Editing Time signature (section)

===Proportions===
{{Main|Mensural notation#Proportions and colorations}}
{|class="wikitable skin-invert-image" style="float:right;clear:right;"
|+Proportion signs{{sfn|Apel|1953|p=150}}
!scope="column"|Proportion
!scope="column" |Notated values
!scope="column"|equivalent to
!scope="column"|Notated values
|-
|[[File:Tempus impf prol min.svg|x30px|Semicircle without dot]] '''2''' or [[Image:Allabreve.svg|12px]]
|[[File:White mensural brevis.svg|x30px]] <br> [[File:White mensural semibrevis.svg|x30px]][[File:White mensural semibrevis.svg|x30px]]
|[[File:Tempus impf prol min.svg|x30px|Semicircle without dot]]
|[[File:White mensural semibrevis.svg|x30px]] <br>  [[File:White mensural minim.svg|x30px]] [[File:White mensural minim.svg|x30px]]
|-
|[[File:Tempus perf prol min.svg|x30px|Circle without dot]] '''2''' or  [[Image:mensural proportion 2.svg|13px]]
|[[File:White mensural brevis.svg|x30px]][[File:White mensural brevis.svg|x30px]][[File:White mensural brevis.svg|x30px]]<br>[[File:Two semibreves.svg|x30px|alt=two semibreves]][[File:Two semibreves.svg|x30px|alt=two semibreves]][[File:Two semibreves.svg|x30px|alt=two semibreves]]
|[[File:Tempus perf prol min.svg|x30px|Circle without dot]]
|[[File:Three semibreves.svg|x30px|alt=three semibreves]]<br>[[File:3x2 minims.svg|x30px|alt=three groups of two minims]]
|-
|[[File:Tempus impf prol min.svg|x30px|Semicircle without dot]] '''3'''
|[[File:White mensural brevis.svg|x30px]][[File:White mensural brevis.svg|x30px]]<br>[[File:Three semibreves.svg|x30px|alt=three semibreves]] [[File:Three semibreves.svg|x30px|alt=three semibreves]] 
|[[File:Tempus impf prol mai.svg|x30px|Semicircle with dot]]
|[[File:Two semibreves.svg|x30px|alt=two semibreves]]<br>[[File:2x3 minims.svg|x30px|alt=two groups of three minims]]
|-
|[[File:Tempus perf prol min.svg|x30px|Circle without dot]] '''3'''
|[[File:White mensural brevis.svg|x30px]][[File:White mensural brevis.svg|x30px]][[File:White mensural brevis.svg|x30px]] <br>[[File:Three semibreves.svg|x30px|alt=three semibreves]] [[File:Three semibreves.svg|x30px|alt=three semibreves]] [[File:Three semibreves.svg|x30px|alt=three semibreves]]
|[[File:Tempus perf prol mai.svg|x30px|alt=Circle with dot]]
|[[File:White mensural semibrevis.svg|x30px]][[File:White mensural semibrevis.svg|x30px]][[File:White mensural semibrevis.svg|x30px]] <br>[[File:3x3 minims.svg|x30px|alt=three groups of three minims]]
|}

Besides showing the organization of beats with [[musical meter]], the mensuration signs discussed above have a second function, which is showing tempo relationships between one section to another, which modern notation can only specify with [[tuplet]]s or  [[metric modulation]]s. This is a fraught subject, because the usage has varied with both time and place: [[Charles Hamm]]<ref>C. Hamm: ''A Chronology of the Works of Guillaume Dufay based on a Study of Mensural Practice'' (Princeton, New Jersey, 1964)</ref> was even able to establish a rough chronology of works based on three distinct usages of mensural signs over the career of  [[Guillaume Dufay]] (1397(?) – 1474). By the end of the sixteenth century [[Thomas Morley]] was able to satirize the confusion in an imagined dialogue:
<blockquote>it was a world to hear them wrangle, every one defending his own for the best. "What? <!-- … -->You keep not time in your proportions." "You sing them false. <!-- … -->What proportion is this?" "Sesquipaltry." <!-- … -->"Nay,<!-- … --> you sing you know not what; it would seem you came lately from a barber's shop where you had 'Gregory Walker' or a [[Courante|Curranta]] played in the new Proportions by them lately found out, called 'Sesquiblinda' and 'Sesquihearkenafter'."

::<small>''Plaine and Easie Introduction to Practicall Musicke'' (1597)<ref>[[Thomas Morley]]: ''Plaine and Easie Introduction to Practicall Musicke'' (1597), quoted in the unsigned "Proportions" in [[New Grove]] XV p. 307 (1980)</ref></small>
</blockquote>
In general though, a slash or the numeral 2 shows a doubling of tempo, and paired numbers (either side by side or one atop another) show ratios instead of beats per measure over note value: in early music contexts {{music|time|4|3}} for example is unrelated to 'third-notes'.{{sfn|Apel|1953|p=189}}

A few common signs are shown:{{sfn|Apel|1953|p=148}}
* [[Image:Allabreve.svg|12px]] ''tempus imperfectum diminutum'', 1:2 proportion (twice as fast);
* [[Image:mensural proportion 2.svg|13px]] ''tempus perfectum diminutum'', 1:2 proportion (twice as fast);
* [[Image:mensural proportion 5.svg|22px]] or [[Image:mensural proportion 4.svg|10px]] ''proportio tripla'', 1:3 proportion (three times as fast, similar to triplets).

In particular, when the sign [[Image:Allabreve.svg|11px]] was encountered, the [[Pulse (music)|tactus]] (beat) changed from the usual whole note (semibreve) to the double whole note (breve), a circumstance called ''[[alla breve]]''. This term has been sustained to the present day, and though now it means the beat is a [[minim (music)|half note]] (minim), in contradiction to the literal meaning of the phrase, it still indicates that the ''tactus'' has changed from a short to a doubled value.

Certain composers delighted in creating mensuration canons, "[[Puzzle canon|puzzle]]" compositions that were intentionally difficult to decipher.<ref>Ernst Friedrich Richter, ''[https://books.google.com/books?id=HNOwAAAAIAAJ A Treatise on Canon and Fugue: Including the Study of Imitation]'', translated from third German edition by  Arthur W. Foote (Boston: Oliver Ditson, 1888): 38. {{pre ISBN}}.</ref>