Okay. so i'm being a real nerd right now, and i've learned about some interesting stuff through some research of my own.

I've been trying to find the relationship between actual music notes and the frequencies.

let's start with a chart here

on your guitar neck, the note known as A4 is A on the second fret of the G string (no dirty thoughts..) so, this note vibrates at frequency of 440hz. now. i'll clear this first, since this is a very mathematical vision of the whole thing, converting frequencies to actual time is ms(milliseconds) = 1/f which means 1 divided by 440hz.

So. A440 is basically what this note is referred as. and there is a very simple formula for finding out the pure frequencies of every single note in all octaves.

Now, pure frequencies are really theorical values for sound techs and other music addicts like me. some instruments come real close to these frequencies, while others (like guitar and bass) vary really lightly due to tuning methods, but that's what makes music good. and bad. depending on your ears.

enough fretting. the formula is:

F = CP * 12thRoot(2)^x

F = Frequency of the note.

CP = Concert pitch (based on the universal 440hz)

x = number of semitones you shift from the A440

I'm sorry if i don't know the proper symbol for the 12th root, but here's a picture that'll show it.


Root Ratios


Okay. so here's a really interesting primer on this formula (the source that helped me figure this stuff out), also explains ratios, which is the next part.

Music meets Math

Now, Ratios are basically what makes a note sound good:

let's take C and G, which are a perfect fifth apart (if you don't know about intervals, sorry, look up on the stuff, it's useful), they have a ratio of 3:2

Now, note frequencies (which are basically the notes) are represented in sine waves in term of graphics.

C and G Sine Wave

A 3:2 ratio means that every 3rd C wave (Green Sine) will mostly match up with every 2nd G wave (Red Sine)

now. the goal of mathematically good sounding notes is basically finding a pattern that seems to repeat itself, in a ratio. like 3:2, 5:4.

here's my source for this:

Music Meets Math 2

There's another function for this. which defines the sine wave for every function (this one i came up with myself, if anyone can prove it wrong, tell me, i'll revise it)

Sin((F^-1)/4)

basically, every time the sine wave reaches a peak amplitude of 1 (Amplitude being the dB level of the note, which doesn't matter in the actual pitch) the period is 1/4th way done, and like i told you earlier, frequency converted in time is 1/f, which
is also f^-1..

F= any frequency obtained using the 12th Root formula.

on its own, a wave is basically useless (in my eyes at least) , but when you compare two different notes, you can see the ratio.

So, where does this apply? basically to professional sound mixers, who sometimes apply EQ according to the actual key of the song, setting each EQ Band to a matching note frequency to bring the life in the key out. and overall understanding that music is indeed math.

(here's the converter that started all this madness for me: http://www.petersontuners.com/support/ctf/index.cfm )

Hope this is interesting to at least some of you!

Yep, pretty cool. Should've had this 2 months ago Thanks

I already know all of that, playing with Fruityloops taught me much

(and doing an astrophysics degree for 2 years also helped a bit)

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