Getting it right ... was Octave Tuning

[BobDavis88@aol.com]

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Alan Barnard writes:
Tune it so the 10th (F3-A4) beats just noticeably faster than the F3-A3 
third. If I am aural tuning I tune to personally tune with fast beating intervals 
(see Potter, 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 
of your temperament octave, which is usually 4:2 or close to it. 
We're confusing two questions. Matthew's original question was how to tune a 
4:2 octave. Several people, myself included, sent the tests, aural and visual. 
Whether that is appropriate for the temperament octave on a particular 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.

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 that 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 movement in the fifths, 
and on most pianos will be unnecessarily narow. However, on some pianos with 
high inharmonicity, a wide temperament octave added to a clean octave below, 
will produce a double octave that is too noisy. It's a balancing act. 

Bob Davis 

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