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	<updated>2026-06-16T02:45:20Z</updated>
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	<entry>
		<id>https://en.xen.wiki/index.php?title=Help:Redirect&amp;diff=231966</id>
		<title>Help:Redirect</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Help:Redirect&amp;diff=231966"/>
		<updated>2026-06-08T03:28:47Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Redirect to Category:All redirect categories using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;#REDIRECT [[Help:Editing#Redirects]]&lt;br /&gt;
&lt;br /&gt;
[[Category:All redirect categories]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
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	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Smart_redirect&amp;diff=231965</id>
		<title>Category:Smart redirect</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Smart_redirect&amp;diff=231965"/>
		<updated>2026-06-08T03:28:47Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Redirect to Category:All redirect categories using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;Smart redirects&#039;&#039;&#039; take one click more than normal [[Help:Editing#Redirects|redirects]] and are therefore easier to expand.&lt;br /&gt;
&lt;br /&gt;
The content is at minimum &#039;&#039;See Some other page&#039;&#039;. Sometimes it will appropriate to clarify the relation between its lemma and the referred page in a whole sentence.&lt;br /&gt;
&lt;br /&gt;
[[Category:All redirect categories]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Category_redirect&amp;diff=231964</id>
		<title>Category:Category redirect</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Category_redirect&amp;diff=231964"/>
		<updated>2026-06-08T03:28:47Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Redirect to Category:All redirect categories using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;Category redirects&#039;&#039;&#039; are used in place of normal [[Help:Editing#Redirects|redirects]] to give additional instructions that are specific to category redirects.&lt;br /&gt;
&lt;br /&gt;
These categories should be empty. Additionally, administrators may delete them if they are no longer necessary.&lt;br /&gt;
&lt;br /&gt;
[[Category:All redirect categories]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Redirects_to_project_namespace&amp;diff=231960</id>
		<title>Category:Redirects to project namespace</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Redirects_to_project_namespace&amp;diff=231960"/>
		<updated>2026-06-08T03:25:47Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Redirects to Category:All redirect categories using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[Category:All redirect categories]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Redirects_from_shortcuts&amp;diff=231959</id>
		<title>Category:Redirects from shortcuts</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Redirects_from_shortcuts&amp;diff=231959"/>
		<updated>2026-06-08T03:25:47Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Redirects to Category:All redirect categories using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[Category:All redirect categories]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Xenharmonic_Wiki:Manual_of_Style/Temperament_pages&amp;diff=231950</id>
		<title>Xenharmonic Wiki:Manual of Style/Temperament pages</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Xenharmonic_Wiki:Manual_of_Style/Temperament_pages&amp;diff=231950"/>
		<updated>2026-06-08T03:18:15Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Xenharmonic Wiki to Category:Xenharmonic Wiki guidelines using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This is a &#039;&#039;&#039;style guide for temperament pages&#039;&#039;&#039;. &lt;br /&gt;
&lt;br /&gt;
For guidance on how to expand or improve existing pages, this page&#039;s sections provide on what to include, and how to name each section. Sections should be added &#039;&#039;as needed&#039;&#039;. Sections in &#039;&#039;italics&#039;&#039; do not denote actual sections, but rather items to add in addition to existing sections or outside of any section. &lt;br /&gt;
&lt;br /&gt;
{{Note| As this guide cannot account for every possible use case, editors are advised to use their best judgment on what to add or not. Additionally, nothing about this guide is set in stone; this guide can (and should!) be updated to fit current developments regarding temperament pages. }}&lt;br /&gt;
