31-limit - Revision history

FloraC: - see also

2026-05-22T08:31:47Z

- see also

← Older revision		Revision as of 08:31, 22 May 2026
Line 22:		Line 22:
	* [https://www.youtube.com/watch?v=HnFX-PdAK4U ''Echo and Narcissus''] (2020)		* [https://www.youtube.com/watch?v=HnFX-PdAK4U ''Echo and Narcissus''] (2020)
	* [https://www.youtube.com/watch?v=li6MHeXWkJU ''Theme for a primate-like creature''] (2024)		* [https://www.youtube.com/watch?v=li6MHeXWkJU ''Theme for a primate-like creature''] (2024)

	~~== See also ==~~
	* [[No-twos 31-limit]]
	* [[User:Contribution/31-limit]] – Includes an enormous table of 31-limit intervals

	[[Category:31-limit\| ]] <!-- main article -->		[[Category:31-limit\| ]] <!-- main article -->
	[[Category:Listen]]		[[Category:Listen]]

FloraC: Expand

2026-05-19T11:11:01Z

Expand

← Older revision		Revision as of 11:11, 19 May 2026
Line 6:		Line 6:
	Like the [[23-limit]], the 31-limit implies a substantial increment in its harmonic contents compared to previous prime limit. Specifically, these things are contained by the 31-limit, but not the 29-limit:		Like the [[23-limit]], the 31-limit implies a substantial increment in its harmonic contents compared to previous prime limit. Specifically, these things are contained by the 31-limit, but not the 29-limit:
	* The [[31-odd-limit\|31-]], [[33-odd-limit\|33-]], and [[35-odd-limit]];		* The [[31-odd-limit\|31-]], [[33-odd-limit\|33-]], and [[35-odd-limit]];
	* Mode 16, 17, and 18 of the harmonic or subharmonic series.		* Mode 16, 17, and 18 of the harmonic or subharmonic series; this means it completes the 5th octave of those series.

			The 31-limit intervals of the 2.3.31 subgroup are mainly [[interseptimal]], with [[32/31]] being a quartertone, [[36/31]] and [[31/27]] being semifourths, and [[31/24]] being a naiadic, with their [[octave complement]]s classified accordingly. While interseptimal intervals are abundant in lower limits, [[31/1\|31]] is the first prime where such intervals occur without combining primes higher than 3. As such, the intervals of 31 are difficult to classify diatonically, but add a contrasting character to the lower limits, in particular [[11/1\|11]] and [[13/1\|13]], which are mainly neutral in quality.

	== Edo approximations ==		== Edo approximations ==

FloraC: Fix a copypasting error

2026-05-19T10:38:33Z

Fix a copypasting error

← Older revision		Revision as of 10:38, 19 May 2026
Line 11:		Line 11:
	[[311edo]] is the smallest edo that is [[consistent]] to the [[31-odd-limit]]. [[1600edo]] is the smallest edo that is [[distinctly consistent]] to the 31-odd-limit.		[[311edo]] is the smallest edo that is [[consistent]] to the [[31-odd-limit]]. [[1600edo]] is the smallest edo that is [[distinctly consistent]] to the 31-odd-limit.

	Edos with increasingly better approximations of the 31-limit ([[monotonicity limit]] ≥ 31 and decreasing [[TE error]]): {{EDOs\| ~~99ef~~, 121ik, 130, 140, 149, 152fgj, 159, 183, 190g, 217, 243e, 270, 311, 388, 422, 525, 566gj, 571, 624jk, 639hj, 643ijk, 653, 692ik, 718, 742i, 863efgjk, 882, 908, 954hj, 1205g, 1289, 1308, 1395, 1578 }}, etc. For a more comprehensive list, see [[Sequence of equal temperaments by error]].		Edos with increasingly better approximations of the 31-limit ([[monotonicity limit]] ≥ 31 and decreasing [[TE error]]): {{EDOs\| 99efk, 121ik, 130, 140, 149, 152fgj, 159, 183, 190g, 217, 243e, 270, 311, 388, 422, 525, 566gj, 571, 624jk, 639hj, 643ijk, 653, 692ik, 718, 742i, 863efgjk, 882, 908, 954hj, 1205g, 1289, 1308, 1395, 1578 }}, etc. For a more comprehensive list, see [[Sequence of equal temperaments by error]].

