Oxford blue has the answer.
'Looping Error' leads to the instrument over reading at anything more than 1g. Significant if recovering from an unusual position on instruments using the turn indicator - you must unload to about 1g to be able to find the wings level position.
A turn co-ordinator (as fitted as a factory item on most spamcans) has the axis of rotation tilted about 30 degrees and rotates the other way. As a result, looping errror is reversed and the instrument undereads at more than 1g which makes it near to useless when recovering from an unusaul position on instruments. For this reason, the club where I instruct has replaced turn co-ordinators with turn and slips on our fleet of PA28s.
Also, if you consider that in a balanced turn you have yaw roll and pitch, the pitch element makes the instrument over-read as the aircraft will be at more than 1g. For this reason, the turn indicator is calibrated to read correctly with this increased g by adjusting the tension on the springs, but at one speed only . The instrument fittted to the Chipmunk in RAF service was actually calibrated to 180 knots, so I don't think this correction is too significant.
But, if an aircraft is flying a turn at 90 degrees angle of bank (theoretical, I know), the turn will be just pitch with no roll and no yaw, and the instrument will read no turn. Therefore the yaw component reduces with increase in angle of bank, so this explains the angle of bank calibration Oxford Blue mentions.
Not an easy subject to be examined on - and of very little significance these days, as if a turn needle is incorporated into a modern instrument display, it's almost certainly derived from INS / IRS information.