&lt;br /&gt;
== &#039;&#039;Introduction&#039;&#039; ==&lt;br /&gt;
This precedes the first section. It should open with [[Template: Infobox regtemp]]. It should include a verbal description that uniquely identifies the temperament in question, preferably in the first paragraph. It must end with a link to the corresponding technical data page for the temperament, as well as a link to the dedicated page for extensions if there is one. &lt;br /&gt;
&lt;br /&gt;
== Theory ==&lt;br /&gt;
=== Interval chain &#039;&#039;or&#039;&#039; interval lattice ===&lt;br /&gt;
An interval chain table should be used for rank-2 temperaments. An interval lattice diagram should be used for rank-3 temperaments. &lt;br /&gt;
&lt;br /&gt;
=== As a detemperament of &#039;&#039;n&#039;&#039;-et ===&lt;br /&gt;
If there is a small equal temperament fit for detempering, this subsection may be added. &lt;br /&gt;
&lt;br /&gt;
=== Notation ===&lt;br /&gt;
Discussion on the notations for the temperament may be added here. &lt;br /&gt;
&lt;br /&gt;
=== Chords and harmony ===&lt;br /&gt;
Discussion on the chords and harmony available in the temperament may be added here. &lt;br /&gt;
&lt;br /&gt;
== Scales ==&lt;br /&gt;
Discussion on the scales available in the temperament as well as links to scala file pages may be added here&lt;br /&gt;
&lt;br /&gt;
== Tunings ==&lt;br /&gt;
This section admits the following subsections: &lt;br /&gt;
* Norm-based tunings: tables for &#039;&#039;p&#039;&#039;-limit norm-based tunings may be added here. &lt;br /&gt;
* Target tunings: tables for &#039;&#039;q&#039;&#039;-odd-limit minimax, least squares, and minimean tunings, and for DR and equal beating tunings may be added here. &lt;br /&gt;
* Tuning spectrum: a table that list edo tunings and eigenmonzo tunings by generator size may be added here. &lt;br /&gt;
&lt;br /&gt;
== Instruments ==&lt;br /&gt;
A gallery of instrument designs may be added here. &lt;br /&gt;
&lt;br /&gt;
== Music ==&lt;br /&gt;
Links to music may be added here. &lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
Links to other pages may be added here. &lt;br /&gt;
&lt;br /&gt;
== External links ==&lt;br /&gt;
Links to outside-wiki resources regarding the temperament and/or its tunings may be added here. &lt;br /&gt;
&lt;br /&gt;
== References ==&lt;br /&gt;
If any works are cited, add them here. &lt;br /&gt;
&lt;br /&gt;
== &#039;&#039;Categories&#039;&#039; ==&lt;br /&gt;
This succeeds the last section. The following categories should be added here: &lt;br /&gt;
* The eponymous category&lt;br /&gt;
* Category: rank-&#039;&#039;r&#039;&#039; temperaments, where &#039;&#039;r&#039;&#039; is the rank of the temperament&lt;br /&gt;
&lt;br /&gt;
The following categories should be added here if applicable: &lt;br /&gt;
* Category: Exotemperaments or Category: Microtemperaments&lt;br /&gt;
* Category: Subgroup temperaments&lt;br /&gt;
* Categories for the temperament families, clans, or collections the temperament belongs to. &lt;br /&gt;
&lt;br /&gt;
== &#039;&#039;Other sections&#039;&#039; ==&lt;br /&gt;
* Extensions&lt;br /&gt;
* Rank-(&#039;&#039;r&#039;&#039; + 1) temperaments&lt;br /&gt;
* Non-octave settings&lt;br /&gt;
* History, terminology or etymology&lt;br /&gt;
* Diagrams&lt;br /&gt;
&lt;br /&gt;
[[Category:Xenharmonic Wiki guidelines]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Xenharmonic_Wiki:Manual_of_Style/Temperament_cataloging&amp;diff=231949</id>
		<title>Xenharmonic Wiki:Manual of Style/Temperament cataloging</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Xenharmonic_Wiki:Manual_of_Style/Temperament_cataloging&amp;diff=231949"/>
		<updated>2026-06-08T03:18:14Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Xenharmonic Wiki to Category:Xenharmonic Wiki guidelines using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This is a &#039;&#039;&#039;guide for where to put and/or find temperament data&#039;&#039;&#039;. &lt;br /&gt;
&lt;br /&gt;
{{Note| As this guide cannot account for all edge cases, editors are advised to use their best judgement on where to put and/or find temperament data. Additionally, nothing about this guide is set in stone; this guide can (and should!) be updated to fit current developments regarding temperament pages. }}&lt;br /&gt;
&lt;br /&gt;
== General rules ==&lt;br /&gt;
Avoid duplication. A temperament should be catalogued exactly once on the wiki. &lt;br /&gt;
&lt;br /&gt;
== Families, clans, and collections ==&lt;br /&gt;
