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596.9996 cents
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In 17-limit Just Intonation, 24/17 is the "first septendecimal tritone," measuring very nearly 597¢. It is the mediant between 7/5 and 17/12, the "second septendecimal tritone." The two septendecimal tritones are each 3¢ away from the 600¢ half-octave, and so they are well-represented in all even-numbered EDO systems, including 12edo. Indeed, the latter system, containing good approximations of the 3rd and 17th harmonics, can use the half-octave as 24/17 and 17/12 in close approximations to chords such as 8:12:17 and 16:17:24. 22edo is another good EDO system for using the half-octave in this way.

See: Gallery of Just Intervals