Re: compound time signature with non duple denominator

[David Wright]

On Wed 02 Nov 2016 at 22:13:54 (+0100), Hans Åberg wrote:
> 
> > On 2 Nov 2016, at 21:08, David Wright <address@hidden> wrote:
> > 
> > On Wed 02 Nov 2016 at 20:10:39 (+0100), Hans Åberg wrote:
> >> 
> >>> On 28 Oct 2016, at 21:48, David Wright <address@hidden> wrote:
> >>> 
> >>> On Fri 28 Oct 2016 at 11:22:00 (-0700), Tobin Chodos wrote:
> >>>> Forgive me if this is a too-easy issue for the list, but: is there a way 
> >>>> to
> >>>> define a time compound time signature such as 4/4 + 1/3?  That is, the
> >>>> measure is four quarter notes long plus one triplet eighth note.
> >>> 
> >>> Isn't this just 13/8? Three triplet eighth notes make a quarter note.
> >>> So it's 3+3+3+3+1 all over 8, and the notes will be written out as
> >>> four dotted quarter notes and an eighth note per measure.
> >> 
> >> Indeed, 12/8 may be complicated notationally if the beats of length 3/8 
> >> are divided into twos and fours, so 4/4 might be preferred.
> > 
> > Now that would be interesting. Are the last three notes of the first
> > bar realistically performable? OTOH splitting the long notes into
> > threes would be straightforward to perform (and to write in 13/8).
> 
> It is, if the tempo is not too high, and one devices a method for counting.
> 
> > The only 13/8 I can recall off-hand is an uncomplicated 6/4+1/8.
> 
> At moderato, 1/4 = 120, 13/16 is performable counting on 2s and 3s. One 
> example is Krivo Sadovsko horo (Bulgaria), 13 = 4+5+4, 4=2+2, 5 = 2+3:
>   https://www.youtube.com/watch?v=3jCuUWnwM28
> Another is Ispayche horo, 13 = 3+2+3+2+3
>   https://www.youtube.com/watch?v=tbU2za0rbzs
> 
> At higher tempo, one may need to count on 3s, 4s, and 5s, especially when 
> clapping hands:
>   https://www.youtube.com/watch?v=aecsGYwtVJM
> This is a Leventikos, in video video, it is in 16 = 4+2+3+4+3, but the clap 
> hands 4+5+4+3.
>   https://en.wikipedia.org/wiki/Leventikos

Correct me if I'm wrong (I'm not familiar with these dances), but
these are just groupings of steady 16th notes, are they not.
My example wasn't.

> This Leventikos is also performed in 12 = 3+2+2+3+2, with quadruplets on the 
> 3s - se my other post in this thread.

OK, the quadruplets add another layer of complexity. The note
durations are now 3+3+3+3+ 4+4+ 4+4+ 3+3+3+3+ 4+4 / 48.
So taking this Leventikos pattern, I've bent the "4/4+1/3" so
that it contains similar tupleticity, to coin a nonce word.

I've broken the 13/8 time signature into the appropriate groups,
3/8+3/8+3/8+3/8+1/8. I've followed this with the 4/4/+1/12
time signature's equivalent notation for the same durations.
The actual rhythm of the individual notes in both cases is
4+4+4+ 3+3+3+3+ 4+4+4+ 3+3+3+3+ 4 / 52.

At the bottom are the versions with undivided notes, with
the 1/12 notes represented in the only way I can think of.

One interesting thing that popped out of my 3/8 notation is
that the odd quaver at the end of each bar can be linked to
the three quavers in the next bar. The upshot is that the
overall rhythm is a repeated (4-slow 4-fast 3-slow 4-fast).

The same rhythm is contained in the 4/4+1/12 notation, but
is it easy to spot? You could make it obvious by writing
   4:2⅔
┌———————┐ over it, and leave people to ponder whether its
speed is the same as the triplet's. Lets' see, 2⅔ is 8/3
so 4:(8/3) is 4*3:8 is 12:8 is 3:2. Success.

Having that 1/8 quaver sitting next to the other three makes
the rhythm quite friendly. If the first beat of the bar is
an undivided dotted crochet, that last quaver is much
harder to time correctly. Of course, we have no idea what
the OP wanted to set to their "4/4+1/3" signature, how it
would be divided etc.

Cheers,
David.

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