> The "problem" with just intonation, if indeed it is a problem, is that if you define two series of notes (call them a scale, if you like) using these integer

> The "problem" with just intonation, if indeed it is a problem, is that if you define two series of notes (call them a scale, if you like) using these integer ratios but starting from two different notes, you will trivially find cases where "the next higher E" is a different frequency. So starting from (say) A and moving by integer ratios gets you to a different (say) F than if you start from (say) B. A nice example is this: On an 7 octave (85 key) piano, if you start on the lowest note and go up in perfect fifths, after going up 12 fifths you will be on the highest note, i.e. up 7 octaves. In just intonation you multiply the frequency by 3/2 to go up a fifth, and you multiply the frequency by 2 to go up an octave. But clearly (3/2)^12 is not equal to 2^7 (129.7ish versus 128).