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The 3136/3125 clippers

🔗Gene Ward Smith <gwsmith@svpal.org>

8/29/2004 12:25:57 PM

I need to do something I can do on autopilot at the moment, so I think
I'll analyze a few clippers. From 3136/3125 I get

[1, 35/32, 28/25, 8/7, 5/4, 32/25, 175/128, 7/5, 10/7, 256/175,
25/16, 8/5, 875/512, 7/4, 25/14, 64/35, 125/64]

and its inverse. This is a good candidate for 6136/6125 planar, which
gives it three major and three minor tetrads. Without tempering, it
has nine 1-5/4-7/4 chords and nine 1-7/5-7/4 chords. If we add 225/224
to 6136/6125, we get orwell, and it then has an otonal and a utonal
pentad, and a boatload of 11 harmony stemming from 176/175 in 11-limit
orwell. The orwell scale (not a modmos) in question is

{-14, -11, -9, -8, -6, -5, -3, -2, -1, 0, 2, 3, 5, 6, 8, 11, 14}

and its inverse. Other commas which might be employed are 3136/3125
and 65625/65526 (both orwell commas), making the whole temperament
story rather complex, but with a decidedly Orwellian flavor.