#1

Quick question: With out going terribly in depth about audio theory, how many Hz are between each half step? Like A=440Hz, so A#=x ? or Is it not even a linear scale?

#2

It's not linear. It's quadratic. Or whatever that's called. An octave up is x2 and an octave down is /2 (or x1/2). I'll have to dig out that Trig lesson sometime, so I can remember that formula.

#3

Its an exponential scale.

Formula

f(x) = 440(2)^(x/12)

where f(x) is the frequency of the pitch, and x is the number of semitones above A440.

Formula

f(x) = 440(2)^(x/12)

where f(x) is the frequency of the pitch, and x is the number of semitones above A440.

#4

Sweet, I've been interested in this stuff for a while actually. Does anyone have any more information regarding this stuff?

#5

To what "stuff" are you referring? Is it the math and physics of music?

#6

Ok, thanks very much

#7

Your starting frequency is 440Hz, then just multiply that by the 12th root of 2 which is about 1.059 and that'll give you A#. Then multiply your new frequency (A#) by 1.059 again. Just keep going. That's how the Ancient Greeks did it I believe.

#8

Your starting frequency is 440Hz, then just multiply that by the 12th root of 2 which is about 1.059 and that'll give you A#. Then multiply your new frequency (A#) by 1.059 again. Just keep going. That's how the Ancient Greeks did it I believe.

No way. The Ancient Greeks constructed scales using simple frequency ratios, like the 3:2 perfect fifth (errm, what we'd call a perfect fifth) and its inverse, the 4:3 perfect fourth (errm...).

3:2 is actually quite close to the 12-edo 2^(7:12), and 4:3 is just as close to 2^(5:12), so 12-edo makes a pretty good 3-limit JI approximation (without the nasty commas).

#9

Sweet, I've been interested in this stuff for a while actually. Does anyone have any more information regarding this stuff?

they used to tune to perfect ratios, but doing so made things sound ok in one key and like poop in other keys so as music progress a couple of hundred years ago they figured out you can tune every note equally (a ratio 1:1.05946309 for a semitone, the 12th root of two) and everything sounds equally out of tune and you can play in any key without any ill consequences

http://en.wikipedia.org/wiki/Musical_temperament

#10

No way. The Ancient Greeks constructed scales using simple frequency ratios, like the 3:2 perfect fifth (errm, what we'd call a perfect fifth) and its inverse, the 4:3 perfect fourth (errm...).

3:2 is actually quite close to the 12-edo 2^(7:12), and 4:3 is just as close to 2^(5:12), so 12-edo makes a pretty good 3-limit JI approximation (without the nasty commas).

Oops, musta got confused with 12tet, Greeks and just maths in general lol! Pretty sure about the calc though, on how to arrive at each new frequency. May go back and do a little light reading!

*Last edited by mdc at Aug 17, 2009,*

#11

To what "stuff" are you referring? Is it the math and physics of music?

Yes, that is exactly what I was referring to. I'm quite interested in physics but unfortunately this type of stuff wasn't covered in either grade 11 or 12 physics (there was actually no sound unit in grade 12).

Also, thanks to seljer, I'll definitely check that out!

#12

Oops, musta got confused with 12tet, Greeks and just maths in general lol! Pretty sure about the calc though, on how to arrive at each new frequency. May go back and do a little light reading!

Yes, you had the first bit correct.