1106edo - Revision history

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

2026-03-13T13:30:00Z

Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

← Older revision		Revision as of 13:30, 13 March 2026
Line 114:		Line 114:
	\| [[Gold]]		\| [[Gold]]
	\|}		\|}
	<nowiki/>* [[Normal forms\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms\|minimal form]] in parentheses if distinct		<nowiki/>* [[Normal forms #Equave-reduced-generator form\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form\|minimal form]] in parentheses if distinct

FloraC: +1

2025-10-27T13:14:01Z

← Older revision		Revision as of 13:14, 27 October 2025
Line 88:		Line 88:
	\| 435.081		\| 435.081
	\| 9/7		\| 9/7
	\| [[Supermajor]]		\| [[Supermajor (temperament)\|Supermajor]]
	\|-		\|-
	\| 2		\| 2

FloraC: Linking & cleanup

2025-10-27T13:13:35Z

Linking & cleanup

← Older revision		Revision as of 13:13, 27 October 2025
Line 5:		Line 5:
	1106edo is a [[zeta peak edo]]. It is strong as a 7-limit system; the only edos lower than it with a lower 7-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] being {{EDOs\| 171, 270, 342, 441, and 612 }}. It is even stronger in the 11-limit; the only ones beating it out now being {{EDOs\| 270, 342, and 612 }}. It is less strong in the 13- and 17-limit, but even so is [[consistency\|distinctly consistent]] through the [[17-odd-limit]].		1106edo is a [[zeta peak edo]]. It is strong as a 7-limit system; the only edos lower than it with a lower 7-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] being {{EDOs\| 171, 270, 342, 441, and 612 }}. It is even stronger in the 11-limit; the only ones beating it out now being {{EDOs\| 270, 342, and 612 }}. It is less strong in the 13- and 17-limit, but even so is [[consistency\|distinctly consistent]] through the [[17-odd-limit]].

	The equal temperament [[tempering out\|tempers out]] {{monzo\| -53 10 16 }} (kwazy comma) and {{monzo\| -13 -46 37 }} (supermajor comma) in the 5-limit; [[4375/4374]] and 52734375/52706752 in the 7-limit; [[3025/3024]] and [[9801/9800]] in the 11-limit; [[4096/4095]], 78125/78078, and 105644/105625 in the 13-limit; [[2500/2499]], [[4914/4913]], and 8624/8619 in the 17-limit. It notably supports [[supermajor]], [[brahmagupta]], and [[orga]] in the 7-limit, and [[semisupermajor]] in the 11-limit. In the higher limits, it supports the 79th-octave temperament [[gold]].		The equal temperament [[tempering out\|tempers out]] {{monzo\| -53 10 16 }} (kwazy comma) and {{monzo\| -13 -46 37 }} (supermajor comma) in the 5-limit; [[4375/4374]] and 52734375/52706752 in the 7-limit; [[3025/3024]] and [[9801/9800]] in the 11-limit; [[4096/4095]], 78125/78078, and 105644/105625 in the 13-limit; [[2500/2499]], [[4914/4913]], and 8624/8619 in the 17-limit. It notably supports [[supermajor (temperament)\|supermajor]], [[brahmagupta]], and [[orga]] in the 7-limit, and [[semisupermajor]] in the 11-limit. In the higher limits, it supports the 79th-octave temperament [[gold]].

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|1106\|columns=12}}		{{Harmonics in equal\|1106\|columns=11}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 1106 factors into {{~~factorization~~\|~~1106~~}}, it has subset edos {{EDOs\| 2, 7, 14, 79, 158, and 553 }}.		Since 1106 factors into {{nowrap\| 2 × 7 × 79 }}, it has subset edos {{EDOs\| 2, 7, 14, 79, 158, and 553 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 114:		Line 114:
	\| [[Gold]]		\| [[Gold]]
	\|}		\|}
	<nowiki/>* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[normal ~~lists~~\|minimal form]] in parentheses if distinct		<nowiki/>* [[Normal forms\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms\|minimal form]] in parentheses if distinct

