Re: compound time signature with non duple denominator

[David Wright]

On Thu 03 Nov 2016 at 10:37:36 (+0100), Hans Åberg wrote:
> 
> > On 3 Nov 2016, at 03:04, David Wright <address@hidden> wrote:
> > 
> > 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.
> 
> Yes, in the definition of the meter, in respons to your question whether it 
> might be performable. 13/8 and even 13/16 is performable at moderato counting 
> on the 1/4s, though I have no example of the 3+3+3+3+1 occurring naturally.

But the three notes I referred to weren't in 13/8 or 13/16 because the
last 3 of 3+3+3+3+1 (in 13/8 time) was a made into a duplet.

> > My example wasn't.
> 
> Then one add another level on the musical line. One example how this occurs 
> metrically is the Leventikos in 12.
> 

I don't know what "another level on the musical line" means.

What I was pointing out was that we have 13/8 consisting of three
dotted crochets followed by a duplet (two in the time of a dotted
crochet) followed by a quaver. The relationship of these notes is
6 6 6 3 3 2 and I think most people would struggle with getting
that last note exactly the correct length.

Of course, if you adopt a pace where you can form that pattern
by grouping 26 rapid claps or whatever, then it can get simpler,
but I was talking in the context of straightforward note values
as sung by, say, a classical singer.

> >> 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.
> 
> Yes, indeed. In the Leventikos, the quadruplet pattern occurs consistently. 
> When performing, there are slower 1/16th contrasted with faster ones. Some 
> performers have triplets on the 2s, and quintuplets occur in Balkan music as 
> well. So it can be more complex.
> 
> > 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.
> 
> A problem with this meter is that the 1/3 at the end is fairly short, so it 
> may be distorted by metric time bends: there is a tendency in Balkan music to 
> shorten the measure at the end.

Hey, that's my point. You call it "metric time bends" and that's fine
in the context of your musical examples.

> So the question is how to bring out the triplet nature. Otherwise replacing 
> the 1/3 with 1/4 or 1/2 might do well, from the practical point of view. The 
> meter 9 = 2+2+2+3 is very common, so at faster tempo, your meter may sound 
> like this one. Some examples:
>   https://www.youtube.com/watch?v=a-2HVFc4k_k
>   https://www.youtube.com/watch?v=78ycWoNozLY

I think you're on a different journey. I'm not trying to "bring out
the triplet nature" in anything. Perhaps you were misled by my second
sentence,

 "Three triplet eighth notes make a quarter note."

The "triplet" in that sentence refers back to the OP's

"the measure is four quarter notes long plus one triplet eighth note".

"One triplet eighth note" defines a duration of time (which the OP
appeared to get wrong in any case). One note cannot form a triplet.

Writing four dotted crochets followed by a quaver, in isolation,
has nothing tripletty about it. It's four steady beats and a kick.
We only use that notation normally when we intend to subdivide it
in a tripletty manner, usually crochet-quaver pairs (or add that
in another part). That's what makes it tripletty.

> > 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).
> 
> Syncopations are common in Balkan music, also on the ornamental level.
> 
> > 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.
> 
> The choice may depend on whether the the 1/4s are divided into triplets or 2s 
> and 4s.

There may be no choice to be made. Perhaps the OP wants four beats and
a kick, and nothing more.

> You might write out both versions, for convenience of the musician. So might 
> have a supporting percussion line with triplets on the 1/4s in the meter 4/4 
> + 1/3, which the other musicians can follow. Then the 4s might be divided 
> into 2s and 4s.

Well you might. But I would be reluctant to put a score in front of
somebody with a quaver having 1:⅔ written over it, or with time
signatures that didn't have powers-of-2 denominators. I guess there
are people here for whom this is normality. My question to them is why
don't they start inventing a glyph hierarchy for note division by
three. We could eliminate a lot of tuplets and dots!

Cheers,
David.