Wikipedia:Reference desk/Archives/Mathematics/2007 March 25

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March 25

Relation between e and music theory

Are there any references on this?

In western music theory, musical notes are tuned to A440. This is the A above middle C, with a frequency of 440Hz. Notes above and below this are calculated with the twelfth root of two. Divide 440 by 2 and you get 220, the frequency of the next lowest A. Keep dividing the number by 2 and you eventually get to 1.71875. This number is close to e-1. You can use (e-1)(12rt2)^n to get a decent estimate of the frequency of musical notes (n=[48,135] for a full keyboard) Is this just a coincidence? --Russoc4 01:41, 25 March 2007 (UTC)

Yes, it's just a coincidence. A = e-1 for that inaudibly low A would correspond to A439.88. The only reason that A440 is used is because 440 is close to 439, which was going to be the standard, but 439 Hz was difficult to reproduce in a laboratory because 439 is a prime number. The only reason A439 was going to be used is because in 1939 the IOS used a different temperature when using the tuning fork that set the French standard pitch established in 1859, which was supposed to be A435. The only reason A435 was used was because that's what the A pitch had gradually inflated to in the years leading up to 1859. The pitch for the A above middle C has basically floated all over the place historically, and it happening to settle on the integer that's closest to 2⁸(e-1) is really totally coincidental.[1] MrRedact 02:44, 25 March 2007 (UTC)

Hmm...interesting. Thanks for the feedback. --Russoc4 04:21, 25 March 2007 (UTC)

Range - Parentheses and Square Brackets

Hello everyone,

I would like to know when to use () and [] when denoting the range of a function, particularly a quadratic function because that is our current unit.

For example, for the quadratic equation y = -(1/2)x^{^2} + 2,

the domain is : (-∞, ∞)

the range is : (-∞, 2]

Why must one use the square bracket after 2 but the parenthesis before and after infinity?

*Note, I have not studied functions and relations yet, so I am using the graphing calculator to make up for that.

See interval (mathematics). A parenthesis means that the endpoint is excluded from the interval; while a square bracket means that endpoint is included in the interval. Infinity is always excluded because is is not a real number. The 2 is included in the "range" of this particular function because the function does attain y=2 (at x=0). For another function this may be different. --Spoon! 21:17, 25 March 2007 (UTC)