1600edo - 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"

2026-03-13T13:38:14Z

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 13:38, 13 March 2026
Line 105:		Line 105:
	\| [[Tetraicosic]]		\| [[Tetraicosic]]
	\|}		\|}
	<nowiki/>* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[normal ~~lists~~\|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

Eufalesio: Added more things

2025-11-22T12:52:30Z

Added more things

← Older revision		Revision as of 12:52, 22 November 2025
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	1600edo is a very strong 37-limit system, being [[consistency\|distinctly consistent]] in the [[37-odd-limit]] with a smaller [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] than anything else with this property until [[4501edo\|4501]].		1600edo is a very strong 37-limit system, being [[consistency\|distinctly consistent]] in the [[37-odd-limit]] with a smaller [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] than anything else with this property until [[4501edo\|4501]].

	It is also the first division past [[311edo\|311]] with a lower [[43-limit]] relative error, being ''almost'' consistent in the [[45-odd-limit]], missing [[50/39]] and [[39/25]], both of which being off by ''52.6%'' by [[patent val]] mapping, which is still just an error of 0.3945 cents.		It is also the first division past [[311edo\|311]] with a lower [[43-limit]] relative error, being ''almost'' consistent in the [[45-odd-limit]], missing only [[50/39]] and [[39/25]], both of which being off by ''52.6%'' by [[patent val]] mapping, which is still just an error of 0.3945 cents.

	In the 5-limit, it supports [[~~kwazy~~]]. In the 11-limit, it supports the rank-3 temperament [[thor]]. In higher limits, it tempers out [[12376/12375]] in the 17-limit and due to being consistent higher than 33-odd-limit it enables the essentially tempered [[flashmic chords]].		In the 7-limit, it supports [[crazy]], it supports In the 11-limit, it supports the rank-3 temperament [[thor]]. In higher limits, it tempers out [[4096/4095]] in the [[13-limit]] (allowing [[schisminic chords]]), [[12376/12375]] in the [[17-limit]], [[6860/6859]] in the 19-limit, and due to being consistent higher than 33-odd-limit it enables the essentially tempered [[flashmic chords]].

	=== ~~Odd~~ harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|1600\|prec=3\|columns=12}}{{Harmonics in equal\|1600\|columns=12\|start=13\|prec=3\|collapsed=true\|title=Approximation of prime harmonics in 1600edo (continued)}}		{{Harmonics in equal\|1600\|prec=3\|columns=12}}{{Harmonics in equal\|1600\|columns=12\|start=13\|prec=3\|collapsed=true\|title=Approximation of prime harmonics in 1600edo (continued)}}

Tristanbay: /* Theory */changed decimal from comma to period

2025-09-25T19:49:04Z

Theory: changed decimal from comma to period

← Older revision		Revision as of 19:49, 25 September 2025
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	1600edo is a very strong 37-limit system, being [[consistency\|distinctly consistent]] in the [[37-odd-limit]] with a smaller [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] than anything else with this property until [[4501edo\|4501]].		1600edo is a very strong 37-limit system, being [[consistency\|distinctly consistent]] in the [[37-odd-limit]] with a smaller [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] than anything else with this property until [[4501edo\|4501]].

	It is also the first division past [[311edo\|311]] with a lower [[43-limit]] relative error, being ''almost'' consistent in the [[45-odd-limit]], missing [[50/39]] and [[39/25]], both of which being off by ''52,6%'' by [[patent val]] mapping, which is still just an error of 0.3945 cents.		It is also the first division past [[311edo\|311]] with a lower [[43-limit]] relative error, being ''almost'' consistent in the [[45-odd-limit]], missing [[50/39]] and [[39/25]], both of which being off by ''52.6%'' by [[patent val]] mapping, which is still just an error of 0.3945 cents.

	In the 5-limit, it supports [[kwazy]]. In the 11-limit, it supports the rank-3 temperament [[thor]]. In higher limits, it tempers out [[12376/12375]] in the 17-limit and due to being consistent higher than 33-odd-limit it enables the essentially tempered [[flashmic chords]].		In the 5-limit, it supports [[kwazy]]. In the 11-limit, it supports the rank-3 temperament [[thor]]. In higher limits, it tempers out [[12376/12375]] in the 17-limit and due to being consistent higher than 33-odd-limit it enables the essentially tempered [[flashmic chords]].
Line 15:		Line 15:
	Since 1600 factors into {{factorization\|1600}}, 1600edo has subset edos {{EDOs\| 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, and 800 }}.		Since 1600 factors into {{factorization\|1600}}, 1600edo has subset edos {{EDOs\| 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, and 800 }}.

