[AH] Re: [sdiy] Where to get special white keys?

[Rich Holmes]

On Feb 27, 2009, at 5:54 AM, cheater cheater wrote:

> I know this sounds dumb, but an octave that is 12 notes long doesn't
> make sense either, and that's what we have right now.

Sure it does, if you understand how western music evolved.

One simple way to look at it is to understand that the octave  
(frequency ratio 2/1) and the perfect fifth (3/2) are the two most  
fundamental intervals in western music. So start at a note and start  
going up by fifths; whenever it gets too high, drop down again by  
octaves.  You get (e.g.) F C G D A E B F# C# G# D# A# and then the  
next note is E# -- which if you're using exactly just fifths and  
octaves is about a quarter of a semitone above F. That's inconvenient  
so shave a little off each fifth and after twelve fifths you come  
back exactly to F. There you are: twelve notes, equally tempered.

> Neither does it make sense to use the word semitone if one semitone
> can be as long as one tone, or as long as a half of it, in some random
> order that i could never really understand. ;-)

No, a semitone is always -- in equal temperament -- half the size of  
a whole tone. But a major scale uses five whole tones and two  
semitones... in some non-random order. The reason for that choice is  
grounded in ancient Greek music theory, but notice in the exercise  
above, if you start on F and you stop at seven notes you get a C  
major scale. You don't want to stop at six notes because that gives  
you too big a gap between A and C... whereas if you stop at eight  
notes you get an awkward run of three semitones in a row (E-F-F#-G),  
and in just intonation they aren't even the same size semitone (F to  
F# is different -- a little smaller if I remember right) -- so seven  
notes it is.

It all makes sense for music based on fifths and octaves, and it  
gives you acceptable major and minor thirds and sixths (frequency  
ratios involving 5, e.g. 6/5, 5/4 ...) . Now if you want to make  
music using ratios involving 7, or if you want better thirds than you  
get in 12-note equal temperament, or if you frankly just want to  
sound weird, then you start looking at other schemes, and inventing  
other schemes... and all sorts of (fun) hell breaks loose...