I apologize for not following this thread too closely but I just checked it and there seems to be some confusion where the "perfect" in perfect 4ths and 5ths and 8ths came from. Let me try and search my memory banks to my undergrad years in music history. It seems to me in medieval times organum was sung in only those intervals which represented the perfection of the heavens. That is the octave and the 4th or fifth as a division. I suspect, thought I can't remember anything being said, the clear intonation probably had some influence here. The imperfect intervals 3rd and 6th were to be avoid if possible and the 2nd and 7th never used. It has been nearly 20 years so feel free to correct me if I am wrong, but I seem to remember this perfect thing predating modern music and notation by centuries. Andrew Remillard going to bed now, hopefully the insomnia is done.
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