Do Music and Numbers Pervade the Universe? A Night of Dionysian Revelry

As you know I have been musing on Pythagoras of Samos recently (Ὁ Πυθαγόρας ὁ Σάμιος). I wrote about him in my blog and in other blogs.

P was a great mathematician. Now it turns almost all bloggers MoR has been discussing with (also on P) have some math capabilities. MoR has instead very little. So he asked his friend Extropian for help.

Extropian is laconic and doesn’t like blogs. So he first sent this movie and just said: “This stuff is Pythagorean.”

He then added: “Here following is the rationale behind the movie.”

He also sent me this paper on Pythagoras & Eugene Wigner that requires a degree in physics to figure out what the hell it means.

Finally he linked to another movie and declared:

“You (more or less) are a pianist but you’ll always be longing for the strings of a guitar, of a violin or of a lute. Pythagoras started a new world-view with the strings of a lyre. You may like this.”

I hope this will not be the music of the future (only because it sounds too robotic). But the 3d animation intuitively shows better than any book on acoustics the relation between the string lengths and the sounds: ie by pressing the strings the robotic fingers change their lengths which produces a change in pitch.

And my friend is right. From the age of 12 I was a decent guitarist then I turned into a pianist at 18, a big mistake, one out of many.

A Crazy Night of Revel

In the spring of 1995 – I’m only apparently digressing – my wife and I came back home from a party. Oh we had had such fun! She though went straight to bed being tired from a hard day at her office. I remained alone in the living room, feeling weird and restless.

There I saw my electronic keyboard, a Korg 01 WFD – now prehistoric – connected to a Mac and two Protei (Proteus 1 and 2.) Before laying my hands on the glowing keys I knew what I needed that night: fat strings sounds more than just piano sounds.

The result was a dozen improvisations that lead to nowhere (l’improvvisazione non porta a nulla, in italiano) and sound now so badly because of analogical worn out tapes and especially when compared to the pro stuff you’ve heard above. They though retain a personal value to me and they ex-press (in the literal meaning of ‘squeeze out’) one of the most authentic musical revelry I ever experienced in my life.

I mean, if Dionysus-Bacchus ever exists I’m pretty sure I met him that night. Another mysterious Dionysian experience is described here. And, Pythagoras and the Dionysian cult are connected, so no digression as I said (in fact Pythagoras was a reformer of Orphism via science. Orpheus was a reformer via music of the religion of Dionysos, the god of wine and unrestrained madness).

3-4 pieces out of 12 I still like a bit. I’m waiting for my digital DAT recorder to be repaired so I can have better sources for my musical ramblings.

Here are 2 from that night in .mp3 format.

Related posts:

Two Piano Improvisations

Examples of Monodic and Polyphonic Music

Manuscript of the Musical Offering. Wikimedia. Public Domain

Ashish, the Geek Wrestler, once asked me for a sort of introduction to Western music. The reason I’m writing this is to save him from metal rock. But the topic is immense and greater than my knowledge, so I guess I can write brief notes on specific aspects, like this one.

One of the characteristics of Western music is polyphony, e.g. music made of melodies that travel independently throughout the composition though harmoniously combined with one another. This whole thing, of combining different melodies together, began in the Middle Ages, possibly by chance, and progressed in the subsequent centuries.

Western music can also be monodic, the opposite of polyphonic, whenever there is either just one melody (monophony) or when a melody prevails over other sounds that serve as mere accompaniment to the main star, the melody itself.

In this nocturne for piano solo by Frédéric Chopin (op. 27 no. 2) we have a cantabile melody, sometimes doubled and with ornaments, accompanied by arpeggios and bass sounds. It is evident here that the melody is the main protagonist, despite the surrounding notes and some voice layering here and there.

Let us first listen to the real thing (we chose Maurizio Pollini for his unromantic interpretation of this romantic work) and we’ll then listen to and view a computer graphical representation of the same work, which favours analysis.

In the computerized version below (by Stephen Malinowski) we notice that the double notes of the melody are not always parallel, which creates like a secondary voice. At the end of the piece there is some slight hint of polyphony. But on the whole this is not a polyphonic piece. Chopin is mainly monodic. Only at the end of his life he inserted some polyphony in his most mature works.

Let us now plunge into the great polyphony of Johann Sebastian Bach (Brandenburg Concerto No.4, iii, Presto.) This music – whose clockwork complexity I hope will not hopelessly bore an unaccustomed ear – is such hard stuff I prefer to propose a computerized version first (also by Stephen Malinowski.)

Different colours and timbers help to mentally separate the different voices. The exercise of following the voices separately is highly educating and can result in great pleasure. No easy thing at first though. I should have chosen a music with less voices (2 or 3 maximum,) but I couldn’t find a Midi music as satisfying as this one, although being able to identify 3 voices (hard already) or  just 2 can be all right at first. The representation is what one usually gets on a Midi sequencer, i.e. a computer software, such as Steinberg Cubase.

Now a version with real players (the performers being unknown to me).

The music of Bach here presented is a fugue (or fugato). In a fugue voices (parts) are not all equal. There is a subject or theme (like a main melody) that is repeated many times at different levels of pitch. It is good exercise as well trying to identify, among the bunch of voices, the subject of a fugue whenever it pops up here and there, which is pretty often.

The study and practice of “the relationship between two or more voices that are independent in contour and rhythm” is called counterpoint. It was highly developed during the Renaissance and was common practice later, during the Baroque period (Wikipedia).
Independent in contour and rhythm. Very important in polyphony. If played or sung separately, voices or melodies still make sense!

One last music by this great German composer: the Brandenburg Concerto No.3 – iii, Allegro, rich with tremendous energy and beauty.