# Which notes should be played together? - Polyrhythm

I'm very new when it comes to polyrhythms and only know some basic theory about them. However, I'm having a very hard time in identifying which notes should be played together in this section which is taken from Rachmaninoff's Op. 23 no. 2. Can someone help me with this and give some general tips how I can tackle this problem?

• Aug 4, 2023 at 18:43
• By the way, some of the confusion here comes from the places where there's a "6" over a quarter note. These aren't "real" quarter notes; they're not a full beat; as Aaron explains, the beat has been split into six parts, sextuplets, and these quarters are just four sextuplets. The first beat in the right hand would have been the same if the engraver had put six sextuplet notes and then tied the first five of them together. Aug 4, 2023 at 20:07
• Oh, and one note: Figuring out the "face value" of these rhythms is the first step, but it doesn't mean that they should necessarily be played in perfectly strict rhythm. Aug 4, 2023 at 20:09

Here is an explanation of the correspondences, which are illustrated in the image at the end of the post.

Beat 1

• RH: The "6" indicates that the beat will be divided into six parts, and the convention in this case is to use sixteenth notes for each division. The initial quarter note equals four sixteenths, the tied sixteenth note is the fifth of the beat, and finally a sixth sixteenth note to round things out.
• LH: Here, the fact that six sixteenth notes are beamed together is understood to mean that those six comprise a single beat.
• Correspondence: Since both hands divide the beat into six, the correspondence is 1:1, counting sixteenth notes as the beat division.

Beat 2

• RH: In this case, the beat is divided into the standard four sixteenth notes (because there is no marking indicating otherwise).
• LH: Like beat 1, there is a six-division of the beat.
• Correspondence: Because the hands divide the beat differently, the usual way to determine how they line up is by taking the least common multiple, and dividing the parts into that many subdivisions. In this case, each part can be divided into 12, with the RH sixteenths each representing 3/12, and each LH sixteenth representing 2/12. Lining things up shows that the RH sixteenth note comes on 10/12, which is exactly halfway between the LH's last two sixteenths, on 9/12 and 11/12.

Beat 3

• RH: The first subdivision of the beat is duple: i.e., eighth notes. This we know because of the single beam connecting the 3 sixteenths to the single eighth. The first half of the beat is then subdivided into 3, as indicated by the "3" above those notes.
• LH: The six-division here is the same as the previous two beats.
• Correspondence: The first three sixteenths in each hand align, then the RH eighth, corresponding to the second half of the beat, aligns with the latter three sixteenths in the LH.

Beat 4 Correspondence: The RH-LH relationship here is the same as in beat 1, keeping in mind that the eighth note in the LH is worth two sixteenth notes. Thus, there are the equivalent of six sixteenth notes in each hand.

• Or more simply: notes that are vertically aligned are played together. Aug 4, 2023 at 20:58
• Yes, as @PiedPiper comments, notes that are vertically aligned (if the typesetting is done sensibly) are to be simultaneous. In the example at hand, there aren't any problems with 3 against 4, or, as in Chopin now and then, 17 against 8. Definitely not intended to be "precise"! :) Aug 4, 2023 at 23:19

To simplify an answer. Assuming the engraving has been properly carried out, use the verticals as a good guide. Any notes which are vertically aligned will be played together. This can be verified by checking the four (in this case) individual beats.

Since there are duplets in both hands, life is a little easier, as a lot of the notes will align vertically, thus will be played together.

Personally, I'd be writing out awkward bars, stretching their physical lengths, so that I could draw verticals, to ascertain which l.h. notes align with which r.h. notes. Then play very slowly, or even simply play the notes on beats 1, 2, 3 and 4 initially, with a metronome. One that can subdivide will be advantageous.

• Thanks! That's also what I learned but I wasn't sure whether all printed piano music adheres to this principle. Aug 5, 2023 at 13:25

However, I'm having a very hard time in identifying which notes should be played together

You have by now plenty advice that is useful for a music playing robot in reply to the wrong question. The question you are really asking here (and for which you are getting replies) is

"I'm having a very hard time in identifying which notes would happen to sound simultaneously if this passage were played by a note playing machine".

Here the left hand has its own melodic lines and rhythms and phrasings and the right hand has its own melodic lines and rhythms and phrasings. You should practice them independently until they come out right on their own (and in reasonable relation to a beating foot or even metronome for a while), get them into their ear, develop a feeling and recognition for them and then piece them together and let them flow independently such that their main accents are in the proper correspondence. Where the phrasing introduces temporal pliancy, keeping the in-phrase timing and character is more important than the matchup of some off-accent notes.

If you structure your music mentally according to the incidentally matching notes instead of the inherent accents, it will sound artificial and stuttering. Essentially you need to commit left and right hand to "muscle memory" separately in order to have listening capacity available for checking that their work runs off in reasonable relation to the main beats of the music.