A101285 Rounded frequencies in Hertz of the notes of the C major music scale beginning at A (A Minor equal-tempered).

55, 62, 65, 73, 82, 87, 98, 110, 123, 131, 147, 165, 175, 196, 220, 247, 262, 294, 330, 349, 392, 440, 494, 523, 587, 659, 698, 784, 880, 988, 1047, 1175, 1319, 1397, 1568, 1760, 1976, 2093, 2349, 2637, 2794, 3136, 3520, 3951, 4186, 4699, 5274, 5588, 6272

Offset: 1

Author

Angela Johansson (angvi798(AT)student.liu.se), Dec 20 2004

Keywords

• nonn

Comments

The scale is equal-tempered ("Wohltemperiert"), introduced by Johann Sebastian Bach.

Subsequence of A101286, obtained by removal of the 5 black keys' frequencies in each block of 12 keys. - R. J. Mathar, Mar 12 2008

Links

• T. Yahaya Abdullah, Music Scales, part of Synthesizers, Music and Television.
• Wikipedia, Equal temperament
• Wikipedia, Aeolian scale

Crossrefs

Cf. A071831, A071832, A071833.

Programs

Maple

A101286x := proc(n) 55*2.0^((n-1)/12.0) ; end: A101285x := proc(n) if n >= 8 then 2*A101285x(n-7) ; else A101286x(op(n,[1,3,4,6,8,9,11])) ; fi ; end: A101285 := proc(n) round(A101285x(n)) ; end: seq(A101285(n),n=1..80) ; # R. J. Mathar, Mar 12 2008

Mathematica

Table[Round[55*2^((Floor[3(4k-1)/7]-1)/12)],{k,1,49}] (* Federico Provvedi, Feb 14 2014 *)

PARI

forstep(i = 0, 100, [2, 1, 2, 2, 1, 2, 2], print(round(55*2^(i/12)))) \\ David Wasserman, Mar 17 2008

Formula

From David Wasserman, Mar 17 2008: (Start)

a(7n) = round(55*2^(n-1/6));

a(7n+1) = 55*2^n;

a(7n+2) = round(55*2^(n+1/6));

a(7n+3) = round(55*2^(n+1/4));

a(7n+4) = round(55*2^(n+5/12));

a(7n+5) = round(110*2^(n-5/12));

a(7n+6) = round(110*2^(n-1/3)). (End)

a(n) = round(55*2^(int(3*(4*k-1)/7-1)/12)). - Federico Provvedi, Feb 14 2014

Extensions

More terms from Jonathan R. Love (japanada11(AT)yahoo.ca) and R. J. Mathar, Mar 08 2007