|
Re: Musical roots may lie in human voice
|
Lowell Prange
|
Aug 19, 2003 16:19 PDT
|
I apologise if my explanation of this is not as simple and elegant as I'd
like.
From the article.
| | This fact, combined with the new finding that preferred musical intervals
are better predicted by the acoustic quirks of the human vocal tract than
by mathematics, leads the scientists to argue that the structure of music
is rooted in our long exposure to the human voice over evolutionary time.
|
I don't think the chromatic scale is as universal through world music as
the author thinks but that would take more research.
I am slowly working through a book on the relationship between music and
mathematics. Mathematics can be limited at times in describing the beauty
of music. Attempts to have computers write music using algorythms are
amusing but fail achieve great art. However, the one thing I figured math
had a better explanation for was the 12 tone scale.
"When any tone is sounded, it produces many faint tones which are known as
overtones. These overtones always always form the same pattern. Here is
the pattern, assuming low E is the sounded tone (the sounded tone is often
called the fundamental in the overtone
series E E B E G# B D E F# G# A# B C# D E"- Ted Green -Jazz
Guitar SIngle Note Soloing Volume 1
(from here it is elementry to get the remaining notes starting the series
again from another note in the series. Like an extension field. The notes
at the end of the series are very high pitched, so we play them in a lower
register but still feel we have a little science on our side.)
This relates to what Pythagorous knew. A vibrating string can be tapped
lightly in the middle causing it to vibrate in two segments, sounding an
octave higher. Dividing it into 3 nodes gets the 3rd noter i the overtone
scale and things get interesting. Dividing it into 4 nodes gets the 4th
note of the overtone scale and 2 octaves above the original, vibrating 4
times as fast) * note an octave is a doubling of freqency and gives many of
the same qualities. that is why E and E an octave higher are both called E
Just having the E and the B, we can derive the entire chromatic
scale. Using the same mutiplier in frequency from E to B, we go from B, B
to F# then to C#, G#, D#, A#, F, C , G , D , A , and E again.
Lets look at this mathematicly.
Imagine we have an E vibrating at 1 HZ (We can't hear one cycle per second
but the numbers are easier to crunch. guitar players tune to an A at 440hz)
the E 1 octave higher would vibrate at 2HZ (the next would be 4HZ the next
would be 8HZ)
then B would vibrate at 3 HZ
9,27,81 would get us F#, C# and G#
Here we see a problem in the mathmatical explanation, We won't get back to
an E of any multiple again, we only get close at the 13th term. That is
why pianos are not tuned in perfect intervals, they are tempered.
The question is how much do we accept this error and still feel justified
in the mathmatical explanation.
I still think the previous article is bunk.
|
|
 |
|
