Pythagorean Tuning & The Pythagorean Comma

Pythagorean Tuning is a tuning scheme
that is constructed by co-relating the ratios
obtained from a chain of perfect 5ths.
In other words, the notes in 1 octave are determined
by their perfect relative 5ths
​from other octaves.

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It's considered an un-tempered scale,
a natural system,
based on the interval of the Perfect 5th (or ratio 3:2).
After the span of 7 pure octaves & 12 pure 5ths a discrepancy develops,
​known as the Pythagorean Comma.

The Pythagorean Comma (PC) represents a measurement of 'left-over space'.
It is also known as the Diatonic Comma,
​as well as the ratio 531441:524288,
which is the numeric value of 1.0136433.

The PC is closely associated in the construction of today's Equal Temperment (ET) Tuning System.

* Pythagorean Tuning may be thought of as inclusive
because it bridges numeric gaps that the
​divisive Just Intonation system does not blanket.