What Catler does

Jon Catler must be busy and not checking this list. He told me, as I
recall, that he tunes his guitars basically in the regular fashion, with
the comma displacement between the third and fourth strings. This gives
him a chain of fourths on the low strings, and a pure utonal triad on top:

E A D G+ B E PITCH NAME (in limit-notation)
4/3 4/3 320/243 5/4 4/3 INTERVAL
1/1 4/3 16/9 6/5 3/2 1/1 DISTANCE FROM E


Yours,
Adam

_________________
Adam B. Silverman
153 Cold Spring Street; A3
New Haven, CT 06511
(203) 782-1765

abs22@pantheon.yale.edu

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>... but isn't there a *pure* JI tuning, based on string
>partials or something?

My answer would be "no": I don't think that any one just intonation
tuning is necessarily more purely JI than any other. But then again, that
depends on what you mean by "pure". As far as I can tell, "pure" has no
specific definition in tuning theory, although it's one of many useful
adjectives, and it's often used as synonymous with "just" itself.

But since JI uses as its basis small whole-number ratios, one can argue
that smaller ratios make the tuning more true to JI principles. If that's
what you mean by "pure JI", then a harmonic-series-fragment tuning would
indeed be a quite pure form of just intonation.




>Based on the C major scale in
>12TET, how should each note be tuned to most closely approximate a pure JI
>tuning? Below is a tuning I found in a book:

I haven't worked out the math specifically, but at a quick glance, those
cent adjustments will give you one of the usual "five-limit" Ptolemaic
diatonic tuning, probably 1:1, 16:15, 9:8, 6:5, 5:4, 4:3, 45:32, 3:2, 8:5,
5:3, 9:5, 15:8 2:1. The 16s (minor third and major sixth) however are
probably exaggerated by a cent or two. Perhaps the table was devised for a
device with two-cent resolution.

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