contents were fully presentable to the senses and in that respect altogether real.
And necessary,  as  Philippe    de  Vitry   allowed,    when    their   purpose was to  make    perfect a   diminished
fifth   or  an  augmented   fourth. As  we  know,   a   certain provision   of  this    kind    was made    by  the earliest
theorists   of  harmony,    when    they    incorporated    B-flat  into    the modal   system  alongside   B   for use in
conjunction with    F.
But when    an  E   was written against the B-flat, one had to  go  outside the system  to  harmonize   it. And
that    was musica  ficta.  The required    E-flat  was not conceptualized  as  we  might   conceptualize   it, as  an
inflection  of  E.  Instead,    it  was conceptualized  as  the upper   member  of  a   melodic semitone,   D–E,    for
which   a   solmization —mi–fa—could    be  inferred.   So  the E   a   semitone    above   D   was a   fa, which   placed  it
in  an  imaginary   or  “feigned”   (ficta) hexachord   with    ut  on  B.  Since   the flat    sign    was itself  a   variant of  the
letter  “B” to  denote  a   B   that    was sung    fa  (in the “soft   hexachord”  on  F)  instead of  mi  (in the “hard
hexachord”  on  G), so  the flat    sign    in  and of  itself  denoted fa  to  a   musician    trained to  sing    in  hexachords.
Thus    a   flat    placed  next    to  an  E   did not mean    “sing   E   a   half    step    lower,” it  meant   “sing   this    note    as  fa.”    The
result  may have    been    the same    so  far as  the listener    was concerned,  but understanding   the different   mental
process by  which   the E   was deduced by  the singer  will    make    clear   the reason  why in  most    cases   musica
ficta   did not have    to  be  expressly   indicated   by  the composer    with    accidentals.    In  many    contexts    the
chromatic   alteration  was mandated    by  rule,   and the rule    was fully   implied in  the solmization,    and so  any
singer  who thought in  terms   of  solmization would   make    the chromatic   adjustment  without being
specifically    told    to  do  so, and,    it  follows,    without even    being   aware   of  the adjustment  as  “chromaticism.”
It  was not a   deviation   from    a   pure    diatonic    norm,   it  was a   preservation    of  pure    diatonic    norms   (in
particular, perfect fourths and fifths) where   they    were    compromised by  a   well-known  kink    in  the diatonic
system.
Musica  ficta   introduced  to  preserve    perfect intervals   was musica  ficta   by  reason  of  (harmonic)
necessity   (in Latin,  causa   necessitatis),  and was considered  perfectly   diatonic.   Just    as  automatic,  and
diatonic,   was musica  ficta   by  long-established    conventions—conventions that    have    left    a   trace   on  familiar
harmonic    practice    in  the form    of  the “harmonic   minor.” They    mainly  affected    the Dorian  mode,   the one
closest to  our minor   mode.   For example,    there   was a   rule    that    a   single  B   between two A’s had to  be  a   B-
flat    (and,   though  it  rarely  required    any adjustment, that    an  F   between two E’s had to  be  F   natural).
Singers learned this    rule    as  a   Latin   jingle: una nota    super   la  /   semper  est canendum    fa  (“One   note
above   la  is  always  sung    fa”).   This    adjustment  had the effect  of  lowering    the sixth   degree  of  the Dorian
scale,  turning it  into    a   sort    of  appoggiatura    or  upper   leading tone    to  fifth   degree, A,  the note    that    formed
the boundary    between the principal   segments    of  the scale.  (And    it  turned  the Dorian  scale,  for all practical
purposes,   into    the minor   scale.) It  was a   grammatical rule,   not an  expressive  device; it  was called  into
play    automatically,  and so  it  did not need    to  be  written down.
There   was a   similar rule    affecting   lower   neighbors   to  the final   in  Dorian  cadences.   Such    notes   were
common  enough  in  Dorian  melodies    to  have    a   name:   subtonium   modi,   as  we  may recall  from    chapter 3.
The rule    about   neighbors   raised  the subtonium,  a   whole   step    below   the final,  to  the subsemitonium,  a   half
step    below.  The effect  was similar to  that    of  borrowing   a   leading tone    in  the minor   mode    and served  the
same    purpose,    strengthening   the grammatical function,   so  to  speak,  of  the cadence.    By  signaling   a   more
definite    close   it  made    the final   more    “final.”    For this    purpose the auxiliary   pitch   had to  be  raised, not
lowered,    thus    forming the lower   note    in  a   mi–fa   pair.   To  indicate    it, a   sign    was needed  that    would   instruct
the singer  to  “sing   mi.”    That    sign,   #,  which   we  call    a   “sharp,”    was originally  derived from    the “square B”
or  b   quadratum   that    functioned  specifically    as  mi  in  the “hard   hexachord.” In  places  like    Dorian
cadences,   where   the subsemitonium   modi    or  leading tone    was called  for by  the routine application of  a
rule,   it  again   could   “go without saying.”    It  did not need    to  be  explicitly  notated,    though  (like   necessary
flats)  it  could   be  notated and frequently, if  haphazardly,    was.
