Um, no, I’m not talking about some mode of Ham radio RF modulation here – I’m referring to musical notation. Here’s Wikipedia’s definition. When you’re done tearing your hair out trying to make sense of that, come back here and I’ll give you my Joe Sixpack definition of metric modulation.
Metric modulation in music is a change in beat structure. In our case here, it is a change in time signature while maintaining the same tempo. The sailent quote from Wikipedia is:
“Usually, such time signatures are mutually prime, e.g., 4/4 and 3/8, and so have no common divisors. “
The attached piece is a reworking of a past project that was done in MuseScore by its original editors, and now reworked in Dorico by me. The third movement of that piece – Mercury, the Winged Messenger has all manner of funky things going on with time signatures.
It’s quite a big deal, this ‘metric modulation’, in that quite a few luminaries in the music community have spilled significant ink writing about it. In fact, if you go back to that past project page of mine on The Planets, you’ll note that the PDF print there is not mine. At the time, I could not figure out how to get Dorico to import The Planets correctly, as the metric tempo changes threw everything off and left me with a total mess… all gibberish. Way off! All I could do at the time was to export from MuseScore as midi data and then work from there in Cubase. At the time (pre version 4) MuseScore was unacceptable for orchestral music rendering!
Here’s an example from page 53 of The Planets. Now, orchestral scores don’t normally include time signature on every single stave, just those where there is a change. So to clue you in, this example system is in 6/8 time, with a tempo of 180bpm (Vivace). Have a look at the staves for Harp, Violin II, Violas, and Cellos – you can see them change over to 2/4 time. Easy, no?
Well, think about it for just a moment. Just those stave’s are marked for 2/4 time have changed, the other have not so they are still in 6/8 time! How do you work out 2/4 playing in time with 6/8? Ouch! Not so easy then.
One way to think of this is in terms of bar measures. It’s plain to see that the bar lines for measures all line up together and it’s obvious the music must play at the same rate – the bars are locked together. If we see 180 bpm @ 6/8 as being primarily the tempo to use we get 60 measures a minute. But with 180 bpm @ 2/4 we get 90 measures a minute. Houston, we have a problem!
Since we’ve declared here by personal fiat that the 180-bpm tempo as applies to 6/8 time is the tempo rate to use since we started with 6/8 to begin with, the 2/4 staves will simply have to play more slowly to go along at the same rate as everyone else. It seems simple enough, but modern computer programs have an issue with this.
The way music is interpreted by a computer varies according to its design. MuseScore has no problem with metric modulation in its scores, most likely because it treats music as a fixed collection of measures and assumes a primary rate based on the above assumptions. Dorico is different. It treats music as a stream of notes and the bar lines for measures are nothing more than artifacts that can be computed from whatever the current time signature is for a particular stave.
This has many advantages such as making it easier to move music around without worrying about things like tied-notes, slurs, and dynamics, which are attached to the notes and move with them. A fixed measure-based system tends to see those things as ornaments, separate from the notes, and make moving and copy-paste operations more difficult.
All good so far. But Dorico currently treats the musical rate (tempo) as based on absolute bpm on each stave individually. What this means is, without some kind of intervention, Dorico will play 60 bars of 6/8 at the same time as 90 bars of 2/4 and this is not what we want at all. We want/need Dorico to play 60 bars of 6/8 at the same time as 60 bars of 2/4, which is what our first way of thinking accomplishes, albeit in a roundabout fashion.
The solution to our dilemma is to use tuplets. Look at the same clip again with hidden items turned on.
See those green flags? Those are flags to indicate that these are 2:3 tuplets and the reason they are shown there is because I’ve hidden them. You won’t see any tuplet markings on the printed score, but Dorico knows they are there. We use 2:3 ratio tuplets because we need to fit two eighth notes into the same place as three eighth notes (6/8 being the master time signature from which our tempo is derived).
This is our trick.
To get a 2/4 key signature displayed, but without really using 2/4 for our actual time signature, we use Dorico’s pickup bar (anacrusis) feature. We created a new time signature of 2/4 which just so happens to include enough extra pickup beats to make it the same length (in time) as a 6/8 measure. We mark the notes within with hidden 2:3 tuples so they fill up the whole bar. Then the next bar we make into a 6/8 time signature (same as everything else), but we hide that time signature so it will not print. (That’s the red flag). From here on out we simply enter everything in as tuplets and then hide the tuplet markings. Problem solved.
Have a look at the full movement if you’re interested. The fun starts at about 1.23 in the attached music clip.