89-limit: Difference between revisions

Fredg999 category edits (talk | contribs)
m Removing from Category:Prime limit using Cat-a-lot
Lériendil (talk | contribs)
mNo edit summary
 
(6 intermediate revisions by 2 users not shown)
Line 1: Line 1:
{{Prime limit navigation|89}}
{{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]].  


It is the highest prime limit that can be represented with [[richie's HEJI extensions]].
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.  


== See also ==
The 89-limit is the highest prime limit that can be represented with [[richie's HEJI extensions]].
* [[Harmonic limit]]
 
{{stub}}


[[Category:89-limit| ]] <!-- main article -->
[[Category:89-limit| ]] <!-- main article -->