# Translation Extraction Trainer

# Session

- Time Spent on Situation:
- Situations solved:
- Average time per situation:
- Time Remaining:

# Description

- Situation Format:
- You are given a series of root tones, you must find the translation number for each of the changes.
- Given two roots r1 and r2, then the translation number is -I(r1, r2), this is because this is the number you would add to each interval in a chord rooted at r1 to see those intervals with respect to r2.

## Shortcuts with proof

- Let k = -I(X,Z), then k (1*12 - k) is always a solution to X Z X
- Proof: Ignoring the Z in the middle we see that to get from X to X you must have shifted 12*j for some j, therefore we know that if you add k semitones to get from X to Z and then you must add 12*j - k semitones to get from Z to X, this is because if you have x1, ..., xn I(x1, xn) = summation( I(x_i, x_(i+1))). (the path to get there)