Maths Meets Music

Mum *sings a note* I’m guessing either a C or a D.
*goes to piano* Oh, it’s a C sharp.
Dad Well, it’s the average of your guesses.
Me Only if it’s a linear relationship.
Dad Of course it is. The C above a middle C has twice the frequency.
Me Then it wouldn’t be linear. It would increase by powers of two.
Dad
Me *consults Wikipedia* Yep, powers of two. Twelve semitones, so to get the frequency of the next semitone, multiply by the twelfth root of two. Middle C is roughly 262 hertz; Tenor C is 523 or so and Soprano C is 1047.
Dad *does the maths* And the fifth, the seventh semitone, is roughly halfway. Maybe that’s why it’s the perfect cadence.
Me *gets calculator* *nearly blasphemes*   2(12√2)7 ≡ 2(2) ∕ (12√2)5!!!! Modelling 2 as n hertz. And the best thing is that the answer is 2.996614154…which rounds to 3, which is halfway between 2 and 4. Aaaaghhh *the romance of logic overwhelms*
Dad So our brains aren’t adding a fixed value between each semitone. They’re actually making a complex geometric calculation.
Me What do you think, Mum?
Mum I stopped listening when you mentioned averages.
Me Yet you’re the only one of us who can sing in tune.
Dad and I *return to calculations* *major excitement*musicalnotes
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One thought on “Maths Meets Music

  1. Pingback: music physics: notes | Cormul

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