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