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

27,3

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

Formula

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

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

Example

.     | 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 .

Prog

(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

Crossrefs

Cf. A214832, A079731, A010774.

Sequence in context: A206916 A336112 A067086 * A005410 A120835 A091374

Adjacent sequences: A254528 A254529 A254530 * A254532 A254533 A254534

Keyword

nonn,fini,full

Author

Reinhard Zumkeller, Feb 01 2015

Extensions

Corrected by Jianing Song, Oct 14 2019

Status

approved