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

The Strange Story of Manius, the Last Roman Soldier in Britannia

Asterix Roman soldier. Click for credits and to enlarge

A silly story I wrote over at The Critical Line, where Richard, a witty lawyer from London, entertains his guests with his vast knowledge and adorable English humour.

Richard though has a problem.

He’s terribly profound in mathematics and so are many of his guests who seem to share the same horrible contagion.

But, it’d be fair to say, I am the one to have a big problem, and, what is this tale but a burst of frustration because of my mathematical ineptitude?

The Tale of Manius

English sheep. Photo by Bernard Durfee (2008). Click for credits and to enlarge

Britannia, 526 CE, in a parallel (and almost identical) universe.

The Western Roman Empire has collapsed. Angles, Saxons and Jutes are invading the Roman province of Britannia from the East. All continental Roman soldiers have gone – but the Romano-Celtic in the West are resisting bravely. Only Manius Papirius Lentulus from Roma has stayed. He lives with the barbarians but risks nothing since he’s considered innocuous by the Angles (or Angli as he says in his language.)

The last Roman soldier has made friends with a few of them: Richard (whom Manius sometimes calls Britannia), Dafna (happened there from a far away land), Cheri, Mr. Crotchety and Phil. In their abstruse language – that Manius understands a bit – they sometimes call him MoR (or, in their weird but cute Latin, Roma.)

A goose has just died for occult reasons MoR isn’t willing to investigate.

A Melodious Sequence, 1,2,3…

Manius felt sorry for the poor goose but also curious about how Cheri might prepare it for lunch.

Approaching Mr. Crotchety he told him he had been so lentus and had forgotten he had something important to tell him.

Dafna was weirdly chanting a melodious sequence of numbers:

“1-2-3-4-5-6-7-8″.

Getting closer in rapture MoR noticed Richard and Phil approaching her as well. Her song seemed the usual diatonic scale kids learn by just pressing the white keys of a keyboard, do-re-mi-fa-sol-la-si-do.

But MoR couldn’t figure out a kinda weirdness in that melody, so a stupid look froze in his face. Richard’s smile became sly instead. Phil was scribbling like crazy on a roll of papyrus.

Britannia finally lost his patience and shoved an elbow into Roma’s ribs.

“Ouch Richard!! Are you crazy??”

Then it finally hit Roma. That devil of a woman!! She was chanting her sequence according to an ancient tuning!

“Yes – said Richard triumphantly – it is the Pythagorean tuning based on a stack of perfect fifths, each tuned in the ratio 3:2. The Babylonian tuning, actually, more than 1 thousand years older than Pythagoras. Starting from D for example, the A is tuned such that the frequency ratio of A and D is 3:2, so if D is tuned to 288 Hz, then the A is tuned to 432 Hz, the E above A is also …..”

Dafna interrupted Richard with an odd smile:

“What he means – she said – is that the Pythagorean love for proportions is evident in this scale’s construction, as all of its tones may be derived from interval frequency ratios based on the first three integers: 1, 2, 3. Isn’t that amazing?”

Surrounded, Outsmarted

Roma felt trapped.

He was surrounded by the Angli and their allies. And they were ALL mathematicians!!

He began to panic. The last Roman soldier in Britannia, outnumbered, outsmarted, began to run wildly uphill and got lost among the sheep never to be seen again.

Sheep in English countryside. Click for credits and to enlarge

The Legend of Roma Continues

A legend says Roma took seven Anglia wives and mixed his blood with the natives.

“Why seven?” asked the Anglia kid to his Anglia grandfather.

The tribe was sitting before a big fire. The summer night was full of stars.

“Because seven is a magic number” replied the Anglia grandfather showily. “The seven hills of Rome, the seven wonders of the world, Jesus saying to Peter to forgive seventy times seven times.”

“But seven – added the Anglia cutie – is also the fourth prime number. It is not only a Mersenne prime (since 23 − 1 = 7) but also a double Mersenne prime since it is itself the exponent for another Mersenne prime, ie 127.”

ψ

The Anglia Grandfather paled.

It’s like he saw all his life fall apart in a second. His mind went back to the time when a Roman soldier had fled wildly uphill and had got lost among the sheep.

Even the Anglia kids!! Even THEM!!

His flight had been useless.

That same feeling of panic, of claustrophobia pervaded him.

He was trapped. Trapped forever.