{{Main| Temperament families and clans }}&lt;br /&gt;
&lt;br /&gt;
A family has a head that is a full-prime-limit temperament. A clan has a head that is a subgroup temperament. Family and clan pages should both be titled after the full-prime-limit temperament. Rarely, a clan may be referred to by the name of the subgroup temperament + family. For example: &lt;br /&gt;
* Archytas family is the rank-3 family of 2.3.5.7 {64/63}; &lt;br /&gt;
* Archytas clan is the rank-2 clan of 2.3.7 {64/63}. &lt;br /&gt;
** &#039;&#039;Archy family&#039;&#039; is an alias of &#039;&#039;archytas clan&#039;&#039;. &lt;br /&gt;
&lt;br /&gt;
Temperament families and clans should only be created when the head temperament is notable by itself, has multiple branches to higher limits, and for the sake of navigability, is within rank-2 to rank-4. The head temperament should be one of the 7-limit tri-prime subgroups (2.3.5, 2.3.7, 2.5.7, and 3.5.7) for rank-2, the 11-limit analog for rank-3, or the 13-limit analog for rank-4. &lt;br /&gt;
&lt;br /&gt;
Besides families and clans, there are pages that collect temperaments of a certain comma on this wiki. These pages are for temperaments one rank lower than its corresponding family, and are used because some temperaments are more closely associated with the comma than any other or otherwise do not belong to any notable family or clan. &lt;br /&gt;
&lt;br /&gt;
Temperament families, clans, and collections are the bread and butter for documenting individual temperaments on this wiki. Temperament data should be placed there whenever applicable. The specific hierarchy of priority is explained as follows. &lt;br /&gt;
&lt;br /&gt;
If a temperament belongs to an existing family or clan, or one that is supposed to exist according to the rules above, consider putting it there. If a temperament belongs to multiple families or clans, determine if it is a [[strong extension]] of the head of each and put it where it is a strong extension of the head. A strong extension is an extension where the generators are not split; it is generally the preferred place for the temperament since the relation between the temperament in question and the head is most clear. And if a temperament is zero or multiple strong extensions at the same time, it may be placed in the family or clan of the simpler subgroup or the simpler head, depending on which is more relevant. &lt;br /&gt;
&lt;br /&gt;
Otherwise, it should be placed in a collection page of the simplest comma tempered out in the temperament. &lt;br /&gt;
&lt;br /&gt;
For example: &lt;br /&gt;
* Hemiwürschmidt is found in Hemimean clan, &#039;&#039;not&#039;&#039; Würschmidt family, since it is a strong extension of didacus, the head of the hemimean clan, and only a weak extension of würschmidt; &lt;br /&gt;
* Dominant is found in Meantone family, since 2.3.5 is simpler than 2.3.7, but schism is found in Archytas clan, since the archytas comma is more &amp;quot;structural&amp;quot; to the temperament. &lt;br /&gt;
&lt;br /&gt;
However, no-2 or no-3 clans should be treated just like collections, since the relation between the members and the head is often not obvious there. &lt;br /&gt;
&lt;br /&gt;
For example: &lt;br /&gt;
* Sensi is found in Sensipent family, &#039;&#039;not&#039;&#039; Sensamagic clan; &lt;br /&gt;
* Miracle is found in Gamelismic clan, &#039;&#039;not&#039;&#039; Quince clan. &lt;br /&gt;
&lt;br /&gt;
== Other pages ==&lt;br /&gt;
=== Very high/low accuracy temperaments ===&lt;br /&gt;
The criteria of inclusion for these pages are given in the introductions. Currently no [[badness]] constraint is in effect but in future there might be. The head of each entry should only be temperaments of the 7-limit tri-prime subgroups for rank-2, the 11-limit analog for rank-3, or the 13-limit analog for rank-4. Extensions may be put there if they meet the criteria above. &lt;br /&gt;
&lt;br /&gt;
=== Equivalence continua ===&lt;br /&gt;
Equivalence continua only hold temperament data of the particular subgroup they are defined in. An equivalence continuum for an equal temperament should only be created if the equal temperament is special in some way, e.g., it is a record 5-limit temperament. Any rank-2 temperament of a 7-limit tri-prime subgroup which does not fit in a family or clan should be placed in an equivalence continuum, when applicable. &lt;br /&gt;
&lt;br /&gt;
=== Miscellaneous 5-limit/7-limit temperaments and catalog of rank-4 temperaments ===&lt;br /&gt;
