A071833 -id:A071833 - cp's OEIS frontend

A071831 Frequency ratios for notes of C-major scale starting at c = 1 (numerators).

1, 9, 5, 4, 3, 5, 15, 2, 9, 5, 8, 3, 10, 15, 4, 9, 5, 16, 6, 20, 15, 8, 9, 10, 32, 12, 40, 15, 16, 18, 20, 64, 24, 80, 30, 32, 36, 40, 128, 48, 160, 60, 64, 72, 80, 256, 96, 320, 120, 128, 144, 160, 512, 192, 640, 240, 256, 288, 320, 1024, 384, 1280, 480, 512, 576, 640, 2048

Offset: 0

N. J. A. Sloane, Jun 10 2002

			The ratios are 1 (c), 9/8 (d), 5/4 (e), 4/3 (f), 3/2 (g), 5/3 (a), 15/8 (b); followed by these 7 numbers multiplied by successive powers of 2.

OEIS index entry for music.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,2).

Cf. A071832, A071833.

Numerator[2^Floor[#/7]Rationalize[2^((-1+Floor[12(1+Mod[#,7])/7])/12),2^-6]]&/@Range[0,70] (* Federico Provvedi, Feb 14 2014 *)

r=[1,9/8,5/4,4/3,3/2,5/3,15/8]; for(n=0,10, a=2^n*r; for(m=1,7, print1(numerator(a[m])", "))) \\ Rick L. Shepherd, Apr 06 2006

A071831(n)=numerator([1,9/8,5/4,4/3,3/2,5/3,15/8][n%7+1]*2^(n\7))  \\ M. F. Hasler, Jun 13 2012

a(n+7) = 2*a(n) for n >= 21. - Rick L. Shepherd, Apr 06 2006

G.f.: (15*x^27 + 9*x^22 + 15*x^20 + 5*x^16 + 9*x^15 + 15*x^13 + 3*x^11 + 5*x^9 + 9*x^8 - 15*x^6 - 5*x^5 - 3*x^4 - 4*x^3 - 5*x^2 - 9*x - 1) / (2*x^7 - 1). - Colin Barker, Feb 14 2014

More terms from Rick L. Shepherd, Apr 06 2006

A071832 Frequency ratios for notes of C-major scale starting at c = 1 (denominators).

Original entry on oeis.org

1, 8, 4, 3, 2, 3, 8, 1, 4, 2, 3, 1, 3, 4, 1, 2, 1, 3, 1, 3, 2, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 3, 1, 3, 1

Offset: 0

N. J. A. Sloane, Jun 10 2002

			The ratios are 1 (c), 9/8 (d), 5/4 (e), 4/3 (f), 3/2 (g), 5/3 (a), 15/8 (b); followed by these 7 numbers multiplied by successive powers of 2.

OEIS index entry for music.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,1).

Cf. A071831, A071833.

Denominator[2^Floor[#/7]Rationalize[2^((-1+Floor[12(1+Mod[#,7])/7])/12),2^-6]]&/@Range[0,70] (* Federico Provvedi, Feb 14 2014 *)
PadRight[{1,8,4,3,2,3,8,1,4,2,3,1,3,4,1,2,1,3,1,3,2},120,{1,1,1,3,1,3,1}] (* Harvey P. Dale, Nov 16 2020 *)

r=[1,9/8,5/4,4/3,3/2,5/3,15/8]; for(n=0,20, a=2^n*r; for(m=1,7, print1(denominator(a[m]),","))) \\ Rick L. Shepherd, Apr 06 2006

A071832(n)=denominator([1,9/8,5/4,4/3,3/2,5/3,15/8][n%7+1]*2^(n\7))  \\ M. F. Hasler, Jun 13 2012

a(n+7) = a(n) for n >= 21; (1,1,1,3,1,3,1 repeats). - Rick L. Shepherd, Apr 06 2006

G.f.: (x^27 + x^22 + 2*x^20 + x^16 + 2*x^15 + 4*x^13 + x^11 + 2*x^9 + 4*x^8 - 8*x^6 - 3*x^5 - 2*x^4 - 3*x^3 - 4*x^2 - 8*x - 1) / ((x - 1)*(x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)). - Colin Barker, Feb 14 2014

More terms from Rick L. Shepherd, Apr 06 2006

A131062 Rounded frequencies of notes in a Pythagorean scale, starting with 260.7 Hertz for a C.

Original entry on oeis.org

261, 293, 330, 348, 391, 440, 495, 521, 587, 660, 695, 782, 880, 990, 1043, 1173, 1320, 1391, 1564, 1760, 1980, 2086

Offset: 1

Hans Isdahl, Sep 24 2007

nonn

The approximate value of 260.7 Hz for the C corresponds to 16/27 * 440 Hz. The frequencies correspond to the ratios [1/1, 9/8, 81/64, 4/3, 3/2, 27/16, 243/128, 2/1].

Wikipedia, Just intonation - Pythagorean tuning.
Wikipedia, Pythagorean tuning.
Index entries for sequences related to music.

Cf. A131071 for the same scale including half-tones.
Cf. A071831/A071832 = A071833/24. - M. F. Hasler, Jun 14 2012
Cf. A101285.

Value of a(8) corrected, sequence extended to 3 octaves and comments added by M. F. Hasler (following suggestions by Franklin T. Adams-Watters and Charles R Greathouse IV), Oct 05 2011

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

Original entry on oeis.org

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

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

nonn

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

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

Cf. A071831, A071832, A071833.

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

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

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

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

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

A101286 Rounded frequencies in Hz of the notes of the chromatic music scale beginning at A.

Original entry on oeis.org

55, 58, 62, 65, 69, 73, 78, 82, 87, 92, 98, 104, 110, 117, 123, 131, 139, 147, 156, 165, 175, 185, 196, 208, 220, 233, 247, 262, 277, 294, 311, 330, 349, 370, 392, 415, 440, 466, 494, 523, 554, 587, 622, 659, 698, 740, 784, 831, 880, 932, 988, 1047, 1109, 1175

Offset: 1

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

nonn

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

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

Cf. A071831, A071832, A071833.

A101286 := proc(n) round( 55*2.0^((n-1)/12.0)) ; end: seq(A101286(n),n=1..80) ; # R. J. Mathar, Mar 12 2008

a(1+n) = round(55*2^(n/12)). - R. J. Mathar, Mar 12 2008

Corrected by T. D. Noe, Nov 02 2006

More terms from R. J. Mathar, Mar 12 2008

A101287 Rounded frequencies in Hz of the notes of the pentatonic music scale beginning at F#.

Original entry on oeis.org

92, 104, 117, 139, 156, 185, 208, 233, 277, 311, 370, 415

Offset: 0

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

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

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

Cf. A071831, A071832, A071833.

cp's OEIS Frontend

A071831 Frequency ratios for notes of C-major scale starting at c = 1 (numerators).

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A071832 Frequency ratios for notes of C-major scale starting at c = 1 (denominators).

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A131062 Rounded frequencies of notes in a Pythagorean scale, starting with 260.7 Hertz for a C.

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

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Maple

Mathematica

PARI

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A101286 Rounded frequencies in Hz of the notes of the chromatic music scale beginning at A.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Formula

Extensions

A101287 Rounded frequencies in Hz of the notes of the pentatonic music scale beginning at F#.

Views

Author

Keywords

Comments

Links

Crossrefs