Minimal consistent EDOs - Revision history

ArrowHead294 at 19:06, 14 August 2025

2025-08-14T19:06:29Z

← Older revision		Revision as of 19:06, 14 August 2025
Line 162:		Line 162:
	[[Category:Consistency]]		[[Category:Consistency]]
	[[Category:Odd limit]]		[[Category:Odd limit]]
	~~</noinclude>~~

ArrowHead294: /* See also */

2025-04-13T18:52:54Z

ArrowHead294 at 18:09, 13 March 2025

2025-03-13T18:09:47Z

← Older revision		Revision as of 18:09, 13 March 2025
Line 1:		Line 1:
	~~<noinclude>~~{{Idiosyncratic terms}}		{{Idiosyncratic terms}}
	An [[edo]] ''N'' is ''[[consistent]]'' with respect to the [[Odd limit\|''q''-odd-limit]] if the closest approximations of the odd harmonics of the q-odd-limit in that edo also give the closest approximations of all the differences between these odd harmonics. It is ''[[distinctly consistent]]'' if every one of those closest approximations is a distinct value, and ''purely consistent''{{idiosyncratic}} if its [[relative interval error\|relative errors]] on odd harmonics up to and including ''q'' never exceed 25%. Below is a table of the smallest consistent, and the smallest distinctly consistent, edo for every odd number up to 135. Odd limits of {{nowrap\|2<sup>''n''</sup> − 1}} are '''highlighted'''.		An [[edo]] ''N'' is ''[[consistent]]'' with respect to the [[Odd limit\|''q''-odd-limit]] if the closest approximations of the odd harmonics of the q-odd-limit in that edo also give the closest approximations of all the differences between these odd harmonics. It is ''[[distinctly consistent]]'' if every one of those closest approximations is a distinct value, and ''purely consistent''{{idiosyncratic}} if its [[relative interval error\|relative errors]] on odd harmonics up to and including ''q'' never exceed 25%. Below is a table of the smallest consistent, and the smallest distinctly consistent, edo for every odd number up to 135. Odd limits of {{nowrap\|2<sup>''n''</sup> − 1}} are '''highlighted'''.
	<~~/noinclude~~>
	{\| class="wikitable center-all"		<onlyinclude>{\| class="wikitable center-all"
	\|+ style="font-size: 105%;" \| Smallest consistent EDOs per odd limit		\|+ style="font-size: 105%;" \| Smallest consistent EDOs per odd limit
	\|-		\|-
Line 145:		Line 145:
	<nowiki />* Apart from 0edo		<nowiki />* Apart from 0edo

	<nowiki />** Purely consistent to the 137-odd-limit<~~noinclude~~>		<nowiki />** Purely consistent to the 137-odd-limit</onlyinclude>

	The last entry, 70910024edo, is consistent up to the 135-odd-limit. The next edo is [[5407372813edo\|5407372813]], reported to be consistent to the 155-odd-limit.		The last entry, 70910024edo, is consistent up to the 135-odd-limit. The next edo is [[5407372813edo\|5407372813]], reported to be consistent to the 155-odd-limit.
Line 157:		Line 157:
	== See also ==		== See also ==
	* [[Consistency limits of small EDOs]]		* [[Consistency limits of small EDOs]]
	* ~~[[User:~~ArrowHead294~~/First 50 purely consistent EDOs by odd limit~~\|First 50 purely-consistent EDOs by odd limit]]		* {{u\|ArrowHead294\|First 50 purely consistent EDOs by odd limit}}

	[[Category:Mapping]]		[[Category:Mapping]]