FloraC: /* Regular temperament properties */ crazy update

2025-03-06T11:31:20Z

Regular temperament properties: crazy update

← Older revision		Revision as of 11:31, 6 March 2025
Line 19:		Line 19:
	! rowspan="2" \| [[Comma list]]		! rowspan="2" \| [[Comma list]]
	! rowspan="2" \| [[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \| Optimal<br />8ve stretch (¢)		! rowspan="2" \| Optimal<br>8ve stretch (¢)
	! colspan="2" \| Tuning error		! colspan="2" \| Tuning error
	\|-		\|-
Line 26:		Line 26:
	\|-		\|-
	\| 2.3		\| 2.3
	\| {{~~monzo~~\| 1753 -1106 }}		\| {{Monzo\| 1753 -1106 }}
	\| {{~~mapping~~\| 1106 1753 }}		\| {{Mapping\| 1106 1753 }}
	\| −0.010		\| −0.010
	\| 0.010		\| 0.010
Line 33:		Line 33:
	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{~~monzo~~\| -53 10 16 }}, {{monzo\| -13 -46 37 }}		\| {{Monzo\| -53 10 16 }}, {{monzo\| -13 -46 37 }}
	\| {{~~mapping~~\| 1106 1753 2568 }}		\| {{Mapping\| 1106 1753 2568 }}
	\| +0.001		\| +0.001
	\| 0.019		\| 0.019
Line 41:		Line 41:
	\| 2.3.5.7		\| 2.3.5.7
	\| 4375/4374, 52734375/52706752, {{monzo\| 46 -14 -3 -6 }}		\| 4375/4374, 52734375/52706752, {{monzo\| 46 -14 -3 -6 }}
	\| {{~~mapping~~\| 1106 1753 2568 3105 }}		\| {{Mapping\| 1106 1753 2568 3105 }}
	\| −0.006		\| −0.006
	\| 0.020		\| 0.020
Line 48:		Line 48:
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 3025/3024, 4375/4374, 5767168/5764801, 35156250/35153041		\| 3025/3024, 4375/4374, 5767168/5764801, 35156250/35153041
	\| {{~~mapping~~\| 1106 1753 2568 3105 3826 }}		\| {{Mapping\| 1106 1753 2568 3105 3826 }}
	\| +0.004		\| +0.004
	\| 0.026		\| 0.026
Line 55:		Line 55:
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 3025/3024, 4096/4095, 4375/4374, 78125/78078, 105644/105625		\| 3025/3024, 4096/4095, 4375/4374, 78125/78078, 105644/105625
	\| {{~~mapping~~\| 1106 1753 2568 3105 3826 4093 }}		\| {{Mapping\| 1106 1753 2568 3105 3826 4093 }}
	\| −0.012		\| −0.012
	\| 0.043		\| 0.043
Line 62:		Line 62:
	\| 2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\| 2500/2499, 3025/3024, 4096/4095, 4375/4374, 4914/4913, 8624/8619		\| 2500/2499, 3025/3024, 4096/4095, 4375/4374, 4914/4913, 8624/8619
	\| {{~~mapping~~\| 1106 1753 2568 3105 3826 4093 4521 }}		\| {{Mapping\| 1106 1753 2568 3105 3826 4093 4521 }}
	\| −0.021		\| −0.021
	\| 0.045		\| 0.045
Line 72:		Line 72:
	\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator		\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
	\|-		\|-
	! Periods<br />per 8ve		! Periods<br>per 8ve
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br />ratio*		! Associated<br>ratio*
	! Temperaments		! Temperaments
	\|-		\|-
Line 94:		Line 94:
	\| 162.749		\| 162.749
	\| 1125/1024		\| 1125/1024
	\| [[~~Kwazy~~]]		\| [[Crazy]]
	\|-		\|-
	\| 2		\| 2
	\| 401\1106<br />(152\1106)		\| 401\1106<br>(152\1106)
	\| 435.081<br />(164.919)		\| 435.081<br>(164.919)
	\| 9/7<br />(11/10)		\| 9/7<br>(11/10)
	\| [[Semisupermajor]]		\| [[Semisupermajor]]
	\|-		\|-
	\| 7		\| 7
	\| 479\1106<br />(5\1106)		\| 479\1106<br>(5\1106)
	\| 519.711<br />(5.424)		\| 519.711<br>(5.424)
	\| 27/20<br />(5120/5103)		\| 27/20<br>(5120/5103)
	\| [[Brahmagupta]] (7-limit)		\| [[Brahmagupta]] (7-limit)
	\|-		\|-
	\| 79		\| 79
	\| 459\1106<br />(11\1106)		\| 459\1106<br>(11\1106)
	\| 498.011<br />(11.935)		\| 498.011<br>(11.935)
	\| 4/3<br />(?)		\| 4/3<br>(?)
	\| [[Gold]]		\| [[Gold]]
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal~~ lists\|minimal form]] in parentheses if distinct		<nowiki/>* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[normal lists\|minimal form]] in parentheses if distinct

