Thanks all for these responses. I'm trying in vain to remember the name in a BBC Radio3 programme some while ago about the Italian composer, just before Gesualdo, who devised the most amazing system to mean that all intervals were perfectly in tune, but the instruments, and singers, had to be tuned with several microtonally different versions of each nominal note to achieve it. I've thought before that it almost argues the existence of a god with a sense of humour, to set the maths so that the octave does want to divide, via the 5ths, into 12 semitones which then don't produce an octave. Back to playing the pipes. Best wishes, Richard. --
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