Re: GDP glossary question: complex meters

[Hans Aberg]

On 26 Feb 2008, at 07:39, Kurt Kroon wrote:

> BACKGROUND
>
> We now have a number of different terms to refer to several closely  
> related
> concepts:
>
> * polymeter
> * polymetric time signature
> * double time signature
> * compound time signature
...

> How can we normalize the terminology?

You can't :-), because there are at least two major incompatible  
terminology systems. The divide sees to go between Germanic (down to  
the Balkans) and Anglo-Latin countries. In the latter, one thinks of  
the meter as subdivided into parts, even if that is not implied by  
the meter definition, and it is called simple if these subdivisions  
are by two. So 2/4 is called simple, even if the piece consist only  
of triplets, as each 1/4 is though of as subdivided into 2 parts.

The Germanic tradition seems to refer on the metric subaccent  
structure. So 2- and 3-time are simple, but 4-time, which is usually  
described as 2+2, is called compound. That is
     >  - (>) -
  4: |  |  |  |    (2+2)
It is though possible to play 4 as
     >  -  -  -
  4: |  |  |  |    (2+2)
Traditional notation does not distinguish between the two, but in  
modern notation, I think one should be able to.


> So ... what are your thoughts?


I think LilyPond needs to mention both: my experience is that anyone  
is used to the one system will not easily adjust to the other.

My own preference is a variation of the Germanic tradition that fits  
well with the complex meters I am used to.

> (
> Elsewhere -- just to add them to the mix -- I've seen:
> * mixed meter / mixed time signatures
> * additive time signatures

I think this in the Germanic tradition, this is the same as compound.

> * alternating time signatures
> )

I think this might be a tune that alternates between meters,  
typically in an irregular fashion, so that one writes out a single  
time signature for it. In old times, if the piece alternates between  
say 6/8 and 3/4, one would just write out one, but today, one may  
want to write
 3 6
 4 8
(no "+" here).

> * polymeter -- the most generic term
>     * sequential polymeter -- Ralph's definition
>         * regular
>         * irregular
>     * simultaneous polymeter -- Valentin's definition
>         * regular and irregular (theoretically)

Harvard Concise agrees with me that polymeter means simultaneous  
(parallel) use of different meters. But it notes that sometimes it is  
used to denote different meters used in succession. The "sequential  
polymeter" might instead be called "alternating meter" (see below).

Following Hindemith, "Elementary Training", which adheres to the  
Germanic tradition (despite the fact the book seems to be written in  
English at Yale), an irregular meter is one which is not repeated  
regularly. So CPP (Common Practice Period) 9 = 3+3+3 would be  
regular, but the Bulgarian Daychovo 9 = 2+2+2+3 would be irregular.

I think the Anglo-Latin tradition uses a different definition, but I  
do not remember it.

> And here's what happens to the list of terms above:
>
> * polymetric time signature
> Deleted: although it implies sequential polymeter, it has too many  
> possible
> interpretations to be useful.

I think such keyword should be in places where they might apply,  
because one is searching for them. For example, I was wanted to  
figure out how to typeset ametric music, but it turns out that  
LilyPond calls in "unmetered", and the difference is hard to capture  
in a search. And failed search may end up as a post to the users  
list :-).

> * double time signature

So in Germanic tradition, this would be 2-time. 3-time is triple  
time. 4=2+2 and 6=3+3 time are compound. And again, the Anglo-Latin  
definitions are different.

> * compound time signature
> * additive time signatures

Or specifically, one must distinguish between "meter" ("time") and  
"time signature". So I think it should be:

* double meter (time)
* compound meter (time)

with no "time signature". - The time signature is what is drawn. The  
meter was often be inferred by some other information in the context,  
like beaming, type of tune, etc.

> * alternating time signatures

Again, dropping "signature", I think alternating meters just mean  
meter changing from measure to measure, normally written out.

An alternation time sigature might be the one above
  3 6
  4 8

  Hans Åberg