In medieval music theory, a change from one hexachord to another, analogous to the modern concept of modulation.
Because the ancient Greek tetrachord-theory could use either a conjunct (synemmenon) or a disjunct (diezeugmenon) tetrachord above the mese (in either the Lesser Perfect System or Greater Perfect System respectively), when mese became associated with the letter-name "A" in medieval European theory, there were two pitches which could occupy the letter-name degree just above it: a "B-flat" or a "B-natural".
For many centuries, these two different pitches were assumed to be a part only of their respective tetrachords, and thus their separate respective systems, the lower pitch belonging to the conjunct tetrachord and the higher pitch belonging to the disjunct. Beginning around 1000, the theory was developed that, if a chant used both notes, it was mutating from one system into the other, somewhat analagous to the later concept of modulation.
In the system of Guido d'Arezzo, which became more or less the standard for a few centuries, there were 3 basic hexachords (starting on G, C, and F), interlocked into a complete system as follows; here each hexachord is given on its own row:
Γ A B C D E F G a b h c d e etc. ut re mi etc. ut re mi fa sol la ut re mi fa sol la ut re mi fa sol la ut re mi fa sol la
(The bottom note was represented by the Greek letter Γ (gamma). The word gamut derives from the full name of this note: gamma ut. The 'h' is supposed to be the 'square-' or 'hard-b' an 'octave' above 'B', and the 'b' is the 'round-' or 'soft-b' a semitone lower; to this day, the German name for B-natural is 'h' (see "German H note") because the notation for this note evolved from the 'square-b' into an 'h', and eventually into the 'natural' accidental symbol.)
It is easy to see from this table that if a chant used 'b' [= "B-flat"] then it was situated in the hexachord based on "F fa ut", and if it used 'h' [= "B natural"] it was in the hexachord of "G sol re ut".
Mutation was effected by changing the syllable on a tone that had more than one syllable available to it. For instance, if a section of a chant was in the "G sol re ut" hexachord and using "B mi", and a "b" was coming up, the "A la mi re" could be used as the mutation-point: it would be entered as "A re" (in the "G sol re ut" hexachord), and left as "A mi" (in the "F fa ut" hexachord), thus enabling the use of "b fa".
Beginning around the time of Marchetto, the practice of mutation was extended to enable to use of many more chromatic notes, by using the same principles on notes other than "A la mi re". The "accidentals" were usually not written in the music, the singers being expected to be able to do it on their own. This practice was called musica ficta.
At first, the goal was mostly to incorporate "Eb" and "F#", but by the end of the 1300s, music was being written that was fully chromatic. After about another 100 years, the accidentals came to have the modern meaning of absolute chromatic pitches.
A similar procedure is used in the more modern method of "fasola".