This particular vehicle had 58,000 miles on it and would set these codes after about a day of driving. The first two codes (P0720 and P0713) are Generic codes, meaning their definition is the same regardless of the vehicle manufacture. Generic codes always have a zero (0) as the first digit. The second digit is a “7” so we know all of the codes are transmission related.
These codes are:
P0720 – Output speed sensor eor.
P0731 – Incorrect gear ratio in 1st gear
The third code is “factory specific”, meaning it may have a different meaning based on the manufacturer. In this case the P1790 means: Fault after shift. Simply put, the computer detected a slip.
As is the case with every vehicle these days, the computer uses an input and output sensor (and sometimes additional speed sensors) to verify the gear ratios. Based on that, the problem with the output sensor would be the first suspect. In this case, the shop discovered the wire harness from the transmission was routed between the engine and bulkhead on the passenger side and had become brittle from heat, damaging the insulation on the output sensor wires.
Repairing the wires fixed the problem.