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So I'm midway through composing a movement of a suite I am working on and I have reached this section that is primarily triplets. It starts off as a solo violin, and then later, more instruments are slowly added back in. I felt the need for rhythmic variety, so what do I do when I have triplets as the primary rhythm? In this case, I went for the polyrhythm option. Polyrhythm has worked for me before to bring rhythmic interest. However, something happened that I did not expect. The rhythms clashed noticeably. I knew rhythmic dissonance was a thing, but that has never occurred in my own works until now. Here is an excerpt that includes the polyrhythm:

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By the way, this passage here starts in G minor and modulates to C minor briefly. Considering that the movement as a whole is in D minor, that's not too surprising. And it can't be the harmony that is making it clash, since outside of a few non-chord tones, all the voices are consonant with each other. That's why I'm thinking that it is the rhythm that is making it clash. However, as I stated before, I have never had rhythmic dissonance happen with polyrhythms before(and that is both for 2:3 and 4:3 polyrhythms).

Here is an example of a piece where I use polyrhythms and don't get this rhythmic dissonance:

https://musescore.com/user/50070/scores/5989028

But it isn't just piano solo for which I have gotten polyrhythms to not be rhythmically dissonant, I have done that for chamber works too. And I have never used polyrhythms outside of x:3 because if triplets are the primary rhythm, rhythmic dissonance is less likely to occur than with say quintuplets as the primary rhythm. And before you say that it is probably the tempo, the tempo that this movement is at is quarter note = 100 BPM, which again, I have wrote polyrhythms at that exact tempo that aren't rhythmically dissonant, so that's ruled out. In fact, I find that the moderate range is where polyrhythm is at its best. Too slow and it might as well be polymeter instead of polyrhythm. Too fast and it might as well be a single rhythm that is very embellished.

So why am I getting this rhythmic dissonance if my tempo is not too fast or too slow and my harmony is consonant? And is there anything I can do to keep the polyrhythm but not have the rhythmic dissonance? Transposing the harmony down I don't really want to do because Violin II is already getting close to its lower bound. If I transpose it down, it will be at its lower bound, an open G, which is not easy to control in terms of intonation and dynamic. Plus, I'm not sure that changing the notes of Violin II would effect the rhythmic dissonance at all.

  • The different parts are very constant with each other when we look at the downbeats. But the off beats (the and of 1, the and of 2, the and of 3) are where the polyrhythm is noticeable. During those off beats, the bottom violin line plays notes that are a half step away from the top violin's note. On beat 1, you have the top violin playing a G on the middle triplet, but the bottom violin comes in with an F# that clashes with the G and sticks out because of the polyrhythm. Likewise on the and of best 2, we have C and B. For the and of beat 3, we have F and Bb. – jdjazz Apr 16 at 5:44
  • One way to test if this is correct is to change the bottom violin line to something like: D-C-G-E-C-A so that the line is alternating between a rise and a fall. This may not be the ultimate line you went, but if you try this, is the dissonance less? If so, I will put this into a full answer. – jdjazz Apr 16 at 5:48
  • Why do you try to avoid dissonance? Don’t you think the dissonance would make it more interesting? Music lives from consonance and dissonance like a picture from light and shadows. – Albrecht Hügli Apr 16 at 6:00
  • @AlbrechtHügli I don’t always try to avoid dissonance because I know that it is needed to some degree. But this polyrhythmic dissonance just stuck out to a degree that on beat dissonance doesn’t. On beat dissonance adds harmonic richness, but the polyrhythmic dissonance really stuck out. – Caters Apr 16 at 6:12
  • I think @jdjazz probably spotted the problem. In the other linked score the polyrhythm voices are much further apart. Here, in m. 53, the voices are right on top of each other, beside the harmonic dissonance that can create a kind of repeated note effect which may not be desired. – Michael Curtis Apr 16 at 6:28
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I suspect the dissonance that you hear is due to the half-step and whole-step intervals between the two violin parts. Because of the polyrhythmic timing, these harmonic clashes are being emphasized. If these half-step intervals were played on the two violins simultaneously, it might sound more intentional. But the staggering can make it sound like a mistake rather than a conscious choice, and delaying the dissonant harmony calls attention to it rather than letting it meld with the melody line.

Here's a little more detail: you are correct that the different parts are very consonant with each other--but only when we look at the downbeats. The offbeats are where the harmonic dissonance occurs. On the "and" of beat 1, you have the two violins playing F# and G at the same time. On the "and" of beat 2, the violins are playing C and B. On the "and" of beat 3, the violins are playing F and Bb.

The half-step intervals are especially dissonant, and they're likely causing what you hear. Something you can try is this: change the bottom violin line to something like: D-C-G-E-C-A. The line will be alternating between a rise and a fall, which may not be what you are looking for, but if it sounds less dissonant to your ear, then it confirms the ideas I've written here.

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    Well I tried changing the bottom violin line to what you suggested and it didn't sound nearly as dissonant as it did before with the rising thirds. – Caters Apr 16 at 16:52
  • Excellent! I think that answers your question--the dissonance was the combination of rhythmic staggering along with the particularly dissonant intervals. – jdjazz Apr 16 at 17:13

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