A132361 A ten-out-of-twelve fractal substitution sequence based on 7th like chords: 1->{1,5,9,12}->{A,Db,F,Ab}, 3->{3,7,11,2}->{B,E, G,Bb}, 4->{4,8,12,3}->{C,Eb,Ab,B}.

11, 7, 3, 2, 12, 8, 4, 3, 3, 4, 12, 8, 8, 3, 4, 12, 12, 9, 5, 1, 9, 1, 5, 12, 3, 4, 12, 8, 1, 5, 12, 9, 1, 5, 12, 9, 12, 9, 5, 1, 9, 1, 5, 12, 3, 4, 12, 8, 3, 4, 12, 8, 1, 5, 12, 9, 9, 1, 5, 12, 12, 9, 5, 1, 2, 11, 7, 3, 2, 2, 3, 11, 7, 7, 2, 3, 11, 7, 2, 3, 11, 2, 11, 7, 3, 2, 2, 3, 11, 7, 2, 3, 11, 7

Offset

1,1

Comments

This sequence uses nine basic tones with {2}->Bb as a terminator. If the triad chords are used only it has less of a blue sound and only has nine tones. It also goes from 4!=24 permutations possible to 3!=6: that significantly lowers the possible out comes for automated output. Substitutions with the permutations increase the variability of this type of sequence.

Links

Table of n, a(n) for n=1..94.

Formula

Substitution function that skip {6,10} and use {2} as a terminator:

s[1] = {12, 9, 5, 1};

s[2] = {2};

s[3] = {11, 7, 3, 2};

s[4] = {12, 8, 4, 3};

s[5] = Permutations[s[1]][[12]];

s[6] = {6};

s[7] = Permutations[s[3]][[12]]; s[8] = Permutations[s[4]][[12]];

s[9] = Permutations[s[1]][[23]];

s[10] = {10};

s[11] = Permutations[s[3]][[23]];

s[12] = Permutations[s[4]][[23]];

Permutations {12,23} are used for spread, but any two combinations of 24:Binomial[24,2]=46 can be used if the first substitutions are the reference state.

Mathematica

Clear[s]
s[1] = {12, 9, 5, 1};
s[2] = {2};
s[3] = {11, 7, 3, 2};
s[4] = {12, 8, 4, 3};
s[5] = Permutations[s[1]][[12]];
s[6] = {6};
s[7] = Permutations[s[3]][[12]]; s[8] = Permutations[s[4]][[12]];
s[9] = Permutations[s[1]][[23]];
s[10] = {10};
s[11] = Permutations[s[3]][[23]];
s[12] = Permutations[s[4]][[23]];
t[a_] := Flatten[s /@ a]; p[0] = {1, 3, 4}; p[1] = t[p[0]];
p[n_] := t[p[n - 1]];
p[3]

Crossrefs

Cf. A132150, A132160.

Sequence in context: A005603 A109828 A048981 * A305273 A236546 A155914

Adjacent sequences: A132358 A132359 A132360 * A132362 A132363 A132364

Keyword

nonn,uned

Author

Roger L. Bagula, Nov 08 2007, Nov 09 2007

Status

approved