In working on the Brahms Rhapsody in G minor, I had to deal with its two-against-three sections...triplets in right hand, duple in left. I'm currently "refreshing" the piece and those are the sections that need the most reworking (esp. measures 40, 48, 52).

In this piece, it's the left hand, the duple that has the melody, so I direct my attention to that hand. I "drive" with the left hand, and let the right hand fall into place in a more subconscious way.

My question is, if this a good general rule, to let the duple drive things? Strictly in terms of rhythm, it's so much easier that way. To focus on the triplets and fit the left hand into that is very difficult for me.

I'm sure there are piece out there where things are reversed, the triplets are more important musically and need to be prominent..which seems intimidating to me. Any thoughts?

never thought of that, but i guess it's the hand with 3 dictates the count. since the 1st note of either 2-note group and 3-note group has to start at the same time, the 2nd note of 3-note group will be played before the 2nd note of 2-note group, or we can say the 2nd note of 2 group has to wait for 2nd note of 3 group played before joining in, and therefore, counting after the 1st note starts from 2nd note of 3 group, which in turn as a dominant force. just my guess anyway.

I think it depends on the context.

If you are playing a piece that does not feature a polyrhythm, is it the right hand with the melody that "drives" or is it the left hand accompaniment that gives impetus to the piece?

What should we use as examples? Say the Chopin Etude Op 10 No 12: Is it the running sixteenth-note figure in the left hand, or is it the chordal figures in the right hand?
In the second movement of the Beethoven, Op 13, is it the upper right hand melody, the inner-voice sixteenths, or the bass that gives movement to the piece?
In the Chopin Fantasie-Impromptu, do the running sixteenth-notes in the right hand or the sextuplets in the left "drive" the piece.

I think you have to ask the same question whether you have polyrhythms or not. In many cases, I think, right and left hands might be equal "co-pilots" although each filling a different function.

I must disagree with you about what hand has the melody in measures 40, 48 and 52 of the Brahms G minor Rhapsody; the notation with the upward stems on the quarter-notes in the right hand clearly - to me - indicates that it is the right hand descending figure on each beat that is the melody. I can't think of the rising arpeggios in the bass as melody compared to what is going on in the right hand. Nevertheless, the two hands work in tandem with each other; I wouldn't say that either one "drives" the other.

I am also confused by the meaning of your statement : "In this piece, it's the left hand, the duple that has the melody, so I direct my attention to that hand. I "drive" with the left hand, and let the right hand fall into place in a more subconscious way." First : apart from the measures mentioned and a few others, there is no duple against triplets, and, Second: I can't see where "in this piece" the left hand has the melody. This piece is in 4/4 (C) time, with a triplet accompaniment throughout and very clearly the right hand has the melody almost exclusively.

Regards,

I try to hear both hands separately and independently. I got familiar with the difference between 2/4 and 3/4, or similar ratios, and try to let each hand do its work.

The left hand has the melody in octaves starting at measure 21. At 23, the left hand is playing a dotted-eighth sixteenth figure against triplets in the right hand, which happens many times in the piece. In my book this counts as duple against triple.

I didn't mean to imply the LH has ALL the melody in this piece...Left hand melody: Measures 21-30, 54-64, the whole last page. LH has an entire motive to itself, for a significant portion of the piece.

I tend to drive with the 3, but I practice driving with both.

I make exercises out of 2 v 3 passages and count aloud, first one hand, then switching to the other.

Wouldn't this be more of a 3 v 4 with most of the 4 missing? That is play all of the 3 but only the first and last notes of the 4?

If you are playing it as a 3 v 2, then the sixteenth note would be played before the last triplet. If you are playing it as 3 v 4 with notes 2 & 3 missing on the 4, then the sixteenth note should be played after the last triplet.

Rich

Actually the mesh between each other like gears.

Two against three works something like this

Together, Left, Right, Left

Three against two:

Together, Right, Left, Right.

Hope this helps.

John

I think that some might argue that the left hand figures in the measures you mention are as much rhythmic devices as actual "melody" and that the F, F, F, E-natural, D, C-sharp D are as much melody as what is going on in the left hand. The only recording I have of the Rhapsody, that of Radu Lupu, certainly seems to treat the left hand as a rhythmic accompaniment while the right hand melody in quarter-notes seems to be predominant.
Moreover, the quarter-note melody is certainly in keeping with the themes in the rest of the piece; throughout the themes are based on a phrase pattern that starts as a pick-up on the fourth beat and continues on beats one, two, and three. To my way of thinking this is echoed in the theme that starts on the fourth beat of measure 20 and continues through 31. When I studied this, I was encouraged to think of the melody as I have just mentioned it, with the left hand being an accompanying figure.

We each, of course, interpret these things as we see and hear them, and I certainly wouldn't vehementaly argue against the melody shifting to the left hand; it's just not how I perceive the work at this point.

Interpret it - right hand or left hand melody at this point - as you will, I don't consider this duple against triple; it's three against four, which is considerably different.

