Every morning I wake up to Radio 3.
One particular morning there was baroque
music playing and the performance had a
perfect hemiola. Now most people don't
really pay much attention to hemiolas
but it really made my day, it was such a
good way to wake up. Later on that same
day I mentioned this to some non-
musician colleagues and one of them said,
"Hemiola,
that sounds like some kind of horrible
disease!".  So please allow me to explain
exactly what a hemiola is and how it
works.
Let's start with some basic maths.  3 times
2 equals 6. 6 can be divided into either
3 groups of 2 or 2 groups of 3.
Music is divided into bars.  If we are in
3 and we combine two bars together we
will have 6 beats in total those 6 beats
can then be redivided. We could
continue with the original time
signature of 2 groups of 3 but we could
also redivide those 6 beats and we
could have 3 groups of 2.  Watch our
juggler, the red ball represents the
downbeat.
He's now juggling in 3/4 time. Now watch
our juggler, again the red ball is the
downbeat but now he's in 2/4 time.
Now watch our juggler as he keeps the tempo
the same but changes the groupings. With
hemiolas the time signature doesn't
change, it's just the groupings of the
notes that change. For that brief moment
the barline is overridden by the
hemiola.  For example if we look at this
music by Lully we can see that the time
signature stays in 3/4 throughout and
the hemiolas
are implied by the melodic and harmonic
movement. Sometimes hemiolas
are quite ambiguous and sometimes
they're not in all the parts at the same time.
Here's another example. If we look at
this excerpt by Geminiani we can see
that two bars of 3/8 have been
combined into one bar of 3/4
so the hemiola is very obvious.
If we are in three and feeling the pulse
as one in a bar then a hemiola will
create an auditory illusion and it will
feel as though the music is speeding up
like this: one two three one two three
one two one two one two one two three
and if I clap that pattern without
counting it would sound like this:
However if we are in three and feeling a
distinct three beats in a bar and we hit
hemiola it will have the opposite
auditory illusion and it will sound as
though the music is slowing down:
one two three one two three one two one
two one two one two three and again
without my counting:
And this is particularly effective if it happens at
the end of a piece or at the end of a
movement signaling the final cadence:
Back to that morning when I was woken up
by my ideal hemiola, what made it so
satisfying? I think that ultimately a
hemiola should make the listener feel as
though he or she is being airborne for
those six beats
and we don't really know where we are
until we've landed safely on the
downbeat after the hemiola. If we return
to our juggler it should feel like this:
and if we return to the Geminiani
excerpt it should sound like this:
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