# True art is irrational.

March 8, 2011 10:42 PM Subscribe

This is what pi sounds like. At least, that's one person's interpretation. There are certainly plenty of others, including touchtone pi, hammered dulcimer pi, violin pi, smooth techno pi, crazy awesome pi, vaguely unsettling pi (sounds best with headphones), and lots of piano pi. Pi has even done a duet with its buddy

(pi as music previously on metafilter)

*e*. Nothing here that tickles your fancy? Think you could do better? Why not make your own pi song? Hell, make two! If you're having trouble remembering all those pesky digits, don't worry: there's a song for that, too.(pi as music previously on metafilter)

That first one was beautiful. Pi in rounds, because pie makes you... round?

posted by Taft at 10:50 PM on March 8, 2011

posted by Taft at 10:50 PM on March 8, 2011

How can you have a π song post and not mention the Hard n Phirm Pi song?

posted by kmz at 10:59 PM on March 8, 2011 [1 favorite]

posted by kmz at 10:59 PM on March 8, 2011 [1 favorite]

*This is the product of the slaves of Base-10. True pi sounds like winning.*

posted by Burhanistan at 1:53 AM

posted by Burhanistan at 1:53 AM

The "others" link is actually pi converted to base-12 (so as to match the number of notes in the chromatic scale) and then assigned notes based on that. Whether it sounds more or less like winning is up to you.

posted by Captain Cardanthian! at 11:02 PM on March 8, 2011 [1 favorite]

You are either 5 days or 60 days too early, you enthusiastic chap. But these shall come in handy for our Pi Party.

(We do Pi day at my house on 31/4, being Australian and all.)

posted by Jilder at 11:11 PM on March 8, 2011 [1 favorite]

(We do Pi day at my house on 31/4, being Australian and all.)

posted by Jilder at 11:11 PM on March 8, 2011 [1 favorite]

*The "others" link is actually pi converted to base-12 (so as to match the number of notes in the chromatic scale) and then assigned notes based on that.*

The assigned notes concept is fun, but seem pretty artificial to me. I've been trying to think of something you could do that might more plausibly claim to be what pi "sounds" like.

Maybe the best idea that's occurred to me is to see what tones related by the actual ratio

`π`sound like (much like the other notes of traditional scale are based on certain ratios to one another). So, A4 440hz*

`π`~ 1382hz ... a somewhat flat equal temperament F6, repeat a couple of times to get some other notes, move up and down octaves to get some kind of scale.

But on the other hand... I also wonder if this is all overkill. We're talking about waves/vibrations when we're talking about music. Lots of pi embedded in there already.

posted by weston at 11:37 PM on March 8, 2011

When it comes to songs based on mathematical constants, I'm partial to 1.618.

posted by The Winsome Parker Lewis at 11:42 PM on March 8, 2011 [1 favorite]

posted by The Winsome Parker Lewis at 11:42 PM on March 8, 2011 [1 favorite]

Well, if no one else is going to bring up Kate Bush, dammit, I will.

posted by mykescipark at 12:26 AM on March 9, 2011 [2 favorites]

posted by mykescipark at 12:26 AM on March 9, 2011 [2 favorites]

Not many people know that Field Marshal Bernard Law Montgomery, 1st Viscount Montgomery of Alamein, had a life-long fascination with pi, instilled in him by a particularly charismatic mathematics teachers, Mr Charles Etherington, during his single term at The King's School, Canterbury.

In his autobiography, The Memoirs of Field Marshal Montgomery, Montgomery wrote "There is little of that time of my life that I can recall with anything approaching pleasure, if I recall it at all, although there remains much that I am not proud of today. But Etherington, at least, made the best of a bad lot with me. He opened the door of geometry, and in particular to that marvellous number between two and three which lives in circles and has no end. It was to be the briefest of glimpses before I and he and it were borne apart..."

But the number was to crop up again in consolation and inspiration, during hard times in both world wars. Tantalisingly, there is only one further mention in the memoirs. "During such periods [of waiting for supplies] there weren't many occasions for thought not contingent on the moment. Now and again, though, there were reminders of the Great War. I mentioned to Lewis [the signaller who ran the HF link to the UK] that we had had a game once based on the digits in that geometical number pi, where each had to make up a new stanza of a song with the words starting with the same letters as those of the number and the tune Twinkle, Twinkle, Little Star. I recalled that we managed some seven or eight verses at one point, but try as I might, I could not remember a one of them. Lewis tried to help, but he could but hinder."

