I know that there is a science behind tempering, especially when applied to various tunings that range from an A=415 standard, to the A=440 current standard, all the way through A being even higher than that, depending on the ensemble. For my take on tempering, at least from a practical perspective when approached from playing trumpet in a wind ensemble, is to simply say that a particular note, take E for instance, is not always the same, and it depends where it is in the chord, and what chord is being played. This was a concept that I first came to understand when I played in a brass quintet where at times we'd break things down in rehearsal and take notes on specific chords so that I'd know whether to listen and push the note a particular direction, up or down, so that it would help the chord to ring the way it was supposed to. While technically everyone may have been "in tune" specifically on their notes, the chord wouldn't ring correctly until that intonation was tempered with certain notes being pushed slightly higher or lower. That's my take on it anyway, and at times I think that "intonation" is actually a combination of comparative intonation and timbre.