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The image below shows Rachmaninoff's Prelude in G minor, Op. 23, No. 5, measure 43 (IMSLP). The treble staff is in 4:4; however, the bass staff has 24 sixteenth notes in it, and though not marked, these are probably meant to be arranged into triplets: every three sixteenth notes fit into the space of two sixteenth notes from the treble staff. Sixteenth notes in the bass staff are therefore shorter than sixteenth notes in the treble staff, and the same goes for eighth notes, etc.

The question is this: the marked note in the middle of the treble staff is linked to a note from the bass staff. What length does that note have? Does it have the length of an eighth note from the treble staff (half a beat), or the length of an eighth note from the bass staff (a third of a beat)? And offset to which note is it played? In other words, does it belong conceptually in the bass staff?

I would go further and actually ask: are there two superimposed F# notes in the bass staff? A sixteenth and an eighth? And what's that eighth doing there? Which staff does it belong to?

Rachmaninoff, Prelude in G minor, Op. 23, No. 5, measure 43

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    When doing arithmetic to understand rhythm patterns, there's no point thinking in staffs. Every voice has to add up to one whole bar, and there are far more than two voices in this music. The cross-staff beam helps you by indicating which notes belong to the same voice.
    – Kilian Foth
    Jun 30, 2021 at 6:28
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    Note that the last part of the highlighted measure implies that an eighth note from the bass staff still takes up half a beat.
    – Dekkadeci
    Jun 30, 2021 at 12:18
  • Kilian: I hear you, but here the voices follow different meter rules depending on which staff they belong in, and so the voice assignments to the staff do matter. That pair of notes sits in both staffs. Dekkadeci: yeah it would seem so. That pair of eighths seems to be conceptually a part of the treble staff.
    – Mihai Danila
    Jun 30, 2021 at 21:04
  • @MihaiDanila no, the triplets do not depend on the staff, but only on the voice. Only one voice has triplets. That voice could also have such a range that some of its notes were written in the upper staff. The voice that has eighth notes could be written entirely in the lower staff. The fact that one voice is distributed across multiple staves is a red herring.
    – phoog
    Jul 1, 2021 at 1:36
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    The main indication of multiple voices is the direction of the stems; the beaming is a secondary indication. There is one voice that is exclusively in the bottom staff and another voice that is sometimes in the bottom staff and sometimes in the top staff. The first three notes in that voice are a G quarter note, an F sharp eighth note, and a G eighth note. The first two of those notes are in the bottom staff. The third note is in the top staff.
    – phoog
    Jul 7, 2021 at 22:28

4 Answers 4

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In this piece there are four distinct "voices" being played simultaneously.

  • The left hand part constitutes one "voice", the "bass voice".
  • The right-hand octaves are the "melody voice".
  • The notes between the octaves that fill out the chords are an "inner harmony voice".
  • The quarter-note G, the F# in question, the G it's beamed with, the A half-note, and the A-B eighth notes in the bass staff all constitute a second "melodic voice" that echos the main melodic voice.

Imagine this piece arranged for orchestra, say, and each of those parts would be given to a different instrument. It's just that the piano can play them all simultaneously.

So for the F# in question, it happens that two voices "sing" it simultaneously: the bass voice sings it as a triplet sixteenth note; the "inner melody" voice sings it as an eighth note. The two voices are indicated, in part, by the double stem. The bass voice continues its arpeggio down from the F#; the inner melody voice continues it up to the G in the treble clef. It's written overlapped to make clear that the left hand should take the note even though it is also a participant in the right-hand part.

Conceptually, the F# has both the length of a triplet sixteenth and an eighth note. When played, the eighth note takes precedence, since it's in the more emphasized voice.

The same situation exists with the G on beat one, which is the same G given in the right-hand octave on that beat. Rather than double-stem the note, it's written twice so that its progression to the left-hand F# is clear.

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  • Thank you for this answer. Does the marked G belong have a triplet eighth length or a simple eighth length? It seems from your answer that the latter is the case: an F# and a G connected by a beam are both conceptually in the treble clef and respect the rules in it. (If so, also see Giovanni's answer below, which claims the opposite.)
    – Mihai Danila
    Jun 30, 2021 at 21:00
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    @MihaiDanila The marked F# and G form and eighth-note pair totaling 1 beat. Both notes are part of the same "voice", they just happen to be written in different staves to indicate which hand should play which.
    – Aaron
    Jun 30, 2021 at 21:03
  • Thank you. And on what basis does that voice follow the meter rules of the treble staff and not those of the bass staff? Does it have to do with the logic of voices that you explained in your answer? (Also, thank you for updating the question to name the piece!)
    – Mihai Danila
    Jun 30, 2021 at 21:05
  • One suggestion: your answer doesn't explicitly state that the inner melody voice follows the meter rules in the treble staff, and that therefore the marked G is a basic eighth. Consider stating that explicitly. (It's also not clear why the F# and the G are part of the inner melody voice; is it because that's the only logical way to think of it due to the octaves taking up the main melody? OTOH, the F# and the G are both marked, just like the octave notes, so why not main melody?)
    – Mihai Danila
    Jun 30, 2021 at 21:08
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    @MihaiDanila Could you clarify what you mean by "meter"? The meter is the same for both staves.
    – Aaron
    Jun 30, 2021 at 21:11
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"Which staff's meter" isn't a particularly useful question, because the two staves have the same meter, which is C, meaning 4/4. Rachmaninoff uses sextuplet sixteenth notes implicitly in the bass voice, which is apparent because of the proportional underlay and because there are 24 of them in the measure. He doesn't write the usual 6 or 3 to indicate this, and he doesn't change the meter.

That the implied tuplet affects only the bass voice is apparent from the fact that all of the other voices comprise eighth notes that have the same duration as three bass notes, quarter notes that have the same duration as six bass notes, and so on. There is no reason to think that the whole staff is affected.

In a comment you wrote

the voices follow different meter rules depending on which staff they belong in

"Depending on which staff they belong in" isn't correct. The bass voice has triplet sixteenths, and all the other voices don't. The staff doesn't matter.

Some further thoughts:

Sixteenth notes in the bass staff are therefore shorter than sixteenth notes in the treble staff...

Actually, some eighth notes in the bass staff (in earlier and later passages) have the same length as those in the treble staff. But, more importantly...

and the same goes for eighth notes, etc.

...is completely untrue. There are no triplet eighth notes anywhere. Every eighth note is 1/8 of a measure, and they all have twice the duration of a "normal" sixteenth note and three times the duration of a triplet sixteenth note.

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This is called cross staff beaming. It's used as an alternative to ledger lines. In this case, the phrasing still belongs to the bass staff, but the pitch is notated in the treble staff.

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  • Thank you for this answer. I'm waiting for Aaron's clarification, but it seems he is claiming that the marked G is a basic eighth note rather than a triplet eighth note.
    – Mihai Danila
    Jun 30, 2021 at 21:00
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    No problem! I agree with Aaron that it is just a normal eighth.
    – Giovanni
    Jul 1, 2021 at 0:44
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You're working under a basic misconception.

"Sixteenth notes in the bass staff are therefore shorter than sixteenth notes in the treble staff, and the same goes for eighth notes, etc."

No. 16ths (and 8ths, and quarters) are the same length everywhere. But those notes in the bass stave aren't 16ths. They're triplet 16ths. Three to an 8th note. It's just that the '3' is omitted. Naughty, but not uncommon when, as here, context makes it obvious that they're triplets.

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