A291454 Number of half tones between successive pitches in a major scale.

2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1

Offset

1,1

Comments

In music theory the repeating sequence '2,2,1,2,2,2,1' is the number of steps of half tones in pitch between the tones of a major scale. Starting at, for example, the tone 'C' that is the first tone of the C major scale, 2 half tones up leads to 'D', which is the second tone in the scale. The scale then is: C,D,E,F,G,A,B and C. Starting at another term in the sequence will produce a different scale; for example, '2,1,2,2,1,2,2' will produce a minor scale.

From Robert G. Wilson v, Aug 25 2017: (Start)

First forward difference of A083026.

Decimal expansion of 737407/3333333. (End)

Links

Muniru A Asiru, Table of n, a(n) for n = 1..1000

Wikipedia, Scale (music)

Formula

a(n) = floor(12*(n+1)/7) - floor(12*n/7). - Federico Provvedi, Oct 18 2018

Dirichlet g.f.: 2*zeta(s) - 7^(-s)*(zeta(s,3/7) + zeta(s)). - Federico Provvedi, Aug 27 2021

Maple

a:=proc(n) floor(12*(n+1)/7-floor(12*n/7)) end: seq(a(n), n=1..110); # Muniru A Asiru, Oct 19 2018

Mathematica

Table[{2, 2, 1, 2, 2, 2, 1}, 15] // Flatten  (* Robert G. Wilson v, Aug 25 2017 *)
Table[Floor[12/7 (k + 1)] - Floor[12/7 k], {k, 1, 100}] (* Federico Provvedi, Oct 18 2018 *)

Prog

(PARI) a(n)=[1, 2, 2, 1, 2, 2, 2][n%7+1] \\ Charles R Greathouse IV, Aug 26 2017
(Magma) [12*(n+1) div 7 - 12*n div 7:  n in [1..80]]; // Vincenzo Librandi, Oct 21 2018

Crossrefs

Cf. A083026, A286748.

Sequence in context: A230259 A085030 A078377 * A105697 A340456 A080757

Adjacent sequences: A291451 A291452 A291453 * A291455 A291456 A291457

Keyword

nonn,easy,hear

Author

Halfdan Skjerning, Aug 24 2017

Status

approved