A132160 Ten tone fractal jazz substitution with {5,10} left out and spacing of either 3 or 4 notes( major or minor ).

1, 4, 6, 9, 4, 7, 8, 1, 12, 6, 11, 2, 3, 9, 6, 12, 1, 4, 7, 8, 1, 12, 7, 11, 3, 4, 8, 4, 11, 12, 1, 4, 6, 9, 12, 3, 4, 8, 9, 6, 11, 2, 3, 11, 7, 8, 2, 3, 2, 6, 11, 3, 6, 7, 11, 12, 9, 6, 12, 1, 6, 11, 2, 3, 12, 3, 4, 8, 9, 1, 4, 6, 9, 4, 7, 8, 1, 12, 7, 11, 3, 4, 8, 4, 11, 12, 1, 4, 6, 9, 12, 3, 4, 8, 9

Offset

1,2

Comments

This substitution is an alternative to the algorithmic function inspired by Oscar Peterson's piano Jazz and in practice can fugue with it ( I've done fugues several times with it).

Links

Table of n, a(n) for n=1..95.

Formula

1-> {1, 4, 6, 9}; 2-> {2, 6, 11}; 3-> {3, 6, 7, 11, 12}; 4-> {4, 7, 8, 1, 12}; 5-> {5}; ( since the substitution starts at {1,4,6,9} and none of them contain 5 or 10, those notes are left out) 6->{6, 11, 2, 3}; 7-> {7, 11, 3, 4}; 8-> {8, 4, 11, 12}; 9-> {9, 6, 12, 1}; 10-> {10}; 11-> {11, 7, 8, 2, 3}; 12-> {12, 3, 4, 8, 9};

Mathematica

Clear[s] s[1] = {1, 4, 6, 9}; s[2] = {2, 6, 11}; s[3] = {3, 6, 7, 11, 12}; s[4] = {4, 7, 8, 1, 12}; s[5] = {5}; s[6] = {6, 11, 2, 3}; s[7] = {7, 11, 3, 4}; s[8] = {8, 4, 11, 12}; s[9] = {9, 6, 12, 1}; s[10] = {10}; s[11] = {11, 7, 8, 2, 3}; s[12] = {12, 3, 4, 8, 9}; t[a_] := Flatten[s /@ a]; p[0] = s[1]; p[1] = t[p[0]]; p[n_] := t[p[n - 1]]; p[3]

Crossrefs

Sequence in context: A076418 A059910 A019837 * A021217 A103550 A321092

Adjacent sequences: A132157 A132158 A132159 * A132161 A132162 A132163

Keyword

nonn,uned

Author

Roger L. Bagula, Nov 02 2007

Status

approved