OFFSET
1,2
COMMENTS
First four chords are based on six tone sequences: A,B,C,D,E,G as "white key like" Ab,Bb,Db,Eb,F,Gb as "black key like" in a {5,5} graph with C and F as the central notes ( notes without black keys associated).
FORMULA
Four functional substitutions of the form: s(n) = {a(n),b(n),c(n),d(n)} where a,b,c,d are pattern functions.
EXAMPLE
1->{1, 6, 10, 12},
2-> {2, 5, 9, 11},
3-> {1, 3, 8, 12},
4-> {2, 4, 7, 11},
5-> {1, 5, 6, 12},
6-> {2, 6, 5, 11},
7-> {1, 7, 4, 12},
8-> {2, 8, 3, 11},
9-> {1, 9, 2, 12},
10-> {2, 10, 5, 11},
11-> {1, 11, 6, 12},
12-> {2, 12, 7, 11}}
MATHEMATICA
(* 12 tone functional substitution*) (* only the first four are remotely chord like*) a[i_] := If[Mod[i, 2] == 0, 2, 1] b[i_] := If[i == 1, 6, If[i == 2, 5, i]] c[i_] := If[i < 10, 11 - i, i - 5] d[i_] := If[Mod[i, 2] == 0, 11, 12] s[i_] := {a[i], b[i], c[i], d[i]} t[a_] := Flatten[s /@ a]; p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]] aa = p[4]
CROSSREFS
KEYWORD
nonn,uned
AUTHOR
Roger L. Bagula, Oct 11 2007
STATUS
approved