43: Transformations of rhythms using Bach's Credo

 There are certain places in the Mass where the rubrics (red text that says basically “be in place X doing thing Y in posture Z with person A helping you out in manner B”, from which we get the term for “grading standards provided to a student along with an assignment) say, especially in the case of a particularly solemn liturgy, “and then the Priest, or the Deacon, or if none are present, the Cantor, intones the [something]”. This could be, for example, the priest singing alone “Gloria in excelsis Deo” which, in a sense, gives the choir permission to start singing the Gloria, and so on.

Once I’ve laid a complete enough theoretical foundation, these articles will switch to discussions, or listening guides, more than instructional material teaching basic theory. And when that day comes, there’ll be more material written here about the Mass in B minor than you could ever imagine.

 But for now, I want to use the first movement of the Credo (the Nicene Creed, in English, “I believe in one God, the Father almighty […] and I look forward to the resurrection of the dead and the life of the world to come.”) to look at some things you can do to a melody, like someone might study rotations, reflections, and translations in high school geometry.

 Like I said, there’s so much more to be said about the Mass in general and about the Credo (the section, and the first movement specifically), but all the context you need for now is this: the main melody is the subject of a 5-voice fugue accompanied by 2 violins, and that subject is very close what the Roman Missal (the book with all the rubrics and prayers the priest prays throughout the Mass) suggests be the melody the priest use to “intone the Credo” whenever that’s asked for. The original is in 8/4 (this time signature is so obscure, there isn’t even a character in the Bravura font I can insert, so this way will have to do), but to make things easier to read, I’ll notate it in to start with. (The whole point of this article is to do things to it that may change that.)

First, here is what the Missal says:

And now here is the subject (with the accompanying bassline):


We can actually just work with the melody for now, but I wanted you to see the bassline first before we discard it.

 Doing so leaves us with:


And perhaps a natural question to ask is “what if we double/halve the note values?”

·       Doubling the values is a process called augmentation (no relation to augmented intervals), and actually gets us right back to Bach’s original

Note that the original starts with a “double-breve” note that means something double a whole note, so 8 beats:

·       Halving is called rhythmic diminution, and applied to the “modified original”, which looks like


 Then, of course, there are more things we can do, like:

·       Reflect the intervals across an axis (for example: an original D above the B in the middle of the treble clef becomes a new G# below B; a minor third above the center “inverts” to a minor third below the center; an A )

·       Print the excerpt backwards (E C# D C# B E F# becomes F# E B C# D C# E)

·       Combine any of these rules (stretch/shrink, reflect, forwards/backwards) how we would like to

This is important for a variety of reasons across different eras. In the harmonic language of the great Baroque contrapuntists like Bach, it provides a wealth of options for how to write fabulously difficult counterpoint (Bach, at times in his cantatas, writes a subject in counterpoint with several degrees of augmentation of the subject; it’s already difficult enough to write counterpoint of a subject against itself, and the fact that he does it so well with the subject against what is functionally a fast-forwarded or slowed-down version of itself makes this all the more impressive). And in the modern period of the 20th century and beyond, it underpins the 12-tone system of Schoenberg and his musical successors. 

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