<HTML>Michael G asks: <BLOCKQUOTE TYPE=CITE style="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT= : 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px">If the second harmonic of the lower note of the 8ve = the first harm.of the higher note then the fundamentals are not exactly an 8ve apart??? </BLOCKQUOTE> Hi Michael, An "octave" can be many things ! Tuners, aural or visual, don't tune a 2:1 octave anywhere in the piano. Here= 's why: Because piano wire does not vibrate harmonically, the partials becom= e progressively sharper, and only one set can match at a time. This is diffe= rent from an organ, the partials of which are harmonic. Take for an example an organ pipe vibrating at 100 Hz. It will be producing = harmonics at 200, 300, 400, 500, and so forth. Doubling in this case = an = octave, so 200, 400, 800, etc. are 8ves. Another pipe vibrating at 200 would= produce harmonics at 400, 600, 800, etc., so the two tones played together = would produce coincident partials at 2:1 (the 2nd partial of the lower coinc= ident with the 1st partial of the upper), as you describe. There would also = be coincidences at 4:2, 6:3, 8:4, etc.  The note would be so in tune th= at it would actuallly sound like a brighter version of the lower note. No be= ats. In the piano example, I'll use made-up numbers, overstated for illustration.= For the 100 Hz. fundamental, because of the inharmonicity endemic to ALL pia= no strings, our phony piano might have octave partials at 201, 403, and 810 = (exaggerated). The upper note might be 200, 401, 806. If you raise it one Hz= . to match at 2:1, or 201Hz:201Hz, you will also have 403:402 and 810:807, s= o the upper harmonics will beat. If you raise it more so that it matches at 4:2, it won't match at 2:1, 6:3, = or 8:4. Some of these beats are of course louder than others, so the "beatle= ss" octave that some tuners describe is a actually a "sweet spot" where a we= ighted average of this beating is reduced to a minimum. It is sometimes an a= ppropriate octave choice, usually in the temperament area, is often an octav= e that doesn't match exactly on ANY coincidence; and is wide of 2:1, less wi= de of 4:2, and slightly narrow of coincidence at 6:3. Other parts of the piano require that the single octaves be stretched a litt= le beyond "clean", so that double and triple octaves sound better. While by = themselves, 4:2 or 6:3 or 8:4 octaves might all sound good, a little slow be= ating is intentionally introduced in the octaves, in order to make the wider= intervals closer to clean. A triple octave higher in the piano can not actu= ally be as clean as possible, without introducing objectionable beats in the= singles and doubles. Octave width can also be voicing dependent. Because our ear averages the bea= ting of the various harmonics depending upon their amplitude, tuners will he= ar a "beatless" octave at a different width in a brightly-voiced piano and d= arker one. I hope this is useful. Regards, Bob Davis </HTML>