User:Fredg999/Sandbox - Revision history

Fredg999: Add draft for lead section of Perfect fourth

2025-04-26T06:33:51Z

Add draft for lead section of Perfect fourth

← Older revision		Revision as of 06:33, 26 April 2025
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			== Perfect fourth ==
			{{Wikipedia\|Perfect fourth}}
			{{About\|the [[interval category]]\|the just perfect fourth\|4/3}}
			In Western music theory, a '''perfect fourth''' is an [[interval]] with a [[frequency ratio]] equal or approximately equal to [[4/3]] (≈498{{c}}). It is a strongly [[consonant]] interval, hence its [[interval quality]] "perfect". A perfect fourth always spans four degrees of a [[diatonic]] scale (e.g. C-F spanning C-D-E-F), hence its [[interval number]] "fourth". In particular, a perfect fourth spans two whole tones (e.g. C-D-E) and one diatonic semitone (e.g. E-F).

			An ''imperfect fourth'' also spans four degrees, but with a different combination of steps. In particular, the augmented fourth spans three whole tones, hence its other name "[[tritone]]". Other fourths may occur in altered diatonic scales, such as the diminished fourth in the harmonic minor scale (e.g. B-E{{flat}}).

			A ''wolf fourth'' (or ''imperfect fourth'', in a second sense) is an interval that attempts to close a [[circle of fourths]], but that fails to approximate a frequency ratio of 4/3. For example, in [[quarter-comma meantone]] temperament, an augmented third (e.g. A{{flat}}-C{{sharp}}) can be used to close the 12-tone circle of fourths, but it falls approximately 36{{c}} flat of a just perfect fourth.

			In microtonal music, an interval may be considered a perfect fourth even if it exhibits only one of the two defining features of a perfect fourth:
			* As intervals in an [[interval region]], perfect fourths only need to have a size close to ≈498{{c}}, no matter the underlying scale or other harmonic context. According to [[Margo Schulter]]'s ''[http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum]'', perfect fourths typically range from approximately 470{{c}} to 530{{c}}. Intervals that are too sharp or too flat to qualify as perfect fourths are often called [[superfourth]]s and [[subfourth]]s respectively.
			* As intervals in a diatonic [[MOS scale]], perfect fourths only need to span two large steps and one small step. This approach allows for sizes ranging from [[7edo\|4\7]] (≈686{{c}}) to [[5edo\|3\5]] (720{{c}}). Intervals inflected by a [[quartertone]] alteration up or down from a perfect fourth are often called [[semi-augmented fourth]]s and [[semi-diminished fourth]]s respectively.

	== Temperament databox ==		== Temperament databox ==
	Using [[User:FloraC/Temperament data]].		Using [[User:FloraC/Temperament data]].

Fredg999: /* Summary of proposed changes (2025-02-17 update) */ Update suggestion for theory/overview

2025-02-17T15:59:57Z

Summary of proposed changes (2025-02-17 update): Update suggestion for theory/overview

← Older revision		Revision as of 15:59, 17 February 2025
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	=== Summary of proposed changes (2025-02-17 update) ===		=== Summary of proposed changes (2025-02-17 update) ===
	; Remove ''Discussion'': The first part of that page would fit better in a "pedagogy" page, while the links should be directly added in the sidebar (see below).		; Remove ''Discussion'': The first part of that page would fit better in a "pedagogy" page, while the links should be directly added in the sidebar (see below).
	; Merge ''General Theory'' and ''Mathematical Theory'' into ''~~Overview~~'': Since General Theory already has some high-level stuff, we might as well want a single overview of tuning theory, with the basic stuff on top. So far my suggestion for the title of that page is "Overview of tuning theory".		; Merge ''General Theory'' and ''Mathematical Theory'' into ''Theory overview'': Since General Theory already has some high-level stuff, we might as well want a single overview of tuning theory, with the basic stuff on top. So far my suggestion for the title of that page is "Overview of tuning theory" (while "Theory overview" would be the shorthand for the sidebar).
	; Add ''Links'': Many websites have a "links" page available through the site's menu, so it would make sense to do the same here, especially since we have the [[Links]] page. By the way, since we have many pages with similar lists of links but for specific aspects, we might want to make this a sort of curated list with a "see also" hatnote in each section.		; Add ''Links'': Many websites have a "links" page available through the site's menu, so it would make sense to do the same here, especially since we have the [[Links]] page. By the way, since we have many pages with similar lists of links but for specific aspects, we might want to make this a sort of curated list with a "see also" hatnote in each section.
	; Rename ''Lists and Galleries'' to ''Lists and tables'': Most pages that are called galleries are not really galleries (of images); however we do have a decent amount of tables. I think ''Lists and tables'' sounds overall better and clearer than ''Lists'' alone. This would imply renaming that page, of course.		; Rename ''Lists and Galleries'' to ''Lists and tables'': Most pages that are called galleries are not really galleries (of images); however we do have a decent amount of tables. I think ''Lists and tables'' sounds overall better and clearer than ''Lists'' alone. This would imply renaming that page, of course.

