I understand what you are saying Duaine... but the point is that if you listen closely enough, you actually DO hear beats and wave-y-nes no matter what you do. Its just that at some few sweet spots you get an illusion that there is a pure octave. The dominant coincidents for any given octave can be brought into line well enough for this to happen in much of the middle part of the piano to the degree one has to listen fairly closely to notice the beating in the whole coincidents partials ladder. But in the extreme ranges... not so extreme actually as one moves down into the bass region... the mesh of beating coincidents along with those that are either beatless or very close to being is very noticeable. The <<pure octave>> is only an illusion. All the comments about coincidents I've read in this thread so far are pretty much right on target. I think perhaps we are getting hung up a bit in semantics ? Cheers RicB To me, a pure octave is when you play C4 and C5 together, and hear no beats or wave-y-ness. Just like tuning unisons of a tri-string and they are in tune when you hear no beats or waves, except they are an octave apart. If C4 is in tune and you hear beats, that means C5 is sharp or flat.
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