1700edo - 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"

2026-03-13T13:33:14Z

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 13:33, 13 March 2026
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	\| [[Leaves]]		\| [[Leaves]]
	\|}		\|}
	<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

ArrowHead294 at 12:33, 21 February 2025

2025-02-21T12:33:15Z

← Older revision		Revision as of 12:33, 21 February 2025
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	== Theory ==		== Theory ==
	1700edo is only [[consistent]] in the [[5-odd-limit]], and there is a large relative delta on the [[harmonic]] [[3/1\|3]]. It has a reasonable approximation to the 2.9.15.21.11.13.17.23 [[subgroup]], or if the harmonic [[5/1\|5]] is desired, the 2.9.5.21.11.23 subgroup. Otherwise, it can be considered in the 2.9.21.11.23.31 [[subgroup]] (not including either 5 or 15). Nonetheless, it tunes the 323 & 2023 temperament [[leaves]] in the 17-limit on the [[patent val]].		1700edo is only [[consistent]] in the [[5-odd-limit]], and there is a large relative delta on the [[harmonic]] [[3/1\|3]]. It has a reasonable approximation to the 2.9.15.21.11.13.17.23 [[subgroup]], or if the harmonic [[5/1\|5]] is desired, the 2.9.5.21.11.23 subgroup. Otherwise, it can be considered in the 2.9.21.11.23.31 [[subgroup]] (not including either 5 or 15). Nonetheless, it tunes the {{nowrap\|323 & 2023}} temperament [[leaves]] in the 17-limit on the [[patent val]].

	=== Odd harmonics ===		=== Odd harmonics ===

Francium: changed EDO intro to ED intro

2025-02-21T06:10:55Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:10, 21 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1700~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 15:58, 15 January 2025

2025-01-15T15:58:56Z

← Older revision		Revision as of 15:58, 15 January 2025
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	\| [[Leaves]]		\| [[Leaves]]
	\|}		\|}
	<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

2024-11-16T13:24:21Z

Partial undo

← Older revision		Revision as of 13:24, 16 November 2024
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	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br />~~Ratio~~*		! Associated<br />ratio*
	! Temperament		! Temperament
	\|-		\|-
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	\| [[Leaves]]		\| [[Leaves]]
	\|}		\|}
	~~{{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 00:50, 16 November 2024

2024-11-16T00:50:44Z

← Older revision		Revision as of 00:50, 16 November 2024
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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		\|+ 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*
	! Temperament		! Temperament
	\|-		\|-
	\| 17		\| 17
	\| 121\1700<br>(21\1700)		\| 121\1700<br />(21\1700)
	\| 85.412<br>(14.824)		\| 85.412<br />(14.824)
	\| 1024/975<br>(8192/8125)		\| 1024/975<br />(8192/8125)
	\| [[Leaves]]		\| [[Leaves]]
	\|}		\|}
	~~<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}}

Eliora: /* Theory */ this fact to subsets

2023-12-10T16:14:52Z

Theory: this fact to subsets

← Older revision		Revision as of 16:14, 10 December 2023
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	== Theory ==		== Theory ==
	1700edo is only [[consistent]] in the [[5-odd-limit]], and there is a large relative delta on the [[harmonic]] [[3/1\|3]]. It has a reasonable approximation to the 2.9.15.21.11.13.17.23 [[subgroup]], or if the harmonic [[5/1\|5]] is desired, the 2.9.5.21.11.23 subgroup. Otherwise, it can be considered in the 2.9.21.11.23.31 [[subgroup]] (not including either 5 or 15). Nonetheless, it tunes the 323 & 2023 temperament [[leaves]] in the 17-limit on the [[patent val]].		1700edo is only [[consistent]] in the [[5-odd-limit]], and there is a large relative delta on the [[harmonic]] [[3/1\|3]]. It has a reasonable approximation to the 2.9.15.21.11.13.17.23 [[subgroup]], or if the harmonic [[5/1\|5]] is desired, the 2.9.5.21.11.23 subgroup. Otherwise, it can be considered in the 2.9.21.11.23.31 [[subgroup]] (not including either 5 or 15). Nonetheless, it tunes the 323 & 2023 temperament [[leaves]] in the 17-limit on the [[patent val]].

	~~One step of 1700edo is the [[relative cent]] for [[17edo]]. It has been named '''iota''' by [[Margo Schulter]] and [[George Secor]].~~

	=== Odd harmonics ===		=== Odd harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 1700 factors into {{factorization\|1700}}, 1700edo has subset edos {{EDOs\| 2, 4, 5, 10, 17, 20, 25, 34, 50, 68, 85, 100, 170, 340, 425, and 850 }}.		Since 1700 factors into {{factorization\|1700}}, 1700edo has subset edos {{EDOs\| 2, 4, 5, 10, 17, 20, 25, 34, 50, 68, 85, 100, 170, 340, 425, and 850 }}.