Regards,

Thinking about this a little more :

The opening eight bars is composed of a melody conceived as follows, always with a pick-up on the fourth beat :

D | Eb, G, Bb
E-natural | F, A, C,
F | E-natural C, G, A, | B-natural, D

and then repeated in a new key

In other words : two short phrases of four notes each, followed by a phrase of seven notes.

The same thing happens beginning at measure 20 (with the A, Bb, A triplet figure conceivably considered as a dominant A to tonic D)
A | D, D, D,
A | D, D, D,
A | F, F, F, E-natural | D, C-sharp, D

and then repeated an octave higher.

This parallel to the rhythm of the opening theme is my (further) justification - or rationalization, if your prefer - for considering the right hand as melody in measures 21 through 30 and further emphasizes Brahms' strong sense of thematic and motivic unity throughout this piece.

Regards,

Whatever works for you; however at least one piano professor disagrees with you.

She considers the right hand an ostinato figure, the left hand melodic. You seriously think the whole dotted-eighth sixteenth business in the left hand, in measures 27-30 especially, is NOT the melody? That's pretty eccentric, IMHO.

As you so eloquently say : "Whatever works for you...." By the same token, whatever works for the piano professor is also evidently fine for her, and fine by me, too. I won't argue the point. I was, however, attempting to give some reasons (justifications, rationalizations) for my approach, but it was not in an attempt to sway you. You are entitled to your views just as, I hope, I am entitled to mine. That's what makes the discussion of interpreting music so interesting.

Eccentric? If you say so.

Regards,

John,

We are talking about a specific piece and not general 3 v 2. I agree with you about 3 v 2, however 3 v 2 is NOT the rhythm in the piece in question.

Here is one of the measures in question:

We're basically talking about 12/8 against 4/4...I think of 4/4, 2/4, 2/2 all as "duple meters." My theory teacher in school referred to things this way. I don't mean to split hairs, but whether you call it duple or quadruple, my question remains unchanged. We have something based in two (subdivided to 16ths) against something in three....

The right hand is clearly an ostinato: that's why it needs to be less than the left hand, not any sort of rhythmic concern.

Make it easy - just sync the sixteenths with the triplets and be done with it. I've never quite understood the reasons for when you do and when you don't play sixteenths as triplets when they appear together with a triplet, but I don't see any overriding contextural reason why you wouldn't in this case. Did Brahms say it was a no-no? Is it generally understood as bad Brahms form to do them that way? Educate me...

Oh, I wouldn't do that - but I would just fudge by playing the sixteenth shortly after the last note of the triplet. I don't think this needs to be terribly mathematically exact.

I don't think it's a difficult or involved polyrhythm and by all means should be followed strictly.

With that kind of rhythm, the last sixteenth in the dotted-eightth sixteenth pattern, can actually fall on the last note in the triplet. This was a common way of writing out this particular pattern amongst many composers including Chopin, in particular Schubert, and even Beethoven.

John

In other areas of the piece, however, there are strict 2 v 3 rhythms (eighth notes against triplets), as well as an elongated version of the measure quoted above...dotted quarter and eighth against 6 triplets.

Neither of those two examples can be fudged by lining things up evenly; they are polyrhythms through and through. So it seems Brahms is playing with 2 (or 4) v. 3 as a rhythmic motif, meaning, it's probably not OK to line the 16th up with the triplet in the above example. He's using that rhythmic tension in a purposeful, motivic fashion.

Careful!

You assuming here that a dotted 8th followed by a sixteenth is a three to one ratio.

But please examine Beethoven's "Moonlight Sonata" (Op. 27 No.2), first movement, and notice that here he uses this notation for a 5 to 1 ratio.

Now, in the Brahms, tempo is going to play a huge factor in how the 16th notes in the LH are played.

http://www.youtube.com/watch?v=4AkV2MllW0A

Here the performer very noticeably slows down a bit. She would not be able to make the rhythm clear, as she interprets it, at a much faster pace.

At a much faster tempo, this would not be possible, or at least it would not be clear.

When the 16th note is played very clearly this way, the actual solution is often:

dotted 8th plus 16th note
=
8th tied to 8th tied to 16th, plus 16th, defined as a tuplet (triplet).

In your edition, it seems very clear that Brahms used the same notation as Beethoven. If you write music, or if you are notating such rhythms in a notation program, you figure out WHY Beethoven, Brahms and others use the 3 to 1 ratio.

It's cleaner notation. It is mathematically incorrect, but it's much easier to write and to read.

So you are not dealing with 3 against 4 here at all.

It's either 3 against 3, or 3 against 6, with the final octave coming on the second half of the value of the third triplet in the RH.

This reminds me of the notation in Schumann's Vogel als Prophet. According to Friskin and Freundlich (in Music for the Piano):
I'm not sure that standard performance practice follows their suggestion, though. (I guess everybody didn't get the memo!)

