

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
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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