The pages Miscellaneous 5-limit temperaments and Miscellaneous 7-limit temperaments hold temperament data of the particular limit given in the title, for rank-2 and rank-3 temperaments, respectively. &lt;br /&gt;
&lt;br /&gt;
Any 5-limit rank-2 temperament which does not fit in a family, nor an equivalence continuum, should go to Miscellaneous 5-limit temperaments. Any 7-limit rank-3 temperament which does not fit in a family should go to Miscellaneous 7-limit temperaments. Any 11-limit rank-4 temperament as well as their extensions which does not fit in a family should go to Catalog of rank-4 temperaments. &lt;br /&gt;
&lt;br /&gt;
=== Subgroup temperaments ===&lt;br /&gt;
Subgroup temperament pages include Subgroup temperaments and the various No-&#039;&#039;p&#039;&#039;&#039;s subgroup temperaments. Any subgroup temperament should go here unless they fit any of the above categories. &lt;br /&gt;
&lt;br /&gt;
=== Fractional-octave temperaments and comma pages ===&lt;br /&gt;
Unless necessary, putting temperament data in these pages should generally be avoided. Fractional-octave temperament pages have poor discoverability, whereas temperament data in comma pages tend to be intrusive for average readers.&lt;br /&gt;
&lt;br /&gt;
[[Category:Xenharmonic Wiki guidelines]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Xenharmonic_Wiki:Manual_of_Style/MOS_pages&amp;diff=231948</id>
		<title>Xenharmonic Wiki:Manual of Style/MOS pages</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Xenharmonic_Wiki:Manual_of_Style/MOS_pages&amp;diff=231948"/>
		<updated>2026-06-08T03:18:14Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Xenharmonic Wiki to Category:Xenharmonic Wiki guidelines using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{mbox|text=This page is maintained by [[Xenharmonic Wiki:WikiProject Mospage|Project Mospage]].}}&lt;br /&gt;
&lt;br /&gt;
{{Infobox MOS|Tuning=5L 2s|debug=1}}&lt;br /&gt;
This is a &#039;&#039;&#039;style guide for mos pages&#039;&#039;&#039;.&lt;br /&gt;
&lt;br /&gt;
The minimum templates for a mos page, for a page that can be considered a stub or otherwise has very little information, is the following:&lt;br /&gt;
&lt;br /&gt;
* [[Template:Infobox MOS|Infobox MOS]]; required, as it categorizes the page&lt;br /&gt;
* [[Template:MOS intro|MOS intro]]; recommended&lt;br /&gt;
* [[Template:MOS intervals|MOS intervals]]; optional, but recommended for small mosses (no more than around 10 notes)&lt;br /&gt;
* [[Template:MOS modes|MOS modes]]; optional, but recommended for small mosses (no more than around 10 notes)&lt;br /&gt;
* [[Template:MOS tuning spectrum|MOS tuning spectrum]]; recommended&lt;br /&gt;
&lt;br /&gt;
For guidance on how to expand or improve existing pages, this page&#039;s sections provide on what to include, and how to name each section. Sections should be added &#039;&#039;as needed&#039;&#039;. Sections in &#039;&#039;italics&#039;&#039; do not denote actual sections, but rather items to add in addition to existing sections or outside of any section. This page uses 5L&amp;amp;nbsp;2s as its running example.&lt;br /&gt;
&lt;br /&gt;
Scale name is included in the lead section rather than its own section, since the main focus of a mos page is &#039;&#039;what it is&#039;&#039;, not &#039;&#039;what it&#039;s called&#039;&#039;. For TAMNAMS-named scales, this is accomplished using the [[Template:TAMNAMS name|TAMNAMS name]] template; in most cases, this is enough information. A name section &#039;&#039;may&#039;&#039; be added if there are contentious names (EG, misnomers), or an in-depth explanation is needed, but for TAMNAMS-named scales, the template already includes either further reasoning or a link to said reasoning.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Disclaimer&#039;&#039;&#039;: as this guide cannot account for every possible use case, editors are advised to use their best judgment on what to add or not. Additionally, nothing about this guide is set in stone; this guide can (and should!) be updated to fit current developments regarding mos pages.&lt;br /&gt;
&lt;br /&gt;
== &#039;&#039;Lead section&#039;&#039; (precedes the first section) ==&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
{{Infobox MOS}}&lt;br /&gt;
{{MOS intro}}&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
The lead section should, at the minimum, consist of [[Template:Infobox MOS]] and the [[Template:MOS intro]]. To ensure proper order of templates when viewed on mobile devices, the infobox should be placed before the intro. Hatnotes should be placed before the infobox. The mos intro is as follows:&lt;br /&gt;
