From jmb184@servtech.com Wed Jun 19 11:42:30 CDT 1996
Article: 75937 of sci.math
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From: jmb184@servtech.com (John Bailey)
Newsgroups: sci.math
Subject: Re: Fundamentals of music
Date: 19 Jun 1996 02:08:57 GMT
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References: <4pkg6o$5gm@news.abs.net> <4pm64j$au4@eccles.dsbc.icl.co.uk> <4q4gen$hmf@muir.math.niu.edu>
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In article <4q4gen$hmf@muir.math.niu.edu>, rusin@vesuvius.math.niu.edu (Dave Rusin) says:
>
>In article <4pm64j$au4@eccles.dsbc.icl.co.uk>,
>Roy Lakin wrote:
>
>>Helmholtz's "Sensations of Tone" showed a 53-keys-to-the-octave keyboard
>>where you would have to move backwards and forwards to transpose keys, so
>>as to position your hands above a slightly different subset.
>>
>
>The 'best' number of tones per interval can be deduced from a
>continued-fraction argument, as another poster noted, although in
>practice there have been some reasonably successful experiments with,
>say, a 19-tone scale.
I find the key layout for a 19 tone scale utterly charming (mathematically)
If you visualize the piano keys for the 12 tone, equi-tempered scale there
are seven white keys and five black in one octave. From any white key
you go up a half tone to the black key for a sharp, and down a half tone
to a black key for a flat. If you now want a 19 tone equi-tempered scale,
you split every black key. For each of the white keys, when you go up
for a sharp, it can now be a different key than going down for a flat from
the next higher white key. Except, now the white keys that did not have
a black key in between before can now have a black key between them.(only
one) Where before there were 7 white and 5 black there are now 7 white,
5x2 split black keys and 2 more new single black keys. Making 19 in all.
This is probably very confusing. If anyone is interested, I will make a
diagram so it is clearer.