Fredg999: /* Summary of proposed changes (2025-02-17 update) */ Add internal link to Links

2025-02-17T15:58:51Z

Summary of proposed changes (2025-02-17 update): Add internal link to Links

← Older revision		Revision as of 15:58, 17 February 2025
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	; Remove ''Discussion'': The first part of that page would fit better in a "pedagogy" page, while the links should be directly added in the sidebar (see below).		; Remove ''Discussion'': The first part of that page would fit better in a "pedagogy" page, while the links should be directly added in the sidebar (see below).
	; Merge ''General Theory'' and ''Mathematical Theory'' into ''Overview'': Since General Theory already has some high-level stuff, we might as well want a single overview of tuning theory, with the basic stuff on top. So far my suggestion for the title of that page is "Overview of tuning theory".		; Merge ''General Theory'' and ''Mathematical Theory'' into ''Overview'': Since General Theory already has some high-level stuff, we might as well want a single overview of tuning theory, with the basic stuff on top. So far my suggestion for the title of that page is "Overview of tuning theory".
	; Add ''Links'': Many websites have a "links" page available through the site's menu, so it would make sense to do the same here. By the way, since we have many pages with similar lists of links but for specific aspects, we might want to make this a sort of curated list with a "see also" hatnote in each section.		; Add ''Links'': Many websites have a "links" page available through the site's menu, so it would make sense to do the same here, especially since we have the [[Links]] page. By the way, since we have many pages with similar lists of links but for specific aspects, we might want to make this a sort of curated list with a "see also" hatnote in each section.
	; Rename ''Lists and Galleries'' to ''Lists and tables'': Most pages that are called galleries are not really galleries (of images); however we do have a decent amount of tables. I think ''Lists and tables'' sounds overall better and clearer than ''Lists'' alone. This would imply renaming that page, of course.		; Rename ''Lists and Galleries'' to ''Lists and tables'': Most pages that are called galleries are not really galleries (of images); however we do have a decent amount of tables. I think ''Lists and tables'' sounds overall better and clearer than ''Lists'' alone. This would imply renaming that page, of course.

Fredg999: /* Summary of proposed changes (2025-02-17 update) */ Avoid term "xenharmonic theory", in favour of "tuning theory" which is more inclusive.

2025-02-17T15:56:31Z

Summary of proposed changes (2025-02-17 update): Avoid term "xenharmonic theory", in favour of "tuning theory" which is more inclusive.

← Older revision		Revision as of 15:56, 17 February 2025
Line 86:		Line 86:
	=== Summary of proposed changes (2025-02-17 update) ===		=== Summary of proposed changes (2025-02-17 update) ===
	; Remove ''Discussion'': The first part of that page would fit better in a "pedagogy" page, while the links should be directly added in the sidebar (see below).		; Remove ''Discussion'': The first part of that page would fit better in a "pedagogy" page, while the links should be directly added in the sidebar (see below).
	; Merge ''General Theory'' and ''Mathematical Theory'' into ''Overview'': Since General Theory already has some high-level stuff, we might as well want a single overview of tuning theory, with the basic stuff on top. So far my suggestion for the title of that page is "Overview of tuning theory"~~; it could just as well be "Overview of xenharmonic theory", too~~.		; Merge ''General Theory'' and ''Mathematical Theory'' into ''Overview'': Since General Theory already has some high-level stuff, we might as well want a single overview of tuning theory, with the basic stuff on top. So far my suggestion for the title of that page is "Overview of tuning theory".
	; Add ''Links'': Many websites have a "links" page available through the site's menu, so it would make sense to do the same here. By the way, since we have many pages with similar lists of links but for specific aspects, we might want to make this a sort of curated list with a "see also" hatnote in each section.		; Add ''Links'': Many websites have a "links" page available through the site's menu, so it would make sense to do the same here. By the way, since we have many pages with similar lists of links but for specific aspects, we might want to make this a sort of curated list with a "see also" hatnote in each section.
	; Rename ''Lists and Galleries'' to ''Lists and tables'': Most pages that are called galleries are not really galleries (of images); however we do have a decent amount of tables. I think ''Lists and tables'' sounds overall better and clearer than ''Lists'' alone. This would imply renaming that page, of course.		; Rename ''Lists and Galleries'' to ''Lists and tables'': Most pages that are called galleries are not really galleries (of images); however we do have a decent amount of tables. I think ''Lists and tables'' sounds overall better and clearer than ''Lists'' alone. This would imply renaming that page, of course.

