I'm currently studying piano music theory and I have a hard time figuring out how much triplets, duplets, quadruplets, quintuplets, sextuplets, and septuplets are worth in different time signatures (simple, compounds hybrid meters)
If anyone has any tricks when they want to know how many beats/notes an irregular grouping is worth, please feel free to respond!
Thank you!
Just looking at your examples, some thoughts that may help are as follows:
I’m assuming triplets don’t give you too much trouble. They’re pretty straightforward.
For the larger groupings, based on your example page, you could think through the following if you get lost:
EXAMPLE: For a grouping of 9 sixteenths, the largest number of sixteenths in that grouping divisible by 4 is 8. 8 sixteenths equals 2 quarter notes, so your grouping fits into the space of two quarter notes.
EXAMPLE: For an grouping of 8 sixteenths, the largest number of sixteenths in that grouping divisible by 3 is 6. 6 sixteenths equals a dotted quarter, so your grouping fits into the space of a dotted quarter.
Hopefully this helps!
Honestly, I don't really "agree" with those crotchet- and minim-beat septuplets. I'd personally add an extra beam to both of those, in part to avoid the issue you're having here where there's an inconsistency between simple and compound metres. It's true that this leaves the pentuplet inconsistency unresolved (and unresolvable, barring something very confusing like quintuplet dotted-quavers), but:
These higher-value tuplets are read contextually, not according to strict rules. If you're in 4/4, and septuplet semiquavers are beamed as a single unit, with three other beats in the bar; well, you know what the composer means.
I assume you understand the length of standard notes and that your question is about the length of the “tuplets”, that is, the ones with a number.
Sadly, the system is not fully consistent, but we come to the weird cases in a moment.
The number in a tuplet is shorthand for a division. That is “3” is mostly short for “3:2”, meaning “three notes in the time of two of the standard length”. In the same way “5” is mostly short for “5:4”. Sometimes it is written like this to avoid confusion.
In 4/4 and 2/2 time signatures, everything is divided in powers of two (2,4,8,16,…) and in these times a tuplet would always fit in the previous power of two:
Well… not always, for higher numbers, some music notators and musicians (like Esther in the other answer) feel for example that 15 should be short for 15:16. So, you might have to look at the context to figure out what is meant.
Another complexity comes with other time signatures: take 6/8 for example. Its bar is divided into 2 dotted 4th notes, then in 6 eight notes, then in 12 sixteenths etc… and so a quintuplet of 5 eight notes is to be played in the duration of 3 eights. Hence here “5” is short for “5:3”
Here is the rule for tuplets with just one number:
Tuplets are usually to be played faster than if the number wasn’t there and should fit equally in a standard time unit, as defined by the time signature.
Common exceptions where tuplets are played slower:
Source: experience & Wikipedia