	One step of it is the [[relative cent]] for [[16edo\|16]]. Its high divisibility, high consistency limit, and compatibility with the decimal system make it a candidate for [[interval size measure]]. One step of 1600edo is already used as a measure called ''śata'' in the context of 16edo [[Armodue theory]]. Similar to the [[Mina]] in the [[27-odd-limit]], All [[45-odd limit]] intervals can be written using integer values of śata, being more in tune than out of tune.		One step of it is the [[relative cent]] for [[16edo\|16]]. Its high divisibility, high consistency limit, and compatibility with the decimal system make it a candidate for [[interval size measure]]. One step of 1600edo is already used as a measure called ''śata'' in the context of 16edo [[Armodue theory]]. Similar to the [[Mina]] in the [[27-odd-limit]], All [[45-odd limit]] intervals can be written using integer values of śata, being more in tune than out of tune.

	== Regular temperament properties ==		== Regular temperament properties ==

Eufalesio: added extra harmonics and more info

2025-09-08T09:44:31Z

added extra harmonics and more info

← Older revision		Revision as of 09:44, 8 September 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	1600edo is a very strong 37-limit system, being [[consistency\|distinctly consistent]] in the [[37-odd-limit]] with a smaller [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] than anything else with this property until [[4501edo\|4501]]. It is also the first division past [[311edo\|311]] with a lower 43-limit relative error.		1600edo is a very strong 37-limit system, being [[consistency\|distinctly consistent]] in the [[37-odd-limit]] with a smaller [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] than anything else with this property until [[4501edo\|4501]].

			It is also the first division past [[311edo\|311]] with a lower [[43-limit]] relative error, being ''almost'' consistent in the [[45-odd-limit]], missing [[50/39]] and [[39/25]], both of which being off by ''52,6%'' by [[patent val]] mapping, which is still just an error of 0.3945 cents.

	In the 5-limit, it supports [[kwazy]]. In the 11-limit, it supports the rank-3 temperament [[thor]]. In higher limits, it tempers out [[12376/12375]] in the 17-limit and due to being consistent higher than 33-odd-limit it enables the essentially tempered [[flashmic chords]].		In the 5-limit, it supports [[kwazy]]. In the 11-limit, it supports the rank-3 temperament [[thor]]. In higher limits, it tempers out [[12376/12375]] in the 17-limit and due to being consistent higher than 33-odd-limit it enables the essentially tempered [[flashmic chords]].

	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|1600}}		{{Harmonics in equal\|1600\|prec=3\|columns=12}}{{Harmonics in equal\|1600\|columns=12\|start=13\|prec=3\|collapsed=true\|title=Approximation of prime harmonics in 1600edo (continued)}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 1600 factors into {{factorization\|1600}}, 1600edo has subset edos {{EDOs\| 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, and 800 }}.		Since 1600 factors into {{factorization\|1600}}, 1600edo has subset edos {{EDOs\| 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, and 800 }}.

	One step of it is the [[relative cent]] for [[16edo\|16]]. Its high divisibility, high consistency limit, and compatibility with the decimal system make it a candidate for interval size measure. One step of 1600edo is already used as a measure called ''śata'' in the context of 16edo [[Armodue theory]].		One step of it is the [[relative cent]] for [[16edo\|16]]. Its high divisibility, high consistency limit, and compatibility with the decimal system make it a candidate for [[interval size measure]]. One step of 1600edo is already used as a measure called ''śata'' in the context of 16edo [[Armodue theory]]. Similar to the [[Mina]] in the [[27-odd-limit]], All [[45-odd limit]] intervals can be written using integer values of śata, being more in tune than out of tune.

