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Level of application
No alteration!

Before going on, be sure to be aware of the principles of mensuration - specially the ternary one, of course - that I won't recall here, to make the story shorter.



Coloration, in the white notation wer'e studying, consists in playing three notes written in black in the same time as two normal white ones. This 3/2 ratio is named sesquialtera in Latin or hemiola in Greekish.
This word of coloration is indeed a remembrance of former times, when ordinary notes were black, and coloured ones were red. And the Ars subtilior, around the 1400s, has even expressed its tricky rythms (2/3, 4/3) with all sorts of symbols : empty red notes, plain red notes, etc, the meaning of which wasn't given explicitely and might depend on the piece of music! White notation has kept the 3/2 ratio, forgetting about nearly all the other ones (however, see comments about the minor color sequence). cordier


Level of application

Thus, two normal - uncoloured - bigger notes of the considered level are replaced by three coloured ones, and the bigger note gives its name to this process:

  • tempus tells about the division of the breve, and thus color temporis consists in playing col_brevecol_brevecol_breve in the same time as brevebreve ;
  • prolatio tells about division of the semibreve, and color prolationis means replacing semibrevesemibreve by col_semibrevecol_semibrevecol_semibreve.
  • eventually, one comes often upon a col_semibrevecol_minime sequence called minor color that we shall study later on, but seldom upon the underlying process (which has got no name), that is, coloration of a minimeminime group, replaced by col_minimecol_minimecol_minime ; we'll see that context allows to avoid confusing these coloured minims with ordinary black semiminims!

The detailed consequences of coloration depends on the preexistent nature of the level of application.

Binary level

A new metrical value is always created, corresponding to our modern triplet. For instance in mens_c mensuration, the replacement of brevebreve by col_brevecol_brevecol_breve can be written, in values of breves: 1 1 <==> 2/3 2/3 2/3. But, the value 2/3 of a breve could not be written without coloration in mens_c mensuration.

Ternary level

A first kind of effect is a change of accentuation due to different splitting of values inside the group. For instance in mens_o mensuration, the same replacement of perfect breves brevebreve by col_brevecol_brevecol_breve suggests a 2 2 2 grouping, instead of the 3 3 original one - here we are counting semibreves.
Apel only mentions this accentuation effect for coloration at a ternary level, thus letting us think it doesn't bring new rhythmic patterns. But, that's not the case! Indeed, a value of 2 is quite common in ternary mensuration, like the breve in brevesemibreve because of the imperfection mechanism; however, I notice that a group of values 2 2 2 cannot be written without coloration in mens_o mensuration.

A question of vocabulary

The word color is used, depending on authors, either in a broad meaning, whatever may be the binary or ternary nature of the application level, or in a more precise one, in which color is said for binary levels only, and hemiola for ternary ones. Here are two examples:

color prolationis  mens_c col_3s_lig      hemiola temporis or major  mens_o col_3b_lig

(Coloration is easily and commonly mixed up with ligatures)

The reader will have easily deduced the name of the two other cases: color temporis, and hemiola prolationis or minor.

Fundamental property

Such blackened notes created at this very application level of coloration are always binary; thus, imperfection can never be applied to them, nor alteration to their subdivisions.

This statement is more precise and weaker than the one made by Apel on his page 126: "Blackened notes are always imperfect. [...] Due to the imperfect quality of blackened notes, none of the principles of imperfection or alteration may be applied to them".

For, we shall see that it's important to distinguish, first, the level at which coloration is applied, from, secondly, the lower and upper levels at which it has different consequences. Failing to do so explicitely, Apel states something which, if taken for granted without comment, is absolutely wrong, and, by the way, impossible to assume in practical cases: he himself invokes several times later an imperfection mechanism applied to originally perfect blackened notes, as we'll see very soon!

At the end of this paragraph, I'd also like to insist on the fact that coloration should never be thought in terms of one note, but of the whole group from which it was born: two normal white notes, replaced by three coloured ones; this principle will help us when coming upon sequences made somewhat unclear by a licence in writing (see below).



Like normal notes, coloured ones are often replaced by smaller ones of total equivalent value, and we've just said that this division toward lower levels will always be binary. Coloration is then distributed from the original note to the smaller ones replacing it. Dots written after these binary coloured notes are, of course, addition dots.

