OFFSET
1,2
COMMENTS
The twelve notes dividing the octave are numbered 1 through 12 sequentially. This sequence begins at a certain note, travels up a perfect fifth (seven semitones) twelve times, and arrives back at the same note. If justly tuned fifths are used, the final note will be sharp by the Pythagorean comma (roughly 23.46 cents or about a quarter of a semitone).
Period 12: repeat [1, 8, 3, 10, 5, 12, 7, 2, 9, 4, 11, 6]. - Omar E. Pol, May 12 2015
LINKS
Alonso del Arte, Alvin Hoover Belt, Daniel Forgues, and Charles R Greathouse IV, The multi-faceted reach of the OEIS: Music
Wikipedia, Circle of fifths
Wikipedia, Pythagorean comma
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,1).
FORMULA
Periodic with period 12: a(n) = 1 + 7*(n-1) mod 12.
From Colin Barker, Nov 15 2019: (Start)
G.f.: x*(1 + 8*x + 3*x^2 + 10*x^3 + 5*x^4 + 12*x^5 + 7*x^6 + 2*x^7 + 9*x^8 + 4*x^9 + 11*x^10 + 6*x^11) / (1 - x^12).
a(n) = a(n-12) for n > 12.
(End)
EXAMPLE
For a(3), 1+7+7 == 3 (mod 12).
For a(4), 1+7+7+7 == 10 (mod 12).
MATHEMATICA
PadRight[{}, 100, {1, 8, 3, 10, 5, 12, 7, 2, 9, 4, 11, 6}] (* Vincenzo Librandi, May 10 2015 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {1, 8, 3, 10, 5, 12, 7, 2, 9, 4, 11, 6}, 108] (* Ray Chandler, Aug 27 2015 *)
PROG
(Magma) [1+7*(n-1) mod(12): n in [1..80]]; // Vincenzo Librandi, May 10 2015
(PARI) a(n)=7*(n-1)%12+1 \\ Charles R Greathouse IV, Jun 02 2015
(PARI) Vec(x*(1 + 8*x + 3*x^2 + 10*x^3 + 5*x^4 + 12*x^5 + 7*x^6 + 2*x^7 + 9*x^8 + 4*x^9 + 11*x^10 + 6*x^11) / (1 - x^12) + O(x^80)) \\ Colin Barker, Nov 15 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Peter Woodward, May 09 2015
EXTENSIONS
Extended by Ray Chandler, Aug 27 2015
STATUS
approved