cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

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

Views

Author

Hans Isdahl, Sep 24 2007

Keywords

Comments

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].

Links

Crossrefs

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

Extensions

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

A214832 Integer part of A440 piano key frequencies, start with A0 = the 1st key.

Original entry on oeis.org

27, 29, 30, 32, 34, 36, 38, 41, 43, 46, 48, 51, 55, 58, 61, 65, 69, 73, 77, 82, 87, 92, 97, 103, 110, 116, 123, 130, 138, 146, 155, 164, 174, 184, 195, 207, 220, 233, 246, 261, 277, 293, 311, 329, 349, 369, 391, 415, 440, 466, 493, 523, 554, 587, 622, 659, 698, 739, 783, 830, 880, 932, 987, 1046, 1108, 1174, 1244, 1318, 1396, 1479, 1567, 1661, 1760, 1864, 1975, 2093, 2217, 2349, 2489, 2637, 2793, 2959, 3135, 3322, 3520, 3729, 3951, 4186
Offset: 1

Views

Author

Jon Perry, Mar 07 2013

Keywords

Comments

A254531(a(k)) = k, k = 1..88. - Reinhard Zumkeller, Feb 04 2015

Examples

			Middle C is 261.626 Hz so a(40) = 261.

Links

Crossrefs

Cf. A059620, A079731, A131062, A101285, A131071.
Cf. A254531, A010774.

Programs

  • Haskell
    a214832 = floor . (* 440) . (2 **) . (/ 12) . fromIntegral . subtract 49
-- Reinhard Zumkeller, Nov 23 2014
  • JavaScript
    for (i=1;i<=88;i++) document.write(Math.floor(Math.pow(2,(i-49)/12)*440)+", ");
  • PARI
    a(n)=floor(440*2^((n-49)/12));

Formula

a(n) = floor[2^((n-49)/12)*440] (Hz) for 1 <= n <= 88.

A319727 Rounded frequencies of notes in the shruti scale of Indian classical music, starting with 260.7 Hertz for C-equivalent note.

Original entry on oeis.org

261, 275, 278, 290, 293, 309, 313, 326, 330, 348, 352, 367, 371, 391, 412, 417, 435, 440, 464, 469, 489, 495, 521, 549, 556, 579, 587, 618, 626, 652, 660, 695, 704, 733, 743, 782, 824, 834, 869, 880, 927, 939, 978, 990
Offset: 1

Views

Author

Jim Singh, Sep 26 2018

Keywords

Comments

A shruti can be interpreted as the smallest interval of pitch the ear can detect and a singer or musical instrument can produce, and accordingly the 'Grama' system divides an octave into 22 parts.
The scale involves 256/243, 25/24 and 81/80 as fractions.
Note that ((81/80)^10) * ((256/243)^7) * ((25/24)^5) = 2.
The frequencies correspond to the ratios [1/1, 256/243, 16/15, 10/9, 9/8, 32/27, 6/5, 5/4, 81/64, 4/3, 27/20, 45/32, 729/512, 3/2, 128/81, 8/5, 5/3, 27/16, 16/9, 9/5, 15/8, 243/128, 2/1].
The start is A-equivalent note = 440 Hz. The initial term (rounded frequency of C-equivalent note) is calculated as (16/27) * 440 Hz = 260.7 Hz.

Links

Crossrefs

Cf. A131071, A131062.

Programs

  • PARI
    Ratios={[1/1, 256/243, 16/15, 10/9, 9/8, 32/27, 6/5, 5/4, 81/64, 4/3, 27/20, 45/32, 729/512, 3/2, 128/81, 8/5, 5/3, 27/16, 16/9, 9/5, 15/8, 243/128];}
a(n)={n--; round(440*16/27*2^(n\22)*Ratios[n%22+1])} \\ Andrew Howroyd, Sep 27 2018

A358029 Decimal expansion of the ratio between step sizes of the diatonic and chromatic semitones produced by a circle of 12 perfect fifths in Pythagorean tuning.

Original entry on oeis.org

1, 2, 6, 0, 0, 1, 6, 7, 5, 2, 6, 7, 0, 8, 2, 4, 5, 3, 5, 9, 3, 1, 2, 7, 6, 1, 2, 2, 6, 0, 3, 9, 2, 4, 2, 3, 3, 7, 1, 8, 1, 1, 5, 5, 7, 9, 2, 3, 2, 7, 6, 7, 8, 3, 3, 4, 1, 0, 6, 5, 2, 0, 1, 6, 1, 6, 2, 0, 8, 7, 4, 8, 0, 0, 8, 3, 1, 2, 2, 7, 8, 4, 6, 8, 8, 1, 4
Offset: 1

Views

Author

Eliora Ben-Gurion, Oct 25 2022

Keywords

Comments

Pythagorean tuning is a form of tuning produced by repeated stacking of the perfect fifth, which has the frequency ratio of 3:2. A circle of 12 perfect fifths is approximately equal to the tuning system predominantly in use in the world today. If the perfect fifth is stacked 12 times and the resulting sequence is octave-reduced, then this divides the octave into 5 chromatic semitones which are equal to 2187/2048 (A229948), and 7 diatonic semitones which are equal to 256/243 (A229943). Diatonic semitones are those which are derived from a circle of 7 perfect fifths, the diatonic scale, and 5 chromatic semitones are a byproduct of an addition of 5 more perfect fifths, that is, another rotation, to the scale.

Examples

			1.2600167526708245359312761226039242337181155792327678334106520161...

Links

Crossrefs

Cf. A131071, A221363, A258054, A257811.
Cf. A229943, A229948.

Programs

  • Mathematica
    RealDigits[(7*Log[3] - 11*Log[2])/(8*Log[2] - 5*Log[3]), 10, 120][[1]] (* Amiram Eldar, Jun 21 2023 *)

Formula

Equals log(2187/2048) / log(256/243).
Equals log(A229948) / log(A229943).
Equals (7*log(3) - 11*log(2))/(8*log(2) - 5*log(3)).
Showing 1-4 of 4 results.

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