First simple examples:    mens_o col_bbss   mens_o col_bssb   mens_o col_ssb1   mens_o col_ssb2

The second example above is a typical case of pure accentual information, shown by the hemiola temporis group col_brevecol_semibrevecol_semibrevecol_breve met under mens_o. For, the same values can be written without coloration by brevesemibreve°semibrevebreve but then we loose the accentual information suggested by col_brevecol_brevecol_breve . BTW, this information is also lost when a modern edition doesn't show passages that were colored in the original!

A few more subtle rythms:    mens_o col_bbmin   mens_o col_minbmin   mens_o col_minbb   mens_cbarre col_minssb

Another hemiola temporis, the group of which is easily recognized despite the embedded white notes!    mens_o col_bb_blanc_b

And here is a beautiful example made of two groups of three black breves:   men_c col_passage1
If you're amazed by the two dotted black semibreves, just think that the two white semibreves that might have replaced them wouldn't have helped one to notice the exact count of values (two groups of three black semibreves, played in the same time as four white breves). This rigorous writing clearly shows complete coloured groups.

Writing licenses
After the discovery of black holes, we now come upon a black rest :-)   mens_o col_minbss
And this one, wouldn't one think it's hesitating between being black or white?   mens_o col_ssbss
Ok, but then... what is its value? Let's have a look: hemiola temporis means replacing two perfect white breves, that is, six white semibreves, by three groups of two black semibreves. Therefore, the count will be the same, whichever color might be the two last symbols! In other words, this license is here allowed by the equality semi-breve=col_semi-breve - a pure accentual effect! (Apel page 131)

Let's not turn our nose up: though surprising, this kind of equality may be useful, provided it does not make us forget the complete group of three values that was created by coloration; this group helps us to find the level of application. Specially under mens_o_pt mensuration, where coloration can be applied to two ternary levels!
Two similar examples taken from the same Chansonnier Nivelle de la Chaussée :   mens_o col_ssbss   mens_o col_ssbb

Of course, such a license is impossible when coloration is applied on a binary level, thus creating new values equal to 2/3 of the original ones! Thus, it even allows one to infere the mensuration when it's not mentionned.
That's what I feel possible (and necessary!) to deduce in this case, for example:   [mens_o] col_bb

And that's right: I've now transcribed this piece, Tout a par moy by Binchois ; the counterpoint works ok under O. And only afterwards I discovered two semibreve rests under the same line in the Cantus part - a reliable proof of tempus perfectum.



Coloured notes can also be grouped at upper level - the one above the application level of coloration : thus  mens_o col_brevecol_brevecol_breve  may sometimes become col_longue  or  col_longuecol_breve   or  col_brevecol_longue  ; quite the same happens in major prolation, where sequences like col_breve or col_brevecol_semibreve or col_semibrevecol_breve may replace the preexistent col_semibrevecol_semibrevecol_semibreve group.

But then, doesn't it seem that at this upper level the bigger notes created by associativity work according to the rules of perfect mensuration ? Well, it is so! That's why I didn't like the early statement made by Apel, according to which coloured notes are always binary; obviously that's not true for the longua in the previous example, and Apel himself gives many such examples, giving this explanation on his page 131 : "The result of coloration in mens_o is usually described as a change from tempus perfectum (B=3S) to tempus imperfectum (B=2S). However, it should be noted that not only does the tempus change but also that the modus simultaneously changes, namely from imperfect (L=2B) to perfect (L=3B)."
Exactly what had said early authors: have a look at the comments about black notes on these documents taken from Blockland and Yssandon.

Restating what I said for distributivity: coloured notes created by associativity at upper level are of a different nature from those first created at the level of application - thus, one should always be aware of the function of these different levels! I'd like to insist, coming back to the example at the beginning of this paragraph: by coloring two longuas, I get three black ones that can be divided binarly (distributivity); on the other hand, the three black breves obtained by coloring two white breves can be grouped according to the rules of a ternary level (associativity). In other words, one thing is to create coloured longuas, another one is to create coloured breves, and then group them from time to time into longuas; that's what took some time for me to understand while reading Apel, but I might be responsible for that..?

