RE: Wilson scale

>}I have a tape McLaren sent me years ago. It has a killer piece that
>}is in a 1-3-5-7 Stellated Hexany tuning that Erv Wilson invented. It is a
>}14 tone just scale. Does anyone have info about just what this is? Is it
>}possible for someone to write out the scale, with both ratios and cents
>}intervals? It sounds like something I'd be interested in
>}investigating...thanks...Hstick
>
>I'm glad you like it -- it's 7-limit!
>
>The hexany by itself is the CPS 2)4 [1,3,5,7], or, if we choose 1*5 as the
>tonic (an arbitrary but convenient choice), the tones
>
>1/1 21/20 6/5 7/5 3/2 7/4
>
>It might be a good idea to play around with this scale first. This scale has
>eight triads that are consonant within the 7-limit. "Stellation" refers to
>the process of adding one note to each triad to form a complete 7-limit
>tetrad:
>
>Triad Completion
>1/1 6/5 7/5 8/5 (1 Odentity)
>6/5 3/2 21/20 9/5 (3 Odentity)
>1/1 3/2 7/4 5/4 (5 Odentity)
>7/5 7/4 21/20 49/40 (7 Odentity)
>7/4 21/20 3/2 21/16 (1 Udentity)
>7/5 7/4 1/1 7/6 (3 Udentity)
>7/5 21/20 6/5 42/25 (5 Udentity)
>1/1 6/5 3/2 12/7 (7 Udentity)
>
>Each of the original six tones serves four tetradic functions, while each of
>the eight new tones serves only one.
>
>Here is the entire scale, in just ratios, cents, and degrees of 31TET (the
>best of your axes for 7-limit):
>
>Ratio cents 31TET
>1/1 0 0
>21/20 84 2
>7/6 267 7
>6/5 316 8
>49/40 351 9
>5/4 386 10
>21/16 471 12
>7/5 583 15
>3/2 702 18
>8/5 814 21
>42/25 898 23
>12/7 933 24
>7/4 969 25
>9/5 1018 26
>
>Of course, McLaren may have chosen a different "tonic," so it really may be a
>particular mode of this scale you are interested in. I suspect his tonic was
>the note called "8/5" above.


SMTPOriginator: tuning@eartha.mills.edu
From: "Paul H. Erlich"
Subject: RE: PLANCK CONSTANT
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