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Article: Shruti Lattice Diagram & Shruti Ratios

 
By Courtesy: Paul Erlich
 
  S. Ramanathan's and Erv Wilson's ratios are

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)

MODERN INDIAN GAMUT

                                   5/4------15/8------45/32
                                   / \       / \       / \
                                  /   \     /   \     /   \
                                 /     \   /     \   /     \
                                /       \ /       \ /       \
                    4/3-------1/1-------3/2-------9/8------27/16
                    / \       / \       / \       /
                   /   \     /   \     /   \     /
                  /     \   /     \   /     \   /
                 /       \ /       \ /       \ /
              16/15------8/5-------6/5-------9/5
If note B is to the east, northeast, or anywhere in between relative to note A, then note B is a harmonic of note A, but note A is not a harmonic of note B.

Here is the lattice diagram for the full 22-shruti scale, as it is normally "rationalized" today:


                        10/9---5/3---5/4--15/8--45/32
                         / \   / \   / \   / \   / \
                        /   \ /   \ /   \ /   \ /   \
256/243-128/81-32/27-16/9---4/3---1/1---3/2---9/8--27/16-81/64-243/256-729/512
                        \   / \   / \   / \   / \   /
                         \ /   \ /   \ /   \ /   \ /
                        16/15--8/5---6/5---9/5--27/20

Explanation of the Lattice Diagram:- Moving one step to the "east" means multiplying by 3:2, or the equivalent, dividing by 4:3.
Moving one step to the "west" means multiplying by 4:3, or the equivalent, dividing by 3:2.

Moving one step to the "northeast" means multiplying by 5:4, or the equivalent, dividing by 8:5.
Moving one step to the "southwest" means multiplying by 8:5, or the equivalent, dividing by 5:4.

Moving one step to the "northwest" means multiplying by 5:3, or the equivalent, dividing by 6:5.
Moving one step to the "southeast" means multiplying by 6:5, or the equivalent, dividing by 5:3.

All these relationships are easy to tune by ear (as _harmonic_ intervals), hence the direct connections shown in the lattice.

C -- 1/1

Db low -- 256/243 (though 135/128 is 2 cents away)
Db high -- 16/15

D low -- 10/9
D high -- 9/8

Eb low -- 32/27
Eb high -- 6/5

E low -- 5/4
E high -- 81/64

F low -- 4/3
F high -- 27/20

F# low -- 45/32
F# high -- 729/512 (though 64/45 is 2 cents away)

G -- 3/2

Ab low -- 128/81
Ab high -- 8/5

A low -- 5/3
A high -- 27/16

Bb low -- 16/9
Bb high -- 9/5

B low -- 15/8
B high -- 243/128

C -- 2/1

You'll find some variations in various works on the subject.

 

 

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