Hi :-) Thanks. I'm no expert in rational temperaments, I just am objecting when you say things that don't sound true. Like "jazz is said to approximate the scal

Hi :-) Thanks. I'm no expert in rational temperaments, I just am objecting when you say things that don't sound true. Like "jazz is said to approximate the scales that could be built off the '7-limit' intervals, which explains its more dissonant nature". (that explains nothing) Or "The only way this would have musical significance.." (only ratios of small integers can 'have musical significance'?) "look at the 7th and 5th notes in a harmonic series" - I played trombone for years. :-) The 7th is flat, sounds out of tune. (Yes I was mostly playing jazz) I don't know why you think I'm writing from the point of view of equal temperament as opposed to harmonic series. But it does sound like you're writing from the point of view of a particular rational temperament - maybe because you just read that book. There are many, dozens or hundreds, of different rational tunings/temperaments/intonations, writing today 'from the point of view' of any one of them about music, as if that's what music 'really' is, would be arbitrary, silly.