Implement mensur@level

[craigsapp]

It would be useful to implement mensur@level which indicates which rhythmic level a (sesquialtera) proportion is applied.

Below is an example work that contains a basic example of sesquialtera applied to only one part, so you can see how the alignment should work between music with/without sesquialtera:

Fortuna desperata, attributed to Josquin des Prez (he likely wrote the contra part), Segovia Manuscript:

https://vmirror.imslp.org/files/imglnks/usimg/a/aa/IMSLP322463-PMLP521914-cancioneiro_de_segovia_parte2.pdf#page=129

Superius part (no sesquialtera):

Tenor part (no sesquialtera):

Contra part (sesquialtera near the end):

The sesquialtera is indicated by the "3" mensuration sign:

The "3" means that within the context of the current mensuration of cut-c, there are now three minims in the time of two minims.

Here is a CMN transcription:

https://josquin.stanford.edu/cgi-bin/jrp?a=notationEditText&f=Jos2711

Section of the full score where sesquialtera is active in the contra part:

There are two possible types of sesquialtera in a fully imperfect mensuration such as C and Cut-C. And in this particular case, it does not really matter, but minor sesquialtera makes the most logical sense, occurring at the prolatio level, where the semibreve is split into three minims rather than two (but the three minims take up the same time as two of the original minims, i.e., they become triplets in CMN).

The other possiblity is major sesquialtera:

which means that there are three semibreves in the time of two original ones. In both cases there will be six minims. Since there are no semibreves in the music it is not totally clear that there are two or three semibreves for each breve. But the melodic contour mostly grouping minims into three implies that there are three minims for each original two rather than three semibreves for each original two semibreves.

How to represent the "3" mensuration is not totally clear. Here is a possibility:

<mensur num="3" modusmaior="2" modusminor="2" tempus="2" prolatio="3" level="minim">

One problem is that this is in the context of Cut-C, so there should also be a 2:1 proportion or slash attribute present as well as an implicit sign of C that is usually not displayed:

<mensur num="3" modusmaior="2" modusminor="2" tempus="2" prolatio="3" level="minim" sign="C" slash="1">

questions:

(1) Should @level be minim or semibrevis for minor sesquialtera (three minims in the time of two minims)?

(2) I believe there is no way to display a "3" mensuration in mensural music currently? I hack it in CMN with:

        <meterSig count="3" unit="2" form="num" />

This mensur does not print anything in verovio:

    <mensur num="3" />

Is there currently a way of displaying a "3" mensuration?

(3) Sesquialtera is a 3:2 proportion. Should this be encoded in mensur@num and mensura@numbase, or something like mensur@proport.num and mensur@proport.numbase?

(4) Note that Cut-C has an implicit porportion of 2:1 due to the slash. How would the 2:1 proportion of the main mensuration sign and the 3:2 proportion both be indicated at the same time.

(5) Note that there are mensuration signs C2, C3, O2, O3 which are not related to sesquialtera (but they can be visually the same as sesquialtera or cancellation of sesquialtera in C and O). How should non-proportion numbers on these mensuration signs be encoded (currently using mensur@num). It is unlikely that these mensuration signs will include sesquialtera (at least I have not seen any cases).

Here is the draft MEI data for this example: fortuna-desperata.zip

The 3 mensuration will probably need to be fixed. Currently it is:

        <mensur xml:id="mensur-L291F1" num="3" numbase="2" modusmaior="2" modusminor="2" tempus="2" prolatio="3" level="minim"/>

[craigsapp]

Here is another case that starts with O3/2 mensuration and then goes into C mensuration (both parts doing the same mensurations at the same time). The meaning of O3/2:

This is equivalent to C with major sesquialtera, with the only difference is that the tempus level is already perfect (so does not need to be perfected as in C). The 3/2 is the sesquialtera proportion that means there are three semibreves in the time of two. Note in the following music that each measure (breve length) should have the same duration, so when switching to C, the perfect breve of O3/2 mensuration has the same duration as the imperfect breve of C mensuration:

In verovio MIDI playback, the C mensuration music is too slow (I would have predicted that the O3/2 was too slow).

The music is otherwise aligned through the entire piece (only two parts are extant):

Here is a zip file containing the draft MEI data for this example: ovetra.zip

Scans of the original edition:

[lpugin]

To your questions:

(1) Should @level be minim or semibrevis for minor sesquialtera (three minims in the time of two minims)?

Up to us to decide. @annplaksin, what did you have in mind?

(2) I believe there is no way to display a "3" mensuration in mensural music currently?

This mensur does not print anything in verovio:

<mensur num="3" />

I will change this and also implement support for showing cases with only @numbase. However, these will probably not make much sense without at least a @sign or a @num, but we can still show a @numbase alone. In that case I would put it one the lowest line and not in the middle.

(3) Sesquialtera is a 3:2 proportion. Should this be encoded in mensur@num and mensura@numbase, or something like mensur@proport.num and mensur@proport.numbase?

