89-limit - Revision history

Lériendil at 15:50, 13 March 2025

2025-03-13T15:50:02Z

← Older revision		Revision as of 15:50, 13 March 2025
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	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]].

			{{stub}}

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

FloraC: Rework on the relation to odd limits and harmonic/subharmonic modes

2024-12-18T09:50:08Z

Rework on the relation to odd limits and harmonic/subharmonic modes

← Older revision		Revision as of 09:50, 18 December 2024
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	{{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]].

	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 mode~~ [[~~Overtone scale~~\|~~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]].		The 89-limit is the highest prime limit that can be represented with [[richie's HEJI extensions]].

	~~== See also ==~~
	* [[Harmonic limit]]

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

BudjarnLambeth at 06:16, 18 February 2024

2024-02-18T06:16:43Z

← Older revision		Revision as of 06:16, 18 February 2024
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 [[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 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 mode [[Overtone scale\|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]].

BudjarnLambeth: Found a way to include both links

2024-02-18T06:16:28Z

Found a way to include both links

← Older revision		Revision as of 06:16, 18 February 2024
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 [[~~overtone~~ scale\|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 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]].

BudjarnLambeth: Changed from 48afdo to overtone scale

2024-02-18T05:34:40Z

Changed from 48afdo to overtone scale

← Older revision		Revision as of 05:34, 18 February 2024
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 [[~~48afdo~~\|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 [[overtone scale\|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]].

BudjarnLambeth: 48afdo link

2024-02-18T05:33:37Z

48afdo link

← Older revision		Revision as of 05:33, 18 February 2024
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 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]].

FloraC: +note on record prime gap

2023-08-01T10:04:21Z

+note on record prime gap

← Older revision		Revision as of 10:04, 1 August 2023
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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.

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

	== See also ==		== See also ==

Fredg999 category edits: Removing from Category:Prime limit using Cat-a-lot

2023-01-03T08:22:30Z

Removing from Category:Prime limit using Cat-a-lot

← Older revision		Revision as of 08:22, 3 January 2023
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	[[Category:89-limit\| ]] <!-- main article -->		[[Category:89-limit\| ]] <!-- main article -->
	~~[[Category:Prime limit]]~~

Fredg999: Created page with "{{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 intona..."

2022-12-31T04:57:53Z

Created page with "{{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 intona..."

New page

{{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.

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

== See also ==
* [[Harmonic limit]]

[[Category:89-limit| ]] 
[[Category:Prime limit]]