On the internet Tuning List, Pat Pagano presented a scale designed by he and David Beardsley, and asked for comments from other list subscribers (Message 19513, Tue Feb 27, 2001 5:24pm). This scale uses a rational tuning, and includes the prime-factors 2, 3, 5, 7, and 17, thus characterizing it as 17-limit, albeit without making any use of the intervening prime-factors 11 and 13.
Because of these missing prime-factors, I (and others) would label it as "7...17-limit", or some other variation such as "7/17-limit". I think it makes sense to recognize in the label that a particular tuning makes use of an inclusive set of fairly low prime-factors with one "special" prime-factor that is larger. This occurs rather often, as here. My first response presented the prime-factor matrix which outlines the values of the exponents of all the prime-factors in the ratios of this scale (Message 19517, Tue Feb 27, 2001 6:43pm):
2 3 5 7 17
2/1 1 0 0 0 0
119/64 - 6 0 0 1 1
85/48 - 4 -1 1 0 1
17/10 - 1 0 -1 0 1
51/32 - 5 1 0 0 1
119/80 - 4 0 -1 1 1
17/12 - 2 -1 0 0 1
1377/1024 -10 4 0 0 1
51/40 - 3 1 -1 0 1
153/128 - 7 2 0 0 1
425/384 - 7 -1 2 0 1
17/16 - 4 0 0 0 1
1/1 0 0 0 0 0
Dan Stearns then created a good ASCII lattice of these pitch relationships (Message 19528, Tue Feb 27, 2001 11:48pm):
425/384
/
/
/
85/48
/ \
/ \ 119/64 1377/1024
/ \ ./ `. /
17/12---17/16----51/32-------153/128
\ 1/1X
\ 119/80
\ /.' `.\
17/10---51/40
Lawrence Ball gave a correct analysis of this scale as a modal species, without actually describing it as such (Message 19537, Wed Feb 28, 2001 4:36am). Additionally, I promised to create Monzo lattices of the scale. Here they are.
Here's the "octave"-equivalent lattice shifted in ratio-space (i.e., transposed) by a 16:17 to show the analysis of this scale as a modal species containing more familiar pitches.
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