OFFSET
1,1
COMMENTS
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.
The scale involves 256/243, 25/24 and 81/80 as fractions.
Note that ((81/80)^10) * ((256/243)^7) * ((25/24)^5) = 2.
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].
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.
LINKS
Wikipedia, Shruti (music)
PROG
(PARI)
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]; }
a(n)={n--; round(440*16/27*2^(n\22)*Ratios[n%22+1])} \\ Andrew Howroyd, Sep 27 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Jim Singh, Sep 26 2018
STATUS
approved