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~~.

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, ~~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 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]].

~~== See also ==~~

* [[Harmonic limit]]

[[Category:89-limit| ]]

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 {{Prime limit navigation|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 '''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, 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 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]].
-== See also ==
+{{stub}}
-* [[Harmonic limit]]
 [[Category:89-limit| ]] <!-- main article -->