11358058edo - Revision history

BudjarnLambeth: Mathematical interest

2025-08-10T22:08:55Z

Mathematical interest

← Older revision		Revision as of 22:08, 10 August 2025
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	{{~~Niche~~}}		{{Mathematical interest}}
	{{Infobox ET		{{Infobox ET
	\| Prime factorization = 2 × 5679029		\| Prime factorization = 2 × 5679029

FloraC: Cleanup. Wrap the harmonics table

2025-07-31T14:30:01Z

Cleanup. Wrap the harmonics table

← Older revision		Revision as of 14:30, 31 July 2025
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	{{Niche}}		{{Niche}}
	{{Infobox ET\|Consistency=35\|Distinct consistency=35~~\|Prime factorization=2 × 5679029~~}}		{{Infobox ET
			\| Prime factorization = 2 × 5679029
			\| Consistency = 35
			\| Distinct consistency = 35
			}}
	{{ED intro}}		{{ED intro}}

	Although its step size is far beyond the human melodic [[just-noticeable difference]], it has been noted for its highly accurate approximation of the 31~~-prime~~-limit, and is consistent up to the ~~36-~~[[Odd prime sum limit\|OPSL]], where it has a lower maximum error (i.e. the error of the least accurate approximation of any interval in the limit from JI) than any smaller [[~~EDO\|~~edo]], meaning it is very likely a [[The Riemann zeta function and tuning\|zeta peak]] edo.		Although its step size is far beyond the human melodic [[just-noticeable difference]], it has been noted for its highly accurate approximation of the [[31-limit]], and is [[consistent]] up to the [[Odd prime sum limit\|36-OPSL]], where it has a lower maximum error (i.e. the error of the least accurate approximation of any interval in the limit from JI) than any smaller [[edo]], meaning it is very likely a [[The Riemann zeta function and tuning\|zeta peak]] edo.

	While not practical to build an acoustic instrument for, one potential use of this system is in electronic music production, where free modulation between higher-limit JI intervals is desired. Instead of keeping track of the intervals directly, the number of steps to the octave for an interval could simply be added or subtracted from one note to get to the next. However, like all other equal temperaments, the consistency of this tuning is limited, and the sequence of intervals may eventually start to deviate from their true JI counterparts.		While not practical to build an acoustic instrument for, one potential use of this system is in electronic music production, where free modulation between higher-limit JI intervals is desired. Instead of keeping track of the intervals directly, the number of steps to the octave for an interval could simply be added or subtracted from one note to get to the next. However, like all other equal temperaments, the consistency of this tuning is limited, and the sequence of intervals may eventually start to deviate from their true JI counterparts.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal		{{Harmonics in equal\|11358058\|columns=9}}
	\| 11358058		{{Harmonics in equal\|11358058\|columns=9\|start=10\|collapsed=true\|title=Approximation of prime harmonics in 11358058edo (continued)}}
	\| columns = 13
	}}

ArrowHead294 at 14:38, 2 June 2025

2025-06-02T14:38:24Z

← Older revision		Revision as of 14:38, 2 June 2025
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	{{Niche}}		{{Niche}}

	{{Infobox ET\|Consistency=35\|Distinct consistency=35\|Prime factorization=2 × 5679029}}		{{Infobox ET\|Consistency=35\|Distinct consistency=35\|Prime factorization=2 × 5679029}}

	{{ED intro}}		{{ED intro}}

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	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal		{{Harmonics in equal
	\|11358058		\| 11358058
	\|columns = 13		\| columns = 13
	}}		}}

Lériendil: changed novelty to niche

2025-03-18T11:38:45Z

changed novelty to niche

← Older revision		Revision as of 11:38, 18 March 2025
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	{{~~Novelty~~}}		{{Niche}}

	{{Infobox ET\|Consistency=35\|Distinct consistency=35\|Prime factorization=2 × 5679029}}		{{Infobox ET\|Consistency=35\|Distinct consistency=35\|Prime factorization=2 × 5679029}}

Francium: changed EDO intro to ED intro

2025-02-20T07:01:06Z

changed EDO intro to ED intro

← Older revision		Revision as of 07:01, 20 February 2025
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	{{Infobox ET\|Consistency=35\|Distinct consistency=35\|Prime factorization=2 × 5679029}}		{{Infobox ET\|Consistency=35\|Distinct consistency=35\|Prime factorization=2 × 5679029}}

	{{~~EDO~~ intro}}		{{ED intro}}

	Although its step size is far beyond the human melodic [[just-noticeable difference]], it has been noted for its highly accurate approximation of the 31-prime-limit, and is consistent up to the 36-[[Odd prime sum limit\|OPSL]], where it has a lower maximum error (i.e. the error of the least accurate approximation of any interval in the limit from JI) than any smaller [[EDO\|edo]], meaning it is very likely a [[The Riemann zeta function and tuning\|zeta peak]] edo.		Although its step size is far beyond the human melodic [[just-noticeable difference]], it has been noted for its highly accurate approximation of the 31-prime-limit, and is consistent up to the 36-[[Odd prime sum limit\|OPSL]], where it has a lower maximum error (i.e. the error of the least accurate approximation of any interval in the limit from JI) than any smaller [[EDO\|edo]], meaning it is very likely a [[The Riemann zeta function and tuning\|zeta peak]] edo.

