1,1

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.

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.

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]

Cf. A132150, A132160.

Sequence in context: A005603 A109828 A048981 this_sequence A087896 A144262 A110093

Adjacent sequences: A132358 A132359 A132360 this_sequence A132362 A132363 A132364

nonn,uned

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 08 2007, Nov 09 2007