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A319280 Numbers that are congruent to {0, 4, 7, 11} mod 12. 4
0, 4, 7, 11, 12, 16, 19, 23, 24, 28, 31, 35, 36, 40, 43, 47, 48, 52, 55, 59, 60, 64, 67, 71, 72, 76, 79, 83, 84, 88, 91, 95, 96, 100, 103, 107, 108, 112, 115, 119, 120, 124, 127, 131, 132, 136, 139, 143, 144, 148, 151, 155, 156, 160, 163, 167, 168, 172, 175, 179 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Key-numbers of the pitches of a major seventh chord on a standard chromatic keyboard, with root = 0.

LINKS

Jianing Song, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

FORMULA

a(n) = a(n-4) + 12 for n > 4.

a(n) = a(n-1) + a(n-4) - a(n-5) for n > 5.

G.f.: x^2*(4 + 3*x + 4*x^2 + x^3)/((1 + x)*(1 + x^2)*(1 - x)^2).

a(n) = (6*n - 4 + (-1)^n + sqrt(2)*cos(Pi*n/2 + Pi/4))/2.

E.g.f.: ((6*x - 3)*cosh(x) + (6*x - 5)*sinh(x) + sqrt(2)*cos(x + Pi/4) + 2)/2.

MATHEMATICA

Select[Range[0, 200], MemberQ[{0, 4, 7, 11}, Mod[#, 12]]&]

LinearRecurrence[{1, 0, 0, 1, -1}, {0, 4, 7, 11, 12}, 100]

PROG

(MAGMA) [n : n in [0..150] | n mod 12 in [0, 4, 7, 11]]

(PARI) x='x+O('x^99); concat(0, Vec(x^2*(4+3*x+4*x^2+x^3)/((1+x)*(1+x^2)*(1-x)^2)))

CROSSREFS

A guide for some sequences related to modes and chords:

Modes:

Lydian mode (F): A083089

Ionian mode (C): A083026

Mixolydian mode (G): A083120

Dorian mode (D): A083033

Aeolian mode (A): A060107 (raised seventh: A083028)

Phrygian mode (E): A083034

Locrian mode (B): A082977

Third chords:

Major chord (F,C,G): A083030

Minor chord (D,A,E): A083031

Diminished chord (B): A319451

Seventh chords:

Major seventh chord (F,C): this sequence

Dominant seventh chord (G): A083032

Minor seventh chord (D,A,E): A319279

Half-diminished seventh chord (B): A319452

Sequence in context: A164888 A023985 A023979 * A214975 A310720 A310721

Adjacent sequences:  A319277 A319278 A319279 * A319281 A319282 A319283

KEYWORD

nonn,easy

AUTHOR

Jianing Song, Sep 16 2018

STATUS

approved

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Last modified August 18 20:02 EDT 2019. Contains 326109 sequences. (Running on oeis4.)