Tristanbay: Tweaked zeta function link

2025-01-15T17:54:01Z

Tweaked zeta function link

← Older revision		Revision as of 17:54, 15 January 2025
Line 5:		Line 5:
	{{EDO intro}}		{{EDO intro}}

	Although its step size is far beyond the human melodic [[just-noticeable difference]], it has been noted for its highly accurate approximation of the 31-prime-limit, and is consistent up to the 36-[[Odd prime sum limit\|OPSL]], where it has a lower maximum error (i.e. the error of the least accurate approximation of any interval in the limit from JI) than any smaller [[EDO\|edo]], meaning it is very likely a [[The Riemann ~~Zeta~~ function and tuning\|zeta peak]] edo.		Although its step size is far beyond the human melodic [[just-noticeable difference]], it has been noted for its highly accurate approximation of the 31-prime-limit, and is consistent up to the 36-[[Odd prime sum limit\|OPSL]], where it has a lower maximum error (i.e. the error of the least accurate approximation of any interval in the limit from JI) than any smaller [[EDO\|edo]], meaning it is very likely a [[The Riemann zeta function and tuning\|zeta peak]] edo.

	While not practical to build an acoustic instrument for, one potential use of this system is in electronic music production, where free modulation between higher-limit JI intervals is desired. Instead of keeping track of the intervals directly, the number of steps to the octave for an interval could simply be added or subtracted from one note to get to the next. However, like all other equal temperaments, the consistency of this tuning is limited, and the sequence of intervals may eventually start to deviate from their true JI counterparts.		While not practical to build an acoustic instrument for, one potential use of this system is in electronic music production, where free modulation between higher-limit JI intervals is desired. Instead of keeping track of the intervals directly, the number of steps to the octave for an interval could simply be added or subtracted from one note to get to the next. However, like all other equal temperaments, the consistency of this tuning is limited, and the sequence of intervals may eventually start to deviate from their true JI counterparts.

Tristanbay: Added EDO intro template and mentioned possibility of being a zeta peak EDO

2025-01-15T17:53:09Z

Added EDO intro template and mentioned possibility of being a zeta peak EDO

← Older revision		Revision as of 17:53, 15 January 2025
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	{{Infobox ET\|Consistency=35\|Distinct consistency=35\|Prime factorization=2 × 5679029}}		{{Infobox ET\|Consistency=35\|Distinct consistency=35\|Prime factorization=2 × 5679029}}

	~~'''11358058edo''', or '''11358058 equal divisions of the octave''', is an equal tuning system with a~~ step size ~~of only about 0.00010565 cents,~~ far beyond the human melodic [[just-noticeable difference]]~~. It~~ has been noted for its highly accurate approximation of the 31-limit, and is consistent up to the 36-[[Odd prime sum limit\|OPSL]], where it has a lower maximum error (i.e. the error of the least accurate approximation of any interval in the limit from JI) than any smaller [[EDO]].		{{EDO intro}}

			Although its step size is far beyond the human melodic [[just-noticeable difference]], it has been noted for its highly accurate approximation of the 31-prime-limit, and is consistent up to the 36-[[Odd prime sum limit\|OPSL]], where it has a lower maximum error (i.e. the error of the least accurate approximation of any interval in the limit from JI) than any smaller [[EDO\|edo]], meaning it is very likely a [[The Riemann Zeta function and tuning\|zeta peak]] edo.

	While not practical to build an acoustic instrument for, one potential use of this system is in electronic music production, where free modulation between higher-limit JI intervals is desired. Instead of keeping track of the intervals directly, the number of steps to the octave for an interval could simply be added or subtracted from one note to get to the next. However, like all other equal temperaments, the consistency of this tuning is limited, and the sequence of intervals may eventually start to deviate from their true JI counterparts.		While not practical to build an acoustic instrument for, one potential use of this system is in electronic music production, where free modulation between higher-limit JI intervals is desired. Instead of keeping track of the intervals directly, the number of steps to the octave for an interval could simply be added or subtracted from one note to get to the next. However, like all other equal temperaments, the consistency of this tuning is limited, and the sequence of intervals may eventually start to deviate from their true JI counterparts.

