303edo - Revision history

ArrowHead294 at 12:30, 21 February 2025

2025-02-21T12:30:21Z

← Older revision		Revision as of 12:30, 21 February 2025
Line 22:		Line 22:
	== Regular temperament properties ==		== Regular temperament properties ==
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
			\|-
	! rowspan="2" \| [[Subgroup]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \| [[Comma list~~\|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
	\|-		\|-
	! [[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	! [[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
Line 34:		Line 35:
	\| {{monzo\| -160 101 }}		\| {{monzo\| -160 101 }}
	\| {{mapping\| 303 480 }}		\| {{mapping\| 303 480 }}
	\| 0.3044		\| +0.3044
	\| 0.3045		\| 0.3045
	\| 7.69		\| 7.69
	\|}		\|}

Francium: changed EDO intro to ED intro

2025-02-21T06:14:22Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:14, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|303~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: Review

2024-01-19T15:07:24Z

Review

← Older revision		Revision as of 15:07, 19 January 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	~~303et~~ is ~~only~~ consistent to the [[3-odd-limit]], with three mappings possible for the 7-limit:		303edo is in[[consistent]] to the [[5-odd-limit]] with three mappings possible for the 7-limit:
	* {{val\|303 480 704 851}} (patent val)		* {{val\| 303 480 704 851 }} ([[patent val]])
	* {{val\|303 480 '''703''' 851}} (303c val)		* {{val\| 303 480 '''703''' 851 }} (303c val)
	* {{val\|303 480 '''703''' '''850'''}} (303cd val)		* {{val\| 303 480 '''703''' '''850''' }} (303cd val)

	~~Using the~~ patent val~~, it~~ tempers out 4294967296/4271484375 and 31381059609/30517578125 in the 5-limit; [[3136/3125]], 177147/175000 and 10616832/10504375 in the 7-limit, [[support]]ing [[gregorian leap day]].		The patent val [[tempering out\|tempers out]] 4294967296/4271484375 and 31381059609/30517578125 in the 5-limit; [[3136/3125]], 177147/175000 and 10616832/10504375 in the 7-limit, [[support]]ing [[gregorian leap day]].

	Using the 303c val, it tempers out [[15625/15552]] and {{monzo\|-83 48 3}} in the 5-limit; [[225/224]], [[4375/4374]] and {{monzo\|36 -7 5 -13}} in the 7-limit.		Using the 303c val, it tempers out [[15625/15552]] and {{monzo\| -83 48 3 }} in the 5-limit; [[225/224]], [[4375/4374]] and {{monzo\| 36 -7 5 -13 }} in the 7-limit, supporting [[catakleismic]]

	Using the 303cd val, it tempers out 15625/15552 and {{monzo\|-83 48 3}} in the 5-limit; [[1029/1024]]~~, 15625/15552~~ and [[43046721/43025920]] in the 7-limit.		Using the 303cd val, it tempers out 15625/15552 and {{monzo\| -83 48 3 }} in the 5-limit; [[1029/1024]] and [[43046721/43025920]] in the 7-limit, supporting [[tritikleismic]].

	=== Prime harmonics ===		=== Prime harmonics ===
Line 22:		Line 22:
	== Regular temperament properties ==		== Regular temperament properties ==
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
	! rowspan="2" \|[[Subgroup]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \|[[Comma list\|Comma List]]		! rowspan="2" \| [[Comma list\|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
	\|-		\|-
	![[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	![[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\|2.3		\| 2.3
	\|{{monzo\|-160 101}}		\| {{monzo\| -160 101 }}
	\|{{mapping\|303 480}}		\| {{mapping\| 303 480 }}
	\| 0.3044		\| 0.3044
	\| 0.3045		\| 0.3045
	\| 7.69		\| 7.69
	\|}		\|}

Francium: Created page with "{{Infobox ET}} {{EDO intro|303}} == Theory == 303et is only consistent to the 3-odd-limit, with three mappings possible for the 7-limit: * {{val|303 480 704 851}} (patent..."

2024-01-11T09:45:49Z

Created page with "{{Infobox ET}} {{EDO intro|303}} == Theory == 303et is only consistent to the 3-odd-limit, with three mappings possible for the 7-limit: * {{val|303 480 704 851}} (patent..."

New page

{{Infobox ET}}
{{EDO intro|303}}

== Theory ==
303et is only consistent to the [[3-odd-limit]], with three mappings possible for the 7-limit:
* {{val|303 480 704 851}} (patent val)
* {{val|303 480 '''703''' 851}} (303c val)
* {{val|303 480 '''703''' '''850'''}} (303cd val)

Using the patent val, it tempers out 4294967296/4271484375 and 31381059609/30517578125 in the 5-limit; [[3136/3125]], 177147/175000 and 10616832/10504375 in the 7-limit, [[support]]ing [[gregorian leap day]].

Using the 303c val, it tempers out [[15625/15552]] and {{monzo|-83 48 3}} in the 5-limit; [[225/224]], [[4375/4374]] and {{monzo|36 -7 5 -13}} in the 7-limit.

Using the 303cd val, it tempers out 15625/15552 and {{monzo|-83 48 3}} in the 5-limit; [[1029/1024]], 15625/15552 and [[43046721/43025920]] in the 7-limit.

=== Prime harmonics ===
{{Harmonics in equal|303}}

=== Subsets and supersets ===
303 factors into 3 × 101, with [[3edo]] and [[101edo]] as its subset edos. [[606edo]], which doubles it, gives a good correction to the harmonics 5 and 7.

== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
! 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
|{{monzo|-160 101}}
|{{mapping|303 480}}
| 0.3044
| 0.3045
| 7.69
|}