music-glossary: proportion
1.244 proportion
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ES: proporción, I: proporzione, F: proportion, D: Proportio, NL: ?, DK:
?, S: ?, FI: suhde.
[Latin: _proportio_] Described in great detail by Gaffurius, in
_Practica musicae_ (published in Milan in 1496). In mensural notation,
proportion is:
1. A ratio that expresses the relationship between the note values
that follow with those that precede;
2. A ratio between the note values of a passage and the ânormalâ
relationship of note values to the metrical pulse. (A special case
of the first definition.)
The most common proportions are:
⢠2:1 (or simply 2), expressed by a vertical line through the
mensuration sign (the origin of the alla breve time signature), or
by turning the sign backwards
⢠3:1 (or simply 3)
⢠3:2 (_sesquialtera_)
To âcancelâ any of these, the inverse proportion is applied. Thus:
⢠1:2 cancels 2:1
⢠1:3 cancels 3:1
⢠2:3 cancels 3:2
⢠and so on.
Gaffurius enumerates five basic types of major:minor proportions and
their inverses:
1. Multiplex, if the major number is an exact multiple of the minor
(2:1, 3:1, 4:2, 6:3); and its inverse, Submultiplex (1:2, 1:3, 2:4,
3:6)
2. Epimoria or Superparticular [orig. _Epimoria seu
Superparticularis_], if the major number is one more than the minor
(3:2, 4:3, 5:4); and its inverse, Subsuperparticular (2:3, 3:4,
4:5)
3. Superpartiens, if the major number is one less than twice the minor
(5:3, 7:4, 9:5, 11:6); and its inverse, subsuperpartiens (3:5, 4:7,
5:9, 6:11)
4. Multiplexsuperparticular, if the major number is one more than
twice the minor (5:2, 7:3, 9:4); and its inverse,
Submultiplexsuperparticular (2:5, 3:7, 4:9)
5. Multiplexsuperpartiens, if the major number is one less than some
other multiple (usually three or four) of the minor (8:3, 11:4,
14:5, 11:3); and its inverse, Submultiplexsuperpartiens (3:8, 4:11,
5:14, 3:11)
He then continues to subdivide each type in various ways. For the
multiplex proportions, for example, he indicates how many times greater
the major number is than the minor:
⢠If two times greater, the proportion is _dupla_. If inverted, itâs
called _subdupla_. Examples: 2:1, 4:2, and 6:3.
⢠If three, _tripla_; and its inversion, _subtripla_. Example: 3:1,
6:2, and 9:3.
⢠If four, _quadrupla_; and its inversion, _subquadrupla_. Example:
4:1, 8:2, and 12:3
Other proportions were possible, but whether they were frequently
used is another question:
⢠33:9, _triplasuperbipartientetertias_
⢠51:15, _triplasuperbipartientequintas_
See also
........
mensural notation.
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