"Compromise temperament" is something of an awkward term, as all temperaments are by definition some sort of compromise. However, this term and the similar term "compromise tuning" have in the harmonica world been used to describe a fine tuning of the harmonica that is neither Just Intonation nor 12 Tone Equal Temperament, but somewhere in between. The idea of these tunings is to give smoother chords than those given by 12TET, without having the harmonica deviate too far from the tuning of the accompanying instruments.
The degree to which the tuning is compromised is a matter of personal preference. Perhaps the most obvious place to start is with what guitarists have come to call "half tempered" tuning. As the name suggests, this involves tuning a given note halfway between its equally tempered value and where it would be if you were to tune justly. As an example, here are a couple of chords (2 3 4 draw and 3 4 5 blow) on a C harp played in three different tunings.
First, here is the 12TET version:
As you can hear, the chords sound rather rough.
Here are the same chords tuned in JI:
Typical nice smooth chords of Just Intonation.
Finally, the same chords tuned midway between the ET and JI versions (the roots of the chords are tuned to +/- 0 cents on the tuner, the fifths are at +1 and the thirds are at about -7.5):
Not surprisingly, this tuning gives chords that are smoother than the ET version, but not quite as smooth as the JI version. Some people prefer the slight beating effect of this sort of tuning, feeling that the JI version is rather lifeless in comparison. Others, after playing compromise tunings for a while, finally decide that they prefer Just Intonation.
Here's a quick and dirty approach to setting up a compromise temperament. First, tune all the roots and fifths to +/-0 on your tuner - on a standard diatonic, this would be holes 1, 3, 4, 6, 7, 9 and 10 blow and 1, 2, 4, 6, 8 and 10 draw. Then tune the major thirds (2, 5 and 8 blow, 3 and 7 draw) to -5 cents. (Of course, it would be best to check all the octaves and tweak accordingly for your own style of playing, rather than simply setting individual notes against the tuner - see other pages in this section for more advice.) If the chords still sound rougher than you would like, try tuning the thirds down to -10 cents. As for holes 5 and 9 draw, try tuning them down by 5 or 10 cents, or even raising them by 5 or 10 cents. On a minor tuned harp, you will need to raise the pitch of the minor thirds and minor sevenths - again +5 cents will smooth them a little, +10 cents will smooth them out a little more.
This sort of tuning is all a matter of personal preference, so there is no substitute for doing a little tweaking and a lot of listening.
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