Fredg999: /* Sidebar revision */ Separate changes already applied in 2023

2025-02-17T15:53:18Z

Sidebar revision: Separate changes already applied in 2023

← Older revision		Revision as of 15:53, 17 February 2025
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	== Sidebar revision ==		== Sidebar revision ==
	=== Summary of proposed changes ===		=== Summary of proposed changes (2025-02-17 update) ===
			; Remove ''Discussion'': The first part of that page would fit better in a "pedagogy" page, while the links should be directly added in the sidebar (see below).
			; Merge ''General Theory'' and ''Mathematical Theory'' into ''Overview'': Since General Theory already has some high-level stuff, we might as well want a single overview of tuning theory, with the basic stuff on top. So far my suggestion for the title of that page is "Overview of tuning theory"; it could just as well be "Overview of xenharmonic theory", too.
			; Add ''Links'': Many websites have a "links" page available through the site's menu, so it would make sense to do the same here. By the way, since we have many pages with similar lists of links but for specific aspects, we might want to make this a sort of curated list with a "see also" hatnote in each section.
			; Rename ''Lists and Galleries'' to ''Lists and tables'': Most pages that are called galleries are not really galleries (of images); however we do have a decent amount of tables. I think ''Lists and tables'' sounds overall better and clearer than ''Lists'' alone. This would imply renaming that page, of course.

			=== Changes applied on 2023-08-04 ===
	; Remove ''Introduction'': That page could be merged into the Main Page, since there's not a lot of information that's not already on the Main Page anyway.		; Remove ''Introduction'': That page could be merged into the Main Page, since there's not a lot of information that's not already on the Main Page anyway.
	; Add ''FAQ'' between ''Random page'' and ''Help'': I suggest renaming ''[[Ask Questions]]'' to ''Frequently asked questions''. That page should offer short answers in addition to links to dedicated articles, as needed. By the way, most of these dedicated articles that we already have are written in a personal/non-neutral style (and are often old, in case that matters for some of them), so we might want to warn readers accordingly.		; Add ''FAQ'' between ''Random page'' and ''Help'': I suggest renaming ''[[Ask Questions]]'' to ''Frequently asked questions''. That page should offer short answers in addition to links to dedicated articles, as needed. By the way, most of these dedicated articles that we already have are written in a personal/non-neutral style (and are often old, in case that matters for some of them), so we might want to warn readers accordingly.
	; Remove ''Conventions'': I don't think that link is worth the space it takes, especially since the page is directly accessible from the top of the ''Help'' page.		; Remove ''Conventions'': I don't think that link is worth the space it takes, especially since the page is directly accessible from the top of the ''Help'' page.
	; Rename ''Pedagogy'' to ''Guides'' and move it to the bottom of its section: "Pedagogy" is a bit vague and sounds like it's more oriented towards educators than learners. Most "pedagogical" pages are guides, since everything else is just a normal page from which readers can learn anyway, at least from my perspective.		; Rename ''Pedagogy'' to ''Guides'' and move it to the bottom of its section: "Pedagogy" is a bit vague and sounds like it's more oriented towards educators than learners. Most "pedagogical" pages are guides, since everything else is just a normal page from which readers can learn anyway, at least from my perspective.
	~~; Remove ''Discussion'': The first part of that page would fit better in a "pedagogy" page, while the links should be directly added in the sidebar (see below).~~
	; Rename ''Orientation'' to ''Approaches'': This seems less vague than "orientation", considering the goal of that page. See also [[Talk:MicrotonalTheory]].		; Rename ''Orientation'' to ''Approaches'': This seems less vague than "orientation", considering the goal of that page. See also [[Talk:MicrotonalTheory]].
	; Merge ''General Theory'' and ''Mathematical Theory'' into ''Overview'': Since General Theory already has some high-level stuff, we might as well want a single overview of tuning theory, with the basic stuff on top. So far my suggestion for the title of that page is "Overview of tuning theory"; it could just as well be "Overview of xenharmonic theory", too.
	; Remove ''Useful Tools'': See [[Talk:Useful Tools]]. We could have a duplicate link to ''Software'' for the sake of independent sections, but I don't think it's worth it.		; Remove ''Useful Tools'': See [[Talk:Useful Tools]]. We could have a duplicate link to ''Software'' for the sake of independent sections, but I don't think it's worth it.
	; Add ''Links'': Many websites have a "links" page available through the site's menu, so it would make sense to do the same here. By the way, since we have many pages with similar lists of links but for specific aspects, we might want to make this a sort of curated list with a "see also" hatnote in each section.
	; Rename ''Lists and Galleries'' to ''Lists and tables'': Most pages that are called galleries are not really galleries (of images); however we do have a decent amount of tables. I think ''Lists and tables'' sounds overall better and clearer than ''Lists'' alone. This would imply renaming that page, of course.
	; Misc. edits: Use sentence case, change some target page titles (already updated or suggested), move LANGAUGES to the bottom (where it's displayed anyway), etc.		; Misc. edits: Use sentence case, change some target page titles (already updated or suggested), move LANGAUGES to the bottom (where it's displayed anyway), etc.

