login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A291454 Number of half tones between successive pitches in a major scale. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

In music theory the repeating sequence '2,2,1,2,2,2,1' is the number steps of half tones upwards 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

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.

Sequence in context: A230259 A085030 A078377 * A105697 A080757 A037196

Adjacent sequences:  A291451 A291452 A291453 * A291455 A291456 A291457

KEYWORD

nonn,easy,hear

AUTHOR

Halfdan Skjerning, Aug 24 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 8 04:16 EDT 2020. Contains 335504 sequences. (Running on oeis4.)