Farey

Well, the Scala command Paul E. referred to is "ratio/farey", the
command "farey" does something different.
It takes two parameters, an interval and the maximum Farey order
(maximum denominator) of the approximating ratio.
For example, rat/fa 115.0 20 gives:

9/8 203.9100 cents, 2^-3.3^2
Deviation: 88.9100 cents, Certainties: 0.0000 0.0000
10/9 182.4037 cents, 2.3^-2.5
Deviation: 67.4037 cents, Certainties: 0.0000 0.0006
11/10 165.0042 cents, 2^-1.5^-1.11
Deviation: 50.0042 cents, Certainties: 0.0000 0.0055
12/11 150.6371 cents, 2^2.3.11^-1
Deviation: 35.6371 cents, Certainties: 0.0003 0.0209
13/12 138.5727 cents, 2^-2.3^-1.13
Deviation: 23.5727 cents, Certainties: 0.0063 0.0438
14/13 128.2982 cents, 2.7.13^-1
Deviation: 13.2982 cents, Certainties: 0.0339 0.0627
15/14 119.4428 cents, 2^-1.3.5.7^-1
Deviation: 4.4428 cents, Certainties: 0.0652 0.0698
16/15 111.7313 cents, 2^4.3^-1.5^-1
Deviation: -3.2687 cents, Certainties: 0.0634 0.0658

The certainties indicate the likelihood of the interval being heard
as such. The first assumes a precision of pitch perception of 0.006
(fine, 0.6%), the second of 0.012 (coarse) within a certain optimal
frequency range. This is explained in an article by Goldstein. The
likelihood decreases with the difference and with the denominator of
the approximation.

Manuel Op de Coul coul@ezh.nl

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On Fri, 20 Sep 1996, Steve Curtin wrote:
> It sounds like something American Masters might do. Can anyone verify this?
> Some of these programs are available on videotape for a reasonable (I think
> around $25) price.

That's about what I paid recently for a tape of their program on Bucky
Fuller. However, American Masters was not on my PBS station Monday
night.

--pH (manynote@library.wustl.edu or http://library.wustl.edu/~manynote)
O
/\ "Foul? What the hell for?"
-\-\-- o "Because you are chalking your cue with the 3-ball."

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