A131214 A seven tone substitution sequence based on "church music" 7th chords: example:A->{A,C,E,G}; A connected heptagon graph substitution: Characteristic polynomial: 4 - 21 x + 49 x^2 - 63 x^3 + 49 x^4 - 21 x^5 + 7 x^6 - x^7.

1, 3, 5, 7, 2, 3, 5, 7, 2, 4, 5, 7, 2, 4, 6, 7, 1, 2, 4, 6, 2, 3, 5, 7, 2, 4, 5, 7, 2, 4, 6, 7, 1, 2, 4, 6, 1, 3, 4, 6, 2, 4, 5, 7, 2, 4, 6, 7, 1, 2, 4, 6, 1, 3, 4, 6, 1, 3, 5, 6, 2, 4, 6, 7, 1, 3, 5, 7, 1, 2, 4, 6, 1, 3, 4, 6, 1, 3, 5, 6, 1, 2, 4, 6, 2, 3, 5, 7, 2, 4, 5, 7, 2, 4, 6, 7, 1, 2, 4, 6, 1, 3, 4, 6, 2

Offset

1,2

Comments

This substitution is suggested by considering the 7 major tones in an octave as interconnected by 7th chords of major tones only ( four tones).

Links

Table of n, a(n) for n=1..105.

Formula

a(n) ={a(n),a(n+2},a(n+4),a(n+6)) Modulo 7

Example

a = Table[If[m == 1,n, If[m > 1 && n + 2*(m - 1) <= 7, n + 2*(m - 1), Mod[n + 2*(m - 1), 7]] ], {n, 1, 7}, {m, 1, 4}]
{{1, 3, 5, 7}, {2, 4, 6, 1}, {3, 5, 7, 2}, {4, 6, 1, 3}, {5, 7, 2, 4}, {6, 1, 3, 5}, {7, 2, 4, 6}}

Mathematica

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

Crossrefs

Sequence in context: A128059 A084763 A179650 * A271833 A357043 A104260

Adjacent sequences: A131211 A131212 A131213 * A131215 A131216 A131217

Keyword

nonn,uned

Author

Roger L. Bagula, Sep 27 2007

Status

approved