Sixth and Twelfth Notes (Tool #41)

If you’ve studied contemporary music you probably have come across definitions of time that aren’t based on 4 (eg. not breves, whole notes, half notes, quarters, eighths, etc.).  Some composers use other definitions of time that aren’t tuplets but aren’t regular notes (including tied or dotted notes).

Two beat durations with which I’m currently experimenting are sixth and twelfth notes.  Sixth notes are equivalent to one quarter note in a quarter note triplet, and twelfth notes are one eighth note in an eighth note triplet.

How are they notated? – They can either be achieved through metric modulation, or writing an incomplete tuplet.  The metric modulation is easier to do in Finale, but making a “2/6” measure is (or so I’ve read) possible.  For example, in one piece I made a “7/12” measure by using a metric modulation that turned the eighth note triplet into the eighth note, and writing a measure of 7/8.  Another way, employed by composers such as Thomas Ades, is to write a bar metered in (eg.) 2/6.

What effects can they have?  What are some ways in which they can be used? – They are effective in throwing a listener’s ear off, since most listeners are usually used to divisions of 4 or 2.  This is particularly effective if they’re thrown in the middle of a “groove” (eg. adding a 5/6 bar in the middle of two 7/8 bars that would normally form a rhythmic groove).  They can also help make open/free passages even freer, by adding in extra abnormal/wide spaces in the passage.  They can also help align instruments progressing at different tempi (if you’re willing to do some math).  These are just a few examples of their possibilities.

Some people argue that these are esoteric techniques, but I argue that using only divisions of 4 or 2 can be just as esoteric to life; in other words, what is more artificial and removed from life than dividing everything by the numbers 4 or 2?  There is more to life that we can describe through music, and life certainly does not confine itself to distinct metrical divisions (just as it doesn’t confine itself to equal temperament).

What do you think?  I’ve found these divisions/beats to be rewarding, but is this this something you’d try?

Happy Composing,


7 thoughts on “Sixth and Twelfth Notes (Tool #41)

  1. This Idea is a great one I figured this out while composing/recording a piece back around 2009/2010 Where I was splicing material from one project and placing it into another, in which it took on a new tempo and/or subdivision/tuplet/ratio. So I had to look at the ticks that make up a beat that make up a bar. I came up with mathematical ways of figuring out any(literally) kind of rhythm and started hypothesizing of synthetically creating more precise meter/Time Signatures. I was told this was similar to avant-garde composers did but in an absolute way. To my knowledge I never heard of anyone doing this before me. So if you think of any division whether triplets(4ths=6ths, 8ths=12ths etc.) or your in betweens like 5ths=quintuples 7ths=sextuplets and so on to infinity, depending on your ratio/tuplet you can get even/odd numbers or even fractions. It’s all relative just like a chord to a tonic(or more precisely the relationship between one note and another). I have been meaning to make more videos on this. Thanks you very much for your post.

  2. I agree that 6th and 12th notes are a very useful concept. But I don’t think they’re “esoteric” in any way. Composers use them all the time, they just don’t call them that. They’re typically used as common time (4/4) with each beat (that is, each 1/4 note) chopped into 3 equal time “steps”. In musical notation this is often indicated by putting a “3” and a tie under each cluster of 3 8th notes to indicate they’re actually 3 12th notes. Very clumsy notation, though!

    So, is there an alternate notation that I don’t know about? It would be much simpler to set the key signature to 12/12 (structured as 4 beats per measure, 3 steps per beat, one 12th note per step), and use actual 12th notes, instead of using 4/4 time and “triplets”. Provided that symbols exist for 12th notes.

    For a couple of examples of how natural-sounding 12th-note melodies are, here are a couple tunes; the first is a tune that’s been running through my head that I think I must have heard somewhere; the second is a stupid little song I composed myself some months ago:

    And, for another example, consider the song “Take Me Out To The Ball Game”: perfect 12/12 meter! But it’s typically written clumsily (8 bars of 4/4 with triplets, or 16 bars of 6/8, or 8 bars of 12/8), whereas, it *should* be written as 8 bars of 12/12, 4 beats per bar, 3 steps (12th notes) per beat.

    1. Thank you for your comment! I agree that the notes are not esoteric, but we use them in very common ways, so that when we use only one 6th or 12th note in a stream of quarters it is quite esoteric. The way we use them in avant-garde composition can expand them beyond their simple “Take Me Out To the Ballgame” uses.

  3. AC

    Twelfth notes are just Triplets. Think about it. One measure in 4/4 time has four beats, each beat can have three triples (one set of three for each of the four beats). 4 x 3 = 12.

    Sixth notes is harder to count but not impossible. For two beats, you just skip the middle note in the first triplet then only play the middle note in the next triplet, or vice versa of course.

    If you really want a brainfuck, try mixing sixteenth notes with twelfth/sixth notes. They come JUST before/after a triplet, almost like a grace note.

    1. That’s exactly right. I think that this brainfracking is good, to mix triplets that don’t fulfill their tuplet brackets–for example two quarter note triplets (6th notes) and one quarter note. That is seen in some scores, but I’m hoping that jarring rhythm (and others like it) appear in more music written nowadays.

    2. Yes you can have any type of tuplet 1 – infinity hypothetically though not practically. I actually made q few Youtube videos explaining whole notes (1s) to 32nd notes (32s) and everynumber in between. Just like our quintuplets and septuplets etc.
      Here is the link, though i need to make a few more for more practical applications this just the introduction.

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