Re: compound time signature with non duple denominator

[Hans Åberg]

> On 3 Nov 2016, at 21:28, David Wright <address@hidden> wrote:
> 
> 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:
>>> 
>>>>> The only 13/8 I can recall off-hand is an uncomplicated 6/4+1/8.

>>> 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.

It was in response to your comment on 13/8 above.

In the Leventikos 12/8, 12 = 3+2+2+3+2, the 3s have duplets metric accents. But 
it is hard to express that via meter. When notation, oen just sums it up. 
Bartok used (4+2+3)/8, that is
  4+2+3
    8
but on the Balkans one would just write 9/8 or 9/16. The beaming can indicate 
metric subaccents, but LilyPond cannot do that automatically, so I just skip it,

>>> 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.

One performer keeps the meter, and the others follow.

> 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.

In irregular meters, the opposite happens: one looses the feeling for exact 
proportions. So one has to unlearn the idea of exact beats. If you want exact 
beats, then you need a sequencer track.

I am not sure exactly what meter you want, but if the proportions are 
3+3+3+3+1, then it will likely feel like a common 9 = 2+2+2+3 with a slight 
time bend shortening the last beat a bit, which is normally done.

The tune Eleno Mome is often played in 7/8, but exists written as 13/16, 13 = 
4+4+2+3, where the 3 has typical 2+1 patterns. In live performances, there 
might be something between 7/8 and 13/16. But exists written as 12/16, 12 = 
3+4+2+3, and a performance plays it as 3+2+2+2+3.

> 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.

On Balkans, they use 3s and 2s, counting on the fingers, for example 11 = 
2+2+3+2+2. This way, smaller differences than be performed.

But you might try using flute articulation t-k and t-k-t patterns.

>>>> 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

Then it sound as a regular 9/8 or 9/16.

>> 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.

So what are your intended metric accents? If the 1/3 at the end is subordinate 
to the i/4, then your meter will sound just like a 9/8 with a slight time bend, 
unless lsowed down to a zeibekiko.

>>> 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.

It is ambiguous, as it stands.

>> 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!

As it is, beaming can indicate subaccent patterns. SO any such notation would 
have to think of that.