Multiple Tempos

• Apr 6, 2017 - 18:16

Did not the great J.S. Bach himself write for multiple tempos in The Art of the Fugue? We can also use this feature to achieve standard strumming techniques and some unusual effects on playback.


Can you describe what you mean in more detail? Do you perhaps means, multiple *time signatures* - as in, one staff wiht one time signature, another with a different time signature, for the same measures? If so, this is already possible (with a few limitations) - see the Handbook under Time signatures - in particular, the section on "Local" time signatures. not sure what that might have to do with strumming or playback effects, but anyhow, that much can be done.

I can think of a few actual cases involving multiple time signatures. One is to have simultaneous equivalent time signatures like 3/2 and 6/4 (written to look like 36/24) to allow switching between duple and triple beat patterns for the same measure duration, as in the Fugue section of Roy Harris's Third Symphony. Another is to extend this to placement of bar lines, as in the middle of the first section of Hindemith's "Mathis der Maler" where the trombones are in 3/2 while the other parts are in 4/4, and the trombone bar lines are offset from those in the other parts. Finally, in the middle section of Ives's "Three Places in New England" in the "dream" sequence, where he puts 4 beats against 3 with offset bar lines.

In reply to by dhfx

an anecdote:
In old times, in my youth ...
Manuel de Falla's work "El Sombrero de Tres Picos / The Three Cornered Hat" was performed by our school symphony orchestra.
It could be played better of course: if the brass and woodwinds were not missed some measures... //towards to end of piece. (Tutti)...
I liked it this wrong played version, and thinking "this is poly-rhythm, this is exactly what I want". :D
Though, the conductor did not agree with me. Because, he was ten years older than he was, until the orchestra found the actual "measure"...
After all, there are various rumors about the number of corners of that Hat :)

In reply to by Joe H

Well, what you describe isn't multiple tempos, it is just different rhythms - like half notes in one staff and eighths in the other. No need for anything fancy to do that. But as I mentioned, there are indeed a few places where Bach does use multiple *time signatures*, so one part can be subdivided into eighths (eg in 2/4) whereas the other subdivided into triplets (eg, in 6/8) at the same time. And as I said, MuseScore already supports this, as explained in the Handbook in the section I mentioned.

So again, what you seem to be talking about is already perfectly possible. If you continue to have trouble, please attach the particular score you are having trouble with and be as precise as possible about what you are trying to do, and we can show you step by step how to do it.

In reply to by Marc Sabatella

Marc - Bach notates this as something like "play at twice the tempo or half the tempo." The scrolling score demonstrates what is meant. The fugue material is only notated once. And then that instruction. The player is to imagine the other stave with the same material only oving at half, twice or quadruple the rate. I see that someone has transcribed AoF on MS. Yet it can not be played back and heard as it is on this Youtube video.

The reason for his notation is to avoid transcribing the material twice. But that was in the old days before we would be sitting at computers demanding to hear the score. Verits99 did the transcription. Anyway to contact that user about this issue?

In reply to by Joe H

If you can show me exactly where in the score it says that, I can try to explain how to add the same notation in MuseScore. And then we can begin to consider the playback. As it is though, it still just isn't clear what you are actually asking for. That video does not appear to be showing different tempos at all that I can tell. It simply has the two lines of the fugue written out independently. That much is also perfectly possible to do in MuseScore, just write them on alternating systems.

In reply to by Marc Sabatella

I noted before that the video shows it at 45:00. And it's quite frequent, and he notates the instructions at the beginning of the piece, I think. In the pieces that use this notation technique, anyway. It should appear in the transcriptions that were done here. Is there some way to contact someone who is familiar with Bach and the Art of Fugue?

In reply to by Joe H

I looked at 45:00, and see no such indication of different tempos in the score. So again, it just isn't clear what you are asking for. The music there does *not* appear to be showing different tempos at all. It is doing exactly what I said above - showing the two liens of the fugue indepedently. They have exactly the same tempo, they just aren't written in a way where the measures all line up exactly. You can achieve that exact effect exactly as I described - using alternating systems.

In reply to by Joe H

This is not true from what I can tell. Watch more closely. The measures go at *precisely* the same rate, but since they are different sizes, they *appear* to move at different rates. But the barlines occur at the same times.

Not sure where you would find someone more familiar with the piece, but for starters, you could probably get the actual score from IMSLP.

In reply to by Joe H

OK, that one does indeed have two measures on one part corresponding to one on the other. This, though, would be done precisely the same way - alternating systems. That is, instead of trying to put the two parts as two staves on a single system - which would require the measures to line up - have a single staff, and have the one system for the top part, the next for the bottom part, and alternating from there.