Fredg999: /* Septimal meantone */ Move TE at the bottom, optimal tunings expanded by default

2024-03-17T01:54:59Z

Septimal meantone: Move TE at the bottom, optimal tunings expanded by default

← Older revision		Revision as of 01:54, 17 March 2024
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	\| Badness = 0.013707		\| Badness = 0.013707
	}}		}}
	{{Databox\|[[Optimal tuning]]s:\|		{{Databox\|[[Optimal tuning]]s:\|defaultstate=expanded\|
	text=		text=
	* [[TE]]: ~2 = 1201.242, ~3/2 = 698.458
	* [[CTE]]: ~3/2 = 696.952		* [[CTE]]: ~3/2 = 696.952
	* [[POTE]]: ~3/2 = 696.495		* [[POTE]]: ~3/2 = 696.495
			* [[TE]]: ~2 = 1201.242, ~3/2 = 698.458
	}}}}		}}}}

Fredg999: /* Temperament databox */ Remove pure generators

2024-03-17T01:50:32Z

Temperament databox: Remove pure generators

← Older revision		Revision as of 01:50, 17 March 2024
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	text=		text=
	* [[TE]]: ~2 = 1201.242, ~3/2 = 698.458		* [[TE]]: ~2 = 1201.242, ~3/2 = 698.458
	* [[CTE]]: ~~~2 = 1200.000,~~ ~3/2 = 696.952		* [[CTE]]: ~3/2 = 696.952
	* [[POTE]]: ~~~2 = 1200.000,~~ ~3/2 = 696.495		* [[POTE]]: ~3/2 = 696.495
	}}}}		}}}}

Fredg999: Add temperament data demo with nested databoxes

2024-03-16T17:45:07Z

Add temperament data demo with nested databoxes

← Older revision		Revision as of 17:45, 16 March 2024
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			== Temperament databox ==
			Using [[User:FloraC/Temperament data]].

			=== Septimal meantone ===
			{{Main\|Septimal meantone}}
			{{Databox\|Temperament data\|defaultstate=expanded\|
			{{User:FloraC/Temperament data
			\| Subgroup = 2.3.5.7
			\| Comma list = 81/80, 126/125
			\| Mapping = {{mapping\| 1 0 -4 -13 \| 0 1 4 10 }}
			\| Mapping generators = ~2, ~3
			\| Wedgie = 1 4 10 4 13 12
			\| Optimal ET sequence = 12, 19, 31, 81, 112b, 143b
			\| Badness = 0.013707
			}}
			{{Databox\|[[Optimal tuning]]s:\|
			text=
			* [[TE]]: ~2 = 1201.242, ~3/2 = 698.458
			* [[CTE]]: ~2 = 1200.000, ~3/2 = 696.952
			* [[POTE]]: ~2 = 1200.000, ~3/2 = 696.495
			}}}}

	== HEJI2Text testing area ==		== HEJI2Text testing area ==
	{\| class="wikitable center-all"		{\| class="wikitable center-all"

