As you have probably noticed, the zig-zag experiment leads us, in
principle, to a slower-than-IOI 400ms isotempo (i.e. 420-430ms). It
seems that the 50ms grid imposed, as a matter of convenience, at the
beginning of this blog, does not help us in this particular case. This
is why I used so many times in the previous entries the word "around" 400ms.
Don't worry. If the perceptual approach towards musical time (that's
what we study here, in case you didn't know) will have an evolution
similar to the Western tuning system, such "adjustments" from the way
our brain naturally processes discrete time will surely occur. Are you
familiar with the major third on your piano? Well, that's a "wrong"
interval, as the natural major third is different (i.e. bigger) and so
are many other intervals tempered by Herr Bach 300 years ago.
But as we now have no idea as to how this evolution will unfold, let us
consider that, after IOI 350ms our 50ms grid should be temporarily enlarged to 75ms
and, as a matter of consequence, our next isotempo to be learned
corresponds well to the 420-430ms (350ms + 75ms = 425ms) value resulted
from the zig-zag experiment.
The magnification of the grid is a natural thing to do as the bigger
the time-intervals to be considered are, the more difficult is for us to
discriminate them accurately. For instance, imagine that you have to tell (cross my heart)
that you can feel the difference between a 60 and a 65 minute
long experience.
The reason for this rests in the fact that our sensory experiences
can be discriminated only if between them there exists at least a "just
noticeable difference"-specific (JND) interval. The JND is a common
place in psychology textbooks and, in the case of time perception, it
may vary from 5% (also called the Weber fraction) and 15% in some
cases. JND simply represents the minimum difference necessary for
similar stimuli to be experienced as different.
Now you can see that, if we keep going with the 50ms grid, at some point we shall have to discriminate
IOI values (such as 1450ms and 1500ms) that are less then 5% apart
(1450 + 5% = 1522; 1500 - 5% = 1425) and, thus, perceptually
undiscernible.
Despite all that, as educated
temporal perception has its own ways, after some practice you will be
able to discriminate both IOI 400ms and IOI 420-430ms as distinct
isotempi. The same goes for IOI 450ms. Whenever unsure, proceed to the
zig-zag test and compare its results to the isotempo you have to name:
if the zig-zag isotempo is slower – you probably deal with a 400ms IOI,
if faster – with a 450ms IOI. This way you will be able to discern and
memorize three tightly spaced isotempi: 400, 420-430 and 450ms.