The Mathematics Behind Indian and Western Music

South Indian Music has 72 complete scales, whereas Western music has 12 major scales. Let’s go deeper into the mathematical combinations of notes that make musical patterns.

Skanda Vivek
Emergent Phenomena
Published in
5 min readDec 31, 2020

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South Indian Melakarta Ragas | Basavarajtalwar

Absolute vs Relative Scales

The fundamental difference between Western classical and Indian music, is that Western music has 12 absolute notes. Each note: C, C#, D, etc. has a specific frequency. Concert C is around 262 Hz for example. Ignore harmonics for now (i.e. the higher pitch or lower pitch version of C).

However, Indian music is relative. In Indian music, notes are marked Sa, Re, Ga, Ma, Pa, Da, Ni, Sa — or short form as below. Note that the end S is the higher pitch version of S.

Mathematical Permutations in Indian Music

Visualizing Raga Combinations | Skanda Vivek

The human ear can distinguish 12 semitones in a scale, the 13th is the harmonic of the first note. In South Indian music, the first and middle notes are fixed (S, P). But the others can be permuted over. Note there are 3 possible R, and three G, but two R and G overlap — the same story with D and N. To find the total combinations of distinct scales (also known as Ragas), we need to use combinations. From 4 possible R, G we can choose 2. From two M, we can choose 1. From 4 D, N we can choose 2.

From these combinations, the number of ragas comes to 4C2*2C1*4C2 = 72. Indian music has 72 distinct scales!

Modes in Western Music

Western music has 12 major scales, all starting from each of the 12 semitones (C, C#, D,….). In addition, there are 7 modes. 7 because a whole scale has 7 distinct notes e.g. C, D, E, F, G, A, B in the C major scale. And each mode starts from the next note. These modes are:

  1. Ionian — C, D, E, F, G, A, B, C
  2. Dorian — D, E, F, G, A, B, C, D
  3. Phrygian — E, F, G, A, B, C, D, E
  4. Lydian — F, G, A, B, C, D, E,

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