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

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in tuning theory[br]- just intonation

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the term just intonation [br]describes the tuning

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of musical intervals [br]so that their frequencies

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are related by small[br]whole number ratios.

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

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so an interval of that size[br]could be referred to as

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justly tuned to a 2/1

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some examples of other [br]important ratios are

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3/2,[br]about 702 cents,[br]

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6/5[br]close to 315 cents[br]

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and 5/4[br]approximately 386 cents.

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why do we place any importance [br]on small whole number ratios

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between frequencies

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because justly in tone intervals [br]have a unique quality

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of smoothness, blending or purity

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at least when used with many[br]standard musical timbres

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

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and here's one tuned to [br]just intonation

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why whole number frequency ratios[br]sound this way

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

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with the harmonic nature[br]of the natural overtone series

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in the complex interaction [br]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[br]it instead of the standard twelve-tone

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Western tuning

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one important issue [br]with using pure JI

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is chromatic drift

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those of us familiar [br]with standard chord progressions

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will immediately recognize the 1-6-2-5[br]chord progression

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which sounds like this in standard[br]Western tuning

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the chords in this progression however

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all arguably approximate pure [br]justly intoned chords

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so if we want to use the purest[br]harmonic intervals

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we can replace the Western intervals[br]with the just pure ones

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but if we do that there are [br]unintended repercussions

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keeping all common tones as unisons[br]and tuning the chords pure

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our final one chord[br]or tonic

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does not arrive back at our[br]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 [br]intervals like 80/81

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

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as the difference [br]between two important ratios

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this chord progression drifts

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by that amount every time through [br]

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hence the term chromatic drift

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this purely tuned chord progression [br]followed by the original one chord

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for comparison [br]sounds like this

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for most chord progressions

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it is impossible to maintain smooth[br]voice leading

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and pure intonation without this[br]chromatic drift

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so either the pitch continually[br]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[br]most musical contexts

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another issue with JI is its[br]complexity

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just intonation has an infinite[br]number of possible ratios

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one for every rational number and[br]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 [br]you want to include in a scale

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

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this can be very cumbersome [br]when taking into account

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modulation and chromatic drift

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both of these problems [br]can be alleviated however

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by temperament - a middle ground[br]between accuracy

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like blending and purity, [br]and practicality

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dealing with things like [br]complexity and drift

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temperament is covered the next video[br]in this series