<HTML>If I tune my octaves not for partial coincidence, but rather for tone, I almost always end up with an octave between a 4:2 and a 6:3, being a bit closer to the 6:3 than the 4:2. This is easily checked by using a M3 - M10th test, seeking an increase to the M10th, then checking the m3 - M6 test for the !2th to  be a slow beat between 1/2 and 1 bps. The m3 will beat at 1/2 to 1 beat a second faster than the m6. I don't choose my octave spread by beats, but by tone quality on a very firm blow at the ends of the keys. Crazy you say? Concert pianists play for tone and projection (I won't say "banging") and unless you tune this way suprising distortions to the tone and power appear. This, of course, requires an "expanded" temperament octave. I never tune my temperament by octave anyway, it must be done for at least an octave and a half to meet the power requirements of each instrument. Incidentally, this is the only way to also achieve good double and triple, dare I say, "piano - wide", octaves, when played  in a robust concert artist style.                                                                                  Michael Meade, RPT     </HTML>