This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A143800 #20 Jun 27 2021 07:55:10 %S A143800 0,12,19,24,28,31,34,36,38,40,42,43,44,46,47,48,49,50,51,52,53,54,54, %T A143800 55,56,56,57,58,58,59,59,60,61,61,62,62,63,63,63,64,64,65,65,66,66,66, %U A143800 67,67,67,68,68,68,69,69,69,70,70,70,71,71,71,71,72,72,72,73,73,73,73,74 %N A143800 In acoustics, using 12-tone equal temperament, the rounded number of semitones in the interval perceived when a vibrating string is divided into n congruent segments. %C A143800 In music, these are known as harmonics. %C A143800 Observe that log_2(n) produces irrational numbers for all n that are not powers of 2, and that dividing a string in half produces an octave interval. %C A143800 Therefore the only harmonics that are perfectly in tune (equal to an interval in 12-TET) are the octaves, which correspond to all harmonics n that are powers of 2. %H A143800 Wikipedia, <a href="http://en.wikipedia.org/wiki/Harmonic_series_(music)">Harmonic series (music)</a> %F A143800 a(n) = round(log_2(n)*12). %e A143800 For n = 3, a(3) = round(log_2(3)*12) = round(19.0195500086539...) = 19 Therefore dividing a string in three equal parts will result in a tone approximately 19 semitones higher, or an octave and a perfect fifth. %p A143800 a:= n-> round(12*log[2](n)): %p A143800 seq(a(n), n=1..70); # _Alois P. Heinz_, Nov 07 2019 %K A143800 easy,nonn %O A143800 1,2 %A A143800 _Cyril Zhang_, Sep 01 2008