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Ugh, stop twitching
of a frightening discovery
music Posted 2001-03-10 10:05:12 by Jim Crawford
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 tuning system.

I've been making note calculations by multiplying each successive halftone by 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.

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