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From: briang@bari.Sun.COM (Brian Gordon)
Newsgroups: comp.music,ba.music,sun.music
Subject: Tuning (e.g. pianos)
Message-ID: <129476@sun.Eng.Sun.COM>
Date: 20 Dec 89 18:46:51 GMT
Sender: news@sun.Eng.Sun.COM
Lines: 50

A couple of weeks ago, there was a comment about the difference in "feel"
between something played in, say, the key of C (on a piano) and the same
thing transposed, say, to C#.  I responded with a comment that this was the
wonderful world of the equal tempered scale, or "deliberate mistuning".

I got a couple of pieces of e-mail asking for more details.  After all, if the
piano is "equally out of tune in all keys", the intervals should be equally
good/bad in all keys, and could not enter into perceived differences.

"No sweat", thinks I, "I'll look that up and post a nice scholarly
explanation."  Well, I haven't found it, and have come up with a couple of
experiments that might help.

Observation: A simple tune, which sounds comfortable on a well tuned piano when
played in the key of C, will sound "brighter" when played on the same piano
when transposed and played in the key of C#.

That could be because there are relative differences (the intervals of a
piano's C# scale are different from those of a C scale), or absolute
differences (we react differencly to the higher frequencies than to the lower
ones).

Experiment: Given recording equipment that can be sped up/slowed down on
playback, record the C# version.  Then, on playback, slow it down enough to
be heard as the C version.  Does it "sound like" the C version, or does it
still sound "brighter", just lower?  Anyone with the gear have the interest?
Or, even better, is this a well known experiment with well know results that
can be read?

Notice that piano tuners already cheat by, for example, "stretching the
octaves".  The further you get from middle C, the greater a ratio it takes to
make an octave "sound right" -- the theoretical 2/1 doesn't work.  A high
octave which is perfectly tuned by freguency (e.g. makes an electronic tuner
happy) sounds flat until the upper note is tweaked up a bit.

I seem to recall stories that, in its heyday, Toscanini's NBC Symphony would
always record things slightly too fast and pitcedh up 1/2, so that, when slowed
down to get into the right key (and speed), they would still be "extra bright".
If that is true (and it worked) that would support version #1 above.

If version #1 is correct, the question then is, how do the differences get
there?  Is it designed into the tempered scale, or is it a distortion, like
stretched octaves, introduced by technicians.  If the latter, how and where?

Any piano tuners and/or theoreticians want to hazzard a guess?

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| Brian G. Gordon	briang@Corp.Sun.COM (if you trust exotic mailers)     |
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