short note, the long being equivalent to two short, or in 3/4 time
[Illustration: musical notation.]. The second mode is the reverse of
the first [Illustration: musical notation.]. The third mode in modern
6/8 time appears as [Illustration: musical notation.]. The principle of
sub-division is thus ternary; "common" time or 2/4 time is a later
modification. So much being admitted, the problem of transposing a tune
written in Gregorian notation without bars, time signature, marks of
expression or other modern devices is obviously a difficult matter. J.
Beck, who has written most recently upon the subject, formulates the
following rules; the musical accent falls upon the tonic syllables of
the words; should the accent fall upon an atonic syllable, the duration
of the note to which the tonic syllable is sung may be increased, to
avoid the apparent discordance between the musical accent and the tonic
syllable. The musical accent must fall upon the rime and the rhythm [28]
adopted at the outset will persist throughout the poem.

Hence a study of the words will give the key to the interpretation of
the tune. If, for instance, the poem shows accented followed by
unaccented syllables or trochees as the prevalent foot, the first "mode"
is indicated as providing the principle to be followed in transposing
the Gregorian to modern notation. When these conditions are reversed the
iambic foot will prevail and the melody will be in the second mode. It
is not possible here to treat this complicated question in full detail
for which reference must be made to the works of J. Beck. But it is
clear that the system above outlined is an improvement upon that
proposed by such earlier students of the subject as Riemann, who assumed
that each syllable was sung to a note or group of notes of equal time
value. There is no evidence that such a rhythm was ever employed in the
middle ages, and the fact that words and music were inseparable in
Provençal lyrics shows that to infer the nature of the musical rhythm