For researchers in the field, Monty's pi song is the holy grail.

posted by Devonian at 1:31 AM on March 9, 2011 [2 favorites]

In his autobiography, The Memoirs of Field Marshal Montgomery, Montgomery wrote "There is little of that time of my life that I can recall with anything approaching pleasure, if I recall it at all, although there remains much that I am not proud of today. But Etherington, at least, made the best of a bad lot with me. He opened the door of geometry, and in particular to that marvellous number between two and three which lives in circles and has no end. It was to be the briefest of glimpses before I and he and it were borne apart..."

But the number was to crop up again in consolation and inspiration, during hard times in both world wars. Tantalisingly, there is only one further mention in the memoirs. "During such periods [of waiting for supplies] there weren't many occasions for thought not contingent on the moment. Now and again, though, there were reminders of the Great War. I mentioned to Lewis [the signaller who ran the HF link to the UK] that we had had a game once based on the digits in that geometical number pi, where each had to make up a new stanza of a song with the words starting with the same letters as those of the number and the tune Twinkle, Twinkle, Little Star. I recalled that we managed some seven or eight verses at one point, but try as I might, I could not remember a one of them. Lewis tried to help, but he could but hinder."

For researchers in the field, Monty's pi song is the holy grail.

posted by Devonian at 1:31 AM on March 9, 2011 [2 favorites]

Hey, hey! That second to last link is an old, old project of mine (did it years ago, as an exercise to teach myself how to work with strings in Actionscript). Always tends to get a bit of traffic whenever March 14 gets near...

posted by avoision at 4:14 AM on March 9, 2011

posted by avoision at 4:14 AM on March 9, 2011

6:56, restate my assumptions:

One, mathematics is the language of nature.

Two, everything around us can be represented and understood through numbers.

Three: If you map into notes the numbers of any system, songs emerge. Therefore, there are songs everywhere in nature. Evidence: YouTube.

posted by adipocere at 4:56 AM on March 9, 2011 [2 favorites]

One, mathematics is the language of nature.

Two, everything around us can be represented and understood through numbers.

Three: If you map into notes the numbers of any system, songs emerge. Therefore, there are songs everywhere in nature. Evidence: YouTube.

posted by adipocere at 4:56 AM on March 9, 2011 [2 favorites]

weston: "

I like this line of thinking, but the pi ratio is already larger than three octaves, and the human range of hearing is only about 11 octaves for someone without hearing damage - so you would get exactly 7 audible notes if you start with the lowest audible frequency (or do you mean transposing each of the multiples of pi up and down octaves?).

Actually, I like that idea and I just plotted out all the audible octave transpositions of the multiples of pi starting at 20 hz. It comes out to 71 unique frequencies.

Partch had this music theory where consonance was a consequence of small number ratios between frequencies (there is some pretty solid math behind that) - given that fact, a scale based on irrational numbers should be pretty massively dissonant. And yeah, based on a cursory glance there are a huge number of nasty discordant intervals in there. As a fan of dissonance I think I would like to try this out.

Kim Cascone's .microsound mailing list is working on a compilation of pi derived music to celebrate pi day again this year, by the way. I may just turn this seed of an idea into a submission there.

posted by idiopath at 5:37 AM on March 9, 2011

*So, A4 440hz*π ~ 1382hz ... a somewhat flat equal temperament F6, repeat a couple of times to get some other notes, move up and down octaves to get some kind of scale.*"I like this line of thinking, but the pi ratio is already larger than three octaves, and the human range of hearing is only about 11 octaves for someone without hearing damage - so you would get exactly 7 audible notes if you start with the lowest audible frequency (or do you mean transposing each of the multiples of pi up and down octaves?).

Actually, I like that idea and I just plotted out all the audible octave transpositions of the multiples of pi starting at 20 hz. It comes out to 71 unique frequencies.

Partch had this music theory where consonance was a consequence of small number ratios between frequencies (there is some pretty solid math behind that) - given that fact, a scale based on irrational numbers should be pretty massively dissonant. And yeah, based on a cursory glance there are a huge number of nasty discordant intervals in there. As a fan of dissonance I think I would like to try this out.

