+@node mensuration sign
+@section mensuration sign
+
+@c TODO: add languages
+
+ES: ?,
+I: ?,
+F: ?,
+D: ?,
+NL: ?,
+DK: ?,
+S: ?,
+FI: ?.
+
+The ancestor of the time signature, mensuration signs were used to indicate the
+relationship between two sets of note durations—specifically, the ratio of
+breves to semibreves (called @notation{tempus}), and of semibreves to minims
+(called @notation{prolatio}).
+
+Each ratio was represented with a single single sign, and was either
+three-to-one (ternary) or two-to-one (binary), as in modern music notation.
+Unlike modern music notation, the @emph{ternary} ratio was the preferred
+one—applied to the @emph{tempus}, it was called @emph{perfect}, and was
+represented by a complete circle; applied to the @emph{prolatio}, it was called
+@emph{major} and was represented by a dot in the middle of the sign. The binary
+ratio applied to the @emph{tempus} was called @emph{imperfect}, and was
+represented by an incomplete circle; applied to @emph{prolatio}, it was called
+@emph{minor} and was represented by the lack of an internal dot. There are four
+possible combinations, which can be represented in modern time signatures with
+and without reduction of note values. (These signs are hard-coded in LilyPond
+with reduction.)
+
+@table @dfn
+@item perfect @emph{tempus} with major @emph{prolatio}
+Indicated by a complete circle with an internal dot. In modern time signatures,
+this equals:
+@itemize
+@item 9/4, with reduction or
+@item 9/2, without reduction
+@end itemize
+
+@item perfect @emph{tempus} and minor @emph{prolatio}
+Indicated by a complete circle without an internal dot. In modern time
+signatures, this equals:
+@itemize
+@item 3/2, with reduction or
+@item 3/1, without reduction
+@end itemize
+
+@item imperfect @emph{tempus} and major @emph{prolatio}
+Indicated by an incomplete circle with an internal dot. In modern time
+signatures, this equals:
+@itemize
+@item 6/4, with reduction or
+@item 6/2, without reduction
+@end itemize
+
+@item imperfect @emph{tempus} and minor @emph{prolatio}
+Indicated by an incomplete circle without an internal dot. In modern time
+signatures, this equals:
+@itemize
+@item 4/4, with reduction or
+@item 2/1, without reduction
+@end itemize
+@end table
+
+The last mensuration sign @emph{looks} like common-time because it @emph{is},
+with note values reduced from the original semibreve to a modern quarter note.
+Being doubly imperfect, this sign represented the (theoretically)
+least-preferred mensuration, but it was actually used fairly often.
+
+This system extended to the ratio of longer note values to each other:
+
+@itemize
+
+ @item maxima to longa, called:
+
+ @itemize
+
+ @item @notation{modus maximorum},
+ @item @notation{modus major}, or
+ @item @notation{maximodus})
+
+ @end itemize
+
+ @item longa to breve, called:
+
+ @itemize
+
+ @item @notation{modus longarum},
+ @item @notation{modus minor}, or
+ @item @notation{modus}
+
+ @end itemize
+
+@end itemize
+
+In the absence of any other indication, these modes were assumed to be
+binary. The mensuration signs only indicated tempus and prolatio, so
+composers needed another way to indicate these longer ratios (called modes.
+Around the middle of the 15th century started to use groups of rests at the
+beginning of the staff, preceding the mensuration sign.
+
+
+Two mensuration signs have survived to the present day: the C-shaped sign,
+which originally designated @notation{tempus imperfectum} and
+@notation{prolatio minor} now stands for @notation{common time}; and the
+slashed C, which designated the same with @notation{diminution} now stands
+for @notation{cut-time} (essentially, it has not lost its original meaning).
+
+@seealso
+@ref{diminution}, @ref{proportion}, @ref{time signature}.
+@c TODO: more cross-references?
+
+
projects / lilypond.git / blobdiff