ArrowHead294: Remove unnecessary escaping of asterisk character

2025-03-04T12:55:10Z

Remove unnecessary escaping of asterisk character

← Older revision		Revision as of 12:55, 4 March 2025
Line 5:		Line 5:
	\|+ style="font-size: 105%;" \| Smallest consistent EDOs per odd limit		\|+ style="font-size: 105%;" \| Smallest consistent EDOs per odd limit
	\|-		\|-
	! Odd<br>limit !! Smallest<br>consistent edo~~{{asterisk}}~~ !! Smallest distinctly<br>consistent edo !! Smallest purely<br>consistent edo~~{{asterisk}}~~ !! Smallest edo<br>consistent to<br>[[Consistency #Generalization\|distance 2]]~~{{asterisk}}~~ !! Smallest edo<br>distinctly consistent<br>to distance 2		! Odd<br>limit !! Smallest<br>consistent edo* !! Smallest distinctly<br>consistent edo !! Smallest purely<br>consistent edo* !! Smallest edo<br>consistent to<br>[[Consistency #Generalization\|distance 2]]* !! Smallest edo<br>distinctly consistent<br>to distance 2
	\|- style="font-weight: bold; background-color: #dddddd;"		\|- style="font-weight: bold; background-color: #dddddd;"
	\| 1 \|\| 1 \|\| 1 \|\| 1 \|\| 1 \|\| 1		\| 1 \|\| 1 \|\| 1 \|\| 1 \|\| 1 \|\| 1

Tristanbay: Removed confusing terminology "accurately consistent" and "distinctly accurate"

2025-01-20T20:10:21Z

Removed confusing terminology "accurately consistent" and "distinctly accurate"

← Older revision		Revision as of 20:10, 20 January 2025
Line 1:		Line 1:
	<noinclude>{{Idiosyncratic terms}}		<noinclude>{{Idiosyncratic terms}}
	An [[edo]] ''N'' is ''[[consistent]]'' with respect to the [[Odd limit\|''q''-odd-limit]] if the closest approximations of the odd harmonics of the q-odd-limit in that edo also give the closest approximations of all the differences between these odd harmonics. It is ''[[distinctly consistent]]'' if every one of those closest approximations is a distinct value, and ''purely consistent''{{idiosyncratic}} if its [[relative interval error\|relative errors]] on odd harmonics up to and including ''q'' never exceed 25%. It is ''accurately consistent''{{idiosyncratic}} if the edo is consistent to [[Consistency #Generalization\|distance 2]], or alternatively put, every ''q''-odd-limit interval in the edo has at most 25% relative error. Below is a table of the smallest consistent, and the smallest distinctly consistent, edo for every odd number up to 135. Odd limits of {{nowrap\|2<sup>''n''</sup> − 1}} are '''highlighted'''.		An [[edo]] ''N'' is ''[[consistent]]'' with respect to the [[Odd limit\|''q''-odd-limit]] if the closest approximations of the odd harmonics of the q-odd-limit in that edo also give the closest approximations of all the differences between these odd harmonics. It is ''[[distinctly consistent]]'' if every one of those closest approximations is a distinct value, and ''purely consistent''{{idiosyncratic}} if its [[relative interval error\|relative errors]] on odd harmonics up to and including ''q'' never exceed 25%. Below is a table of the smallest consistent, and the smallest distinctly consistent, edo for every odd number up to 135. Odd limits of {{nowrap\|2<sup>''n''</sup> − 1}} are '''highlighted'''.
	</noinclude>		</noinclude>
	{\| class="wikitable center-all"		{\| class="wikitable center-all"
	\|+ style="font-size: 105%;" \| Smallest consistent EDOs per odd limit		\|+ style="font-size: 105%;" \| Smallest consistent EDOs per odd limit
	\|-		\|-
	! Odd <br>limit !! Smallest <br>consistent edo{{asterisk}} !! Smallest distinctly <br>consistent edo !! Smallest purely <br>consistent edo !! Smallest ~~accurately~~ <br>consistent ~~edo~~ !! Smallest distinctly <br>~~accurate edo~~		! Odd<br>limit !! Smallest<br>consistent edo{{asterisk}} !! Smallest distinctly<br>consistent edo !! Smallest purely<br>consistent edo{{asterisk}} !! Smallest edo<br>consistent to<br>[[Consistency #Generalization\|distance 2]]{{asterisk}} !! Smallest edo<br>distinctly consistent<br>to distance 2
	\|- style="font-weight: bold; background-color: #dddddd;"		\|- style="font-weight: bold; background-color: #dddddd;"
	\| 1 \|\| 1 \|\| 1 \|\| 1 \|\| 1 \|\| 1		\| 1 \|\| 1 \|\| 1 \|\| 1 \|\| 1 \|\| 1

