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.