409edo - Revision history

ArrowHead294 at 12:58, 21 February 2025

2025-02-21T12:58:08Z

← Older revision		Revision as of 12:58, 21 February 2025
Line 13:		Line 13:
	== 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 25:		Line 26:
	\| {{monzo\| -648 409 }}		\| {{monzo\| -648 409 }}
	\| {{mapping\| 409 648 }}		\| {{mapping\| 409 648 }}
	\| 0.2311		\| +0.2311
	\| 0.2311		\| 0.2311
	\| 7.88		\| 7.88
Line 32:		Line 33:
	\| {{monzo\| -44 26 1 }}, {{monzo\| 12 19 -15 }}		\| {{monzo\| -44 26 1 }}, {{monzo\| 12 19 -15 }}
	\| {{mapping\| 409 648 1148 }}		\| {{mapping\| 409 648 1148 }}
	\| 0.2266		\| +0.2266
	\| 0.1888		\| 0.1888
	\| 6.43		\| 6.43
Line 39:		Line 40:
	\| 117649/117612, 5038848/5021863, 134775333/134217728		\| 117649/117612, 5038848/5021863, 134775333/134217728
	\| {{mapping\| 409 648 1148 1415 }}		\| {{mapping\| 409 648 1148 1415 }}
	\| 0.1503		\| +0.1503
	\| 0.2102		\| 0.2102
	\| 7.16		\| 7.16
Line 46:		Line 47:
	\| 729/728, 19773/19712, 50421/50336, 718848/717409		\| 729/728, 19773/19712, 50421/50336, 718848/717409
	\| {{mapping\| 409 648 1148 1415 1513 }}		\| {{mapping\| 409 648 1148 1415 1513 }}
	\| 0.1963		\| +0.1963
	\| 0.2093		\| 0.2093
	\| 7.13		\| 7.13

Francium: changed EDO intro to ED intro

2025-02-21T05:51:35Z

changed EDO intro to ED intro

← Older revision		Revision as of 05:51, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|409~~}}		{{ED intro}}

	== Theory ==		== Theory ==

Francium: /* Music */ +music

2024-08-01T14:01:56Z

Music: +music

← Older revision		Revision as of 14:01, 1 August 2024
Line 54:		Line 54:
	; [[Francium]]		; [[Francium]]
	* "End Of Sartorius Membranes" from ''End of Sartorius Membranes'' (2024) – [https://open.spotify.com/track/5aNPRLUiI5PIvhKEl2XPc9 Spotify] \| [https://francium223.bandcamp.com/track/end-of-sartorius-membranes Bandcamp] \| [https://www.youtube.com/watch?v=QuxTb_pyG2Y YouTube]		* "End Of Sartorius Membranes" from ''End of Sartorius Membranes'' (2024) – [https://open.spotify.com/track/5aNPRLUiI5PIvhKEl2XPc9 Spotify] \| [https://francium223.bandcamp.com/track/end-of-sartorius-membranes Bandcamp] \| [https://www.youtube.com/watch?v=QuxTb_pyG2Y YouTube]
			* "Look Lady?" from ''Questions'' (2024) – [https://open.spotify.com/track/3alyeoProiPiuxHyXZB1Ii Spotify] \| [https://francium223.bandcamp.com/track/look-lady Bandcamp] \| [https://www.youtube.com/watch?v=jqPSMmkw8HM YouTube] – snape in 409edo tuning

	[[Category:Listen]]		[[Category:Listen]]

Francium: +music

2024-02-20T12:04:24Z

+music

← Older revision		Revision as of 12:04, 20 February 2024
Line 50:		Line 50:
	\| 7.13		\| 7.13
	\|}		\|}

			== Music ==
			; [[Francium]]
			* "End Of Sartorius Membranes" from ''End of Sartorius Membranes'' (2024) – [https://open.spotify.com/track/5aNPRLUiI5PIvhKEl2XPc9 Spotify] \| [https://francium223.bandcamp.com/track/end-of-sartorius-membranes Bandcamp] \| [https://www.youtube.com/watch?v=QuxTb_pyG2Y YouTube]

			[[Category:Listen]]

