Search: id:A143800
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%I A143800
%S A143800 0,12,19,24,28,31,34,36,38,40,42,43,44,46,47,48,49,50,51,52,53,54,54,55,
%T A143800 56,56,57,58,58,59,59,60,61,61,62,62,63,63,63,64,64,65,65,66,66,66,67,
%U A143800 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 log2(n) produces irrational numbers for all n that are not 
               powers of 2,
%C A143800 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,
%C A143800 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(log2(n)*12)
%e A143800 For n = 3, a(3) = round(log2(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.
%o A143800 (Other) //language: C/C++ #include <stdio.h> #include <math.h> //for 
               log #define round(x) (x<0?ceil((x)-0.5):floor((x)+0.5)) int main(){ 
               const NUMBER_OF_TERMS = 100; //change for more or fewer terms const 
               TONES_PER_OCTAVE = 12; //change for different number of increments 
               making an octave long harmonic; for(harmonic=1; harmonic<=NUMBER_OF_TERMS; 
               ++harmonic){ printf("%ld ", (long) round(log(harmonic)/log(2)*TONES_PER_OCTAVE)); 
               } return 0; }
%Y A143800 Equals to round(log2(A000027)*12), since A000027 represents the natural 
               numbers.
%Y A143800 Sequence in context: A100541 A056688 A107911 this_sequence A003335 A030609 
               A053752
%Y A143800 Adjacent sequences: A143797 A143798 A143799 this_sequence A143801 A143802 
               A143803
%K A143800 easy,nonn
%O A143800 1,2
%A A143800 Cyril Zhang (cyril.zhang1(AT)gmail.com), Sep 01 2008

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