	{{Note\| [[Wart notation]] is used to specify the [[val]] chosen for the edo. In the above list, "~~99ef~~" means taking the second closest approximations of harmonics 11 and 13. }}		{{Note\| [[Wart notation]] is used to specify the [[val]] chosen for the edo. In the above list, "99efk" means taking the second closest approximations of harmonics 11, 13, and 31. }}

	== Music ==		== Music ==

FloraC: + edo approximation. - stub mark

2026-05-19T10:37:49Z

+ edo approximation. - stub mark

← Older revision		Revision as of 10:37, 19 May 2026
Line 7:		Line 7:
	* The [[31-odd-limit\|31-]], [[33-odd-limit\|33-]], and [[35-odd-limit]];		* The [[31-odd-limit\|31-]], [[33-odd-limit\|33-]], and [[35-odd-limit]];
	* Mode 16, 17, and 18 of the harmonic or subharmonic series.		* Mode 16, 17, and 18 of the harmonic or subharmonic series.

			== Edo approximations ==
			[[311edo]] is the smallest edo that is [[consistent]] to the [[31-odd-limit]]. [[1600edo]] is the smallest edo that is [[distinctly consistent]] to the 31-odd-limit.

			Edos with increasingly better approximations of the 31-limit ([[monotonicity limit]] ≥ 31 and decreasing [[TE error]]): {{EDOs\| 99ef, 121ik, 130, 140, 149, 152fgj, 159, 183, 190g, 217, 243e, 270, 311, 388, 422, 525, 566gj, 571, 624jk, 639hj, 643ijk, 653, 692ik, 718, 742i, 863efgjk, 882, 908, 954hj, 1205g, 1289, 1308, 1395, 1578 }}, etc. For a more comprehensive list, see [[Sequence of equal temperaments by error]].

			{{Note\| [[Wart notation]] is used to specify the [[val]] chosen for the edo. In the above list, "99ef" means taking the second closest approximations of harmonics 11 and 13. }}

	== Music ==		== Music ==
Line 17:		Line 24:
	* [[No-twos 31-limit]]		* [[No-twos 31-limit]]
	* [[User:Contribution/31-limit]] – Includes an enormous table of 31-limit intervals		* [[User:Contribution/31-limit]] – Includes an enormous table of 31-limit intervals

	~~{{Stub}}~~

	[[Category:31-limit\| ]] <!-- main article -->		[[Category:31-limit\| ]] <!-- main article -->
	[[Category:Listen]]		[[Category:Listen]]

Lériendil at 15:45, 13 March 2025

2025-03-13T15:45:48Z

← Older revision		Revision as of 15:45, 13 March 2025
Line 17:		Line 17:
	* [[No-twos 31-limit]]		* [[No-twos 31-limit]]
	* [[User:Contribution/31-limit]] – Includes an enormous table of 31-limit intervals		* [[User:Contribution/31-limit]] – Includes an enormous table of 31-limit intervals

			{{Stub}}

	[[Category:31-limit\| ]] <!-- main article -->		[[Category:31-limit\| ]] <!-- main article -->
	[[Category:Listen]]		[[Category:Listen]]

FloraC: +rank, lattice representation, relation to odd limits and harmonic/subharmonic modes

2024-12-17T15:42:28Z

+rank, lattice representation, relation to odd limits and harmonic/subharmonic modes

← Older revision		Revision as of 15:42, 17 December 2024
Line 1:		Line 1:
	{{Prime limit navigation\|31}}		{{Prime limit navigation\|31}}
	The '''31-limit''' consists of [[just intonation]] [[interval]]s whose [[ratio]]s contain no [[prime factor]]s higher than 31. It is the 11th [[prime limit]] and is ~~thus~~ a superset of the [[29-limit]] and a subset of the [[37-limit]].		The '''31-limit''' consists of [[just intonation]] [[interval]]s whose [[ratio]]s contain no [[prime factor]]s higher than 31. It is the 11th [[prime limit]] and is a superset of the [[29-limit]] and a subset of the [[37-limit]].

