Tuning Theory 1: Just Intonation ("Microtonal" Theory)

In this video I gloss over why Just Intonation is TOTALLY AWESOME and then convince you it SUCKS.

Also, please ignore my instinctual figured bass that I added to the last chord in the I vi ii V I, but didn't add to any others...

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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