FloraC: Review

2024-01-19T15:20:11Z

Review

← Older revision		Revision as of 15:20, 19 January 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	409et is ~~only~~ consistent to the [[3-odd-limit]]. ~~Using~~ the patent val~~, it~~ tempers out ~~2460375/2458624 and 201768035/201326592 in the 7-limit; 1073741824/1071794405, 161280/161051, 1835008/1830125, 2097152/2096325, 496125/495616, 117649/117612, 226492416/226474325,~~ [[~~441~~/~~440~~]]~~, 2460375/2458624, 201768035/201326592, 24057/24010,~~ [[~~5632~~/~~5625~~]], ~~16808715/16777216, 4108797/4096000 and 102487/102400 in the 11-limit. It~~ [[support]]s [[~~rank-4~~]] [[~~werckismic~~]] and [[~~snape~~]].		409et is in[[consistent]] to the [[5-odd-limit]]. In the 7-limit, the 409c [[val]] {{val\| 409 648 '''949''' 1148 }} is about as viable as the [[patent val]] {{val\| 409 648 '''950''' 1148 }}. The 409c val [[tempering out\|tempers out]] [[15625/15552]] and [[16875/16807]], [[support]]ing [[sqrtphi]]. The patent val tempers out [[3136/3125]] and [[19683/19600]], supporting [[subpental]].

	=== Odd harmonics ===		=== Odd harmonics ===
Line 13:		Line 13:
	== 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\|-648 409}}		\| {{monzo\| -648 409 }}
	\|{{mapping\|409 648}}		\| {{mapping\| 409 648 }}
	\| 0.2311		\| 0.2311
	\| 0.2311		\| 0.2311
	\| 7.88		\| 7.88
	\|-		\|-
	\|2.3.7		\| 2.3.7
	\|{{monzo\|-44 26 1}}, {{monzo\|12 19 -15}}		\| {{monzo\| -44 26 1 }}, {{monzo\| 12 19 -15 }}
	\|{{mapping\|409 648 1148}}		\| {{mapping\| 409 648 1148 }}
	\| 0.2266		\| 0.2266
	\| 0.1888		\| 0.1888
	\| 6.43		\| 6.43
	\|-		\|-
	\|2.3.7.11		\| 2.3.7.11
	\|117649/117612, 5038848/5021863, 134775333/134217728		\| 117649/117612, 5038848/5021863, 134775333/134217728
	\|{{mapping\|409 648 1148 1415}}		\| {{mapping\| 409 648 1148 1415 }}
	\| 0.1503		\| 0.1503
	\| 0.2102		\| 0.2102
	\| 7.16		\| 7.16
	\|-		\|-
	\|2.3.7.11.13		\| 2.3.7.11.13
	\|729/728, 19773/19712, 50421/50336, 718848/717409		\| 729/728, 19773/19712, 50421/50336, 718848/717409
	\|{{mapping\|409 648 1148 1415 1513}}		\| {{mapping\| 409 648 1148 1415 1513 }}
	\| 0.1963		\| 0.1963
	\| 0.2093		\| 0.2093
	\| 7.13		\| 7.13
	\|}		\|}

Francium: Created page with "{{Infobox ET}} {{EDO intro|409}} == Theory == 409et is only consistent to the 3-odd-limit. Using the patent val, it tempers out 2460375/2458624 and 201768035/201326592 in..."

2024-01-15T15:42:40Z

Created page with "{{Infobox ET}} {{EDO intro|409}} == Theory == 409et is only consistent to the 3-odd-limit. Using the patent val, it tempers out 2460375/2458624 and 201768035/201326592 in..."

New page

{{Infobox ET}}
{{EDO intro|409}}

== Theory ==
409et is only consistent to the [[3-odd-limit]]. Using the patent val, it tempers out 2460375/2458624 and 201768035/201326592 in the 7-limit; 1073741824/1071794405, 161280/161051, 1835008/1830125, 2097152/2096325, 496125/495616, 117649/117612, 226492416/226474325, [[441/440]], 2460375/2458624, 201768035/201326592, 24057/24010, [[5632/5625]], 16808715/16777216, 4108797/4096000 and 102487/102400 in the 11-limit. It [[support]]s [[rank-4]] [[werckismic]] and [[snape]].

=== Odd harmonics ===
{{Harmonics in equal|409}}

=== Subsets and supersets ===
409edo is the 80th [[prime edo]]. [[1227edo]], which triples it, gives a good correction to the harmonic 5.

== 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|-648 409}}
|{{mapping|409 648}}
| 0.2311
| 0.2311
| 7.88
|-
|2.3.7
|{{monzo|-44 26 1}}, {{monzo|12 19 -15}}
|{{mapping|409 648 1148}}
| 0.2266
| 0.1888
| 6.43
|-
|2.3.7.11
|117649/117612, 5038848/5021863, 134775333/134217728
|{{mapping|409 648 1148 1415}}
| 0.1503
| 0.2102
| 7.16
|-
|2.3.7.11.13
|729/728, 19773/19712, 50421/50336, 718848/717409
|{{mapping|409 648 1148 1415 1513}}
| 0.1963
| 0.2093
| 7.13
|}