Octave Tuning

[BobDavis88@aol.com]

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Matthew writes:
When I tune the temperament octave (A3-A4), it needs to be a 4:2 octave, 
correct?  
No. Read the many replies which said that it should usually be wider than 
that.
And one way to test this octave is to play the A two octaves above the lower 
note as the test key, to hear the partials in the octave, am I right?
Not exactly, but read Don Rose's comments on ghosting.
  If the octave you are testing has no beat whatsoever, you have a perfect 
temperament octave, is this true?
No. There is no such thing as a beatless octave. An octave which is not 
beating at one level, such as 4:2, will be beating at all other coincident 
partials, such as 2:1, 6:3, 8:4. The higher the beatless coincident is in the chain, 
the wider the octave. A good compromise octave is usually pretty quiet, though, 

Matthew,

If you have kept this trail of posts on octave tuning, please go back and 
re-read it, and the links to which you were referred, including the ones to the 
AccuTuner manual Appendices F and H. People are happy to spend time helping 
you, but you've got to do your homework and read the replies. At the risk of 
repetition, I include, directly below, a copy of my post from last week on this 
subject:
Bob Davis
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Matthew's original question was how to tune a 4:2 octave. Several people, 
myself included, sent the tests, aural and visual. Whether that [meaning 4:2] 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. [It's wider] 

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. 

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