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A254531 a(n) is the position of the piano key whose frequency is closest to n Hz, start with A0 = the 1st key. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 21 00:11 EST 2022. Contains 350473 sequences. (Running on oeis4.)