Pythagorean Tuning is named after Pythagoras (570 BC-495 BC),the Greek mathematician best known for Geometry (The Pythagorean Theorem, anyone?). This particular tuning system tunes pitches by fifths-- an interval that was assumed to be "perfect" sounding: especially during later centuries, such as the Middle Ages. In terms of its harmonic ratio, the perfect fifth is 3:2 (or 3/2). This means that the octave harmonic of 2/1 is divide by 1/3--which , in mathematical terms, means that the reciprocal of 2/1 has to be multiplied by the reciprocal of 1/3:
1/2*3/1= 3/2
What does this have to do with Pythagorean Tuning, you ask? Well, 3/2 can be added or subtracted to other interval ratios (which really means multiplying them together). Using that ratio, you can "log 10" it and multiply by the constant.
But, what if your calculated cent value is WAY too high? That means that the interval ratio is in the wrong octave (It's over 2/1). The way to fix this problem, when adding large ratios, is to multiply them by 1/2-- and repeat the process if the resulting ratio is still too large. To subtract intervals that are in the wrong octave, multiply them by the reciprocal (2/1) and keep going until the end ratio is within octave range.
Of course, Pythagorean Tuning can be rather murky sometimes: especially when thinking in terms of 12 half-steps. Starting at "C," the perfect fifth (3/2) can be multiplied by itself: moving up one fifth after the other. Consequently, the ratios and cents become progressively problematic because they move into the wrong octave and include strange accidental notes. The same can be said of the perfect fourth (4/3), which can be multiplied by itself when moving down in fourths.