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From: ark@rabbit.UUCP (Andrew Koenig)
Newsgroups: net.music
Subject: Re: Tempered scales
Message-ID: <2574@rabbit.UUCP>
Date: Wed, 7-Mar-84 14:10:40 EST
Article-I.D.: rabbit.2574
Posted: Wed Mar  7 14:10:40 1984
Date-Received: Thu, 8-Mar-84 08:23:37 EST
References: <6082@decwrl.UUCP>
Organization: AT&T Bell Laboratories, Murray Hill
Lines: 12

Pianos are generally tuned with "stretched octaves."  In other words,
the high notes on the keyboard are slightly higher than one would
expect and the low notes are slightly lower.

Perhaps one reason for this is that the upper partials of an individual
piano string are also stretched:  the second harmonic (say) is very
slightly more than twice the frequency of the fundamental.  It would
therefore make sense to tune the upper notes to match the actual harmonics
of the lower notes.

The out-of-tune harmonics are one of the things that makes a piano sound
like a piano.