In another thread, Ian Russell spoke of, and linked to, Colin Pykett's discussion of widening and narrowing the octave. http://www.pykett.org.uk/impureoctaves.htm#Summary
We've often discussed temperaments that widen the octave to achieve equal beating octaves and M5's here. And the well temperaments create M3's that are closer to just in some keys than M3's in ET. Meantone, of course, places more emphasis on M3's being closer to just, too.
But has anyone tried working with narrowing the octave to create less wide M3's for an ET or quasi-ET, per Pykett? (The UT's and meantone assume at least a pure octave and often, in practice, a stretch to a 2:1 or wider octave, yes?) Is it possible to narrow the octave and slowly stretch in expanding past the temperament? Would the M5's just beat too much against the octave? (Not sure what intervals, if any, could be made to be beat equally.) And, clearly, the 2nd partial of the lower octave note will beat against the fundamental of the higher note, so inharmonicity would be an immediate problem. Jeff--an insurmountable problem?
(Bill--My first thought was that such a temperament would that take us in the direction of a temperament ordinaire--a meantone that tried for better M5's. But even a temperament ordinaire starts with the assumption of a "perfect" octave.)