My question here is do we really need the proportion to be given if we have @level? The proportion will always be 3:2 in a sesquialtera, won't it? Or are you thinking for @level not to be required?

(4) Note that Cut-C has an implicit porportion of 2:1 due to the slash. How would the 2:1 proportion of the main mensuration sign and the 3:2 proportion both be indicated at the same time.

See above. If we assume an implicit 3:2 proportion for the sequialtera encoded with @level, then @num and @numbase remain free for the Cut-C proportion. The only problem is having a what for not showing them, which I think relates to the question below.

(5) Note that there are mensuration signs C2, C3, O2, O3 which are not related to sesquialtera (but they can be visually the same as sesquialtera or cancellation of sesquialtera in C and O). How should non-proportion numbers on these mensuration signs be encoded (currently using mensur@num). It is unlikely that these mensuration signs will include sesquialtera (at least I have not seen any cases).

These are cases where I think we need a distinct attribute to encode the logical value when it does not correspond to the visual one, or when there is no visual one. @num.log and @numbase.log would solve questions (4) and (5). For example,

For non-proportion numbers, (e.g., a C3), you would do:

<mensur num="3" num.log="1" sign="C"/>

For a Cut-C, you would do

<mensur num.log="2" sign="C" slash="1"/>

However, for that particular case, I wonder if we should not expect the 2:1 proportion to be inferred from the visual information (the slash). At least this is what I thought you would want to have from this discussion.

In verovio MIDI playback, the C mensuration music is too slow (I would have predicted that the O3/2 was too slow)

The MIDI playback applies the num="3" and numbase="2" proportion. I guess this is why it is is faster than C.

[craigsapp]

<mensur num="3" /> I will change this and also implement support for showing cases with only @numbase. However, these will probably not make much sense without at least a @sign or a @num, but we can still show a @numbase alone. In that case I would put it one the lowest line and not in the middle.

As you note, "3" mensuration has no meaning in isolation and there is an implicit @sign which can be either C or O (which is found earlier in the music). So it will be necessary to supply the implicit information, particularly @tempus and @prolatio.

A question is: should the implicit information be extracted automatically from the previous <mensur> in the music, or should it be required to be given within the <mensur num="3" />. Sometimes the 3 mensuration is cancelled by using a 2 (not very often in JRP repertory), or by repeating the original sign, such as Cut-C. Tinctoris likes fully explicit proportions, so I think he would have something such as 2/3 to cancel the 3/2 proportion.

Preferably the 3 mensuration in isolation will be centered on the middle line. In the first example given above, I think it is just for continuity that the 3 is at the bottom of the staff, since there is no meaning for it being there other than the notes are near the bottom of the staff.

[annplaksin]

at 1) According to the (very hard to find) paragraph in the documentation, @level contains the note level that is affected. In the case of three minims in the time of two minims it would be:

<mensur num="3" numbase="2" level="minima" />

at 2) I think it works with <proport>:

<proport num="3"/>

at 3) When @level is used, I guess, we still need to use @num/@numbase to define how the given note level will be affected.

at 4): If every part has a Cut-C, I think, there is no reason to use num/numbase for the implicit proportion. Because, I assume, a proportion is always a comparison. The question in the case of Cut-C is: 2:1 compared to what? Also, the 2:1 is not always a question of tempo, but also a question of tactus.

regarding the last comment: Giving @tempus and @prolatio is absolutely crucial for the case of "3". Not to give the information of an earlier sign but because the "3" will change the mensuration implicitly. The most common case is sesquialtera following an imperfect tempus. Something like that in a case of Cut-C followed by a 3:

<mensur sign="C" slash="1" prolatio="2" tempus="2" />
[... some music...]
<mensur num="3" numbase.log="2" level="semibrevis" tempus="3" />

[craigsapp]

My question here is do we really need the proportion to be given if we have @level? The proportion will always be 3:2 in a sesquialtera, won't it? Or are you thinking for @level not to be required?

@level is required since mathematically it can be applied at two possible rhythmic levels. The first case above is very simple and does not include any semibreves to resolve which one in this case, so it is not totally obvious since it works either on the semibreve or minim levels.

Perhaps @level should be described as @level="tempus" and @level="prolatio" @annplaksin? When at @level="tempus" that would mean the semibreves are in 3:2 proportion and a perfection of the breves (if they are not already perfected as in the second full example above). @level="prolatio" would mean the minims are in 3:2 proportion and a perfection of the semibreve (if it is not already perfected).

I would not have problems with @level implying a 3:2 proportion (and perfection as needed). But given the name, it seems that it should mean to apply some proportion at the specified level (not necessarily sesquialtera). Otherwise the attribute should be called @sesquialtera if it has a fixed proportion meaning.

For @slash="1", I think that is reasonable to assume a 2:1 proportion is implicitly built in. When mixed with other mensurations at the same time, such as C and Cut-C, this is the meaning of the slash. When the music only has Cut-C, then the meaning of the slash becomes more ambiguous and changes over time (i.e, it does not always mean play twice as fast as C). But those ambiguities can be handled by adjusting the tempo.

