Re 3,9,17,19 based scales

Xmaxmixmax and Dan Stearns: I located my old notes on 19-limit
approximations to the chromatic gamut discussed in Tuning Digests 2055
and 2056. Unfortunately, I had misremembered the scale I mentioned in an
earlier post (2057?) unless there is yet another one lurking in the back
issues of the Journal of the Acoustic Society of America in the late
40's and 50's. In any case, the reference to the scale I had in mind is
T. E. Simonton. 1953. Integral Ratio Chromatic Temperament. JASA 25(6):
1167. I'm not quite sure of the date as my old index card is very faded
-- it could be 1951 or even 1957. The scale is below and includes
ratios of 5, being based on the sequence (15:)16:17:18:19:20 as 1/1
17/16 9/8 19/16 5/4 4/3 17/12 3/2 19/12 5/3 16/9 17/9 2/1.

Replacing the 5/4 with 24/19 and the 5/3 with 32/19 produces Dan
Stearn's scale in TD 2056. One can construct this scale by building the
harmonic series 16:17:18:19 up from 1/1 and 4/3 and the corresponding
subharmonc series down from 3/2 and 2/1. This procedure generates both
of the tritone-flanking intervals 17/12 and 24/17, which differ by 6
cents. Probably either could be used, or one might just as well use 600
cents (square root of 2) in place of either for an error of only 3
cents.

A somewhat similar scale is Wronski's, described on page 105 of Jocelyn
Godwin's book "Music and the Occult." Its ratios are 1/ 1 17/16 9/8
85/72 5/4 4/3 17/12 51/32 27/16 85/48 17/9 2/1.

I discoverd that both of the above scales and 4 variants were in one of
my JiCalc stacks (JCC) for the Macs. Two 7-tone scales based on similar
premises have also been constructed by Dan and me and are in the stack
as well.

--John