ArrowHead294 at 16:50, 18 February 2025

2025-02-18T16:50:34Z

← Older revision		Revision as of 16:50, 18 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1106~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 18:16, 15 January 2025

2025-01-15T18:16:28Z

← Older revision		Revision as of 18:16, 15 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	1106edo is a [[zeta peak edo]]. It is strong as a 7-limit system; the only edos lower than it with a lower 7-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] being {{EDOs\| 171, 270, 342, 441 and 612 }}. It is even stronger in the 11-limit; the only ones beating it out now being {{EDOs\| 270, 342 and 612 }}. It is less strong in the 13- and 17-limit, but even so is [[consistency\|distinctly consistent]] through the [[17-odd-limit]].		1106edo is a [[zeta peak edo]]. It is strong as a 7-limit system; the only edos lower than it with a lower 7-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] being {{EDOs\| 171, 270, 342, 441, and 612 }}. It is even stronger in the 11-limit; the only ones beating it out now being {{EDOs\| 270, 342, and 612 }}. It is less strong in the 13- and 17-limit, but even so is [[consistency\|distinctly consistent]] through the [[17-odd-limit]].

	The equal temperament [[tempering out\|tempers out]] {{monzo\| -53 10 16 }} (kwazy comma) and {{monzo\| -13 -46 37 }} (supermajor comma) in the 5-limit; [[4375/4374]] and 52734375/52706752 in the 7-limit; [[3025/3024]] and [[9801/9800]] in the 11-limit; [[4096/4095]], 78125/78078, and 105644/105625 in the 13-limit; [[2500/2499]], [[4914/4913]], and 8624/8619 in the 17-limit. It notably supports [[supermajor]], [[brahmagupta]], and [[orga]] in the 7-limit, and [[semisupermajor]] in the 11-limit. In the higher limits, it supports the 79th-octave temperament [[gold]].		The equal temperament [[tempering out\|tempers out]] {{monzo\| -53 10 16 }} (kwazy comma) and {{monzo\| -13 -46 37 }} (supermajor comma) in the 5-limit; [[4375/4374]] and 52734375/52706752 in the 7-limit; [[3025/3024]] and [[9801/9800]] in the 11-limit; [[4096/4095]], 78125/78078, and 105644/105625 in the 13-limit; [[2500/2499]], [[4914/4913]], and 8624/8619 in the 17-limit. It notably supports [[supermajor]], [[brahmagupta]], and [[orga]] in the 7-limit, and [[semisupermajor]] in the 11-limit. In the higher limits, it supports the 79th-octave temperament [[gold]].
Line 28:		Line 28:
	\| {{monzo\| 1753 -1106 }}		\| {{monzo\| 1753 -1106 }}
	\| {{mapping\| 1106 1753 }}		\| {{mapping\| 1106 1753 }}
	\| ~~−0~~.010		\| −0.010
	\| 0.010		\| 0.010
	\| 0.99		\| 0.99
Line 42:		Line 42:
	\| 4375/4374, 52734375/52706752, {{monzo\| 46 -14 -3 -6 }}		\| 4375/4374, 52734375/52706752, {{monzo\| 46 -14 -3 -6 }}
	\| {{mapping\| 1106 1753 2568 3105 }}		\| {{mapping\| 1106 1753 2568 3105 }}
	\| ~~−0~~.006		\| −0.006
	\| 0.020		\| 0.020
	\| 1.83		\| 1.83
Line 56:		Line 56:
	\| 3025/3024, 4096/4095, 4375/4374, 78125/78078, 105644/105625		\| 3025/3024, 4096/4095, 4375/4374, 78125/78078, 105644/105625
	\| {{mapping\| 1106 1753 2568 3105 3826 4093 }}		\| {{mapping\| 1106 1753 2568 3105 3826 4093 }}
	\| ~~−0~~.012		\| −0.012
	\| 0.043		\| 0.043
	\| 3.94		\| 3.94
Line 63:		Line 63:
	\| 2500/2499, 3025/3024, 4096/4095, 4375/4374, 4914/4913, 8624/8619		\| 2500/2499, 3025/3024, 4096/4095, 4375/4374, 4914/4913, 8624/8619
	\| {{mapping\| 1106 1753 2568 3105 3826 4093 4521 }}		\| {{mapping\| 1106 1753 2568 3105 3826 4093 4521 }}
	\| ~~−0~~.021		\| −0.021
	\| 0.045		\| 0.045
	\| 4.11		\| 4.11
Line 114:		Line 114:
	\| [[Gold]]		\| [[Gold]]
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if ~~it is~~ distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

