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Re: compound time signature with non duple denominator


From: Hans Åberg
Subject: Re: compound time signature with non duple denominator
Date: Thu, 3 Nov 2016 10:37:36 +0100

> 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.

> My example wasn't.

Then one add another level on the musical line. One example how this occurs 
metrically is the Leventikos in 12.

>> 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.

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

> 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.

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.






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