Re: A theory question (or why do some notes sound right?)


"Gary Rosen" <garymrosen@xxxxxxxxxxx> wrote in message
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"RichL" <rpleavitt@xxxxxxxxx> wrote in message
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Gary Rosen <garymrosen@xxxxxxxxxxx> wrote:
"Brian Running" <brunning@xxxxxxx> wrote in message
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Derek Tearne wrote:

Music theory can be used to work out what will sound right or wrong
in any given situation and explain why.

I agree with everything you've said, Derek, except this. Music
theory doesn't explain why something sounds good to us. That's
entirely within our minds. There's no scientific explanation, much
less a music-theory explanation, of why two or three notes with a
certain mathematical ratio of frequencies sound the way they do.
And, there's no right or wrong -- otherwise, there would be one
perfect song, and all the others would be wrong somehow. Thank god
that's not the case!

While it is obvious that music theory isn't exactly "cut and dried"
like the theory of gravity, there is considerable mathematical
justification for the diatonic scale which forms the basis of most
Western music (and I don't mean as in "Country and Western", podner).


There is "mathematical justification" for just intonation, in which the
frequencies of notes in a scale are related by ratios of integers. And
the western just scale is only one of many that can be constructed in
such a fashion.

Unfortunately for this argument, we don't use just intonation for the
most part any more because it's not invariant with respect to changes in
key, whereas the equal-tempered scales are. And the western
equal-tempered scale is in a sense totally arbitrary with successive
notes having a ratio of 2 raised to the 1/12 power.

In a "just" diatonic scale, the notes are in the following ratios:

C D E F G A B C
1 9/8 5/4 4/3 3/2 5/3 15/8 2

(This may not come out aligned in proportional font)

The "errors" introduced by equal temperatment in cents are:

0 +4 -14 -2 +2 -16 -12 0

(a cent is one-hundredth of a semitone)

The fourth and fifth (F and G in the C scale) are pretty damn close. The
third (E) is a little more problematic. Bb (16/9) is -4, Eb (6/5) is +16.
Not too bad a compromise to buy the ability to change keys within a
song that has opened up so many possibilities for music.

- Gary Rosen

The errors I calculated above are correct in magnitude, but have
the wrong sign, e. g. tempered E is 14 cents sharp to just E, not
14 cents flat as my list implies. If anyone other than Rich is reading
this any more :^).

- Gary Rosen


.

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