	== Regular temperament properties ==		== Regular temperament properties ==

FloraC: /* Regular temperament properties */ crazy update

2025-03-06T11:33:03Z

Regular temperament properties: crazy update

← Older revision		Revision as of 11:33, 6 March 2025
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	! 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
	\|-		\|-
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	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{~~monzo~~\| -53 10 16 }}, {{monzo\| 26 -75 40 }}		\| {{Monzo\| -53 10 16 }}, {{monzo\| 26 -75 40 }}
	\| {{~~mapping~~\| 1600 2536 3715 }}		\| {{Mapping\| 1600 2536 3715 }}
	\| −0.0003		\| −0.0003
	\| 0.0228		\| 0.0228
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	\| 2.3.5.7		\| 2.3.5.7
	\| 4375/4374, {{monzo\| 36 -5 0 -10 }}, {{monzo\| -17 5 16 -10 }}		\| 4375/4374, {{monzo\| 36 -5 0 -10 }}, {{monzo\| -17 5 16 -10 }}
	\| {{~~mapping~~\| 1600 2536 3715 4492 }}		\| {{Mapping\| 1600 2536 3715 4492 }}
	\| −0.0157		\| −0.0157
	\| 0.0332		\| 0.0332
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	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 3025/3024, 4375/4374, {{monzo\| 24 -1 -5 0 1 }}, {{monzo\| 15 1 7 -8 -3 }}		\| 3025/3024, 4375/4374, {{monzo\| 24 -1 -5 0 1 }}, {{monzo\| 15 1 7 -8 -3 }}
	\| {{~~mapping~~\| 1600 2536 3715 4492 5535 }}		\| {{Mapping\| 1600 2536 3715 4492 5535 }}
	\| −0.0172		\| −0.0172
	\| 0.0329		\| 0.0329
Line 50:		Line 50:
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 3025/3024, 4096/4095, 4375/4374, 78125/78078, 823875/823543		\| 3025/3024, 4096/4095, 4375/4374, 78125/78078, 823875/823543
	\| {{~~mapping~~\| 1600 2536 3715 4492 5535 5921 }}		\| {{Mapping\| 1600 2536 3715 4492 5535 5921 }}
	\| −0.0087		\| −0.0087
	\| 0.0356		\| 0.0356
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	\| 2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\| 2500/2499, 3025/3024, 4096/4095, 4375/4374, 14875/14872, 63888/63869		\| 2500/2499, 3025/3024, 4096/4095, 4375/4374, 14875/14872, 63888/63869
	\| {{~~mapping~~\| 1600 2536 3715 4492 5535 5921 6540 }}		\| {{Mapping\| 1600 2536 3715 4492 5535 5921 6540 }}
	\| −0.0163		\| −0.0163
	\| 0.0331		\| 0.0331
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	\|+ 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
	\|-		\|-
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	\| 162.75		\| 162.75
	\| 1125/1024		\| 1125/1024
	\| [[~~Kwazy~~]]		\| [[Crazy]]
	\|-		\|-
	\| 32		\| 32
Line 86:		Line 86:
	\|-		\|-
	\| 32		\| 32
	\| 121\1600<br />(21/1600)		\| 121\1600<br>(21/1600)
	\| 90.75<br />(15.75)		\| 90.75<br>(15.75)
	\| 48828125/46294416<br />(?)		\| 48828125/46294416<br>(?)
	\| [[Windrose]]		\| [[Windrose]]
	\|-		\|-
	\| 32		\| 32
	\| 357\1600<br />(7\1600)		\| 357\1600<br>(7\1600)
	\| 267.75<br />(5.25)		\| 267.75<br>(5.25)
	\| 245/143<br />(?)		\| 245/143<br>(?)
	\| [[Germanium]]		\| [[Germanium]]
	\|-		\|-
	\| 80		\| 80
	\| 629\1600<br />(9\1600)		\| 629\1600<br>(9\1600)
	\| 471.75<br />(6.75)		\| 471.75<br>(6.75)
	\| 130/99<br />(?)		\| 130/99<br>(?)
	\| [[Tetraicosic]]		\| [[Tetraicosic]]
	\|}		\|}
	<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 13:53, 20 February 2025

2025-02-20T13:53:25Z

← Older revision		Revision as of 13:53, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1600~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 18:43, 15 January 2025

