Newsgroups: comp.speech
Path: pavo.csi.cam.ac.uk!warwick!pipex!uunet!haven.umd.edu!purdue!news.cs.indiana.edu!lynx!nmsu.edu!opus!ted
From: ted@nmsu.edu (Ted Dunning)
Subject: Re: Fundamental Frequencies of the Musical Notes
In-Reply-To: ted@nmsu.edu's message of Sat, 2 Jan 1993 00:38:24 GMT
Message-ID: <TED.93Jan2094107@lole.nmsu.edu>
Sender: usenet@nmsu.edu
Reply-To: ted@nmsu.edu
Organization: Computing Research Lab
References: <1993Jan1.105401.46023@kuhub.cc.ukans.edu> <TED.93Jan1134723@lole.nmsu.edu>
	<TED.93Jan1173824@lole.nmsu.edu>
Date: Sat, 2 Jan 1993 16:41:07 GMT
Lines: 21



a kind reader has pointed out that my previous postings are not
terribly clear.

basically,

well-tempered is the system where half-tones are separated by a factor
of 2^(1/12)

natural temper is the system derived from simple fractions.  it is
close to the well-tempered tuning if you look at the numbers, but not
if you listen to the chords.

this kind reader also points out that there is a variation on natural
tempering in which some of the later notes in the circle are tweaked
a bit to make things come closer overall.  this is called mean
tempering and is essentially what piano tuners do when they walk up
and down using different intervals from the first few keys that they
tune from a reference.