			The 31-limit is a rank-11 system, and can be modeled in a 10-dimensional lattice, with the primes 3 to 31 represented by each dimension. The prime 2 does not appear in the typical 31-limit lattice because [[octave equivalence]] is presumed. If octave equivalence is not presumed, an eleventh dimension is needed.

			Like the [[23-limit]], the 31-limit implies a substantial increment in its harmonic contents compared to previous prime limit. Specifically, these things are contained by the 31-limit, but not the 29-limit:
			* The [[31-odd-limit\|31-]], [[33-odd-limit\|33-]], and [[35-odd-limit]];
			* Mode 16, 17, and 18 of the harmonic or subharmonic series.

	== Music ==		== Music ==
Line 9:		Line 15:

	== See also ==		== See also ==
	* [[31-odd-limit]]
	* [[No-twos 31-limit]]		* [[No-twos 31-limit]]
	* [[User:Contribution/31-limit]] – Includes an enormous table of 31-limit intervals		* [[User:Contribution/31-limit]] – Includes an enormous table of 31-limit intervals

Lériendil at 11:08, 3 September 2024

2024-09-03T11:08:18Z

← Older revision		Revision as of 11:08, 3 September 2024
Line 11:		Line 11:
	* [[31-odd-limit]]		* [[31-odd-limit]]
	* [[No-twos 31-limit]]		* [[No-twos 31-limit]]
			* [[User:Contribution/31-limit]] – Includes an enormous table of 31-limit intervals

	[[Category:31-limit\| ]] <!-- main article -->		[[Category:31-limit\| ]] <!-- main article -->
	[[Category:Listen]]		[[Category:Listen]]

Francium: +categories

2024-07-19T18:40:05Z

+categories

← Older revision		Revision as of 18:40, 19 July 2024
Line 13:		Line 13:

	[[Category:31-limit\| ]] <!-- main article -->		[[Category:31-limit\| ]] <!-- main article -->
			[[Category:Listen]]

Francium: /* Music */ +music

2024-07-19T18:38:00Z

Music: +music

← Older revision		Revision as of 18:38, 19 July 2024
Line 6:		Line 6:
	* [https://www.youtube.com/watch?v=oTk3gWguv6I ''Soul Box''] (2020)		* [https://www.youtube.com/watch?v=oTk3gWguv6I ''Soul Box''] (2020)
	* [https://www.youtube.com/watch?v=HnFX-PdAK4U ''Echo and Narcissus''] (2020)		* [https://www.youtube.com/watch?v=HnFX-PdAK4U ''Echo and Narcissus''] (2020)
			* [https://www.youtube.com/watch?v=li6MHeXWkJU ''Theme for a primate-like creature''] (2024)

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

FloraC: Rework intro and see also

2024-01-07T10:40:13Z

Rework intro and see also

← Older revision		Revision as of 10:40, 7 January 2024
Line 1:		Line 1:
	{{Prime limit navigation\|31}}		{{Prime limit navigation\|31}}
	'''31-limit''' is the 11th [[prime limit]] and is thus a superset of the [[29-limit]] and a subset of the [[37-limit]]~~. In 31-limit [[just intonation]], all ratios in the system will contain no primes higher than 31~~.		The '''31-limit''' consists of [[just intonation]] [[interval]]s whose [[ratio]]s contain no [[prime factor]]s higher than 31. It is the 11th [[prime limit]] and is thus a superset of the [[29-limit]] and a subset of the [[37-limit]].

	== Music ==		== Music ==
Line 8:		Line 8:

	== See also ==		== See also ==
	* [[~~Harmonic~~ limit]]		* [[31-odd-limit]]
	* [[No-twos 31-limit]]		* [[No-twos 31-limit]]

	[[Category:31-limit\| ]] <!-- main article -->		[[Category:31-limit\| ]] <!-- main article -->