22 Shruti Research Topics

Topic 15 : Importance of the Pythagorean Scale : 'Pythagorean Limma'

Dr. Vidyadhar Oke   Pythagorean Scale is important because, an extremely important number called "Pythagorean Limma" is hidden in this scale. Pythagoras analyzed the % distances between the above consecutive notes and found them as under. (Refer to following table)

Table shows % distances between notes in Pythagorean scale

% distances between notes in Pythagorean scale

Thus, Pythagoras found that the distances between S-R, R-G, G-M, P-D, and D-N as 12.5%, and that between M-P and N-S' as 5.3497942 %. He considered this distance as 'Limma' meaning 'left over' in Greek. This means that when we go on adding 12.5% from S, the 'left over' distance ending in P is the same as that ending in S'. This is the 'Pythagorean Limma'. It's value is 1.053497942, rounded off to 1.0535, because; as shown above, 1.4238281 x 1.0535 = 1.5; and 1.8984375 x 1.0535 = 2.

This measurement of 1.053497942 (or 1.0535) appears in the fundamental construction of 22 Shrutis.

Pythagoras was a great Mathematician, Musicologist, and an Astronomer. To him, number was everything. He considered 4 sets of numbers. For him,

  • 'only numbers' constituted ------------------------------------- -> Mathematics
  • 'numbers and space' constituted ----------------------------- -> Geometry
  • 'numbers and time' constituted ------------------------------- -> Music
  • 'numbers with space and time', all together, constituted -> Astronomy

He saw a great unity in all creations in nature, and felt that music was a 'Melody of Spheres (Planets)'. He trusted that musical notes and the orbital distances between planets would have a relation.

Thus, his musical octave gave us the extremely important 'Pythagorean Limma', of 5.3497942, rounded off to 5.35%.

Topic 14 : Pythagoraen Octave (Scale)
END OF Topic 15.

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Topic 16 : 'Syntonic Comma' or 'Ptolemic Comma'
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