etc. }

These forms were rather typical than stringently binding as Dante
himself notes (_De Vulg. El._, ii, 11); many variations were [26]
possible. The first seems to have been the most popular type. The poem might also
conclude with a half stanza or _tornada_, (French _envoi_). Here, as in
the last couplet of the Arabic _gazul_, were placed the personal
allusions, and when these were unintelligible to the audience the
_joglar_ usually explained the poem before singing it; the explanations,
which in some cases remain prefixed to the poem, were known as the
_razos_.

Troubadour poems were composed for singing, not for recitation, and the
music of a poem was an element of no less importance than the words.
Troubadours are described as composing "good" tunes and "poor" words, or
vice versa; the tune was a piece of literary property, and, as we have
said, if a troubadour borrowed a tune he was expected to acknowledge its
origin. Consequently music and words were regarded as forming a unity,
and the structure of the one should be a guide to the structure of the
other. Troubadour music is a subject still beset with difficulties[13]:
we possess 244 tunes written in Gregorian notation, and as in certain
cases the same poem appears in different MSS. with the tune in
substantial agreement in each one, we may reasonably assume that we have
an authentic record, as far as this could be expressed in Gregorian
notation. The chief difference between Troubadour and Gregorian music
lies in the fact that the former was syllabic in character; in other [27]
words, one note was not held over several syllables, though several
notes might be sung upon one syllable. The system of musical time in the
age of the troubadours was based upon the so-called "modes," rhythmical
formulae combining short and long notes in various sequences. Three of
these concern us here. The first mode consists of a long followed by a
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 ob