A west end show is going on tour and they have a marimba tuning problem; the marimba is tuned to A440Hz, but the musical samples are recorded at A442Hz. So the notes have come to me for re-tuning.
During the first cycle of tuning, I make a record of where the notes are presently, the results are below.
In the graph, the two smooth lines represent what the tuning should be, and where I need to raise the pitch to. The wiggly lines show that the tuning of the notes is actually all over the place.
The biggest problem area is the third partial which is consistently flat.
In simple terms, to raise the pitch, the note needs to be shortened in length, removing material in the centre of the note increases the flexibility of the bar, which lowers the pitch. It is harder to raise the pitch than to lower it, furthermore, shortening the length affects all the longitudinal harmonics, whereas harmonics can be somewhat targeted when tuning down.
Therefore, I raised the pitch of these notes so that all the harmonics were at, or above the target pitch, then the harmonics that were sharp were brought down into tune.