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

261, 275, 278, 290, 293, 309, 313, 326, 330, 348, 352, 367, 371, 391, 412, 417, 435, 440, 464, 469, 489, 495, 521, 549, 556, 579, 587, 618, 626, 652, 660, 695, 704, 733, 743, 782, 824, 834, 869, 880, 927, 939, 978, 990

Offset: 1

Author

Jim Singh, Sep 26 2018

Keywords

• nonn

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)

Crossrefs

Cf. A131071, A131062.

Programs

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