"Just the question of the stretch that has always been a bone of contention amongst my peers. It has always been a 'matter of opinion', which is not quite perfect tuning IMO. Best regards, David" Ok, Let's take a little deeper look into this topic. The common misconception seems to be that by using one of the tests to set a particular octave match (2:1, 4:2, 6:3 etc) we can set the "perfect octave". We focus our attention and our ears to rule out any other information except one partial from the lower note and one partial from the upper note. I did a little experiment on two pianos, a Baldwin studio upright(243) and a Steinway D. I set 2:1, 4:2 and then 6:3 octaves between A4 and A3, then measured the fundamental of A3. The number represents in cents how far the octave was stretched. Then I set the octave justby ear as a unison would be tuned to determine the "sweet spot", or ideal placement. Baldwin 2:1 -.6 4:2 -2.9 6:3 -6.7 "ideal" -1.3 Steinway 2:1 -.2 4:2 -1.3 6:3 -3.1 "ideal" -2.0 You can see that the "ideal" octave is some sort of combination of the "pure" single-partial octave types. Lesser pianos may have a wider range between the octave types, as well as a difference between which partial matches is the location of the "ideal octave". Likewise, throughout the scale the partial choices change. I find that some pianos really like a 6:3 match for a section of the bass, or a 4:1 double octave match for certain portions of the treble... Most of my tunings end up using a mix of multiple partial matches to control the stretch. Ron Koval Chicagoland
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