

A133210


A functional 12 tone Musical substitution sequence based on the chord like pattern in: 1>{1,6,10,11} or Ab,Db,F,Gb 2>{2,5,9,12} or A,C,E,G 3>{3,8,11,1} or Bb,Eb,Gb,Ab 4>{4,7,12,2} or B,D,G,A Characteristic Polynomial: 16 x^2 + 36 x^3 + 36 x^4  215 x^5 + 355 x^6  368 x^7 + 285 x^8  161 x^9 + 59 x^10  12 x^11 + x^12.


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1, 6, 10, 12, 2, 6, 5, 11, 2, 10, 5, 11, 2, 12, 7, 11, 2, 5, 9, 11, 2, 6, 5, 11, 1, 5, 6, 12, 1, 11, 6, 12, 2, 5, 9, 11, 2, 10, 5, 11, 1, 5, 6, 12, 1, 11, 6, 12, 2, 5, 9, 11, 2, 12, 7, 11, 1, 7, 4, 12, 1, 11, 6, 12, 2, 5, 9, 11, 1, 5, 6, 12, 1, 9, 2, 12, 1, 11, 6, 12, 2, 5, 9, 11, 2, 6, 5, 11, 1, 5, 6
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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).


LINKS

Table of n, a(n) for n=1..91.


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

Cf. A133159, A131979.
Sequence in context: A248757 A136812 A109397 * A324975 A141467 A361109
Adjacent sequences: A133207 A133208 A133209 * A133211 A133212 A133213


KEYWORD

nonn,uned


AUTHOR

Roger L. Bagula, Oct 11 2007


STATUS

approved