ArrowHead294: Partial undo

2024-11-16T12:34:46Z

Partial undo

← Older revision		Revision as of 12:34, 16 November 2024
Line 14:		Line 14:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~{comma basis begin}}~~		{\| class="wikitable center-4 center-5 center-6"
			\|-
			! rowspan="2" \| [[Subgroup]]
			! rowspan="2" \| [[Comma list]]
			! rowspan="2" \| [[Mapping]]
			! rowspan="2" \| Optimal<br />8ve stretch (¢)
			! colspan="2" \| Tuning error
			\|-
			! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.3		\| 2.3
Line 57:		Line 66:
	\| 0.045		\| 0.045
	\| 4.11		\| 4.11
	~~{{comma basis end}~~}		\|}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{{rank-2 ~~begin}}~~		{\| class="wikitable center-all left-5"
			\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
			\|-
			! Periods<br />per 8ve
			! Generator*
			! Cents*
			! Associated<br />ratio*
			! Temperaments
	\|-		\|-
	\| 1		\| 1
Line 97:		Line 113:
	\| 4/3<br />(?)		\| 4/3<br />(?)
	\| [[Gold]]		\| [[Gold]]
	~~{{rank-2 end}~~}		\|}
	~~{{orf}}~~		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

ArrowHead294 at 04:23, 16 November 2024

2024-11-16T04:23:42Z

← Older revision		Revision as of 04:23, 16 November 2024
Line 14:		Line 14:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~\| class="wikitable center-4 center-5 center-6"~~		{{comma basis begin}}
	~~! rowspan="2" \| [[Subgroup]]~~
	~~! rowspan="2" \| [[Comma list\|Comma List]]~~
	~~! rowspan="2" \| [[Mapping]]~~
	~~! rowspan="2" \| Optimal<br>8ve Stretch (¢)~~
	~~! colspan="2" \| Tuning Error~~
	\|-
	~~! [[TE error\|Absolute]] (¢)~~
	~~! [[TE simple badness\|Relative]] (%)~~
	\|-		\|-
	\| 2.3		\| 2.3
	\| {{monzo\| 1753 -1106 }}		\| {{monzo\| 1753 -1106 }}
	\| {{mapping\| 1106 1753 }}		\| {{mapping\| 1106 1753 }}
	\| -0.010		\| −0.010
	\| 0.010		\| 0.010
	\| 0.99		\| 0.99
Line 41:		Line 33:
	\| 4375/4374, 52734375/52706752, {{monzo\| 46 -14 -3 -6 }}		\| 4375/4374, 52734375/52706752, {{monzo\| 46 -14 -3 -6 }}
	\| {{mapping\| 1106 1753 2568 3105 }}		\| {{mapping\| 1106 1753 2568 3105 }}
	\| -0.006		\| −0.006
	\| 0.020		\| 0.020
	\| 1.83		\| 1.83
Line 55:		Line 47:
	\| 3025/3024, 4096/4095, 4375/4374, 78125/78078, 105644/105625		\| 3025/3024, 4096/4095, 4375/4374, 78125/78078, 105644/105625
	\| {{mapping\| 1106 1753 2568 3105 3826 4093 }}		\| {{mapping\| 1106 1753 2568 3105 3826 4093 }}
	\| -0.012		\| −0.012
	\| 0.043		\| 0.043
	\| 3.94		\| 3.94
Line 62:		Line 54:
	\| 2500/2499, 3025/3024, 4096/4095, 4375/4374, 4914/4913, 8624/8619		\| 2500/2499, 3025/3024, 4096/4095, 4375/4374, 4914/4913, 8624/8619
	\| {{mapping\| 1106 1753 2568 3105 3826 4093 4521 }}		\| {{mapping\| 1106 1753 2568 3105 3826 4093 4521 }}
	\| -0.021		\| −0.021
	\| 0.045		\| 0.045
	\| 4.11		\| 4.11
	\|}		{{comma basis end}}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+Table of~~ rank-2 ~~temperaments by generator~~
	\|-
	~~! Periods<br>per 8ve~~
	! Generator*
	! Cents*
	! Associated<br>Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 1		\| 1
Line 96:		Line 81:
	\|-		\|-
	\| 2		\| 2
	\| 401\1106<br>(152\1106)		\| 401\1106<br />(152\1106)
	\| 435.081<br>(164.919)		\| 435.081<br />(164.919)
	\| 9/7<br>(11/10)		\| 9/7<br />(11/10)
	\| [[Semisupermajor]]		\| [[Semisupermajor]]
	\|-		\|-
	\| 7		\| 7
	\| 479\1106<br>(5\1106)		\| 479\1106<br />(5\1106)
	\| 519.711<br>(5.424)		\| 519.711<br />(5.424)
	\| 27/20<br>(5120/5103)		\| 27/20<br />(5120/5103)
	\| [[Brahmagupta]] (7-limit)		\| [[Brahmagupta]] (7-limit)
	\|-		\|-
	\| 79		\| 79
	\| 459\1106<br>(11\1106)		\| 459\1106<br />(11\1106)
	\| 498.011<br>(11.935)		\| 498.011<br />(11.935)
	\| 4/3<br>(?)		\| 4/3<br />(?)
	\| [[Gold]]		\| [[Gold]]
	\|}		{{rank-2 end}}
	~~<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct~~		{{orf}}

