Re: [tuning] Octave stretch web page

The cited web address
http://www.mmk.ei.tum.de/persons/ter/top/octstretch.html
doesn't work for me. Is this address correct?

Some comments on the discussion:

With simultaneous periodic tones it is easy to adjust them very
accurately to a 2:1 frequency ratio just "by ear" When the frequencies differ ever so slightly from that ratio, beats are heard. Accurate tuning to 2:1 thus is merely a matter of making the beats as slow as possible ....

But piano tuners I've met don't do it that way. Instead, they use a third reference tone to which both test tones beat at rates in a range more easily perceived and measured, and one of the test test tones is adjusted to cause those beat rates to become equal. Not only can this be more accurate than listening for slow rolls, but easier, since one also immediately knows which test tone is sharper/flatter.

[JP] Wasn't it Alexander Ellis who said that the only POSSIBLE way to tune a piano accurately was by the "beating" method... not by any other kind of "auditory" experience??

Because of piano string inharmonicity, the very concept of "accurate" piano tuning is debatable. Piano tuning is a fine art of compromise, even without consideration of octave stretching. Fortunately, there are beat-counting tuning strategies (series of beat tests) that lead to reasonable compromises, if special care is taken across the 'breaks' on the piano harp) and these strategies incorporate various amounts of octave stretching as well.

[JP] I can see why piano tuners used the "beating" method for so many years...

The good ones still do.

[PE] But tuning a melodic octave by ear, you can still do so with enough
accuracy to notice that it's not a 2:1 ratio.

True, especially in the high and low ranges as noted, but unfortunately, the 'best' ratio will be different for different listeners. I've heard tuners reveling in stories about the ridiculous amounts of octave stretching demanded by this or that concert pianist.

John Thaden wrote,

>The cited web address
>http://www.mmk.ei.tum.de/persons/ter/top/octstretch.html
>doesn't work for me. Is this address correct?

Yup. Something seems to be down at the mmk.ei.tum.de site right now . . .
please try again later.

Thanks for your other comments -- they were helpful.