ArrowHead294: /* See also */

2025-01-13T13:21:50Z

ArrowHead294 at 00:04, 5 January 2025

2025-01-05T00:04:54Z

← Older revision		Revision as of 00:04, 5 January 2025
Line 1:		Line 1:
	<noinclude>{{Idiosyncratic terms}}		<noinclude>{{Idiosyncratic terms}}
	An [[edo]] ''N'' is ''[[consistent]]'' with respect to the [[Odd limit\|''q''-odd-limit]] if the closest approximations of the odd harmonics of the q-odd-limit in that edo also give the closest approximations of all the differences between these odd harmonics. It is ''[[distinctly consistent]]'' if every one of those closest approximations is a distinct value, and ''purely consistent''{{idiosyncratic}} if its [[relative interval error\|relative errors]] on odd harmonics up to and including ''q'' never exceed 25%. It is ''accurately consistent''{{idiosyncratic}} if the edo is consistent to [[Consistency #Generalization\|distance 2]], or alternatively put, every ''q''-odd-limit interval in the edo has at most 25% relative error. Below is a table of the smallest consistent, and the smallest distinctly consistent, edo for every odd number up to 135. Odd limits of {{nowrap\|2<sup>''n''</sup> − 1}} are '''highlighted'''.</noinclude>		An [[edo]] ''N'' is ''[[consistent]]'' with respect to the [[Odd limit\|''q''-odd-limit]] if the closest approximations of the odd harmonics of the q-odd-limit in that edo also give the closest approximations of all the differences between these odd harmonics. It is ''[[distinctly consistent]]'' if every one of those closest approximations is a distinct value, and ''purely consistent''{{idiosyncratic}} if its [[relative interval error\|relative errors]] on odd harmonics up to and including ''q'' never exceed 25%. It is ''accurately consistent''{{idiosyncratic}} if the edo is consistent to [[Consistency #Generalization\|distance 2]], or alternatively put, every ''q''-odd-limit interval in the edo has at most 25% relative error. Below is a table of the smallest consistent, and the smallest distinctly consistent, edo for every odd number up to 135. Odd limits of {{nowrap\|2<sup>''n''</sup> − 1}} are '''highlighted'''.
			</noinclude>
	{\| class="wikitable center-all"		{\| class="wikitable center-all"
	\|+ style="font-size: 105%;" \| Smallest consistent EDOs per odd limit		\|+ style="font-size: 105%;" \| Smallest consistent EDOs per odd limit

Xenllium at 07:19, 24 November 2024

2024-11-24T07:19:05Z

← Older revision		Revision as of 07:19, 24 November 2024
Line 53:		Line 53:
	\| 45 \|\| 17461 \|\| 17461 \|\| 20567 \|\| 19735901 \|\| 19735901		\| 45 \|\| 17461 \|\| 17461 \|\| 20567 \|\| 19735901 \|\| 19735901
	\|-		\|-
	\| 47 \|\| 20567 \|\| 20567 \|\| 20567 \|\| \|\|		\| 47 \|\| 20567 \|\| 20567 \|\| 20567 \|\| 152797015 \|\| 152797015
	\|-		\|-
	\| 49 \|\| 20567 \|\| 20567 \|\| 459944 \|\| \|\|		\| 49 \|\| 20567 \|\| 20567 \|\| 459944 \|\| \|\|

