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

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

Author

Reinhard Zumkeller, Feb 01 2015

Keywords

• nonn
• fini
• full

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

• 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

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