Quick mathematical summary of the problem:

An octave is a 2:1 ratio between frequencies, so 880 hz is one octave above 440 hz. A perfect fifth is a 3:2 ratio between frequencies, so 660 hz is a perfect fifth above 440.

In the modern western system of music, twelve perfect fifths is harmonically equal to seven octaves. In other words,

(2/1)7 == (3/2)12

Unfortunately, we know this is mathematically untrue.

Furthermore, three major thirds is harmonically equal to one octave:

(2/1) == (5/4)3

This also is mathematically untrue.

Hilarity ensues.