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From: geoff@callan.UUCP (Geoff Kuenning)
Newsgroups: net.music
Subject: Re: Tempered scales
Message-ID: <129@callan.UUCP>
Date: Sat, 24-Mar-84 21:57:35 EST
Article-I.D.: callan.129
Posted: Sat Mar 24 21:57:35 1984
Date-Received: Tue, 27-Mar-84 00:31:07 EST
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Organization: Callan Data Systems, Westlake Village, CA
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Chris Isbell says:

>	According to my calculations, the equal tempered major 
>	third has a frequency ratio of 1.2599..., while the just third is 
>	exactly 1.25. This is an error of 0.8 percent. (An error of a whole 
>	semitone is 6 percent.) I have not taken any scientific measurement of 
>	the tuning errors in modern woodwind instruments, but my subjective 
>	experience is that this error *is* significant.

Indeed, this should be significant.  Piano tuners measure tuning errors as a
percentage of a semitone, called 'cents'.  My tuner tells me that the human
ear can distingish half a 'cent' in tuning error (when comparing two notes);
this works out to a 0.03 percent error using the units of the paragraph
above.  A 0.8 percent error works out to about 13 'cents'.  My piano was
recently 20 'cents' out of tune, and it was *GROSS* to my ear.

Incidentally, I note that some of this apparently depends on ear training.  As
a modern listener, I find that most early instruments sound out-of-tune.  I
always attributed this to their being harder to play, but apparently this is
actually because I have learned to prefer equally-tempered scales to
"correctly-tuned scales".

	Geoff Kuenning
	...!ihnp4!sdcrdcf!trwrb!wlbr!callan!geoff