Proportion signs as implicit mensurations

[annplaksin]

As promised on the SIG meeting I try my best to summarize the problem.
First, I would like to point on that this issue is highly related to that discussion on Verovio: staffDef@proport.numbase without @proport.num? #863

The problem in mensural notation is, that meanings can change slightly over time and location. This is mainly the reason why I appreciate approaches giving the meaning as well as the sign itself.
Anna Maria Busse Berger pointed out in her book "Mensuration and Proportion Signs. Origins and Evolution" (Oxford, 1993) the vast differences of proportion signs, on the one hand considered to be like mensuration signs, on the other hand as a sign mainly for diminuition. (in short, p. 228)

This comes along with consequences in interpreting proportion signs:

• Proportion signs interpreted as mensurations affect the relations of note levels. A fraction given with @num/@numbase affect in those cases not all note levels:
  E.g. sesquialtera as implicit mensuration after a cut C shortens the semibrevis by a third and every smaller note level in consequence as well. But larger note levels remain unchanged.
• Proportion signs as implicit mensuration signs could affect perfection/imperfection.
  In the mentioned example, rules of perfection needs to be applied on breves.
• Proportion signs as implicit mensurations are not cumulative while understood as independent entity are cumulative. (Busse-Berger, p. 196)
• Proportions do not always compare semibreves (Busse-Berger, p. 212)

Therefore, we have a messy relationship between proportion signs and its meanings. A sesquialtera for example could be a diminuition by a third could be an implicit mensuration change. And it could be marked with a 3, a 3/2 or a 3 with a circle above.

A music example for a sesquialtera as implicit mensuration change is Josquins Tu solus qui facis mirabilia. There are a lot more and more complex as well.
As well, I don't want to discuss all the cases made in Busse-Berger's book, but I value it as a compilation of complication.
For now, this summary hopefully serves as a starting point for a discussion on how to deal with proportions. Because we should find a way to deal with it.

[lpugin]

I recall discussions about introducing more gestural alternative for attributes. For example, having both mensur@num and mensur@num.ges. Of course, this would not solve all the issues listed above. However, allowing for a distinct encoding of the visual and gestural domain when they do not concur is a quite powerful feature of MEI and I suspect it also to be a useful one here.

[annplaksin]

I would like to point out to following examples, both Tu solus qui faci mirabilia:
http://www.e-codices.unifr.ch/en/csg/0463/31v CSGall463, 31v (Tschudi Liederbuch)
https://digi.vatlib.it/view/MSS_Capp.Sist.41 Capp.Sist.41 155v

Here we have different proportion signs meaning the same. A sesquialtera with an implicit change of mensuration from tempus imperfectum to tempus perfectum, that means rules of imperfection come into play.

[annplaksin]

Please see as well music-encoding/music-encoding#686 about the encoding of "3"