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Calculating geometric complexity and badness   Message List  
Reply Message #5598 of 20696 |
Re: Calculating geometric complexity and badness

--- In tuning-math@yahoogroups.com, "wallyesterpaulrus <wallyesterpaulrus@y...>"
<wallyesterpaulrus@y...> wrote:

> probably gene's typos . . .

Here are my Maple routines:


qw11 := proc(q)
# 11-limit weighted quadratic form

local a,b,c,d;
a := ordp(q,3);
b := ordp(q,5);
c := ordp(q,7);
d := ordp(q,11);
ln(3)^2*a^2+ln(5)^2*b^2+ln(7)^2*c^2+ln(11)^2*d^2+
ln(3)^2*a*b+ln(3)^2*a*c+ln(3)^2*a*d+ln(5)^2*b*c+ln(5)^2*b*d+ln(7)^2*c*d end:


gc11 := proc(l)
# complexity of 11-limit linear wedgie

sqrt(37.4669556799257*l[1]^2+19.8578149236787*l[2]^2+13.8576504872655*l[3]^2+
8.43459044261178*l[4]^2-9.24811506924099*l[2]*l[3]-
12.9637247061659*l[1]*l[2]-6.02856647730047*l[1]*l[3]-
6.41005295068753*l[3]*l[4]-2.95953128437572*l[1]*l[4]-
4.54006536578504*l[2]*l[4]) end:


gpc11 := proc(l)
# complexity of 11-limit planar wedgie

sqrt(18.1878630999135*l[1]^2
+13.2165141603747*l[2]^2
+8.13090525300357*l[3]^2
+6.57565648053141*l[4]^2
+4.20601082222387*l[5]^2
+2.76216685071556*l[6]^2
+9.98976207451545*l[1]*l[2]
-4.90415316714511*l[1]*l[3]
+4.65474179366984*l[1]*l[4]
-2.28509613536279*l[1]*l[5]
-.721921985754273*l[1]*l[6]
+6.45350417171744*l[2]*l[3]
+5.37666377942441*l[2]*l[4]
+1.44384397150855*l[2]*l[5]
-1.56317414960855*l[2]*l[6]
+3.00701812111700*l[3]*l[5]
-1.56317414960855*l[3]*l[6]
+3.84182937372243*l[4]*l[5]
+2.39798540221390*l[4]*l[6]
+2.39798540221390*l[5]*l[6]) end:






Wed Jan 22, 2003 3:19 am

genewardsmith
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Message #5598 of 20696 |
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I've just finished computing the coefficients to calculate geometric complexity directly from the wedgie up to the 11 limit; an aggravating but potentially...
Gene Ward Smith <gene...
genewardsmith Offline Send Email
Jan 19, 2003
2:48 pm

... That's all the wedgie is for a single comma? I take it this would be the chromatic uv in the linear case? ... Cool. I can do that. ;) ... You mean...
Carl Lumma <clumma@...>
clumma Offline Send Email
Jan 19, 2003
8:16 pm

I wrote.. ... D'oh, I meant commatic. -C....
Carl Lumma <clumma@...>
clumma Offline Send Email
Jan 20, 2003
8:26 am

I get a slightly different result calculating geometric complexity for meantone using the 5 limit comma formula. Should it be 4.132030727? Thanks. Also I was...
Paul G Hjelmstad
paulhjelmstad Offline Send Email
Jan 21, 2003
10:15 pm

... for ... Thanks. ... include ... probably gene's typos . . . ... for rms ... optimal ... you mean p=2? that *is* rms -- "root mean square". are you looking ...
wallyesterpaulrus <wa...
wallyesterpa... Offline Send Email
Jan 21, 2003
11:12 pm

... Here are my Maple routines: qw11 := proc(q) # 11-limit weighted quadratic form local a,b,c,d; a := ordp(q,3); b := ordp(q,5); c := ordp(q,7); d :=...
Gene Ward Smith <gene...
genewardsmith Offline Send Email
Jan 22, 2003
3:19 am

Thanks. Sorry to be lagging so far behind, but I am making progress. Now, could you just show me how complexity is calculated for meantone (the easiest example...
Paul G Hjelmstad
paulhjelmstad Offline Send Email
Jan 22, 2003
4:38 pm
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