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%I #20 Jun 27 2021 07:55:10
%S 0,12,19,24,28,31,34,36,38,40,42,43,44,46,47,48,49,50,51,52,53,54,54,
%T 55,56,56,57,58,58,59,59,60,61,61,62,62,63,63,63,64,64,65,65,66,66,66,
%U 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 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 In music, these are known as harmonics.
%C 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 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 Wikipedia, <a href="http://en.wikipedia.org/wiki/Harmonic_series_(music)">Harmonic series (music)</a>
%F a(n) = round(log_2(n)*12).
%e 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 a:= n-> round(12*log[2](n)):
%p seq(a(n), n=1..70); # _Alois P. Heinz_, Nov 07 2019
%K easy,nonn
%O 1,2
%A _Cyril Zhang_, Sep 01 2008