&lt;br /&gt;
{{MOS intro|Scale Signature=5L 2s}}&lt;br /&gt;
Other important info can include the following:&lt;br /&gt;
&lt;br /&gt;
* Whether the mos can be thought of a warping of another, more familiar mos or edo. Examples:&lt;br /&gt;
** 4L&amp;amp;nbsp;3s can be seen as a warped diatonic scale (5L&amp;amp;nbsp;2s), where one large step is replaced with a small step.&lt;br /&gt;
** 5L&amp;amp;nbsp;1s can be seen as the equal-tempered whole-tone scale (6edo) but with one step that is larger than the others.&lt;br /&gt;
* Usage, discovery, and noteworthy temperaments the mos corresponds to.&lt;br /&gt;
* Under what conditions is the mos proper. This is only recommended for mosses with notable near-mos forms, as this information is included in the intro already.&lt;br /&gt;
Sections that would be otherwise too short, such as temperament-related information, can be added in the lead section instead.&lt;br /&gt;
&lt;br /&gt;
What the mos is referred to may also be included here. Names that see common use should be added here; proposed names are assumed to be idiosyncratic until proven otherwise.&lt;br /&gt;
&lt;br /&gt;
Subsections for this follow the format for TAMNAMS, in which the following are described in their own subsections:&lt;br /&gt;
&lt;br /&gt;
== Scale properties ==&lt;br /&gt;
=== Intervals ===&lt;br /&gt;
The use of TAMNAMS is advised for describing the names of its intervals and scale degrees. The mos intervals template gives ranges for each of the intervals present in the mos.&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
{{MOS intervals}}&lt;br /&gt;
&amp;lt;/pre&amp;gt;{{MOS intervals|Scale Signature=5L 2s}}&lt;br /&gt;
&lt;br /&gt;
=== Modes ===&lt;br /&gt;
Listings of the scale&#039;s modes, or rotations of its step patterns, are added here. This can include mode names in use by the general community. Names that have not received use by the broader community use should be treated as idiosyncratic, and if applicable, the person who had proposed the names should be stated. Example: &#039;&#039;person-name&#039;&#039; has proposed/advocated for the following names...&lt;br /&gt;
&lt;br /&gt;
Listing mode names &#039;&#039;specific&#039;&#039; to a tuning or temperament is not advised. Linking to such mode names is allowed.&amp;lt;pre&amp;gt;&lt;br /&gt;
{{MOS modes}}&lt;br /&gt;
&amp;lt;/pre&amp;gt;{{MOS modes|Scale Signature=5L 2s}}&lt;br /&gt;
&lt;br /&gt;
Scale degree qualities (major, minor, etc) can be show using the template shown.&amp;lt;pre&amp;gt;&lt;br /&gt;
{{MOS mode degrees}}&lt;br /&gt;
&amp;lt;/pre&amp;gt;{{MOS mode degrees|Scale Signature=5L 2s}}&lt;br /&gt;
&lt;br /&gt;
== Theory ==&lt;br /&gt;
Subsections include:&lt;br /&gt;
&lt;br /&gt;
* Low harmonic entropy scales&lt;br /&gt;
* Temperament interpretations&lt;br /&gt;
Other subsections include:&lt;br /&gt;
&lt;br /&gt;
* Any theory described by musicians/theorists&lt;br /&gt;
* Tetrachordal analysis or similar&lt;br /&gt;
&lt;br /&gt;
== Tuning ranges ==&lt;br /&gt;
Discussions about specific tuning ranges, and what JI ratios are approximated, can be given. Hatnotes to appropriate temperament pages are also advised.&lt;br /&gt;
&lt;br /&gt;
Tuning ranges include:&lt;br /&gt;
&lt;br /&gt;
* &#039;&#039;&#039;Simple tunings&#039;&#039;&#039; - Step ratios 2:1, 3:1, and 3:2&lt;br /&gt;
* &#039;&#039;&#039;Soft-of-basic&#039;&#039;&#039; &#039;&#039;&#039;tunings&#039;&#039;&#039; - Step ratios softer than 2:1&lt;br /&gt;
* &#039;&#039;&#039;Hard-of-basic&#039;&#039;&#039; &#039;&#039;&#039;tunings&#039;&#039;&#039; - Step ratios harder than 2:1&lt;br /&gt;
&lt;br /&gt;
Sections for smaller ranges can be used instead. Such ranges include:&lt;br /&gt;
* &#039;&#039;&#039;Ultrasoft tunings&#039;&#039;&#039; - Step ratio tunings between 1:1 to 4:3&lt;br /&gt;
* &#039;&#039;&#039;Parasoft tunings&#039;&#039;&#039; - Step ratio tunings between 4:3 to 3:2&lt;br /&gt;
* &#039;&#039;&#039;Hyposoft tunings&#039;&#039;&#039; - Step ratio tunings between 3:2 to 2:1, which can be split even further if needed:&lt;br /&gt;
** &#039;&#039;&#039;Quasisoft tunings&#039;&#039;&#039; - Step ratio tunings between 3:2 to 5:3&lt;br /&gt;
** &#039;&#039;&#039;Minisoft tunings&#039;&#039;&#039; - Step ratio tunings between 5:3 to 2:1&lt;br /&gt;
* &#039;&#039;&#039;Hypohard tunings&#039;&#039;&#039; - Step ratio tunings between 2:1 to 3:1, which can be split even further if needed:&lt;br /&gt;
