Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 6/24/83; site rabbit.UUCP Path: utzoo!watmath!clyde!burl!ulysses!allegra!alice!rabbit!ark 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.