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in this video I'll be discussing one
of the most critical topics

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in tuning theory
- just intonation

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the term just intonation 
describes the tuning

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of musical intervals 
so that their frequencies

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are related by small
whole number ratios.

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we already know that
the ratio 2/1 is 1200 cents

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so an interval of that size
could be referred to as

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justly tuned to a 2/1

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some examples of other 
important ratios are

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3/2,
about 702 cents,


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6/5
close to 315 cents


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and 5/4
approximately 386 cents.

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why do we place any importance 
on small whole number ratios

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between frequencies

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because justly in tone intervals 
have a unique quality

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of smoothness, blending or purity

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at least when used with many
standard musical timbres

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here's a dominant seventh chord played
in standard Western tuning

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and here's one tuned to 
just intonation

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why whole number frequency ratios
sound this way

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is beyond the scope of this video
just to know it has to do

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with the harmonic nature
of the natural overtone series

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in the complex interaction 
between multiple sine waves

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that results in what's called beating

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now if just intonation or JI for short

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has these positive qualities why not use
it instead of the standard twelve-tone

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Western tuning

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one important issue 
with using pure JI

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is chromatic drift

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those of us familiar 
with standard chord progressions

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will immediately recognize the 1-6-2-5
chord progression

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which sounds like this in standard
Western tuning

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the chords in this progression however

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all arguably approximate pure 
justly intoned chords

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so if we want to use the purest
harmonic intervals

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we can replace the Western intervals
with the just pure ones

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but if we do that there are 
unintended repercussions

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keeping all common tones as unisons
and tuning the chords pure

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our final one chord
or tonic

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does not arrive back at our
original pitch

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instead it arrives at 80/81

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about 21 cents below the starting pitch

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tiny, nearly one over one 
intervals like 80/81

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are referred to as "commas"
and often show up in just intonation 


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as the difference 
between two important ratios

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this chord progression drifts

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by that amount every time through 


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hence the term chromatic drift

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this purely tuned chord progression 
followed by the original one chord

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for comparison 
sounds like this

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for most chord progressions

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it is impossible to maintain smooth
voice leading

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and pure intonation without this
chromatic drift

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so either the pitch continually
drifts or the pitch has to be jarringly

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corrected at some point

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neither of these options is desirable in
most musical contexts

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another issue with JI is its
complexity

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just intonation has an infinite
number of possible ratios

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one for every rational number and
requires an infinite number of

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dimensions to represent it

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one for each prime number

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the more of these just intervals 
you want to include in a scale

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the more difficult they will be
to organize, play and notate

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this can be very cumbersome 
when taking into account

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modulation and chromatic drift

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both of these problems 
can be alleviated however

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by temperament - a middle ground
between accuracy

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like blending and purity, 
and practicality

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dealing with things like 
complexity and drift

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temperament is covered the next video
in this series