# How to clearly notate tuplets, both "simple" and "complex," in irregular meters

(There's a bunch here, sorry. I've used bold text to outline the flow of the main content of the question.)

Basically, I'm transcribing the rhythms of a song, mostly in a 6/4 & 4/4 feel, though every now & then the music deviates into a small series of "glitchy syncopations," to put it one way. in the midst of all this, there's a single bar of 5/8 containing a normal (simple) quarter-note triplet (3 quarters in place of 2) followed by a single articulated 8th note. this got me wondering: if I used such rhythms in a composition which remained in 5/8 time extensively, and wanted to also incorporate a triplet which spans the entire 5/8 bar (a slightly more complex tuplet) how would I notate that?

The answer seemed simple at first to me: use 3 beamed eighth notes, spaced appropriately, topped with the ratio notation: 3:5. this indicates that there are 3 eighth notes in place of 5? correct?? (see image below)

However, when this figure is compared to the "simple" quarter note triplet mentioned before, there's a possible discrepancy in clarity concerning speed / duration: aside from the differences between note spacing of the components within each triplet, the 3:5 triplet in bar 2, below, (which SHOULD represent a slower/longer triplet than the one in bar 1) suggests that it is faster than the standard quarter-note triplet. which is fully untrue, and seems a tad too misleading for my liking.

Am I missing something crucial? like... if the meter is odd / imperfect / irregular, are the rules for notating tuplets altered? in other words, is my notation of the first, simple quarter-note triplet wrong? and is that notation (three quarters with a bracket) better suited for the triplet which spans the entire 5/8 measure?

Off the top of my head I know of one source: Alexander Scriabin's Prelude in C (Op. 11 No.1): the meter is 2/2, but the general feel is a subdivision of quintuple eighth-note groupings, accents often notated and implied on the 1st and 3rd notes of each quintuplet. The composer never uses tuplet symbols to indicate that 5 eighths take the place of 4 (at least in none of the scores I've seen) but the music makes the subdivision quite clear.

Anyways, in a few places the left hand plays a figure of 3 quarter notes, again, never notated with any tuplet signs, but implied to be a triplet pitted against the quintuplet: 3 quarters in place of 5 eighths (aka a normal quarter-note triplet pitted against the standard pulse of the time sig: 2/2), rather than a quarter note triplet taking the place of 4 out of 5 of the eighth-notes from the quintuplet... or any other rhythm. the distinction between these triplets may seem slight but I believe it makes a difference which one is observed.

I realize since the time signature is 2/2 and not 5/8, there may be a difference between this example and my hypothetical, but if my assumption about Scriabin's triplets here being 3:5 is correct, then my very first posited notation of the "simple" quarternote triplet in a 5/8 context may be fallacious, and I should be treating said "simple" tuplet with a more special approach. maybe the following:

Using the 8th-note triplet, explicitly labeled with a "3:4" ratio (above left), instead of the standard quarter note triplet notation, seems a clearer solution. its result is the same as (quarters)3:2 but leaves room for the usage of the 3 quarter grouping to represent triplet which fills the duration of a 5/8 bar, like my assumption of Scriabin. (above, right

One more possible notation:

Is this just one of those kinks in our system of notation? or is there a ~standard protocol based on precedence in sources? If you've read all this thanks so much.

• Scriabin's notation here is just a mess, if it really was Scriabin's in the first place. Your excerpts look like they came from the first Russian edition, which has so many misprints it looks like they were fired at the pages from a shotgun. For example in that first prelude, the MM mark as printed is a dirge, not "vivace" - and there's even a wrong clef change, later on! I guess proof reading and vodka don't mix well (bad pun...).
– user19146
Commented Jul 5, 2018 at 15:57

Wow, very interesting question, and your opening example really shows the problem very well!

If I understand your entire question correctly, then I recommend not viewing the Scriabin as 3:5.

The left hand triplets are really 3:2, in the sense that you are playing 3 quarter notes in the span or 2 notated quarter notes. The 3:5 is the relationship between the hands, not the relationship to the notated meter, which is an important distinction to make. This is especially important in a piece like this Scriabin prelude, where the right hand is off doing something unexpected: a 5:4 relationship.

In other words, you want to notate it to show the relationship between what's being played and the notated subdivisions. Reading the Scriabin as 3:5 would be incorrect, because that 3:5 is the relationship among the hands themselves.

This is why the second measure of your second example is not ideal, because that quarter-note triplet indicates "3 quarter notes to be played in the span of 2 quarter notes (=4 eighth notes)," which leaves one eighth note unaccounted for in that measure.

I personally prefer the bottom example, because it leaves no doubt as to the notated intent. (But I don't have a source suggesting that this way is optimal.) This notation might catch a sight reader off guard, but based on these rhythms, I doubt sight reading will be a priority :-)

• You definitely understood my question! Your input is very helpful, thanks. It was only today, while typing up this question, that I realized the prelude's left hand triplet obviously relates to the half note pulse of the stated 2/2 signature---a huge DUH moment. Even though I practice this prelude every other day. I'll be sure to think of that relationship in those terms now, though it was valuable, I think, to hammer into my mind what a 3:5 polyrhythm sounds and feels like. things are a lot clearer now, and I'm sure this is a rare problem, but fun to work through nonetheless. cheers! Commented Apr 19, 2018 at 23:55

I'm not sure I entirely agree with Richard's answer. Certainly standard notation is to indicate a triplet using notes which would "normally" take longer than the triplet, e.g. three eighth notes for a triplet covering a quarter note.
Your stated problem occurs because 5/8 time can only be "contracted" in this way by using quarter notes. So if I (and I have 50 years' experience with reading oddball scores) were to see in 5/8 time, a quarter-note triplet followed with an eighth rest, I would certainly see the triplet as covering 4 eighth notes. If I see just a quarter-note triplet, I would blink a couple times and make the three notes cover all five eighth notes.
Definitely do not write the full-measure triplet with eighth notes, as that violates the "contraction" rule.
Yes, this means the quarter-note triplet means different things depending on whether there's an eighth rest in the same measure, but that's just the way it is.

To answer if this one of the kinks in our system, I would just say that our system has not caught up to all of these rhythmic possibilities. I have not done enough looking at scores from musics around the world to see how polyrhythms are notated in different places. But this kind of polyrhythm has just not been common enough in western music to have a standard notation in place for it. Even if this rhythm has become very common, it still takes time for an agreed-upon notation to gain common use. It would be more common to see a measure of 1/2 with a quintuplet of 8th notes in the RH and triplet quarter notes in the LH. But that does not explain the best way to notate it in 5/8.

That being said, I agree with both Richard and Carl. I believe the 3:5 above the triplet enhances the understanding of the rhythm, but I don't think it is necessary. Like Carl, I think I would blink a few times and then understand that the triplet quarter notes should fill the measure.