89-limit: Difference between revisions
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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. | '''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 mode 48 of the harmonic series, which is to say that all of the first 96 harmonics are in the 89-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, as it corresponds to the 95-odd-limit and thus [[48afdo|mode 48 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]]. | The 89-limit is the highest prime limit that can be represented with [[richie's HEJI extensions]]. | ||