Kim Cascone's .microsound mailing list is working on a compilation of pi derived music to celebrate pi day again this year, by the way. I may just turn this seed of an idea into a submission there.

posted by idiopath at 5:37 AM on March 9, 2011

adipocere: "

I think this is much less profound than people make it out to be.

Let's try the visual analog:

"If we map into colored pixels the numbers of any system, images emerge. Therefore there is art everywhere in nature."

Trivially true, but not interesting to (look at/ hear) until you have a good mapping system, an open mind, and/or some good drugs.

posted by idiopath at 5:39 AM on March 9, 2011

*If you map into notes the numbers of any system, songs emerge. Therefore, there are songs everywhere in nature.*"I think this is much less profound than people make it out to be.

Let's try the visual analog:

"If we map into colored pixels the numbers of any system, images emerge. Therefore there is art everywhere in nature."

Trivially true, but not interesting to (look at/ hear) until you have a good mapping system, an open mind, and/or some good drugs.

posted by idiopath at 5:39 AM on March 9, 2011

Oh, absolutely. That's why I was mocking it by deliberately mangling a quote from the film

posted by adipocere at 6:39 AM on March 9, 2011 [1 favorite]

*Pi*.posted by adipocere at 6:39 AM on March 9, 2011 [1 favorite]

> given that fact, a scale based on irrational numbers should be pretty massively dissonant.

In the equal-tempered tuning, the "standard" tuning that's on pretty well every piano, clarinet, xylophone or whatever sold in the US, the ratio between any pair of notes except octaves is, in fact, irrational (because the ratio between a white note and the black note next to it is the twelfth root of two...)

posted by lupus_yonderboy at 8:11 AM on March 9, 2011

In the equal-tempered tuning, the "standard" tuning that's on pretty well every piano, clarinet, xylophone or whatever sold in the US, the ratio between any pair of notes except octaves is, in fact, irrational (because the ratio between a white note and the black note next to it is the twelfth root of two...)

posted by lupus_yonderboy at 8:11 AM on March 9, 2011

*I like this line of thinking, but the pi ratio is already larger than three octaves, and the human range of hearing is only about 11 octaves for someone without hearing damage - so you would get exactly 7 audible notes if you start with the lowest audible frequency (or do you mean transposing each of the multiples of pi up and down octaves?).*

Yeah. Arguably we do this with conventional scale... the harmonic series that gives rise to the ratios we use for our intervals climbs octaves fairly quickly too, but we map it into intervals inside an octave.

Sortof, anyway -- I realize that some focus more on string length ratios than the overtone series, but even there I think you can make it work: if string length L is an octave, find the length ℓ

_{k}for which ℓ

_{k}*

`π`*k = L, for k=1 and whatever else might strike your fancy.

posted by weston at 9:16 AM on March 9, 2011

lupus_yonderboy: "

D'oh - supposedly I actually knew that already :) My composition teacher would shake his head in shame. I could hide behind the word "should" like a weasel, but what I meant would have been better stated "an irrational number that is not a factor of any small whole number". There don't seem to be any small number ratios in the multiples of pi translated up and down octaves (other than the 2:1, 4:1 etc. generated by the very act of transposition). And the 12th root of 2 is good at hitting that "close enough" zone where you aren't so much in extreme dischord as slightly off key. The multiples of pi (or e I would also guess) seem to hit that uncanny valley of extreme dischord between sweet intervals much more reliably.

posted by idiopath at 10:37 AM on March 9, 2011

*the ratio between any pair of notes except octaves is, in fact, irrational*"D'oh - supposedly I actually knew that already :) My composition teacher would shake his head in shame. I could hide behind the word "should" like a weasel, but what I meant would have been better stated "an irrational number that is not a factor of any small whole number". There don't seem to be any small number ratios in the multiples of pi translated up and down octaves (other than the 2:1, 4:1 etc. generated by the very act of transposition). And the 12th root of 2 is good at hitting that "close enough" zone where you aren't so much in extreme dischord as slightly off key. The multiples of pi (or e I would also guess) seem to hit that uncanny valley of extreme dischord between sweet intervals much more reliably.

posted by idiopath at 10:37 AM on March 9, 2011

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posted by foot at 10:46 PM on March 8, 2011