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I have never understood if these two note values are supposed to be played in the same way:

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Mathematically, I can understand that they are the same, since both of them have 6 notes that are being played in 1 beat, but they are symbolized different.

Usually, the way I have seen the sixteenth triplets is like this:

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(a line connecting the two groups).

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The difference between a sextuplet and two triplets is that the two triplets are clearly substructured into two units. The sextuplet in contrast may either be substructured into three groups of two notes, or it may not be substructured at all.

If you have one ascending run (for example) written as sextuplets, chances are that the composer intends you to not make the fourth note stand out in any manner.

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    So, the difference is that in the triplets that the 1st and the 4th note stands out, whereas on the sextuplet only the first one does?
    – Shevliaskovic
    Dec 26, 2014 at 10:27
  • That's pretty much right. Although it might also suggest phrasing of notes, as well as actual accents. And, if accents are supposed to be obvious, it would also make sense to use accent markings.
    – Bob Broadley
    Dec 26, 2014 at 10:39
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    I think when there is a difference, you have nailed precisely what it is... but there are different conventions that different composers/publishers use and it is quite possible that the composer does NOT intend any difference between the two figures. Matters of phrasing such as this can be notated as much as possible with similar grouping techniques but technically speaking, the barring of notes is in no way required to influence their phrasing patterns.
    – Darren Ringer
    Dec 26, 2014 at 23:54
  • Exactly. As @DarrenRinger says, different beamings may suggest different accents or phrasing, but to explicitly show these, you should use accent marks and phrasing slurs.
    – Bob Broadley
    Dec 27, 2014 at 22:09
  • Except that there are times when accent marks (which imply dynamic accents) and slurs (which tend to imply that the last note under the slur is detached from the notes that follow it) aren't entirely appropriate. Indeed, there are instruments for which dynamic accents aren't really possible, e.g., harpsichord and organ. On instruments such as these, tuplets are usually picked out by agogic accents, i.e., slightly dwelling on the first note of the group. In such cases, beaming is the proper way of going about the notation.
    – user16935
    Dec 28, 2014 at 2:47
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You are right. They have exactly the same rhythmic values. It would make more sense to use the sextuplets unless:

  • the music obviously accents two groups of three notes per beat.

  • the music often intersperses quavers (8th) notes with groups of triplet semiquavers (16th).

In either case where you use triplet semiquavers, I would group pairs of them with a single beam, as shown in your last example. Unless, of course, you are in a time signature which has a longer beat, such as compound time or 2/2, in which case you could group 3 and 4 groups of triplet semiquavers with single beams, respectively.

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It's like the difference between 6/8 and 3/4, the first being subdivided into two units, the second in 3. However, in many cases there is only one accent on the first note of a sextuplet. Anyway, when written as two triplets the accents are clearly on the first and (possibly a bit weaker) on the fourth note. This little article describes the different rhythmic interpretations of the sextuplet.

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The sextuplet can also be six in the time of three, six in the time of four and Six in the time of five. It all depends on the specifics of the piece and how the rhythms work. So yes very much different than the regular three in the time of two.

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