FloraC: Expand on theory

2023-10-31T10:38:40Z

Expand on theory

← Older revision		Revision as of 10:38, 31 October 2023
Line 5:		Line 5:
	1106edo is a [[zeta peak edo]]. It is strong as a 7-limit system; the only edos lower than it with a lower 7-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] being {{EDOs\| 171, 270, 342, 441 and 612 }}. It is even stronger in the 11-limit; the only ones beating it out now being {{EDOs\| 270, 342 and 612 }}. It is less strong in the 13- and 17-limit, but even so is [[consistency\|distinctly consistent]] through the [[17-odd-limit]].		1106edo is a [[zeta peak edo]]. It is strong as a 7-limit system; the only edos lower than it with a lower 7-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] being {{EDOs\| 171, 270, 342, 441 and 612 }}. It is even stronger in the 11-limit; the only ones beating it out now being {{EDOs\| 270, 342 and 612 }}. It is less strong in the 13- and 17-limit, but even so is [[consistency\|distinctly consistent]] through the [[17-odd-limit]].

	It notably supports [[supermajor]], [[brahmagupta]], and [[orga]] in the 7-limit, and ~~notably~~ [[semisupermajor]] in the 11-limit. In the higher limits, it supports the 79th-octave temperament [[gold]].		The equal temperament [[tempering out\|tempers out]] {{monzo\| -53 10 16 }} (kwazy comma) and {{monzo\| -13 -46 37 }} (supermajor comma) in the 5-limit; [[4375/4374]] and 52734375/52706752 in the 7-limit; [[3025/3024]] and [[9801/9800]] in the 11-limit; [[4096/4095]], 78125/78078, and 105644/105625 in the 13-limit; [[2500/2499]], [[4914/4913]], and 8624/8619 in the 17-limit. It notably supports [[supermajor]], [[brahmagupta]], and [[orga]] in the 7-limit, and [[semisupermajor]] in the 11-limit. In the higher limits, it supports the 79th-octave temperament [[gold]].

	=== Prime harmonics ===		=== Prime harmonics ===
Line 32:		Line 32:
	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{monzo\| -53 10 16 }}, {{monzo\| 40 -~~56 21~~ }}		\| {{monzo\| -53 10 16 }}, {{monzo\| -13 -46 37 }}
	\| {{mapping\| 1106 1753 2568 }}		\| {{mapping\| 1106 1753 2568 }}
	\| +0.001		\| +0.001
Line 88:		Line 88:
	\| 9/7		\| 9/7
	\| [[Supermajor]]		\| [[Supermajor]]
			\|-
			\| 2
			\| 150\1106
			\| 162.749
			\| 1125/1024
			\| [[Kwazy]]
	\|-		\|-
	\| 2		\| 2

