Stretch: What's it all about?

[D. B. Stang]

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I am kind of a newbie, so if this topic is a dead horse that's already
been beaten a few times, forgive
me.
What I would like to do is briefly describe my understanding of stretch
and ask for comments about
whether I am getting the idea or not.
Randy Potter states the following: "We are simply trying to match our
tuning to the amount of
inharmonicity in the piano". (Randy Potter course book, section 1.6).
"You do not put any stretch in
the piano. The piano told you how much to stretch it. ... using 17ths
and 3: and 4: octave tests, you
would end up with a perfectly stretched piano". (section 1.7)  What he
is saying is, minimize
octave beating, and then a piano is stretched correctly.
Well, recently I bought the Reyburn Cyber Tuner, which has a "Octave
Tuning Style" feature, which
gives the user a range of 9 levels of stretch you can choose from; "1"
being "pure" (beat speed for
the 4:2 octave at A2-A4 = 0), and "9" (beat speed = 0.8/sec.) I was
immediately confused because
this contradicts Potter, who says a piano is tuned "right" when octave
beating is minimized, period.
Meanwhile, I can remember a physics professor explaining that human
hearing is "imperfect"
because when we hear a pure octave, we think it's a little bit narrow,
so pianos are stretched in
order to make octaves sound more correct to the human ear.
No one has ever explained all this to me succinctly. What I have
concluded in my own little
pea-brain is that there are two distinct kinds of stretch: what I will
call "objective" and "subjective".
The objective stretch is that which compensates for a piano's
inharmonicity.
The subjective stretch is the amount beyond the objective part, which
makes it sound good to the
listener. So when people use the word "stretch", they're not always
talking about the same thing;
sometimes they mean the objective part of it, sometimes they mean the
subjective part of it,
sometimes they mean both parts, and sometimes they don't know what
they're talking about.
Right ??
Any guidance on this subject is welcome.





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