** &#039;&#039;&#039;Minihard tunings&#039;&#039;&#039; - Step ratio tunings between 2:1 to 5:2&lt;br /&gt;
** &#039;&#039;&#039;Quasihard tunings&#039;&#039;&#039; - Step ratio tunings between 5:2 to 3:1&lt;br /&gt;
* &#039;&#039;&#039;Parahard tunings&#039;&#039;&#039; - Step ratio tunings between 3:1 to 4:1&lt;br /&gt;
* &#039;&#039;&#039;Ultrahard tunings&#039;&#039;&#039; - Step ratio tunings between 4:1 to 1:0&lt;br /&gt;
&lt;br /&gt;
The mos tunings template shows cent values for varying step ratios.&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
{{MOS tunings|Step Ratio=2/1; 3/1; 3/2}}&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
{{MOS tunings|Step Ratio=2/1; 3/1; 3/2|Scale Signature=5L 2s}}&lt;br /&gt;
&lt;br /&gt;
== Scales ==&lt;br /&gt;
Links to scala file pages can be added here, as well as links to pages regarding step variations (typically modmos scales) of the mos.&lt;br /&gt;
&lt;br /&gt;
== Scale tree ==&lt;br /&gt;
The tuning spectrum template (or scale tree) can be provided using the corresponding template. A handmade table can also be used if the template is found too limiting, such as by substituting the template.&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
{{MOS tuning spectrum}}&lt;br /&gt;
&amp;lt;/pre&amp;gt;{{MOS tuning spectrum|Scale Signature=5L 2s}}&lt;br /&gt;
&lt;br /&gt;
== Music ==&lt;br /&gt;
Links to music can be added here.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
Links to other pages can be added here.&lt;br /&gt;
&lt;br /&gt;
== External links ==&lt;br /&gt;
Links to outside-wiki resources regarding the mos and/or its tunings can be added here.&lt;br /&gt;
&lt;br /&gt;
== References ==&lt;br /&gt;
If any works are cited, add them here.&lt;br /&gt;
&lt;br /&gt;
== &#039;&#039;Categories&#039;&#039; (succeeds the last section) ==&lt;br /&gt;
The mos infobox automatically categorizes the mos by note count and under the category of abstract mos patterns. Any other categories can be added here.&lt;br /&gt;
&lt;br /&gt;
== &#039;&#039;Other sections not discussed here&#039;&#039; ==&lt;br /&gt;
* Gallery - recommended location is before Music&lt;br /&gt;
* Notation - recommended location is after Intervals. Notation schemes shouldn&#039;t be added unless it has notable use by multiple composers or its use is ubiquitous, as with 5L 2s. If there are multiple notation schemes, this section may be made into a subpage, though this should be a last resort.&lt;br /&gt;
* Approaches&lt;br /&gt;
* Genchain&lt;br /&gt;
* Trivia&lt;br /&gt;
&lt;br /&gt;
[[Category:Xenharmonic Wiki guidelines]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Quartertone&amp;diff=209227</id>
		<title>Quartertone</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Quartertone&amp;diff=209227"/>
		<updated>2025-09-03T21:08:36Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;A &#039;&#039;&#039;quartertone&#039;&#039;&#039; or &#039;&#039;&#039;quarter tone&#039;&#039;&#039; is an [[interval]] which is similar in size to a single step of [[24edo]], which is 50 [[cents]]. This makes &amp;quot;quartertone&amp;quot; an [[interval region]], similar to &amp;quot;seventh&amp;quot; or &amp;quot;major third&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
== Properties ==&lt;br /&gt;
In harmony, quarter tones tend to be perceived as [[dissonant]]. As such, the [[harmonic entropy]] model is generally tuned to portray them as having the highest harmonic entropy of any interval. In melody, they tend to produce a &amp;quot;bending&amp;quot; or &amp;quot;melting&amp;quot; effect. Due to this effect, they are often used as grace notes to smoothen and add color to the transition between more distant intervals.&lt;br /&gt;
&lt;br /&gt;
In the classical and folk traditions of [[Arabic, Turkish, Persian|Arabia]], [[Indian|North India]], [[Indian|South India]], [[Arabic, Turkish, Persian|Iran]] and [[Arabic, Turkish, Persian|Turkey]], quartertones are not used as melodic intervals in their own right, but they are used as critical building blocks of larger melodic units. They are particularly used to build [[neutral]] intervals such as neutral seconds and neutral thirds (it should be noted that each of these traditions has multiple flavors of major, minor and neutral seconds, thirds, etc.)&lt;br /&gt;
&lt;br /&gt;
