Posted 2001-03-10 10:05:12 by
Working on an update of grapesynth (big
changes, big bugs, doesn't run well on my P133, don't hold your breath),
I've noticed a somewhat disturbing anomaly in the western style twelve-tone
I've been making note calculations by multiplying each successive halftone
pow(2, 1.0/12). The twelfth root of two, in more readable terms. This
has the effect of multiplying the frequency by two every octave.
After seven of these calculations, or a “perfect fifth,” the frequency is
very near to 1.5 of the original.
pow(pow(2, 1.0/12), 7) is about 1.4983.
I know it's not a rounding error, because I've checked against several
frequency tables, and they show the same anomaly.
I've heard that the perfect fifth interval is supposed to be a 3/2
difference in frequency, and it makes sense to me that the fewer cycles
it takes for waves to match up, the better they would complement each
other. Octaves take two cycles of the higher wave and only one of the
lower; a “true” perfect fifth would take three and two; more dissonant
intervals would take many more.
So what I'm saying is: something's very wrong here. I don't know what it
is. Not having a background in conventional music theory, I don't know
who to talk to about this scandal or even what questions to ask, So I've
put this text on my web site for one to two people a month to look at.
Here's hoping one of them is more familiar with this problem than I am.