You're both describing two similar consequences of the same mathematical fact: 2^(7/12) is close to 3/2: * The reason that in their 12-note graph the red line

You're both describing two similar consequences of the same mathematical fact: 2^(7/12) is close to 3/2: * The reason that in their 12-note graph the red line very nearly overlaps with the seventh green line is that (2^(1/12))^7 is very close to 3/2. * The reason that twelve fifths nearly make an octave -- (3/2)^12 is ~2^7 -- is that if you use 2^(7/12) to approximate 3/2 then it's (2^(7/12))^12 which is exactly 2^7. Since you're applying the approximation twelve times instead of once, that also explains why we've gone from being off by 0.11% to 1.4%.