<HTML><HEAD> <META charset=US-ASCII http-equiv=Content-Type content="text/html; cha= rset=US-ASCII"> <META content="MSHTML 6.00.2800.1106" name=GENERATOR></HEAD> <BODY style="FONT-SIZE: 10pt; FONT-FAMILY: Arial; BACKGROUND-COLOR: #fffff= f"> <DIV> <DIV>Alan Barnard writes:</DIV> <BLOCKQUOTE style="PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: blue = 2px solid"><SPAN class=781230321-22092004><FONT face=Arial>Tune it so th= e 10th (F3-A4) beats just noticeably faster than the F3-A3 third. If I am au= ral tuning I tune to personally tune with fast beating intervals (see P= otter, Coleman, etc.) BUT it is very handy to be able to tune and recognize = good 5ths and 4ths in your temperament to use as checks--including a check o= f your temperament octave, which is usually 4:2 or close to it. </FONT></SPA= N></BLOCKQUOTE></DIV> <DIV>We're confusing two questions. Matthew's original question was how to t= une a 4:2 octave. Several people, myself included, sent the tests, aural and= visual. Whether that is appropriate for the temperament octave on a particu= lar piano is a second question. Tuning so that "the 10th is just noticeably = faster than the third" might produce a good width of octave, but it is NOT a= 4:2.</DIV> <DIV> </DIV> <DIV>A clean 4:2 octave IS wide at 2:1, and narrow at 6:3. Most aural tuners= naturally gravitate towards a temperament octave that is very slightly wide= of 4:2 ("the 10th is just noticeably faster than the third"), which will be= substantially wide of 2:1 and a tiny narrow of 6:3. This gives an octave th= at is pretty clean-sounding, and produces fifths which are pretty clean and = fourths that aren't too trashy. Any octave size can be divided into 12 equal= half steps. A true 4:2 octave will produce cleaner fourths and more mo= vement in the fifths, and on most pianos will be unnecessarily narow. Howeve= r, on some pianos with high inharmonicity, a wide temperament octave ad= ded to a clean octave below, will produce a double octave that is too n= oisy. It's a balancing act. </DIV> <DIV> </DIV> <DIV>Bob Davis </DIV></BODY></HTML>