A319279 Numbers that are congruent to {0, 3, 7, 10} mod 12.

0, 3, 7, 10, 12, 15, 19, 22, 24, 27, 31, 34, 36, 39, 43, 46, 48, 51, 55, 58, 60, 63, 67, 70, 72, 75, 79, 82, 84, 87, 91, 94, 96, 99, 103, 106, 108, 111, 115, 118, 120, 123, 127, 130, 132, 135, 139, 142, 144, 147, 151, 154, 156, 159, 163, 166, 168, 171, 175, 178

Offset

1,2

Comments

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

Apart from the offset the same as A013574. - R. J. Mathar, Sep 27 2018

Links

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

Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-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*(3 + x + 2*x^2)/((x^2 + 1)*(x - 1)^2).

a(n) = (6*n - 5 + sqrt(2)*cos(Pi*n/2 + Pi/4))/2.

E.g.f.: ((6x - 5)*e^x + sqrt(2)*cos(x + Pi/4) + 4)/2.

Mathematica

Select[Range[0, 200], MemberQ[{0, 3, 7, 10}, Mod[#, 12]]&]
LinearRecurrence[{1, 0, 0, 1, -1}, {0, 3, 7, 10, 12}, 100]

Prog

(Magma) [n : n in [0..150] | n mod 12 in [0, 3, 7, 10]]
(PARI) x='x+O('x^99); concat(0, Vec(x^2*(3+x+2*x^2)/((x^2+1)*(x-1)^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): A319280

Dominant seventh chord (G): A083032

Minor seventh chord (D,A,E): this sequence

Half-diminished seventh chord (B): A319452

Sequence in context: A105135 A225552 A147683 * A013574 A235915 A310178

Adjacent sequences: A319276 A319277 A319278 * A319280 A319281 A319282

Keyword

nonn,easy

Author

Jianing Song, Sep 16 2018

Status

approved