Friday, May 29, 2009

Is Irrational Music Even Possible?

Nick's last post making fun of people who can't do math got me thinking:

There are whole notes, quarter notes, 64th notes, triplets, etc... Notice these are are divisions of beats using rational numbers.

Is it even possible to have legitimate music composed of notes that represent an irrational division of beats? For example could a song ever be written using "pi notes" or "e notes"? Instead of 3/4 or 6/8 time, is it even possible to have 1/sqrt(2) time? Must divisions in music *always* be rational numbers?

Does anyone know enough music theory to know if this is an established fact, or are we humans just not smart/creative enough to do music outside of rational numbers? Are our brains wired so that irrational beats just wouldn't sound good?

Anyways, it looks like musicians are really confined in this regard. I mean the full measure of the musical patterns looks like zero compared to what could be accomplished if irrational patterns were allowed.

Oooh, here comes some cookies, I've got to go!


  1. I think the quantum nature of music displays some underlying metaphysical truth regarding our existence. Because a "quantum" representation of music is what we tend to produce I think that shows something about how the universe works.

  2. That is the universe is not irrational ;-)

  3. Well, to input a little semi-serious music theory into a non-serious post: Sure, I guess you could have an irrationally divisioned note, but that would really take infinite precision in the duration of the sound. This is the part that's not possible. A "1/pi"th note would sound very much (probably for most people indistinguishably) like a triplet note. Also, if you invoke quantum mechanics, having a quantum of sound duration (think phonons) would imply some sort of inherent rationalization in music, even if you could get down to a "1/1.509E33"th notes.

    Similarly, I guess you could have 1/sqrt(2) time, but it would be useless. The time signature is to tell you how many beats there are in a measure -- in a practical sense, how many times is the conductor going to swing his hand in between the down beats -- and how long each beat is. If the conductor swings his hand sqrt(10) times in between each down beat, he would only be in sync with the down beat at the start of the song, thus rendering the conductor useless for the rest of the song.

    However, I guess, if you had a song written with 4-sqrt(2) time, and used 1/sqrt(2)th notes, you would get four of those per measure, so that might actually work out. However, I would probably just re-normalize everything and call those quarter notes, thus messing up your entire system, bwahhahahahah!!!

  4. HI BRAVO....... you're not alone....

    I come to 1.5091905E+33 too !!!! WELCOME

    based on natural frequencies (and EXP LN(2)/12
    Octave 96 (human, or 101 (natural count from 1 Hz)

    re 1.45704E+33
    entredeux 1.51E+33 Hz > Amplitude 0.00000001 ?????????

    the confins of universality possible =?=?

    I find it between
    ré dieze 1.54368E+33
    less than proton, .... so I seems like tachyons or quarcks or phonons, or the ultimate boson ?

    call me through e-mail to discuss calculation .... if interest in quantics mecanics...


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