If you tune the intervals between different pairs of notes
exactly, then the intervals and notes defined by our standard
keyboard don't quite fit together; this is just a sad fact of
maths. To make them fit, you have to tune the intervals slightly
wrong, which is called "tempering" the intervals, and the
pattern of how you temper all the different intervals on the
keyboard is called a "temperament". The commonest way of doing
this in modern times is simply to space the notes in the octave
evenly, known as "equal temperament" - this give fifths that are
slightly flat (too narrow), and major thirds that are markedly
sharp (too wide), but all by the same amount for a given type of
interval. On instruments like the organ, the effect of the sharp
thirds, in particular, is very apparent, because of the evenly
held sounds from the pipes. So temperaments are used which make
the most commonly used major thirds closer to the correct tuning
- but this can only be done by making other thirds worse; hence
the idea of good