In [[regular temperament]] theory and [[equal tuning]] theory, quartertones are sometimes used as melodic intervals in their own right, or sometimes not, depending which temperament is being used. In [[superpyth]] temperament for example, quartertones are usually treated as substantial melodic steps. By contrast, [[meantone]] usually treats them as only structural units for building larger neutral intervals. This difference may be due to how early or late quartertones appear on the [[generator]] chain (early in superpyth, late in meantone).&lt;br /&gt;
&lt;br /&gt;
== Upper and lower bounds ==&lt;br /&gt;
&amp;quot;Quartertone&amp;quot; is a slightly blurry region.&lt;br /&gt;
&lt;br /&gt;
It is not clear exactly what a &amp;quot;tone&amp;quot; is (what this interval should be a quarter &#039;&#039;of&#039;&#039;). The most often used definition is a step of [[6edo]], which is 200 cents: the standard 12edo whole tone. However, the [[just]] whole tone, [[9/8]] (203.9 cents), could also be used, which would make the &#039;average&#039; quarter tone 51 rather than 50 cents.&lt;br /&gt;
&lt;br /&gt;
The lower bound of the &amp;quot;quartertone&amp;quot; region might be somewhere around 40 cents: below this, intervals become more like a &amp;quot;fifth tone&amp;quot; or &amp;quot;sixth tone&amp;quot;. The upper bound might be somewhere around 60 cents: above this, intervals become more like a &amp;quot;third tone&amp;quot;. &lt;br /&gt;
&lt;br /&gt;
Though, it is also possible to call all of the above &amp;quot;quartertone&amp;quot; and make the bounds much wider: something in the ball park of 30 cents to 70 cents.&lt;br /&gt;
&lt;br /&gt;
== Examples ==&lt;br /&gt;
The [[EDO]]s: {{EDOs|21, 22, 23, 24, 25, 26, 27, 28 &amp;amp; 29}} use a quartertone as their smallest step size. EDOs slightly larger or smaller are sometimes argued to do the same. This makes quartertones structurally important to those EDOs. They may sometimes also be used as melodic intervals depending on the approach taken.&lt;br /&gt;
&lt;br /&gt;
24edo is sometimes called &amp;quot;&#039;&#039;&#039;the quartertone scale&#039;&#039;&#039;&amp;quot; or &amp;quot;&#039;&#039;&#039;the quarter tone scale&#039;&#039;&#039;&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
A sampling of just intervals that sit towards the middle of the quartertone range: [[36/35]], [[100/97]], [[33/32]].&lt;br /&gt;
&lt;br /&gt;
A sampling of just intervals that sit towards the outskirts of the quartertone range: [[50/49]], [[49/48]], [[45/44]], [[128/125]], [[28/27]], [[27/26]], [[25/24]], [[23/22]].&lt;br /&gt;
&lt;br /&gt;
[[Category:Interval regions]]&lt;br /&gt;
[[Category:Quartertone]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Navatone&amp;diff=209226</id>
		<title>Navatone</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Navatone&amp;diff=209226"/>
		<updated>2025-09-03T21:08:31Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;The &#039;&#039;&#039;navatone&#039;&#039;&#039; is the name of a musical interval that is made up of nine [[Tone|whole tones]]. The term is also used to refer to any pitch in the neighborhood of 1800{{cent}}, or any interval which is one [[octave]] above a [[tritone]].&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|+Some commonly used navatones&lt;br /&gt;
!Ratios&lt;br /&gt;
![[Prime limit]]&lt;br /&gt;
|-&lt;br /&gt;
|[[45/16]], [[25/9]]&lt;br /&gt;
|5&lt;br /&gt;
|-&lt;br /&gt;
|[[20/7]], [[14/5]]&lt;br /&gt;
|7&lt;br /&gt;
|-&lt;br /&gt;
|[[17/6]]&lt;br /&gt;
|17&lt;br /&gt;
|-&lt;br /&gt;
|[[23/8]]&lt;br /&gt;
|23&lt;br /&gt;
|-&lt;br /&gt;
|[[31/11]]&lt;br /&gt;
|31&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
== Etymology ==&lt;br /&gt;
&#039;&#039;&#039;Nava-&#039;&#039;&#039; is the Sanskrit numeral prefix for nine.&lt;br /&gt;
&lt;br /&gt;
[[Category:Interval regions]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Gentle_region_(extended_version)&amp;diff=209225</id>
		<title>Gentle region (extended version)</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Gentle_region_(extended_version)&amp;diff=209225"/>
		<updated>2025-09-03T21:08:31Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;This is an extended version of the &#039;&#039;&#039;[[Gentle_region|Gentle region]] article.&#039;&#039;&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
-----&lt;br /&gt;
[[Margo_Schulter|Margo Schulter]], in a [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_105200.html#105202 tuning list posting], defined the &amp;quot;gentle region&amp;quot; of temperaments with a fifth as generator as that of fifths about 1.49 to 2.65 cents sharp; later [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_106239.html#106239 amending that] to from 1.49 to 3.04 cents sharp.&lt;br /&gt;
