Here's a geek
ier take on it.
An octave is an exact doubling of pitch
, a.k.a. frequency
. A above middle C
ly defined as 440 Hz1
s above the A string on a guitar
which is 110 Hz
). What that "440 Hz
" means in plain English2
is that the thing producing the sound is making four hundred and forty complete back-and-forth motions per second3
, and pushing the air back and forth at the same rate.
Within an octave
, the frequency
of each note (semitone
, I should say; we're using both black and white keys) is greater than the next lower one by a factor of 1.0594631 (4)
, the 12th root of 2. Why? Because that way, you double your frequency
every twelve semitones
, and the pitch
es you get happen to be at useful ratios from each other. Two pitch
es will sound nice together5
if the ratio
of their frequencies
is relatively simple: An octave
(A + A, 2:1) sounds very pleasant, or "consonant
"; a "perfect fifth
" (A + E, 2:3) sounds nice, and a perfect fourth
(A + D, 3:4) also sounds nice. Weird or "dissonant
" ones like the augmented fourth
(A + D#, 32:45) sound like crap, but they can be useful as flavoring: You wouldn't eat a handful of salt
, but a little bit is a good thing.
The important thing here is that the ratio
between two notes in one octave
(say, A 110 and E ~164.8) will be the same as the ratio
between the same two notes in a different octave
(like A 440 and E ~659.3). And if A 110 sounds good with E ~164.8, you can safely assume that it'll sound good with E ~659.3 because that's the way fraction
I've left out some of the most interesting stuff, like harmonics
, but this is probably enough for one day. Anyhow I'm not gonna try to explain harmonics
without illustrations. Maybe when I hit level 6 I'll put a bitmap
with some waveform
s in my home node. Aren't you excited?!
== cycles per second
There's no such thing.
This assumes that you've got it tuned
perfectly, and in the real world that never quite happens, but it should be reasonably close. If it's a stringed instrument and you tune it much too high, you'll wreck the thing. The crucial thing is to agree with the other strings on the same instrument, and with any other instrument
s you may be playing along with.
This is tempered intonation
. The first volunteer to explain just intonation
vs. tempered intonation
gets a cupcake and my undying admiration
. In brief, tempered intonation
is a pragmatic fudge factor
thing: The ratio
s between notes are all made to come out slightly
wrong, instead of some being perfect and others being lousy.
This page seems moderately informative: http://home.earthlink.net/~kgann/tuning.html
5 von Helmholtz
spent hundreds of pages on the gory details
, but "they sound nice together" will do fine :)
is right about subjectivity and harmony
is full of math, but let us not forget that you can't reduce
it to math. There's a lot of squishy stuff in there too, which I tend do discuss only with words like "whoa" and "cool". I'm just a fuckin' punk with a guitar
; he's a musician
That bit about F# and Gb scares me. With fret
s, it's the same note, so I can avoid thinking about it. And I will, too.