89-limit: Difference between revisions
Jump to navigation
Jump to search
m Changed from 48afdo to overtone scale |
m Found a way to include both links |
||
| Line 2: | Line 2: | ||
'''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 [[ | 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 the [[48afdo|48]]th [[Overtone scale|mode 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]]. | ||
Revision as of 06:16, 18 February 2024
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 the 48th mode 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.