FloraC: Adopt template: Factorization; misc. cleanup

2023-10-31T10:29:50Z

Adopt template: Factorization; misc. cleanup

← Older revision		Revision as of 10:29, 31 October 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	1106edo is a [[~~The Riemann zeta function and tuning #Zeta EDO lists\|~~zeta peak edo]]. It is strong as a 7-limit system; the only edos lower than it with a lower 7-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] being {{EDOs\| 171, 270, 342, 441 and 612 }}. It is even stronger in the 11-limit; the only ones beating it out now being {{EDOs\| 270, 342 and 612 }}. It is less strong in the 13- and 17-limit, but even so is ~~distinctly~~ [[consistent]] through the [[17-odd-limit]].		1106edo is a [[zeta peak edo]]. It is strong as a 7-limit system; the only edos lower than it with a lower 7-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] being {{EDOs\| 171, 270, 342, 441 and 612 }}. It is even stronger in the 11-limit; the only ones beating it out now being {{EDOs\| 270, 342 and 612 }}. It is less strong in the 13- and 17-limit, but even so is [[consistency\|distinctly consistent]] through the [[17-odd-limit]].

	It notably supports [[supermajor]], [[brahmagupta]], and [[orga]] in the 7-limit, and notably [[semisupermajor]] in the 11-limit. In the higher limits, it supports the 79th-octave temperament [[gold]].		It notably supports [[supermajor]], [[brahmagupta]], and [[orga]] in the 7-limit, and notably [[semisupermajor]] in the 11-limit. In the higher limits, it supports the 79th-octave temperament [[gold]].
Line 11:		Line 11:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 1106 factors into ~~2 × 7 × 79~~, it has subset edos {{EDOs\| 2, 7, 14, 79, 158, and 553 }}.		Since 1106 factors into {{factorization\|1106}}, it has subset edos {{EDOs\| 2, 7, 14, 79, 158, and 553 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 26:		Line 26:
	\| 2.3		\| 2.3
	\| {{monzo\| 1753 -1106 }}		\| {{monzo\| 1753 -1106 }}
	\| {{~~val~~\| 1106 1753 }}		\| {{mapping\| 1106 1753 }}
	\| -0.010		\| -0.010
	\| 0.010		\| 0.010
Line 33:		Line 33:
	\| 2.3.5		\| 2.3.5
	\| {{monzo\| -53 10 16 }}, {{monzo\| 40 -56 21 }}		\| {{monzo\| -53 10 16 }}, {{monzo\| 40 -56 21 }}
	\| {{~~val~~\| 1106 1753 2568 }}		\| {{mapping\| 1106 1753 2568 }}
	\| +0.001		\| +0.001
	\| 0.019		\| 0.019
Line 40:		Line 40:
	\| 2.3.5.7		\| 2.3.5.7
	\| 4375/4374, 52734375/52706752, {{monzo\| 46 -14 -3 -6 }}		\| 4375/4374, 52734375/52706752, {{monzo\| 46 -14 -3 -6 }}
	\| {{~~val~~\| 1106 1753 2568 3105 }}		\| {{mapping\| 1106 1753 2568 3105 }}
	\| -0.006		\| -0.006
	\| 0.020		\| 0.020
Line 47:		Line 47:
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 3025/3024, 4375/4374, 5767168/5764801, 35156250/35153041		\| 3025/3024, 4375/4374, 5767168/5764801, 35156250/35153041
	\| {{~~val~~\| 1106 1753 2568 3105 3826 }}		\| {{mapping\| 1106 1753 2568 3105 3826 }}
	\| +0.004		\| +0.004
	\| 0.026		\| 0.026
Line 54:		Line 54:
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 3025/3024, 4096/4095, 4375/4374, 78125/78078, 105644/105625		\| 3025/3024, 4096/4095, 4375/4374, 78125/78078, 105644/105625
	\| {{~~val~~\| 1106 1753 2568 3105 3826 4093 }}		\| {{mapping\| 1106 1753 2568 3105 3826 4093 }}
	\| -0.012		\| -0.012
	\| 0.043		\| 0.043
Line 61:		Line 61:
	\| 2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\| 2500/2499, 3025/3024, 4096/4095, 4375/4374, 4914/4913, 8624/8619		\| 2500/2499, 3025/3024, 4096/4095, 4375/4374, 4914/4913, 8624/8619
	\| {{~~val~~\| 1106 1753 2568 3105 3826 4093 4521 }}		\| {{mapping\| 1106 1753 2568 3105 3826 4093 4521 }}
	\| -0.021		\| -0.021
	\| 0.045		\| 0.045
Line 69:		Line 69:
	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
			\|+Table of rank-2 temperaments by generator
			\|-
	! Periods<br>per 8ve		! Periods<br>per 8ve
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br>Ratio		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-		\|-