the following article describes "stretch tuning" for piano:

https://www.postpiano.com/support/updates/tech/tuning.htm

here is my opinion (for the record):

a piano which is tuned precisely to equal tempered tuning will sound out-of-tune, due to the human ear's predilection to expect the higher notes to progressively sharpen while the lower notes "should" progressively flatten.

this is most likely due to the same effect that occurs in natural pythagorean tuning.

equal tempered tuning fixes the problem of not being able to play in twelve keys, and then "stretch tuning" fixes the fix (if you get my drift).

when i was tuning pianos as a job, the piano tuners who showed me the tricks of the trade explained it to me in the terms i describe above.

they told me that once you're into the next octave above middle c that you start sharpening at about the rate of a cent per half-octave and then the top notes are tuned by ear (electronic tuners have a heck of a time with those super-high frequencies).

and then you do the same for the bottom end.

using their formulae, i tuned hundreds of pianos and even though my "stretch" max'd out at generally no higher than about twelve cents, those babies sounded good to me.

the link above regarding "inharmonicity" told me something that those old piano tuners never did (maybe they didn't know about it or thought that since i was just a teenager then that the topic would have been over my head - who knows ...)

the point i want to make here is that a stretch of 12 cents is much closer to the variance caused by the pythagorean comma than the 35 cents referenced in the above link.

35 cents is waaaay more than the pythagorean comma.

i always take everything with a grain of salt, and it would be interesting to hear other piano tuners' takes on this subject.
There is one comment, leave a comment.
my two cents:)i took a class just because i like playing a piano in tune and couldn't afford paying someone. tuned around.
aural vs electronic, me electronic. sanderson. found too many pianos that were way overcompensated and inconsistant in the bass and high end, mostly spinets.
most pianos need pitch raise these days for the common man due to funds and sanderson is nice for that. i think double octave tuning suits my taste.
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