LilyPond Music Glossary: 1.190 mensuration sign

## 1.190 mensuration sign

ES: signo de mensuración, I: ?, F: signe de mensuration, D: Mensurzeichen, 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 tempus), and of semibreves to minims (called 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 ternary ratio was the preferred one—applied to the tempus, it was called perfect, and was represented by a complete circle; applied to the prolatio, it was called major and was represented by a dot in the middle of the sign. The binary ratio applied to the tempus was called imperfect, and was represented by an incomplete circle; applied to prolatio, it was called 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.)

perfect tempus with major prolatio

  Indicated by a complete circle with an internal dot. In modern time signatures, this equals:

  - 9/4, with reduction or
  - 9/2, without reduction
perfect tempus and minor prolatio

  Indicated by a complete circle without an internal dot. In modern time signatures, this equals:

  - 3/2, with reduction or
  - 3/1, without reduction
imperfect tempus and major prolatio

  Indicated by an incomplete circle with an internal dot. In modern time signatures, this equals:

  - 6/4, with reduction or
  - 6/2, without reduction
imperfect tempus and minor prolatio

  Indicated by an incomplete circle without an internal dot. In modern time signatures, this equals:

  - 4/4, with reduction or
  - 2/1, without reduction

The last mensuration sign looks like common-time because it 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:

- maxima to longa, called:
  - modus maximorum,
  - modus major, or
  - maximodus)
- longa to breve, called:
  - modus longarum,
  - modus minor, or
  - modus

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 tempus imperfectum and prolatio minor now stands for common time; and the slashed C, which designated the same with diminution now stands for cut time (essentially, it has not lost its original meaning).

#### See also

diminution, proportion, time signature.

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