Tristanbay: /* Prime harmonics */Expanded the prime harmonics table by a couple of columns

2024-04-29T08:08:37Z

Prime harmonics: Expanded the prime harmonics table by a couple of columns

← Older revision		Revision as of 08:08, 29 April 2024
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	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|11358058}}		{{Harmonics in equal
			\|11358058
			\|columns = 13
			}}

Tristanbay: Corrected a grammatical issue and bolded some stuff in the beginning

2024-04-29T08:06:05Z

Corrected a grammatical issue and bolded some stuff in the beginning

← Older revision		Revision as of 08:06, 29 April 2024
Line 3:		Line 3:
	{{Infobox ET\|Consistency=35\|Distinct consistency=35\|Prime factorization=2 × 5679029}}		{{Infobox ET\|Consistency=35\|Distinct consistency=35\|Prime factorization=2 × 5679029}}

	11358058edo, or 11358058 equal divisions of the octave, is an equal tuning system with a step size of only about 0.00010565 cents, far beyond the human melodic [[just-noticeable difference]]. It has been noted for its highly accurate approximation of the 31-limit, and is consistent up to the 36-[[Odd prime sum limit\|OPSL]], where it has ~~the~~ lower maximum error (i.e. the error of the least accurate approximation of any interval in the limit from JI) of any ~~previous~~ [[EDO]].		'''11358058edo''', or '''11358058 equal divisions of the octave''', is an equal tuning system with a step size of only about 0.00010565 cents, far beyond the human melodic [[just-noticeable difference]]. It has been noted for its highly accurate approximation of the 31-limit, and is consistent up to the 36-[[Odd prime sum limit\|OPSL]], where it has a lower maximum error (i.e. the error of the least accurate approximation of any interval in the limit from JI) than any smaller [[EDO]].

	While not practical to build an acoustic instrument for, one potential use of this system is in electronic music production, where free modulation between higher-limit JI intervals is desired. Instead of keeping track of the intervals directly, the number of steps to the octave for an interval could simply be added or subtracted from one note to get to the next. However, like all other equal temperaments, the consistency of this tuning is limited, and the sequence of intervals may eventually start to deviate from their true JI counterparts.		While not practical to build an acoustic instrument for, one potential use of this system is in electronic music production, where free modulation between higher-limit JI intervals is desired. Instead of keeping track of the intervals directly, the number of steps to the octave for an interval could simply be added or subtracted from one note to get to the next. However, like all other equal temperaments, the consistency of this tuning is limited, and the sequence of intervals may eventually start to deviate from their true JI counterparts.

Tristanbay: Added info about OPSL consistency and error

2024-04-29T05:28:03Z

Added info about OPSL consistency and error

← Older revision		Revision as of 05:28, 29 April 2024
Line 3:		Line 3:
	{{Infobox ET\|Consistency=35\|Distinct consistency=35\|Prime factorization=2 × 5679029}}		{{Infobox ET\|Consistency=35\|Distinct consistency=35\|Prime factorization=2 × 5679029}}

	11358058edo, or 11358058 equal divisions of the octave, is an equal tuning system with a step size of only about 0.00010565 cents, far beyond the human melodic [[just-noticeable difference]]. It has been noted for its highly accurate approximation of the 31-limit.		11358058edo, or 11358058 equal divisions of the octave, is an equal tuning system with a step size of only about 0.00010565 cents, far beyond the human melodic [[just-noticeable difference]]. It has been noted for its highly accurate approximation of the 31-limit, and is consistent up to the 36-[[Odd prime sum limit\|OPSL]], where it has the lower maximum error (i.e. the error of the least accurate approximation of any interval in the limit from JI) of any previous [[EDO]].

	While not practical to build an acoustic instrument for, one potential use of this system is in electronic music production, where free modulation between higher-limit JI intervals is desired. Instead of keeping track of the intervals directly, the number of steps to the octave for an interval could simply be added or subtracted from one note to get to the next. However, like all other equal temperaments, the consistency of this tuning is limited, and the sequence of intervals may eventually start to deviate from their true JI counterparts.		While not practical to build an acoustic instrument for, one potential use of this system is in electronic music production, where free modulation between higher-limit JI intervals is desired. Instead of keeping track of the intervals directly, the number of steps to the octave for an interval could simply be added or subtracted from one note to get to the next. However, like all other equal temperaments, the consistency of this tuning is limited, and the sequence of intervals may eventually start to deviate from their true JI counterparts.