89-limit: Difference between revisions
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{{Prime limit navigation|89}} | {{Prime limit navigation|89}} | ||
'''89-limit''' is the 24th [[prime limit]] and is | The '''89-limit''' consists of [[just intonation]] [[interval]]s whose [[ratio]]s contain no [[prime factor]]s 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-odd-limit|89-]], [[91-odd-limit|91-]], [[93-odd-limit|93-]], and [[95-odd-limit]]; | |||
* Mode 45, 46, 47 and 48 of the harmonic or subharmonic series. | |||
The 89-limit is the highest prime limit that can be represented with [[richie's HEJI extensions]]. | |||
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Latest revision as of 15:50, 13 March 2025
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-, 91-, 93-, and 95-odd-limit;
- Mode 45, 46, 47 and 48 of the harmonic or subharmonic series.
The 89-limit is the highest prime limit that can be represented with richie's HEJI extensions.
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