Summarizing, coloration of two normal notes at some level will give rise to:
More examples

We now will be able to find many examples, since real music often involves both distributivity and associativity:
Passages (cantus & altus) of 9 black semibreves:   c_barre col_assoc_1a    c_barre col_assoc_1b
This excerpt from A la pesca ogn'homo by Iannis Plice exhibits distributivity (black minims, not semiminims!) and associativity (black breves imperfected by neighbouring semibreves). Notice also the addition dot applied to a binary black semibreve (level of application). For, we have here color prolationis, thus to be read under black mens_o, so to say (a color temporis would create three black binary breves, thus six black semibreves when starting with two white breves, or twelve when starting with two such sequences, but never nine).

I've put on a different page another example taken from the Manuscrit italien des frottole.

The bass part of this piece shows a minor color sequence, which will be studied later on; for now, let's just take its transcription for granted.

Same manuscript, pages 138-139, under c_barre  tenor rusticus_ten  altus rusticus_alt
In each part, one sees that the semiminim and the next two notes must be understood as subdivisions of a binary black breve; thus we have here color temporis. The tenor shows two coloured minims, while in the altus the two notes written like fuses are obviously semiminims, so written, in my opinion, to avoid any confusion with colored minims!

Same manuscript, pages 162-163, under c_barre  tenor mortefai_ten  altus mortefai_alt
Ternary division is here shown by the sequence of col_brevecol_semibreve rythms, and by their horizontal spacing (thanks to the scribe!). Hence we have a case of color prolationis - notice, once more, the three coloured minims in the tenor part.

Same manuscript, page 130, Cantus, second line: c_barre orcheson
Here the scribe makes explicit the ternary division, probably because we have a rather unfrequent case of coloration, that is, the one replacing minimeminime by col_minimecol_minimecol_minime (three coloured minims). The col_semibrevecol_minime at the beginning, called minor color is however quite frequent, even if its transcription is sometimes questionable (see further) - here there's no doubt about a ternary evaluation. As for the last coloured group (that is, the first one read backwards), it involves imperfection of the last coloured semibreve on the left side.

Symbolic usage
Under white notation, coloured really means black, thus some pieces were entirely written in black just to illustrate their meaning of relief or sadness. Have a look at the right side, where you see the cantus of Josquin Deprez's famous deploration on the death of Jean Ockeghem - coloration is there nothing but an illustration, without any mensurational consequence. josq_depl
And here is the contra of Andati accesi mei suspiri, a piece taken from the same Manuscrit italien des frottole (page 71).
This color prolationis could have been as well notated by tempus perfectum in white values.


No alteration!

We've seen that black notes can be grouped at upper level according to the rules of a ternary mensuration. It's nearly true, for colored notes are never altered.
You might like to just accept this new rule; after all, that's only one more to be memorized :-) As for me, I'd like to prove that this is not an exception, but rather a logical consequence of the fact that the reason having lead to introduce alteration of white notes doesn't exist any more for coloured ones.

Reason for alteration of white notes (reminder)

Before its introduction, a 1 2 3 rhythm could not be written, for, in the first candidate sequence semibrevebrevebreve the next to last breve, before its similar sister on the right side, must be equal to 3 (simila ante similem perfecta). Thus the artifice of alteration - legal, in principle, only when it is necessary - leads to write this rhythm as a semibrevesemibrevebreve sequence, in which the value of the second semibreve is doubled.

This reason disappears with colored notes

First example : coloring the tempus, the three resulting black breves are built binary, thus one can't even think of alteration for black semibreves.

Second example : coloring the prolatio, we get three black semibreves. Grouping at upper level may then make this sequence appear as col_semibrevecol_breve ; but, the total value of the group remaining unchanged, we see that the so created black breve, which did not exist before as a ternary note, is equal to 2/3 of this total without ambiguity (let's save some space for this poor lonely col_semibreve !). In other words, this black breve is, so to say, born imperfect, and thus the 1 2 rhythm can be - and must be - written without using the artifice of alteration.

As a matter of fact, alteration became old fashioned earlier than coloration [Apel page 136] : "Blackened notes are also frequently used in later sources (after 1550) for the expression of the iambic rhythm which was formerly indicated by alteration, e.g.: mens_o semibrevesemibrevesemibrevebrevesemibrevecol_semibrevecol_brevebreve  instead of  mens_o semibrevesemibrevesemibrevebrevesemibreve°semibrevesemibrevebreve "

Thank you for your patience: other paragraphs to come...