Fredg999: /* HEJI2Text testing area */ Test new Template:HEJI

2024-01-01T08:29:14Z

HEJI2Text testing area: Test new Template:HEJI

← Older revision		Revision as of 08:29, 1 January 2024
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	== HEJI2Text testing area ==		== HEJI2Text testing area ==
	{\| class="wikitable center-all"		{\| class="wikitable center-all"
	\|+ 8:16 scale on E~~<span class="heji">~~e~~</span>~~		\|+ 8:16 scale on E{{HEJI\|e}}
	! HEJI (normal)		! HEJI (normal)
	! Ratio		! Ratio
	! HEJI (big)		! HEJI (big)
	\|-		\|-
	\| ~~<span class="heji">~~e~~</span>~~E		\| {{HEJI\|e}}E
	\| 1/1		\| 1/1
	\| <big>~~<span class="heji">~~e~~</span>~~E</big>		\| <big>{{HEJI\|e}}E</big>
	\|-		\|-
	\| ~~<span class="heji">~~n~~</span>~~F		\| {{HEJI\|n}}F
	\| 9/8		\| 9/8
	\| <big>~~<span class="heji">~~n~~</span>~~F</big>		\| <big>{{HEJI\|n}}F</big>
	\|-		\|-
	\| ~~<span class="heji">~~m~~</span>~~G		\| {{HEJI\|m}}G
	\| 5/4		\| 5/4
	\| <big>~~<span class="heji">~~m~~</span>~~G</big>		\| <big>{{HEJI\|m}}G</big>
	\|-		\|-
	\| ~~<span class="heji">~~4e~~</span>~~A		\| {{HEJI\|4e}}A
	\| 11/8		\| 11/8
	\| <big>~~<span class="heji">~~4e~~</span>~~A</big>		\| <big>{{HEJI\|4e}}A</big>
	\|-		\|-
	\| ~~<span class="heji">~~e~~</span>~~B		\| {{HEJI\|e}}B
	\| 3/2		\| 3/2
	\| <big>~~<span class="heji">~~e~~</span>~~B</big>		\| <big>{{HEJI\|e}}B</big>
	\|-		\|-
	\| ~~<span class="heji">~~0~~</span>~~C		\| {{HEJI\|0}}C
	\| 13/8		\| 13/8
	\| <big>~~<span class="heji">~~0~~</span>~~C</big>		\| <big>{{HEJI\|0}}C</big>
	\|-		\|-
	\| ~~<span class="heji"><~~e~~</span>~~D		\| {{HEJI\|e}}D
	\| 7/4		\| 7/4
	\| <big>~~<span class="heji"><~~e~~</span>~~D</big>		\| <big>{{HEJI\|e}}D</big>
	\|-		\|-
	\| ~~<span class="heji">~~m~~</span>~~D		\| {{HEJI\|m}}D
	\| 15/8		\| 15/8
	\| <big>~~<span class="heji">~~m~~</span>~~D</big>		\| <big>{{HEJI\|m}}D</big>
	\|-		\|-
	\| ~~<span class="heji">~~e~~</span>~~E		\| {{HEJI\|e}}E
	\| 2/1		\| 2/1
	\| <big>~~<span class="heji">~~e~~</span>~~E</big>		\| <big>{{HEJI\|e}}E</big>
	\|}		\|}

Fredg999: Five pillars moved to main namespace

2023-12-28T16:46:24Z

Five pillars moved to main namespace

← Older revision		Revision as of 16:46, 28 December 2023
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	~~== Five pillars ==~~
	~~{{Wikipedia\|Wikipedia:Five pillars}}~~
	~~The fundamental principles of the [[Xenharmonic Wiki]] may be summarized in five "pillars", derived from those of {{w\|Wikipedia}}:~~

	~~=== The Xenharmonic Wiki is a specialized encyclopedia ===~~
	The Xenharmonic Wiki is a '''complementary resource to Wikipedia'''; in that sense, the scope of the Xenharmonic Wiki can be compared to that of wikis hosted on websites such as Fandom in that they are specialized encyclopedias, whereas Wikipedia is a general-purpose encyclopedia with stricter guidelines regarding its content and structure (see {{w\|WP:5P1}}).

	~~=== The Xenharmonic Wiki is written from a neutral point of view ===~~
	Almost the same as Wikipedia: {{w\|WP:5P2}}. The main difference is that '''original research is allowed on the Xenharmonic Wiki'''. There are a number of [[Conventions#Original research\|conventions]] in place to help readers distinguish between established ideas or terms and emergent ones. In addition, some pages are dedicated to editors' personal experiences, interpretations and opinions on various matters, and such pages should always be identifiable as such.

	~~=== The Xenharmonic Wiki is free content that anyone can use, edit, and distribute ===~~
	~~Same as Wikipedia: {{w\|WP:5P3}}~~

	~~=== The Xenharmonic Wiki's editors should treat each other with respect and civility ===~~
	~~Same as Wikipedia: {{w\|WP:5P4}}~~

	~~=== The Xenharmonic Wiki has no firm rules ===~~
	~~Same as Wikipedia: {{w\|WP:5P5}}~~

	== HEJI2Text testing area ==		== HEJI2Text testing area ==
	{\| class="wikitable center-all"		{\| class="wikitable center-all"