cp's OEIS Frontend

A319727 Rounded frequencies of notes in the shruti scale of Indian classical music, starting with 260.7 Hertz for C-equivalent note.

%I A319727 #11 Sep 28 2018 22:12:12
%S A319727 261,275,278,290,293,309,313,326,330,348,352,367,371,391,412,417,435,
%T A319727 440,464,469,489,495,521,549,556,579,587,618,626,652,660,695,704,733,
%U A319727 743,782,824,834,869,880,927,939,978,990
%N A319727 Rounded frequencies of notes in the shruti scale of Indian classical music, starting with 260.7 Hertz for C-equivalent note.
%C A319727 A shruti can be interpreted as the smallest interval of pitch the ear can detect and a singer or musical instrument can produce, and accordingly the 'Grama' system divides an octave into 22 parts.
%C A319727 The scale involves 256/243, 25/24 and 81/80 as fractions.
%C A319727 Note that ((81/80)^10) * ((256/243)^7) * ((25/24)^5) = 2.
%C A319727 The frequencies correspond to the ratios [1/1, 256/243, 16/15, 10/9, 9/8, 32/27, 6/5, 5/4, 81/64, 4/3, 27/20, 45/32, 729/512, 3/2, 128/81, 8/5, 5/3, 27/16, 16/9, 9/5, 15/8, 243/128, 2/1].
%C A319727 The start is A-equivalent note = 440 Hz. The initial term (rounded frequency of C-equivalent note) is calculated as (16/27) * 440 Hz = 260.7 Hz.
%H A319727 Wikipedia, <a href="http://en.wikipedia.org/wiki/shruti_(music)">Shruti (music)</a>
%o A319727 (PARI)
%o A319727 Ratios={[1/1, 256/243, 16/15, 10/9, 9/8, 32/27, 6/5, 5/4, 81/64, 4/3, 27/20, 45/32, 729/512, 3/2, 128/81, 8/5, 5/3, 27/16, 16/9, 9/5, 15/8, 243/128];}
%o A319727 a(n)={n--; round(440*16/27*2^(n\22)*Ratios[n%22+1])} \\ _Andrew Howroyd_, Sep 27 2018
%Y A319727 Cf. A131071, A131062.
%K A319727 nonn
%O A319727 1,1
%A A319727 _Jim Singh_, Sep 26 2018