[annplaksin]

Perhaps @level should be described as @level="tempus" and @level="prolatio" @annplaksin?

No. Tempus describes the relation between brevis and semibrevis level. This is the main indicator if rules of imperfection or alteration should be applied. Level describes which note level is affected by a succesive proportion.

[craigsapp]

No. Tempus describes the relation between brevis and semibrevis level. This is the main indicator if rules of imperfection or alteration should be applied. Level describes which note level is affected by a succesive proportion.

OK, that sounds good.

In the first example given above, that would mean that @level="minim" should be used (but in this case @level="semibrevis" is also possible since there are no semibreves to resolve which level the sesquilatera/perfection is happening on).

[craigsapp]

Here is an analysis of the second example which has O3/2 at the start and goes into C. I extracted the timemap values for the measure just before and after the C mensuration starts:

There is a 3:2 proportion being added, but at the wrong rhythmic level. The durations of each measure (i.e., the durations of the breves) should be equal, since the proportion is not applied to the breve level. In the above example the first measure (breve) is 2700 units, while the second is 4050, which is a relation of 3:2 between the meaures (breves). The breve level should remain 1:1.

Instead the 3:2 proportion should be applied to the semibreve level. This should make semibreves 3:2 between the two measures. Currently there is a 9:4 relation between the semibreves in the first measure compared to the second measure.

Here is a rhythm chart for O3/2 that should be happening:

(I adjusted the charts so the proportions are under the rhythmic levels as @annplaksin wants). So the <mensur> should be (as it is in the example data):

<menur sign="O" num="3" numbase="2" modusmaior="2" modusminor="2" tempus="3" prolatio="2" level="semibrevis" />

Verovio is currently doing this:

which is <mensur level="brevis" /> instead of <mensur level="semibrevis" />.

Here is one way of detecting the problem:

In terms of modern notation, the semibreves are triplet semibreves in O3/2, so in modern notation the two measures are:

[lpugin]

I think looking at the current implementation of the timemap in Verovio is confusing since it applies the proportion from the base level - which is why you end up with a 9:4.

What is not clear to me is the difference between a @level="brevis" and the C3 and O (column 2 and 5) in the example you give in this discussion. The proportion on the brevis level seems to duplicate the tempus being perfect. What I am misunderstanding here?

[craigsapp]

Here is a schematic of what is currently being done using the timemap values as an example:

And what should be done:

I am using 4050 for the duration of the breve in C as a reference. The problem to resolve is why the breve duration in O3/2 is not equal to the breve in C.

Conceptually what seems to be happening is that the longa is perfected on the left for O3/2. The theoretical longa would have a duration of 8100, so the breve is 1/3 = 2700 while for C the breve is 1/2 of a longa = 4050. This is where the extra 3:2 proportion is coming from to generate the 9:4 proportions at the semibreve level.

Something is causing the breves between the two mensurations to not have the same durations, but they need to be the same.

[craigsapp]

Here is a schematic that seems to make things clearer:

The gray boxes are the durations of the notes. The 3:2 proportion is applied at the semibreve level. This causes the original perfect breve duration to shorten to 2/3 of its original length, and now the breve duration in O3/2 is the same as the breve in C.

O mensuration is given on the right for comparison. The breve in O has a duration of 1.5 (3:2) times longer than the breve in C due to the perfection of the tempus. The sesquialtera being applied in O3/2 is making the breve have the same duration in C and O3/2.

[craigsapp]

Here is a demonstration of how @level works:

Note that C3/2 is not usually fully spelled out (except for Tincoris who compliains that proportions should be fully spelled out). Most typically 3 is used to represent the same thing, but also C3 is used (and in most if not all cases in JRP, the C is replaced with a Cut-C) [And note C3 is also a separate mensuration sign describing the divisions of the modusminor and tempus levels]. Also note that to cancel sesquialtera, often 2 is given as the mensuration sign, although in JRP most cancellations are done by given the original mensuration sign before the sesquialtera.

Whenever there is a sesquialtera, that implies that the given rhythm level is perfected so that the 3:2 proportion can be applied to their durations, making three of the perfected notes fit into the time of two of the imperfect notes. Before the Petrucci style sesquialtera mensuration signs, there is an additional implied change from 2 to 3 for the given level that the sesquialtera is done at. With a mensuration sign such as 03/2, the level is already perfected, so the step of perfecting the rhythmic level is not needed.

Notice in the above figure that there are six minims in either major sesquialtera (left side) or minor sesquialtera (right side). The original example Fortuna desperata at the top of this thread has six minims in the time of four, so either type of sesquialtera can be used since there are no semibreves to resolve which one. But if you look at the pattern of the minims, they look like they are grouped into threes, making minor sesquialtera a better description of what is happening.

[lpugin]

How does this look?

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