Xenllium at 06:22, 24 November 2024

2024-11-24T06:22:47Z

← Older revision		Revision as of 06:22, 24 November 2024
Line 5:		Line 5:
	\|+ style="font-size: 105%;" \| Smallest consistent EDOs per odd limit		\|+ style="font-size: 105%;" \| Smallest consistent EDOs per odd limit
	\|-		\|-
	! Odd<br />limit !! Smallest<br />consistent edo{{asterisk}} !! Smallest distinctly<br />consistent edo !! Smallest purely<br />consistent edo !! Smallest accurately<br />consistent edo !! Smallest distinctly<br />accurate edo		! Odd <br>limit !! Smallest <br>consistent edo{{asterisk}} !! Smallest distinctly <br>consistent edo !! Smallest purely <br>consistent edo !! Smallest accurately <br>consistent edo !! Smallest distinctly <br>accurate edo
	\|- style="font-weight: bold; background-color: #dddddd;"		\|- style="font-weight: bold; background-color: #dddddd;"
	\| 1 \|\| 1 \|\| 1 \|\| 1 \|\| 1 \|\| 1		\| 1 \|\| 1 \|\| 1 \|\| 1 \|\| 1 \|\| 1
Line 29:		Line 29:
	\| 21 \|\| 94 \|\| 282 \|\| 311 \|\| 8539 \|\| 8539		\| 21 \|\| 94 \|\| 282 \|\| 311 \|\| 8539 \|\| 8539
	\|-		\|-
	\| 23 \|\| 94 \|\| 282 \|\| 311 \|\| 16808		\| 23 \|\| 94 \|\| 282 \|\| 311 \|\| 16808 \|\| 16808
	\| 16808
	\|-		\|-
	\| 25 \|\| 282 \|\| 388 \|\| 311 \|\| 16808		\| 25 \|\| 282 \|\| 388 \|\| 311 \|\| 16808 \|\| 16808
	\| 16808
	\|-		\|-
	\| 27 \|\| 282 \|\| 388 \|\| 311 \|\| 16808		\| 27 \|\| 282 \|\| 388 \|\| 311 \|\| 16808 \|\| 16808
	\| 16808
	\|-		\|-
	\| 29 \|\| 282 \|\| 1323 \|\| 311 \|\| 16808		\| 29 \|\| 282 \|\| 1323 \|\| 311 \|\| 16808 \|\| 16808
	\| 16808
	\|- style="font-weight: bold; background-color: #dddddd;"		\|- style="font-weight: bold; background-color: #dddddd;"
	\| 31 \|\| 311 \|\| 1600 \|\| 311 \|\| 16808		\| 31 \|\| 311 \|\| 1600 \|\| 311 \|\| 16808 \|\| 16808
	\| 16808
	\|-		\|-
	\| 33 \|\| 311 \|\| 1600 \|\| 311 \|\| 16808		\| 33 \|\| 311 \|\| 1600 \|\| 311 \|\| 16808 \|\| 16808
	\| 16808
	\|-		\|-
	\| 35 \|\| 311 \|\| 1600 \|\| 311 \|\| 16808		\| 35 \|\| 311 \|\| 1600 \|\| 311 \|\| 16808 \|\| 16808
	\| 16808
	\|-		\|-
	\| 37 \|\| 311 \|\| 1600 \|\| 311 \|\| \|\|		\| 37 \|\| 311 \|\| 1600 \|\| 311 \|\| 324296 \|\| 324296
	\|-		\|-
	\| 39 \|\| 311 \|\| 2554 \|\| 311 \|\| \|\|		\| 39 \|\| 311 \|\| 2554 \|\| 311 \|\| 2398629 \|\| 2398629
	\|-		\|-
	\| 41 \|\| 311 \|\| 2554 \|\| 311 \|\| \|\|		\| 41 \|\| 311 \|\| 2554 \|\| 311 \|\| 19164767 \|\| 19164767
	\|-		\|-
	\| 43 \|\| 17461 \|\| 17461 \|\| 20567 \|\| \|\|		\| 43 \|\| 17461 \|\| 17461 \|\| 20567 \|\| 19735901 \|\| 19735901
	\|-		\|-
	\| 45 \|\| 17461 \|\| 17461 \|\| 20567 \|\| \|\|		\| 45 \|\| 17461 \|\| 17461 \|\| 20567 \|\| 19735901 \|\| 19735901
	\|-		\|-
	\| 47 \|\| 20567 \|\| 20567 \|\| 20567 \|\| \|\|		\| 47 \|\| 20567 \|\| 20567 \|\| 20567 \|\| \|\|
Line 153:		Line 146:

