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.

A010774 Decimal expansion of 12th root of 2.

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane

Keywords

Comments

This number figures in our standard 12-tone tuning of music today.
It represents the frequency ratio of a semitone in equal temperament. The equal-tempered chromatic scale divides the octave, which has a ratio of 2:1, into twelve parts of equal ratio: [2^(n/12), 2^((n+1)/12)), 0 <= n <= 11. - Daniel Forgues, Feb 28 2013

Examples

			2^(1/12) = 1.059463094359295264561825294946341700779204317494...

References

  • D. Coulter, Digital Audio Processing. Berkeley, California: Focal Press (2000) p. 30
  • Ian Stewart, Professor Stewart's Incredible Numbers, London, Profile Books, 2015, pp. 217-228.

Links

Crossrefs

Cf. A103922, A010768.
Cf. A214832, A254531.

Programs

Formula

Equals Product_{k>=0} (1 + (-1)^k/(12*k + 11)). - Amiram Eldar, Jul 29 2020
Equals sqrt(A010768). - Hugo Pfoertner, May 31 2024

A131071 12-note scale in Hertz (rounded to integers).

Original entry on oeis.org

261, 275, 293, 309, 330, 348, 366, 391, 412, 440, 464, 495, 521
Offset: 1

Views

Author

Hans Isdahl, Sep 24 2007

Keywords

Links

Crossrefs

Cf. A131062 for the corresponding C major scale. [M. F. Hasler, Oct 07 2011]
Cf. A214832.

Formula

The scale involves 9/8 and 256/243 as fractions and the start is A = 440 Hz.
The initial term (rounded frequency of the C) is calculated as 16/27 * 440 Hz = 260.74 Hz, cf. the Wikipedia page on Pythagorean tuning for the ratios of the frequencies. - M. F. Hasler, Oct 07 2011

A254531 a(n) is the position of the piano key whose frequency is closest to n Hz, start with A0 = the 1st key.

Original entry on oeis.org

1, 1, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 22
Offset: 27

Views

Author

Reinhard Zumkeller, Feb 01 2015

Keywords

Examples

			.     | Frequency [Hz] | Piano key | Pitch
.   i | f = A079731(i) |      a(f) |
.  ---+----------------+-----------+------
.   0 |             28 |         1 |  A0
.   1 |             55 |        13 |  A1
.   2 |            110 |        25 |  A2
.   3 |            220 |        37 |  A3
.   4 |            440 |        49 |  A4    A440
.   5 |            880 |        61 |  A5
.   6 |           1760 |        73 |  A6
.   7 |           3520 |        85 |  A7 .

Links

Crossrefs

Cf. A214832, A079731, A010774.

Programs

  • Haskell
    a254531 = (+ 49) . round . (* 12) . logBase 2 . (/ 440) . fromIntegral
  • PARI
    a(n) = round(12*log(n/440)/log(2))+49 \\ Jianing Song, Oct 14 2019

Formula

a(n) = round(12*log_2(n/440)) + 49, 27 <= n <= 4308.
a(A214832(k)) = k for k = 1..88.

Extensions

Corrected by Jianing Song, Oct 14 2019

A079731 Fundamental piano frequencies in Hertz rounded to nearest integer.

Original entry on oeis.org

28, 55, 110, 220, 440, 880, 1760, 3520
Offset: 0

Views

Author

Ralf Stephan, Feb 18 2003

Keywords

Links

Crossrefs

Cf. A214832, A254531.

Formula

a(n)=round(27.5*2^n), n=0...7.
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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