Baroque triplets + dotted rhythms

• Dec 1, 2022 - 06:28

I'm trying to typeset some Baroque music, where triplets are accompanied by dotted rhythms. It is a very common notation convention: a dotted eighth note + sixteenth note is understood as a quarter note + eighth note under a triplet. The first example here is from the Prelude in D major, from WTC2, BWV 874. On the left is the example in modern notation, and on the right is the original notation, but with wrong vertical spacing (and wrong playback).


The second example is how it should look like, taken from a scan of the Bach-Gesellschaft Ausgabe edition.


Could you please guide me, step by step, how to do this?


If you can, typeset it according to modern standards so today's musicians will understand it without thinking you've made an editorial rhythmic error.

But if you need to reproduce this (for example for educational purposes): use tuplets to make your notations match. Since playback is supposed to be in triplet feel, that is what we start from: correct time positions.
Then you create a tuplet for each time duration to alter its notational duration to match your intent.

In reply to by jeetee

That's the solution, your example perfectly explains it. Thank you!

And yes, I feel I do need to do it like this, because I do not dare changing what Bach wrote. If Bach used this notation for his music, I'll use this notation for his music. I do not see myself worthy of being Bach's editor. But that's just my personal opinion, neither here nor there. The technical part of this question has been answered.

In reply to by kresimir

Wait. You know Bach wrote this like this? Do you know when the version you are using was published. I found a version that looks just like yours that was published in the mid 1800's. Who knows from what source. Yes, it may have been the practice 250 years ago to write and play this way. Did you know that technically, none of the instruments Bach wrote for exist, or are used, today? Should we play his two part inventions on piano? Trumpet and horn parts were written for valveless instruments. For example.
Glad your question has been answered.

In reply to by bobjp

Yes, bobjp. Of course Bach wrote like this. Pretty much everyone in Bach's time wrote music like this. For this specific piece we don't have his manuscript facsimile, but I do have the second best thing, a facsimile of a manuscript by his pupil (and son-in-law) Johann Christoph Altnikol. Here is the measure in question (in soprano+bass clef):


And yes, of couse I know when version I posted above was published, I already wrote what edition that is, the Bach-Gesellschaft Ausgabe edition. It's from 1866. This doesn't change anything. Here is the same measure from Neue Bach-Ausgabe, from 1995:


This is simply the proper way to notate Baroque music. Nobody who knows anything about Baroque music is confused by this. It is very similar to Jazz where swing notes are not notated correctly rhythmically, but no Jazz player gets confused by the notation. And I was certainly not about to change four centuries of tradition, just because I didn't know how to do it in MuseScore. Frankly, I would sooner abandon MuseScore and use something else. Fortunately, that won't be necessary.

Just to prove that Bach did use this notation style, here are the first few measures from the very famous chorale "Jesus bleibet meine Freude" from cantata no. 147, in the author's manuscript:


What is even more interesting here is that the mixed time signature is explicit. Notice, the first violin part is in 9/8, but the second violin is in 3/4, as well as all other parts which do not have the "triplet" rhythm. However, it is clear here that the dotted rhythms in 3/4 are not to be played as written here, that is in 3 to 1 ratio, like they normally are (because they would clash with the "triplets" above), but in 2 to 1, or in other words, as if they were a quarter note plus an eight note under a triplet. So when typesetting this score, the same adjustment of vertical spacing would have to be done, otherwise the sixteenth notes in the second violin part would be too far to the right.

Regarding the claim that "none of the instruments Bach wrote for exist, or are used, today", there is no need to comment on that, beyond saying that it is patently untrue (utterly absurd, even) and, in any case, entirely irrelevant for this discussion.

In reply to by kresimir

Thanks for your input. Obviously, I am not an expert on Baroque notation. Much like you are not an expert on Baroque instruments. Though not pertinent to this discussion.
There is a school of thought that suggests that everything was played with a swing like feel. Which would support this type of notation. Truth is that we don't really know how music was performed. There is almost no information about it. Ask yourself why. Possibly because the vast majority of the population of Europe never heard any of Bach's music. Or any of the other composers music. Maybe in church, or at the opera. The latter being for the elite population. You had to be a member of a patron's court to hear regular concerts.
Besides, just because composers wrote things that way doesn't make it correct. It makes it the best way they could write it. And yes, everyone knew what it meant. But they didn't have to satisfy mathematically correct software. So you have to resort to tricks to get it to look and playback the way you want.

In reply to by bobjp

Sure; the main thing to keep in mind from 4 to 5 is the difference between correct playback timing (step 4) and correct notation result (step 7). I've placed them side-by-side here for convenience:
We want our notes to play for the actual duration of one thing, but we want that note to look like a different duration. This means we have to trick the notation into showing a different amount of notational duration to fit inside that actual duration; and the way to do so is by using a tuplet.

General note about Tuplet Ratios

A Tuplet ratio consists of two numbers: A : B.
The second number (B) indicates which base duration we want to use in the tuplet. It does so by saying how many notes of the chosen duration fit inside the total tuplet duration.

A (hopefully clarifying ;-) ) example:
Starting from a 1/4th rest a tuplet of ratio A : 2 will use a 1/8th note as its base duration inside the tuplet; because one can fit 2 1/8th notes inside a 1/4th duration.
Similarly, starting from the same 1/4th rest, a tuplet of ratio A : 4 will use a 1/16th note as its base duration inside the tuplet; because 4/16ths = 1/4th.
Finally, if we would use the same ratio (A : 4) but now start from a 1/8th note, the resulting base duration will equal to a 1/32nd duration.

The first number (A) tells you how many notes of the chosen duration will end up in the tuplet.
A tuplet in the form 3 : B (also called a triplet) will end up with 3 notes in the chosen base duration. A tuplet using 25 : B will end up with 25 base durations inside it instead.

Now let's bring that knowledge together in our example scenario:

Starting from the first note, treble staff, voice 1

We want our note to play for the duration of the 1/4th rest as in measure 4. But we want that note to look like a dotted 1/8th note (as in step 7).
Since a dotted 1/8th isn't a clean divider of the starting duration (1/4th) we need to look at it a different way. A dotted 1/8th has a total duration of 1/8 + 1/16(the dot) = 3/16ths. So if our tuplet can end up with 3 16th notes, we'd have achieved our goal. We thus start by presuming a tuplet ratio of 3 : B if we can find a B that'll result in 1/16th base duration.

And we can!
Because 1/16th is a clean division of our total starting duration (1/4th). Normally, there'd fit 4 16ths into this 1/4th. As a consequence our second tuplet ratio number thus becomes A : 4

Bringing it together means we need a tuplet with a ratio of 3 : 4 starting from the quarter rest to end up with 3/16ths instead. Once we have those, we can combine those 3/16ths back into a single dotted 1/8th notation, as was our goal.

Next up: 2nd note, treble staff, voice 1

Now we want to show that 1/8th duration as a 1/16th duration instead. Keeping in mind the tuplet ratio logic: "Give me A notes of the type that would normally fit B times inside this"
Normally, there'd fit 2 16ths into a 1/8th note, so that would be the number we want for our base duration. And we only want to end up with 1 of them.
Our resulting ratio thus becomes 1 : 2

The others

In this scenario, the other tuplet tricks are identical to the one explained. Just as for that first beat, the intent is to use the original/actual triplet for the correct playback duration interpretation; but then use tuplet ratios to show different notational durations in their stead.

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