Notes from Brahms

A few days ago I happened to mention a GKC quote about musical notation, and promised a little more insight, both into GKC on music, and into musical notation. Both are deep, though not too deep to consider, at least in fragments. And while I proceed with today's work, hoping to get to my promised story about addition, I will entertain you with Brahms and GKC:

That all men are equal is a matter of abstract theory; that most men are equal is a matter of common fact. And as it is with altitude of stature, so it is with altitude in any one of the arts. At the one end there are a few who can do it perfectly; at the other end there are (I am told) a few who can only do it horribly or who cannot do it at all. Between the two stretch the interminable lines of that everlasting legion who can do it. There is such a thing as being able to read and write, being able to sow and reap, being able to play golf or read the Greek alphabet. And the difference between those who can do it and those who can't do it is much more absolute and abysmal (to a true philosopher) than any difference in the degree of value or vileness with which it is done. I know, as every man knows, the things I can, in this literal sense, do. I can swim: I cannot ride. I can play chess: I cannot play bridge. I can scull: I cannot punt. I can read Greek lettering: I cannot read Arabic lettering. In this strong, sound, fundamental sense, I can write literature; whereas I could not write music. Or, if you like to put it so, I can't play the piano, but I can play the fool. But the distinction is decisive. I can do it; and therefore I am a trader and not a thief. And I would sooner call myself a journalist than an author; because a journalist is a journeyman. He has a real working human trade; he even has a trade-union.
[GKC, Preface to A Miscellany of Men, emphasis added]

Now, to see some of the fantastically complex detail of real music, here is the first seven measures of the 3rd movement of Brahms' 4th symphony:



This is what a computer scientist might call "parallel programming" (I wonder whether it should be called CRCW or ERCW?) - but I will spare you the details. This is what the conductor uses as he conducts the orchestra. Here, you see sixteen lines of independent instructions (processes, in some systems). Actually, some lines are themselves executing parallel "threads", like the oboes... ah, but you need to know the German terms for the instruments. Here is the list of the required instruments:

Kleine Flöte = piccolo (little flute)
Große Flöte = flute (big flute)
2 Hoboen = two oboes
2 Klarinetten in C = two clarinets in C
2 Fagotte = 2 bassoons
Kontrafagott = contrabass bassoon
4 Hörner = 4 horns: 2 in F, 2 in C
2 Trompeten in C = 2 trumpets in C
Pauken in F-G-C = 3 timpani (kettledrums) tuned to F, G, C
Triangel = triangle
Violine I and II = first and second violins
Bratsche = violas
Violoncell = cellos
Kontrabaß = basses ("double bass")

Now, consider the "2 Hoboen" line, where we see two notes at the very first beat. An oboe can only play one note at a time, but Brahms wants two players, so one plays the top notes in the line, the other plays the bottom note. But if you study the score, you will see that there are other instruments also playing the same notes! Compare the upper notes in that line with the Violine I line, and its lower notes with the Violine II line - in the first measures they are the same - so the oboes are playing in unison with the violins.

There's more - much more excitement here - while these notes are moving downwards in pitch, the notes of the cellos and basses are moving upwards! Wow, high tech. And this is just a symphony, and just the first seven measures... If you really want some tech stuff, check out the counterpoint of a Bach fugue! And the classical artists are not the only ones who do this; even rock music does such things!

Well, I cannot give you an entire lesson in musical notation today, nor even begin to consider what implications this notation has for computing, or for more distant things like a university, or the Papacy - all essays for another day. But you might think a little, and hopefully I will have a story for you soon.