in this video I'll be discussing one
of the most critical topics
in tuning theory
- just intonation
the term just intonation
describes the tuning
of musical intervals
so that their frequencies
are related by small
whole number ratios.
we already know that
the ratio 2/1 is 1200 cents
so an interval of that size
could be referred to as
justly tuned to a 2/1
some examples of other
important ratios are
3/2,
about 702 cents,
6/5
close to 315 cents
and 5/4
approximately 386 cents.
why do we place any importance
on small whole number ratios
between frequencies
because justly in tone intervals
have a unique quality
of smoothness, blending or purity
at least when used with many
standard musical timbres
here's a dominant seventh chord played
in standard Western tuning
and here's one tuned to
just intonation
why whole number frequency ratios
sound this way
is beyond the scope of this video
just to know it has to do
with the harmonic nature
of the natural overtone series
in the complex interaction
between multiple sine waves
that results in what's called beating
now if just intonation or JI for short
has these positive qualities why not use
it instead of the standard twelve-tone
Western tuning
one important issue
with using pure JI
is chromatic drift
those of us familiar
with standard chord progressions
will immediately recognize the 1-6-2-5
chord progression
which sounds like this in standard
Western tuning
the chords in this progression however
all arguably approximate pure
justly intoned chords
so if we want to use the purest
harmonic intervals
we can replace the Western intervals
with the just pure ones
but if we do that there are
unintended repercussions
keeping all common tones as unisons
and tuning the chords pure
our final one chord
or tonic
does not arrive back at our
original pitch
instead it arrives at 80/81
about 21 cents below the starting pitch
tiny, nearly one over one
intervals like 80/81
are referred to as "commas"
and often show up in just intonation
as the difference
between two important ratios
this chord progression drifts
by that amount every time through
hence the term chromatic drift
this purely tuned chord progression
followed by the original one chord
for comparison
sounds like this
for most chord progressions
it is impossible to maintain smooth
voice leading
and pure intonation without this
chromatic drift
so either the pitch continually
drifts or the pitch has to be jarringly
corrected at some point
neither of these options is desirable in
most musical contexts
another issue with JI is its
complexity
just intonation has an infinite
number of possible ratios
one for every rational number and
requires an infinite number of
dimensions to represent it
one for each prime number
the more of these just intervals
you want to include in a scale
the more difficult they will be
to organize, play and notate
this can be very cumbersome
when taking into account
modulation and chromatic drift
both of these problems
can be alleviated however
by temperament - a middle ground
between accuracy
like blending and purity,
and practicality
dealing with things like
complexity and drift
temperament is covered the next video
in this series