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A 7-limit JI detempering of Blackjack

🔗Gene W Smith <genewardsmith@juno.com>

5/8/2002 8:31:26 PM

Here is a symmetrical JI scale related to Blackjack, obtained by
detempering Blackjack by what I call "Euclidean reduction", where I
choose the scale step nearest to unity in the symmetrical 7-limit
octave-equivalent lattice. In the one case where there was a tie I broke
in in favor of 49/40 and 80/49 rather than 60/49 and 49/30; the latter
giving an alternative version.

Here is the scale:

1, 49/48, 15/14, 35/32, 8/7, 7/6, 49/40, 5/4, 21/16, 4/3, 7/5, 10/7, 3/2,
32/21, 8/5, 80/49, 12/7, 7/4, 64/35, 28/15, 96/49

Here is the (symmetrical) pattern of scale steps:

49/48, 360/343, 49/48, 256/245, 49/48, 21/20, 50/49, 21/20, 64/63, 21/20,
50/49, 21/20, 64/63, 21/20, 50/49, 21/20, 49/48, 256/245, 49/48, 360/343,
49/48