Steven

Brahms uss what is known as hemiola. These links here will explain it better than I can.

http://www.rrcs.org.uk/MembersSite/Hemiola.htm

http://unconqueredsound.blogspot.com/2006/01/fun-with-hemiolas-part-1.html

http://unconqueredsound.blogspot.com/2006/02/fun-with-hemiolas-part-2.html

And of course good old Wikipedia
http://en.wikipedia.org/wiki/Hemiola

This may clarify the this situation once and for all.

John

This is one point in the discussion of this piece on which I totally agree with you.

Regards,

Gary D.

I don't think I can agree with you on this, failed mathematician that I may be.[/b]

If you were to base each beat on 100 units :
The left hand dotted-eighth plus sixteenth would sound on 1 and 75
The right hand triplets would sound on
1, 33, and 66.

You are suggesting that the last sixteenth-note would come at 83, (halfway between 66 and 100) which is late.

Of course, no one is going to be that precise in playing this, I understand, but I think it's misleading to suggest that the last sixteenth-note in the left hand comes exactly between the last triplet of one group and the first of the next.

When I studied this piece - and I still have the teacher's notes on my score - he clearly wrote : "left hand barely later than right hand" [triplet understood], and he was not only quite a stickler for artistic performance as well as adherence to scores' note values, but he is also considered somewhat of an "expert" on performing Brahms. To say that I was not totally successful in realizing his notes is beside the point; I believe, in principle, his direction is correct and that the last sixteenth-note comes just after the last triplet and not halfway between the last note of one triplet and the first of the next.

Of course we are splitting hairs, but isn't that one of the things that makes this Forum so much fun?

Regards,

Actually, I'm suggesting something a bit different. I'm suggesting that Brahms clearly wants the 16th note to come later than the last note of the triplet, and I'm suggesting a logical and practical way to make that happen.

Here is what happens, in my experience. As you accelerate the tempo, the triplets in the RH will remain in rhythm (I think you'd agree that they must), but where the final LH 16th note falls will change because of physical limitations for the simple reason that it is very hard to move very quickly from the 16th note octave to the next 8th note octave.

In other words, practicing it very slowly, in a way that is mathematically correct, might be practical for a student who has never been faced with this kind of problem before, but what actually happens is going to change as the tempo increases.

By maintaining a very strict rhythm in the RH and making sure that the last LH notes come after the last triplet note, the "effect" falls right into place. The perfomance I linked to may show the LH coming closer to a triplet 32nd note simply because the pianist plays that section markedly slower. I don't totally dislike what she did, but she is definitely taking a huge liberty, because there is no indication of a "meno mosso" tempo in any score I've seen. Her slower tempo might allow her to come closer to a true 32nd note (1/6th), but even so I suspect that a careful midi analysis would show that those LH octaves are starting to fall closer to where you think they should be, and a full tempo performace is going to "condense" what happens until the there will be less and less time between the LH and RH. A much more serious problem would be to have that 16th note slide back in rhythm with the LH, which would be just plain wrong in this case.

To make a very long idea short: I totally agree with your teacher about where these notes need to fall, not because of mathematics, but because it is what is going to happen. I just think what we are talking about is outside of a 2 againts 3 problem or a 3 against 4 problem.
But he is right! Because that's what is going to *happen*! No matter how you practice this, at full tempo the only danger is that the LH will be together with the RH. As long as it is entering later and does not disturb the RH rhythm, it has to be that way!
Yes, it does make it fun. In the "real world", I swear I could go years without talking about something like this. Normally my job is just to show people how to do things, and they have no idea of the thinking that goes behind finding solutions.

By the way, for me this is a perfect example of what happens when the tempo is pushed too much.

http://www.youtube.com/watch?v=M683J04gJg8

This pianist totally loses the effect, sacrificing everything to speed. If he cut back just a little, he could do it right, and most of his wrong notes would go away too.

Bruce,

As an update to what we were talking about:

I just took the passage we were discussing (Brahms) and played it first very slowly, putting the 16th notes on the second half of the value of the last RH triplets.

Then I accelerated just one measure, finally reaching full tempo. I repeated it many times then.

I used DP and a midi program to record what I did, real time.

Then I slowed the recording down to half speed, to analyze what is really happening.

It showed clearly that at full tempo, the 16th note octaves actually do fall closer and closer to the final RH triplet notes when the tempo is accelerated.

I think this is just what has to happen, physically, and it also suggests that if the tempo continues to accelerate, at some point the 16ths note will actually fall so close to the last notes of the triplet that the notated rhythm will be destroyed.

This suggests to me that the real key to playing this or any other passage like it is not to play it too fast and make the "non troppo" part of the tempo indication extremely important to observe!

Those are very good reasons.

It's funny, but for many years (something like four decades) it never even occurred to me that that the sixteenths and triplets could be played together, but last year I was going through the piece once again, and out of the blue, I thought of the notation convention that says that usually the sixteenth in that dotted patten will fit to the triplet. So I tried it out. Although I wasn't convinced it was really the only right solution, it also didn't sound completely wrong either. I sort of like it.