: it was geometry and mathematics laid out on paper, “order” with the potential to be demonstrated in sonic form, the divine geometry of the music of the spheres, etc., etc., and it was studied as a science (i.e. part of the Medieval Quadrivium, with geometry, mathematics and astronomy) rather than a rhetorical art (i.e. part of the Trivium, with grammar, logic and rhetoric). It goes against all our instincts to remember that this was so, but that’s the way it was. In this respect composers who indulge in Augenmusik are not therefore necessarily guilty of a crime against music.

Black Dogs Defined

This is the best of me; for the rest, I ate, and drank, and slept, loved and hated, like another: my life was as the vapour and is not; but this I saw and knew; this, if anything of mine, is worth your memory.

(John Ruskin, Sesame and Lilies)

Whatever people say I am, that’s what I’m not.

(Alan Sillitoe, Saturday Night and Sunday Morning)

This is my letter to the world, that never wrote to me.

(Emily Dickinson, This is my letter to the world)

Safe upon the solid rock the ugly houses stand:
Come and see my shining palace built upon the sand!

(Edna St. Vincent Millay, Second Fig)

R.A.D. Stainforth

I was born before The Beatles’ first LP and brought up in the reeking slums of Jericho. I am in love with a woman called Hazel and in love with her daughter, also called Hazel, both of whom I met at Alcoholics Anonymous.

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