2025-01-15T18:43:09Z

← Older revision		Revision as of 18:43, 15 January 2025
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	\| {{monzo\| -53 10 16 }}, {{monzo\| 26 -75 40 }}		\| {{monzo\| -53 10 16 }}, {{monzo\| 26 -75 40 }}
	\| {{mapping\| 1600 2536 3715 }}		\| {{mapping\| 1600 2536 3715 }}
	\| ~~−0~~.0003		\| −0.0003
	\| 0.0228		\| 0.0228
	\| 3.04		\| 3.04
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	\| 4375/4374, {{monzo\| 36 -5 0 -10 }}, {{monzo\| -17 5 16 -10 }}		\| 4375/4374, {{monzo\| 36 -5 0 -10 }}, {{monzo\| -17 5 16 -10 }}
	\| {{mapping\| 1600 2536 3715 4492 }}		\| {{mapping\| 1600 2536 3715 4492 }}
	\| ~~−0~~.0157		\| −0.0157
	\| 0.0332		\| 0.0332
	\| 4.43		\| 4.43
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	\| 3025/3024, 4375/4374, {{monzo\| 24 -1 -5 0 1 }}, {{monzo\| 15 1 7 -8 -3 }}		\| 3025/3024, 4375/4374, {{monzo\| 24 -1 -5 0 1 }}, {{monzo\| 15 1 7 -8 -3 }}
	\| {{mapping\| 1600 2536 3715 4492 5535 }}		\| {{mapping\| 1600 2536 3715 4492 5535 }}
	\| ~~−0~~.0172		\| −0.0172
	\| 0.0329		\| 0.0329
	\| 4.39		\| 4.39
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	\| 3025/3024, 4096/4095, 4375/4374, 78125/78078, 823875/823543		\| 3025/3024, 4096/4095, 4375/4374, 78125/78078, 823875/823543
	\| {{mapping\| 1600 2536 3715 4492 5535 5921 }}		\| {{mapping\| 1600 2536 3715 4492 5535 5921 }}
	\| ~~−0~~.0087		\| −0.0087
	\| 0.0356		\| 0.0356
	\| 4.75		\| 4.75
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	\| 2500/2499, 3025/3024, 4096/4095, 4375/4374, 14875/14872, 63888/63869		\| 2500/2499, 3025/3024, 4096/4095, 4375/4374, 14875/14872, 63888/63869
	\| {{mapping\| 1600 2536 3715 4492 5535 5921 6540 }}		\| {{mapping\| 1600 2536 3715 4492 5535 5921 6540 }}
	\| ~~−0~~.0163		\| −0.0163
	\| 0.0331		\| 0.0331
	\| 4.41		\| 4.41
Line 103:		Line 103:
	\| [[Tetraicosic]]		\| [[Tetraicosic]]
	\|}		\|}
	<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

2024-11-16T12:25:03Z

Partial undo

← Older revision		Revision as of 12:25, 16 November 2024
Line 16:		Line 16:

	== 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]] (%)
	\|-		\|-
	\| 2.3.5		\| 2.3.5
Line 52:		Line 61:
	\| 0.0331		\| 0.0331
	\| 4.41		\| 4.41
	~~{{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
	\|-		\|-
	\| 2		\| 2
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	\| 130/99<br />(?)		\| 130/99<br />(?)
	\| [[Tetraicosic]]		\| [[Tetraicosic]]
	~~{{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 04:45, 16 November 2024

2024-11-16T04:45:46Z

← Older revision		Revision as of 04:45, 16 November 2024
Line 16:		Line 16:

	== 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]] (%)~~
	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{monzo\| -53 10 16 }}, {{monzo\| 26 -75 40 }}		\| {{monzo\| -53 10 16 }}, {{monzo\| 26 -75 40 }}
	\| {{mapping\| 1600 2536 3715 }}		\| {{mapping\| 1600 2536 3715 }}
	\| -0.0003		\| −0.0003
	\| 0.0228		\| 0.0228
	\| 3.04		\| 3.04
Line 36:		Line 28:
	\| 4375/4374, {{monzo\| 36 -5 0 -10 }}, {{monzo\| -17 5 16 -10 }}		\| 4375/4374, {{monzo\| 36 -5 0 -10 }}, {{monzo\| -17 5 16 -10 }}
	\| {{mapping\| 1600 2536 3715 4492 }}		\| {{mapping\| 1600 2536 3715 4492 }}
	\| -0.0157		\| −0.0157
	\| 0.0332		\| 0.0332
	\| 4.43		\| 4.43
Line 43:		Line 35:
	\| 3025/3024, 4375/4374, {{monzo\| 24 -1 -5 0 1 }}, {{monzo\| 15 1 7 -8 -3 }}		\| 3025/3024, 4375/4374, {{monzo\| 24 -1 -5 0 1 }}, {{monzo\| 15 1 7 -8 -3 }}
	\| {{mapping\| 1600 2536 3715 4492 5535 }}		\| {{mapping\| 1600 2536 3715 4492 5535 }}
	\| -0.0172		\| −0.0172
	\| 0.0329		\| 0.0329
	\| 4.39		\| 4.39
Line 50:		Line 42:
	\| 3025/3024, 4096/4095, 4375/4374, 78125/78078, 823875/823543		\| 3025/3024, 4096/4095, 4375/4374, 78125/78078, 823875/823543
	\| {{mapping\| 1600 2536 3715 4492 5535 5921 }}		\| {{mapping\| 1600 2536 3715 4492 5535 5921 }}
	\| -0.0087		\| −0.0087
	\| 0.0356		\| 0.0356
	\| 4.75		\| 4.75
Line 57:		Line 49:
	\| 2500/2499, 3025/3024, 4096/4095, 4375/4374, 14875/14872, 63888/63869		\| 2500/2499, 3025/3024, 4096/4095, 4375/4374, 14875/14872, 63888/63869
	\| {{mapping\| 1600 2536 3715 4492 5535 5921 6540 }}		\| {{mapping\| 1600 2536 3715 4492 5535 5921 6540 }}
	\| -0.0163		\| −0.0163
	\| 0.0331		\| 0.0331
	\| 4.41		\| 4.41
	\|}		{{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~~
	\|-		\|-
	\| 2		\| 2
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	\|-		\|-
	\| 32		\| 32
	\| 121\1600<br>(21/1600)		\| 121\1600<br />(21/1600)
	\| 90.75<br>(15.75)		\| 90.75<br />(15.75)
	\| 48828125/46294416<br>(?)		\| 48828125/46294416<br />(?)
	\| [[Windrose]]		\| [[Windrose]]
	\|-		\|-
	\| 32		\| 32
	\| 357\1600<br>(7\1600)		\| 357\1600<br />(7\1600)
	\| 267.75<br>(5.25)		\| 267.75<br />(5.25)
	\| 245/143<br>(?)		\| 245/143<br />(?)
	\| [[Germanium]]		\| [[Germanium]]
	\|-		\|-
	\| 80		\| 80
	\| 629\1600<br>(9\1600)		\| 629\1600<br />(9\1600)
	\| 471.75<br>(6.75)		\| 471.75<br />(6.75)
	\| 130/99<br>(?)		\| 130/99<br />(?)
	\| [[Tetraicosic]]		\| [[Tetraicosic]]
	\|}		{{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: Adopt template: Factorization; misc. cleanup

