A kind of alternate tuning in which the intervals between notes in the scale are based on small integer ratios. So your intervals sound pure, since your ear is naturally attuned to hearing such "true" intervals, and the trick is to balance/approximate the intervals so they're even enough to allow some transposition without having any number in the ratios too big.

In the system of Just Intonation (as used by Harry Partch), each pitch is represented by a ratio of two integers a/b that expresses its relation to the tonic, the central pitch on which the tuning is based. The tonic itself is represented by the ratio 1/1 or the interval of a unison, which basically means the two pitches are the same.

Because of the way the cochlea of the inner ear is designed, pitches that differ from each other by one or more factors of two (octaves) will sound inexplicably like the same pitch even though one is higher than the other. They're the same pitch class in different registers. Because of this octave equivalence, ratios can be multiplied or divided by 2 without change in meaning, so they are customarily so adjusted as to fall between 1/1 (the tonic) and 2/1 (its octave doubling). For example, 10/3 would be divided by 2 to get 5/3, and 1/5 would be multiplied by 2 three times to get 8/5. That way all the possible pitches, even those far beyond the range of human hearing, can be condensed down into a single octave and represented by numbers between 1 and 2.

Since the tonic and all its octave doublings are basically the same pitch, the first really different pitch we come across is 3/2. This pitch has a very consonant relationship to the tonic, almost exactly the same as the conventional (equal-tempered) interval of a perfect fifth. The reason this interval is so consonant is because of the smallness of the numbers in its ratio (in simplest form), and all the ratios follow this rule, from the perfect consonance of 1/1 to an infinity of dissonance expressed by irreducible fractions with ever-larger numerators and denominators. Around 11 or 13 the ear stops being able to recognize integer ratios as consonances to the point where they sound like random noise.

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