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Definitions of tuning terms
© 1998 by Joseph L. Monzo
All definitions by Joe Monzo unless otherwise cited
mutation
A change from one
hexachord to another.
Because the ancient
Greek theory could use either a
conjunct
(synemmenon) or a disjunct
(diezeugmenon) tetrachord
above the mese (in either the
Lesser or Greater Perfect System respectively),
when mese became associated with the letter-name "A"
in medieval European theory, there were two pitches
that could occupy the letter-name
degree just above it:
a "B-flat" or a "B natural".
For many centuries, they 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:
(The bottom note was represented by the Greek letter G 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 half-tone lower; to this day, the German
name for B-natural is 'h' because the notation for this note
evolved from the 'square-b' into an 'h', and eventually into
the 'natural' accidental.)
It is easy to see from this table that if a chant
used 'b' [= "B-flat"] then it was 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.
[from Joe Monzo, JustMusic:
A New Harmony]
Updated: 2002.1.12
G 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
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