Really  skillful    British extemporizers,  going   all the way back    to  the time    of  Giraldus    Cambrensis,
could   come    up  with    much    more    impressive  harmonizations, not only    in  three   parts   but in  four    or  even
more.   Desiderius  Erasmus (Erasmus    of  Rotterdam), the great   humanist    scholar and a   great   Anglophile,
reported    in  amazement,  following   one of  his many    visits  to  England toward  the end of  the fifteenth   century,
that    in  English churches    “many   sing    together,   but none    of  the singers produce those   sounds  which   the notes
on  the page    indicate.”  (This   sounds  a   lot like    Giraldus,   in  fact,   except  that    the Welsh   singers he  described
did not use books   at  all.)
We  can share   in  Erasmus’s   amazement   if  we  travel  forward in  time    a   bit for a   quick   look    at  the latest
and most    advanced    treatise    on  supra   librum  singing from    the British Isles.  A   manual  copied  in  Scotland
around  1580,   but summing up  two or  three   hundred years’  worth   of  singers’    lore,   ends    with    a   final   chapter
on  “countering”    in  which   twelve  rules   are given   that,   when    mastered    over    considerable    time,   enabled a
quartet of  singers to  take    a   simple  line    of  plainchant  (like   Ex. 11-22a) and from    it  work    up  on  the spot    a
polyphonic  realization like    the one shown   in  the treatise’s  final   didactic    example.    The tenor   sings   a   highly
embellished version of  the cantus  firmus  at  the original    pitch   (each   measure beginning   and ending  with    the
notated pitch,  but with    the middle  filled  most    fancifully),    and the other   parts   carol   away    even    more
ornately,   albeit  according   to  strict—and, no  doubt,  well-kept—secret    formulas    (Ex.    11-22b).
EX. 11-22A Heir beginnis    countering, presumed    cantus  firmusEX. 11-22B Heir beginnis    countering, final   example,    mm. 1–6