An anomaly in the traditional western twelve-tone musical scale

I've been making note calculations by multiplying each successive note by pow(2, 1.0/12), a.k.a. the twelfth root of two. This has the desired effect of multiplying the frequency by two every twelve half-tones, a.k.a. every octave.

After seven of these calculations, a.k.a. a perfect fifth, the calculated frequency is very, very close 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 with an unlimited-precision calculator to my satisfaction. I know it's not an error in my algorithm, because my calculated data matches that of several published frequency tables, which show the same anomaly.

I've heard that the perfect fifth interval is supposed to be a difference of exactly 1.5, and it makes sense to me that the fewer cycles two waves require to match up, the better they would complement each other. Octaves would take two cycles of the higher pitched wave and one of the lower; a "true" perfect fifth would take three and two; more dissonant intervals would take many more.

What I'm saying is that something is 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'm putting it here in hopes that someone more knowledgable will be able to enlighten me.

This little problem that you have put your finger on has bedeviled musical traditions for some millenia.
Read all about it in why it's fundamentally impossible to tune a piano perfectly and equal temperament.

Also notice that it is somewhat dangerous to call the temperament you were using traditional western, since from the Middle Ages to now we have gone through at least three temperaments, namely just intonation that was substituted around 1500 by the meantone temperament, now largely superseded by the equal temperament.