2023-10-30T13:59:42Z

Adopt template: Factorization; misc. cleanup

← Older revision		Revision as of 13:59, 30 October 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	1600edo is a very strong 37-limit system, being distinctly consistent in the 37-limit with a smaller [[Tenney-~~Euclidean_temperament_measures~~#TE simple badness\|relative error]] than anything else with this property until [[4501edo\|4501]]. It is also the first division past [[311edo\|311]] with a lower 43-limit relative error.		1600edo is a very strong 37-limit system, being [[consistency\|distinctly consistent]] in the [[37-odd-limit]] with a smaller [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] than anything else with this property until [[4501edo\|4501]]. It is also the first division past [[311edo\|311]] with a lower 43-limit relative error.

	In the 5-limit, it supports [[kwazy]]. In the 11-limit, it supports the rank-3 temperament [[thor]]. In higher limits, it tempers out [[12376/12375]] in the 17-limit and due to being consistent higher than 33-odd-limit it enables the essentially tempered [[flashmic chords]].		In the 5-limit, it supports [[kwazy]]. In the 11-limit, it supports the rank-3 temperament [[thor]]. In higher limits, it tempers out [[12376/12375]] in the 17-limit and due to being consistent higher than 33-odd-limit it enables the essentially tempered [[flashmic chords]].
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	1600~~'s divisors are~~ {{EDOs\|1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, 800}}.		Since 1600 factors into {{factorization\|1600}}, 1600edo has subset edos {{EDOs\| 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, and 800 }}.

	One step of it is the [[relative cent]] for [[16edo\|16]]. Its high divisibility, high consistency limit, and compatibility with the decimal system make it a candidate for interval size measure. One step of 1600edo is already used as a measure called ''śata'' in the context of 16edo [[Armodue theory]].		One step of it is the [[relative cent]] for [[16edo\|16]]. Its high divisibility, high consistency limit, and compatibility with the decimal system make it a candidate for interval size measure. One step of 1600edo is already used as a measure called ''śata'' in the context of 16edo [[Armodue theory]].
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	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{~~Monzo~~\| -53 10 16 }}, {{monzo\| 26 -75 40 }}		\| {{monzo\| -53 10 16 }}, {{monzo\| 26 -75 40 }}
	\| {{mapping\| 1600 2536 3715 }}		\| {{mapping\| 1600 2536 3715 }}
	\| -0.0003		\| -0.0003
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	=== 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
	\|-		\|-
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	\| 17.25		\| 17.25
	\| ?		\| ?
	\|[[Dam]] / [[dike]] / [[polder]]		\| [[Dam]] / [[dike]] / [[polder]]
	\|-		\|-
	\| 32		\| 32