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89-limit is the 24th prime limit and is thus a superset of the 83-limit and a subset of the 97-limit. In 89-limit just intonation, all ratios in the system will contain no primes higher than 89.

The prime 89 is the start of a record prime gap ending at 97, the previous record prime gap being the one corresponding to the 23-limit. Thus, it marks a potential stopping point for prime limits, as it corresponds to the 95-odd-limit and thus the 48th mode of the harmonic series, which is to say that all of the first 96 harmonics are in the 89-limit.

The 89-limit is the highest prime limit that can be represented with richie's HEJI extensions.

See also