			One step of 1700edo is the [[relative cent]] for [[17edo]]. It has been named '''iota''' by [[Margo Schulter]] and [[George Secor]].

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

FloraC: Expand; +subsets and supersets

2023-10-30T13:31:00Z

Expand; +subsets and supersets

← Older revision		Revision as of 13:31, 30 October 2023
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	== Theory ==		== Theory ==
	1700edo is only [[consistent]] in the [[5-odd-limit]], and there is a large relative delta on the ~~3rd~~ harmonic. ~~From~~ a ~~regular temperament theory perspective~~, ~~its best usage~~ is ~~as a~~ 2.9.11.21.23.31 [[subgroup]] ~~tuning because all other harmonics up to 29th have more than 25% error~~. Nonetheless, it tunes the 323 & 2023 temperament [[leaves]] in the 17-limit on the patent val.		1700edo is only [[consistent]] in the [[5-odd-limit]], and there is a large relative delta on the [[harmonic]] [[3/1\|3]]. It has a reasonable approximation to the 2.9.15.21.11.13.17.23 [[subgroup]], or if the harmonic [[5/1\|5]] is desired, the 2.9.5.21.11.23 subgroup. Otherwise, it can be considered in the 2.9.21.11.23.31 [[subgroup]] (not including either 5 or 15). Nonetheless, it tunes the 323 & 2023 temperament [[leaves]] in the 17-limit on the [[patent val]].

	One step of 1700edo is the [[relative cent]] for [[17edo]]. It has been named '''iota''' by [[Margo Schulter]] and [[George Secor]].		One step of 1700edo is the [[relative cent]] for [[17edo]]. It has been named '''iota''' by [[Margo Schulter]] and [[George Secor]].
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	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|1700}}		{{Harmonics in equal\|1700}}

			=== Subsets and supersets ===
			Since 1700 factors into {{factorization\|1700}}, 1700edo has subset edos {{EDOs\| 2, 4, 5, 10, 17, 20, 25, 34, 50, 68, 85, 100, 170, 340, 425, and 850 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
	=== 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*
	! Temperament		! Temperament
	\|-		\|-

FloraC: Cleanup; clarify the title row of the rank-2 temp table

2023-10-15T14:48:09Z

Cleanup; clarify the title row of the rank-2 temp table

← Older revision		Revision as of 14:48, 15 October 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|1700}}		{{EDO intro\|1700}}

	== Theory ==		== Theory ==
	1700edo is consistent in the 5-odd-limit, ~~although~~ there is a large relative delta on the 3rd harmonic. From a regular temperament theory perspective, ~~it's~~ best usage is as a 2.9.11.21.23.31 subgroup tuning because all other harmonics up to 29th have more than 25% error. Nonetheless, it tunes the 323 & 2023 temperament [[leaves]] in the 17-limit on the patent val.		1700edo is only [[consistent]] in the [[5-odd-limit]], and there is a large relative delta on the 3rd harmonic. From a regular temperament theory perspective, its best usage is as a 2.9.11.21.23.31 [[subgroup]] tuning because all other harmonics up to 29th have more than 25% error. Nonetheless, it tunes the 323 & 2023 temperament [[leaves]] in the 17-limit on the patent val.

	One step of 1700edo is the [[relative cent]] for [[17edo]]. It has been named '''iota''' by [[Margo Schulter]] and [[George Secor]].		One step of 1700edo is the [[relative cent]] for [[17edo]]. It has been named '''iota''' by [[Margo Schulter]] and [[George Secor]].

	=== Odd harmonics ===		=== Odd harmonics ===
	{{~~harmonics~~ in equal\|1700}}		{{Harmonics in equal\|1700}}

	== Regular temperament properties ==		== Regular temperament properties ==
	=== Rank-2 temperaments===		=== Rank-2 temperaments===
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	!Periods		! Periods<br>per 8ve
	per 8ve		! Generator*
	!Generator		! Cents*
	~~(Reduced)~~		! Associated<br>Ratio
	!Cents		! Temperament
	~~(Reduced)~~
	!Associated
	Ratio
	!Temperament
	\|-		\|-
	\|17		\| 17
	\|121\1700<br>(21\1700)		\| 121\1700<br>(21\1700)
	\|85.412<br>(14.824)		\| 85.412<br>(14.824)
	\|1024/975<br>(8192/8125)		\| 1024/975<br>(8192/8125)
	\|[[Leaves]]		\| [[Leaves]]
	\|}		\|}
			<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

BudjarnLambeth at 06:56, 9 July 2023

2023-07-09T06:56:38Z

← Older revision		Revision as of 06:56, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|1700}}		{{EDO intro\|1700}}
	== Theory ==		== Theory ==