	<nowiki />** Purely consistent to the 137-odd-limit<noinclude>		<nowiki />** Purely consistent to the 137-odd-limit<noinclude>


	The last entry, 70910024edo, is consistent up to the 135-odd-limit. The next edo is [[5407372813edo\|5407372813]], reported to be consistent to the 155-odd-limit.		The last entry, 70910024edo, is consistent up to the 135-odd-limit. The next edo is [[5407372813edo\|5407372813]], reported to be consistent to the 155-odd-limit.

Fitzgerald Lee at 10:39, 29 October 2024

2024-10-29T10:39:53Z

← Older revision		Revision as of 10:39, 29 October 2024
Line 29:		Line 29:
	\| 21 \|\| 94 \|\| 282 \|\| 311 \|\| 8539 \|\| 8539		\| 21 \|\| 94 \|\| 282 \|\| 311 \|\| 8539 \|\| 8539
	\|-		\|-
	\| 23 \|\| 94 \|\| 282 \|\| 311 \|\| 16808?		\| 23 \|\| 94 \|\| 282 \|\| 311 \|\| 16808
	\| 16808?		\| 16808
	\|-		\|-
	\| 25 \|\| 282 \|\| 388 \|\| 311 \|\| 16808?		\| 25 \|\| 282 \|\| 388 \|\| 311 \|\| 16808
	\| 16808?		\| 16808
	\|-		\|-
	\| 27 \|\| 282 \|\| 388 \|\| 311 \|\| 16808?		\| 27 \|\| 282 \|\| 388 \|\| 311 \|\| 16808
	\| 16808?		\| 16808
	\|-		\|-
	\| 29 \|\| 282 \|\| 1323 \|\| 311 \|\| 16808?		\| 29 \|\| 282 \|\| 1323 \|\| 311 \|\| 16808
	\| 16808?		\| 16808
	\|- style="font-weight: bold; background-color: #dddddd;"		\|- style="font-weight: bold; background-color: #dddddd;"
	\| 31 \|\| 311 \|\| 1600 \|\| 311 \|\| 16808?		\| 31 \|\| 311 \|\| 1600 \|\| 311 \|\| 16808
	\| 16808?		\| 16808
	\|-		\|-
	\| 33 \|\| 311 \|\| 1600 \|\| 311 \|\| 16808?		\| 33 \|\| 311 \|\| 1600 \|\| 311 \|\| 16808
	\| 16808?		\| 16808
	\|-		\|-
	\| 35 \|\| 311 \|\| 1600 \|\| 311 \|\| 16808?		\| 35 \|\| 311 \|\| 1600 \|\| 311 \|\| 16808
	\| 16808?		\| 16808
	\|-		\|-
	\| 37 \|\| 311 \|\| 1600 \|\| 311 \|\| \|\|		\| 37 \|\| 311 \|\| 1600 \|\| 311 \|\| \|\|

← Older revision		Revision as of 18:52, 13 April 2025
Line 157:		Line 157:
	== See also ==		== See also ==
	* [[Consistency limits of small EDOs]]		* [[Consistency limits of small EDOs]]
	* {{u\|ArrowHead294\|~~First 50 purely~~ consistent EDOs by odd limit}}		* {{u\|ArrowHead294\|Purely consistent EDOs by odd limit}}

	[[Category:Mapping]]		[[Category:Mapping]]

← Older revision		Revision as of 13:21, 13 January 2025
Line 157:		Line 157:
	== See also ==		== See also ==
	* [[Consistency limits of small EDOs]]		* [[Consistency limits of small EDOs]]
			* [[User:ArrowHead294/First 50 purely consistent EDOs by odd limit\|First 50 purely-consistent EDOs by odd limit]]

	[[Category:Mapping]]		[[Category:Mapping]]