Or, if you prefer to have the measure actually align, simply hide every other barline in the other part. Again, perfectly doable with MuseScore already.

In reply to by Joe H

BTW, it's also important to realize that this video doesn't show the actual score - it is a computer animation. Bach didn't write it the way you are seeing it here, with the two lines on separate staves that don't align, nor was it published that way to my knowledge. The actual score is written traditionally. See for example…, which shows both XII and XV as they are normally written - perfectly normal measures. Bach simply wrote the line out twice as slow in one voice, as I said in my original response. The computer animation you are watching in the video is just trying to show how it would look if it had been written out using the same note note values but player twice as fast. It was never meant to be a score you'd actually read from - it's just a teaching video.

But *if* you wanted to produce a hard copy of the computer animation shown in the video - with the lines written separately - you could do it in MuseScore as I have been suggesting.

In reply to by Joe H

@Joe H... You wrote:
I noted before that the video shows it at 45:00.
As Marc states:
I looked at 45:00, and see no such indication of different tempos in the score.

Here's a You Tube screenshot at 44:59


Here's the actual score:


In the You tube video there is no tempo difference in playback of the two staves. One staff has to move faster (or slower) across the You Tube screen so that the barlines cross the red cursor at the same time.
(That's why standard notation aligns barlines - even to the point of stretching one measure of, for example, a single whole note in the bass clef, played against a string of 16ths in the treble clef. The barlines must line up to avoid the very confusion you write about.)

Additionally, you wrote:
OK. I'll have to take another look. Maybe I read something wrong. Nope. Try again at 57:00.
Well... at 57:00 the two staves do exhibit different tempos for a completely different reason. The bass clef note durations are changed from the original score (perhaps as a teaching/analysis exercise).


I was all prepared to concede that I must have read something wrong, because now I remember that his instructions were not regarding tempo but the pitch at which the contrapunctus must be transposed to and the inversions of the cantus firmus. How I conflated that with tempo instructions is just poor memory. I did say that he did not notate this. There was some sort of instructions for the pianist to transpose this in their mind while playing.

However, I do believe that the Master would highly approve of having multiple tempos - that is staves that are above or below eachother in which the measures are measured at different tempos - usually multiples or submultiples of a tempo.

Yes, this could be achieved by transposing the beats in a meter - writing quarter notes against half notes renders the same effect. The great advantage of multiple meters is that you do not have to refigure the original stave. You simply copy and paste it and plug in a distinct tempo for the complementary stave.

Like I say, the Art of Fugue could then be played and read correctly as it appears in the scrolling score. Also, I could do all the calculations for playable strum techniques easier with this tool.

In reply to by Joe H

I wouldn't be so bold as to put words into Bach's mouth. All I know is, he did *not* in fact write anything of the sort. And I would hate to be asked to read something like that. But as I have said several times, if you wish to create a score using such experimental notation (and hopefully pay the musician well who is forced to read it!), you can do it in exactly the way I described.

In reply to by Joe H

Yes, poly-rhythm can be written.
But poly-tempo doesn't seem possible.

As Archimedes said: "Give me a place to stand, and I shall move the world."
Our "stand" is tempo. Without it, nothing will happen.


Let's think of two measures, with different metronomes: one 60 (bottom) and the other 90 (top).
While reading the second measure below, we need to read the third measure above.
After a while, the distance constantly increasing, we must have eyes like chameleons so that we can read... Also, on a line-break, we might need to be at a cross-eyed.

At this point, you can say: "It will always be in the same line."
But in this case, there is no need for a different tempo.
If they are on the same vertical line, they can be written in the same tempo.

Yet, we have agreed that Bach did write in multiple tempo, attested to by the Art of the Fugue. Tempos that are multiples or submultiples of the original tempo of the cantus firmus.

In reply to by Joe H

No, that's the the *same* tempo, just half or double the *rhythmic value*. As I said in my very first response, he wrote quarter notes in one staff, eighths in the other, etc. The same tempo, just different rhythmic values. Again, what you see in that video is *not* what Bach wrote, is a computer-generated animation showing what it would look like *if* it were written using the same rhythmic values but different tempos. And as I keep pointing out, if you really want to do something even Bach would never have done, you are welcome to. MuseScore already allows it, using the technique I have described. But it is not recommended, because it is not easily readable - it is really only useful for compute-generated animations, not actual printed scores.

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