[Ardour-Dev] Tempo Maps and Complex Meters

[Ben Bell]

I'm afraid this mail is borderline brain-dump material. I've been
kicking these things around for a while but haven't really got a full
grip on them.

This mail is the result of two things: The first is trying to record
various pieces of music in Ardour which do vaguely unusual things
rhythmically -- frequent meter changes, odd time signatures and so on.
The second is trying to track down and fix a bug which causes anyone
doing the above to end up with a scrambled tempo map because of
something screwy occasionally happening in the calculations when moving
tempo or time signature changes around.

In general though, for pieces where the tempo and time signature varies,
ardour's tools aren't really up to the job (e.g. moving or copying
sections of audio with associated meter and tempo changes).


Tempo maps and complex meters in Ardour
=======================================

Perhaps I should start with a simple question and an assumption of the
answer:
Q: Why do we care about tempo and meters in Ardour?
A: Tempos and meters are fundamentally there to allow us to create a
   grid upon which we can align regions in a musically relevant way.

This is slightly different from the answer you might get from someone
involved in notation, where there is an element of communication and
expression of intent which is important. But if you're not producing
notation it really is about a grid of divisions and subdivisions to
which you can align musical components. The metronome, which might
feature prominently in someone else's answer to this question, is
actually just an audible representation of this grid.

For anything with changes to the meter or tempo, we start to encounter
questions on how to handle them, both in terms of the tempo map itself
but also in terms of the implicit effects that editing it has on regions
and tracks. Likewise, if you have some audio recorded over a set of
tempo or meter changes and you want to move or copy it, in most cases
you'll want to reflect these changes on the tempo map too.

When manipulating the tempo map in such a way as to move bars around
there is a question as to what to do with regions on that time line.
Some may be intended to be aligned relative to bars and beats, some by
absolute time. I'd have thought that in most cases this was a
characteristic of a track rather than individual regions and that would
simplify the UI (a selection on the track).

Some pieces (particulary avant garde pieces) can have polyrhythmic
meters where one part is played in a different signature to another.
Refering to the per-track BBT/seconds alignment idea above this could be
generalised to a selection from one of several time lines, one of which
is seconds and others can be independent or related tempo maps. If we
imagine tempo maps as another type of track, with all the
cut/paste/drag/copy operations that normal tracks have then this starts
looking like quite a flexible way of going about things.  There is
obviously more to think about here but it feels like the right sort of
direction to me.

Another thing to consider is progressive changes to tempo (i.e.
accelerando and decelerando, but also potentially tracking the minor and
arbitrary fluctuations rhythm that a live performance entails).

More complex time signatures also start raising issues. Something I'd
personally find useful is divisions and subdivisions when marking bars.
Something in 9/8 for example might be counted as 2, 3, 4 or it might be
counted as 3, 3, 3. Having a click that sounded like this (ahem)
X.x..x... or X..x..x..  and likewise a grid with two levels of emphasis
would be very helpful in track some of these things. I suppose it's a
nice to have wishlist item.

Another question is that of irrational (and worse) meters. I'm not an
expert on this area at all but from what I've seen of it I'd argue that,
mathematically, a lot of these things can be expressed using rational
meters. While I'd accept that a lot of notational devices such as meters
like 4/5, (2/3)/4 or have their place as communicative and expressive
features of notation, when it actually comes to rhythmic alignment
they're superfluous. Anything with a non power-of-two denominator is, I
believe, musically identical to the same thing written with a
power-of-two denominator[1]. I believe they've been used in polyrhythmic
music to make parts line up in notation but again I think the reason for
this is clarity of notation, not anything rhythmically significant.

Time signatures along the lines of (2/3)/4 or, say, 3.7/4 are perhaps
useful but in all practical cases (once you take into account the fact
that we don't have infinite time resolution) can be represented by
rational time signatures, or approximated sufficiently closely as to be
indistinguishable.  I'm expecting someone here to dive in and correct
me, but is there really a practical difference between 3.7/4 and 30/32
with emphasis on 8, 16, 24?  Likewise, mid-bar time signature changes
are easily represented as two time signature changes -- one to shorten
the bar that is to be aborted early and a second to introduce the
desired new time signature. Perhaps this is all blind prejudice on my
part :)

One more thought that crops up which didn't fit neatly anywhere above:
sometimes it is useful to stop the BBT count, have a free-form section
which is purely measured in seconds, and then start the BBT counting
again. Notionally you could imagine this as a 1 beat bar of arbitrary
tempo to make it take exactly n seconds.


Anyway, apologies for the rambling and disorgised form of the mail. Does
anyone have any thoughts on this? There must be other people out there
recording rhythmically complex music in ardour who have some perspective
on this.

Ben


[1] Actually, anything written with any denominator is musically
    identical when rewritten with a different denominator. It's just a
    mapping to the tempo.


-- 
+-----Ben Bell - "A song, a perl script and the occasional silly sig.-----+
  ///      email: bjb at deus.net            www: http://www.deus.net/~bjb/
  bjb    Don't try to drive me crazy... 
  \_/                                        ...I'm close enough to walk.