## Topic 47: Useful mathematical information for all 22 scales beginning from 22 shrutis

The ratios in-between the 22 shrutis must be considered as 'Normal Shrutyantar'.

If we shift the scale serially, some of the ratios change, and their table is given below.

Thus, in a 22-Shruti-Harmonium, if the scale is changed some shrutis are not available as can be seen in the following table.

The table below shows the Normal Shrutyantaras (normal available shrutis) in all 22 scales and non-available or wrong shrutis available in Red.

In the following table:

1. 1
Vertical Column A gives Shruti numbers.
2. 2
Vertical Column B gives Shruti titles.
3. 3
3. Vertical Column 1 gives the Normal shruti percentages.
4. 4
Vertical Columns 2 to 22 give the respective Shadja in that column in Magenta, and % distances from the same of the remaining Shrutis in the same vertical column. For explanation, in Vertical column 2, r1 is the Shadja, and shrutis shown in Red are wrong or not available, if r1 is taken as Shadja.
5. 5
The horizontal line with arrow pointing to the right ( -> ) at the bottom of every vertical column shows the no.of Shrutis available. For eg. with r1 (in vertical column 2), only 16 out of 22 Shrutis are available when r1 is taken as Shadja.

In other words, this table is a 'Ready-Reckoner' for the selection of Shrutis in different scales.