A079731 -id:A079731 - cp's OEIS frontend

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

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

Jon Perry, Mar 07 2013

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

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

BGfL, A Virtual Keyboard
Wikipedia, Piano Key Frequencies
Wikipedia, Twelfth root of two
Index entries for sequences based on music

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

Cf. A254531, A010774.

a214832 = floor . (* 440) . (2 **) . (/ 12) . fromIntegral . subtract 49
-- Reinhard Zumkeller, Nov 23 2014

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));
```

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

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

Reinhard Zumkeller, Feb 01 2015

			.     | 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 .

Reinhard Zumkeller, Table of n, a(n) for n = 27..4308
Wikipedia, Piano Key Frequencies
Wikipedia, Twelfth root of two
Index entries for sequences based on music

Cf. A214832, A079731, A010774.

a254531 = (+ 49) . round . (* 12) . logBase 2 . (/ 440) . fromIntegral

a(n) = round(12*log(n/440)/log(2))+49 \\ Jianing Song, Oct 14 2019

a(n) = round(12*log_2(n/440)) + 49, 27 <= n <= 4308.

a(A214832(k)) = k for k = 1..88.

Corrected by Jianing Song, Oct 14 2019

cp's OEIS Frontend

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

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