One of the alternative ways of describing the positions of the Dance of Shiva is to talk about one hand with respect to the other.
Since the positions for each arm are exactly the same (1, 2, 3, 4, a, b, c and d) and the movement possibilites from each position are the same (zero, forwards, transquarter, backwards, change, change forwards, change transquarter, change backwards) you can use movements as a way of describing the relative position of one arm to the other. You can use your left arm as the reference position.
If your arms are in position 1-1 using the normal dance of shiva coordinate system, you could say that relative to the left arm the right arm is doing a zero move, i.e. it is in the same position. You could therefore label 1-1 as 1-zero. All other positions where both arms are in the same position could be labeled as 2-zero, 3-zero, 4-zero, a-zero etc.
If the hands are in position 1-2 then here the right hand is 1 position ahead of position 2 or a forward move ahead. So 1-2 could be called 1-forwards.
The table of correlations is below. Just so you are aware,
| 1-1 | 1-Ze | a-a | a-Z | 1-a | 1-Ch | a-1 | 1-Ch |
| 1-2 | 1-Fw | a-b | a-F | 1-b | 1-CF | a-2 | a-CF |
| 1-3 | 1-Tq | a-c | a-Tq | 1-c | 1-CT | a-3 | a-CT |
| 1-4 | 1-Bw | a-4 | a-Bw | 1-d | 1-CB | a-4 | a-CB |
| 2-2 | 2-Ze | b-b | b-Ze | 2-b | 2-Ch | b-2 | b-Ch |
| 2-3 | 2-Fw | b-c | b-Fw | 2-c | 2-CF | b-3 | b-CF |
| 2-4 | 2-Tq | b-d | b-Tq | 2-d | 2-CT | b-4 | b-CT |
| 2-1 | 2-Bw | b-a | b-Bw | 2-a | 2-CB | b-1 | b-CB |
| 3-3 | 3-Ze | c-c | c-Ze | 3-c | 3-Ch | c-3 | c-Ch |
| 3-4 | 3-Fw | c-d | c-Fw | 3-d | 3-CF | c-4 | c-CF |
| 3-1 | 3-Tq | c-a | c-Tq | 3-a | 3-CT | c-1 | c-CT |
| 3-2 | 3-Bw | c-b | c-Bw | 3-b | 3-CB | c-2 | c-CB |
| 4-4 | 4-Ze | d-d | d-Ze | 4-d | 4-Ch | d-4 | d-Ch |
| 4-1 | 4-Fw | d-a | d-Bw | 4-a | 4-CF | d-1 | d-CB |
| 4-2 | 4-Tq | d-b | d-Tq | 4-b | 4-CT | d-2 | d-CT |
| 4-3 | 4-Bw | d-c | d-Bw | 4-c | 4-CB | d-3 | d-CB |
Table of Relative Position Coordinates and their equivalents. Normal dance of shiva coordinates are in the grey columns. Relative position coordinates are in the white columns.
Part of the dance of shiva can be recognizing patterns.
In this case, using this system of coordinates can enable you to see patterns of changes within patterns of movements.
For example doing a set of Forwards moves from 1-1 you see the following patterns:
The hand positions are always in the same position relative to each other.
Doing a set of Forward-Backward Moves you would get this result:
In this case in every other position the arms relate via either a zero move or a transquarter move.
From 1-2 the movements look like this:
If you, like I have trouble with the Forward-Backward (or Backwards forward sets) especially when the arms are staggered, the above pattern (forwards, backwards, forwards, backwards) may give you a way of quickly figuring out where each arm goes. You can think of the position of the first arm, say from 1 to 2, and then use the 2 position as a reference for the position that the right arm moves to, 2 backwards=1.