89-limit

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The 89-limit consists of just intonation intervals whose ratios contain no prime factors higher than 89. It is the 24th prime limit and is a superset of the 83-limit and a subset of the 97-limit.

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 due to a substantial increment in its harmonic contents. Specifically, these things are contained by the 89-limit, but not the 83-limit:

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