&lt;br /&gt;
Gentle-tempered tone systems are thus &amp;quot;mild&amp;quot; (or, as the name says, &amp;quot;gentle&amp;quot;) versions of [[Superpyth]] temperament. They allow harmony in the style of medieval Pythagorean harmony, usable for &amp;quot;Neo-gothic&amp;quot; harmony systems; besides, they are possible temperament frameworks for [[Arabic, Turkish, Persian| middle-eastern (Arabic, Turkish, Persian)]] tuning systems, with the special property of delivering a common framework for both Arabic and Turkish music, differing in the degree of tempering. When the tempering of the fifth is &amp;quot;very gentle&amp;quot;/near-just, the interval notated as C-Fb in standard sheet notation (8 fifths down) will be close to a 5/4 major third, as used in Turkish music; while sharper tempering will give this interval the character of a neutral third, as important in Arabic music. (The interval notated as C-E will have the character of a larger Pythagorean—or super-Pythagorean—major third.)&lt;br /&gt;
&lt;br /&gt;
We can consider the first region to extend from fifths of size 17\29 to 64\109, and the extended region to reach 47\80. If we remove the restriction to tempering based on chains of fifths, we find that notable equal divisions in the smaller gentle region include multiples of {{EDOs| 29, 46, 75, 104, 109, 121, 145, 155, 162, 167, 179, 191, 201, 213, 225 and 237, plus 63 and 80 }} in the extended region.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! colspan=&amp;quot;2&amp;quot; | Generator&lt;br /&gt;
! Cents&lt;br /&gt;
! 2-3-7(b)-11-13(b)&lt;br /&gt;
! &amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0); display: block; text-align: center;&amp;quot;&amp;gt;&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0); display: block; text-align: center;&amp;quot;&amp;gt;Half 8/7+ 1\3 7/6&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0); display: block; text-align: center;&amp;quot;&amp;gt;1\3 8/7+ Half 7/6&amp;lt;/span&amp;gt;&amp;lt;/span&amp;gt;&amp;lt;/span&amp;gt;&lt;br /&gt;
! 8/7+7/6&lt;br /&gt;
! Notes&lt;br /&gt;
|-&lt;br /&gt;
| (7+10)\29&lt;br /&gt;
| &lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 289.655+413.793&lt;br /&gt;
| {{val| 29 46 81 100 107 }}&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 2\29+3\29&lt;br /&gt;
&lt;br /&gt;
82.759+124.138&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 6\29+6\29&lt;br /&gt;
&lt;br /&gt;
248.276+248.276&lt;br /&gt;
| &lt;br /&gt;
|-&lt;br /&gt;
| (25+36)\104&lt;br /&gt;
| &lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 288.4615+415.385&lt;br /&gt;
| {{val| 104 165 292 360 385 }}&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 5\52+&#039;&#039;23\312&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
115.385+&#039;&#039;88.4615&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0); text-align: start;&amp;quot;&amp;gt;&#039;&#039;5\78+23\208&#039;&#039;&amp;lt;/span&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0); text-align: start;&amp;quot;&amp;gt;&#039;&#039;76.923+132.692&#039;&#039;&amp;lt;/span&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 5\52+23\104&lt;br /&gt;
&lt;br /&gt;
230.769+265.385&lt;br /&gt;
| &lt;br /&gt;
|-&lt;br /&gt;
| (18+26)\75&lt;br /&gt;
| &lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 288+416&lt;br /&gt;
| &amp;amp;lt; 75 119 210~211 259 277| &lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 7\75+&#039;&#039;17\225&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
112+&#039;&#039;90.667&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0); text-align: start;&amp;quot;&amp;gt;&#039;&#039;14\225+17\150&#039;&#039;&amp;lt;/span&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0); text-align: start;&amp;quot;&amp;gt;&#039;&#039;74.667+136&#039;&#039;&amp;lt;/span&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 14\75+17\75&lt;br /&gt;
&lt;br /&gt;
224+272&lt;br /&gt;
| &lt;br /&gt;
|-&lt;br /&gt;
| &lt;br /&gt;
| (47+68)\196&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 287.755+416.3265&lt;br /&gt;
| &amp;amp;lt; 196 311 549-551 678 725| &lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | &#039;&#039;37\392+44\588&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;113.265+89.796&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0); text-align: start;&amp;quot;&amp;gt;&#039;&#039;37/588&#039;&#039;+11/98&amp;lt;/span&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0); text-align: start;&amp;quot;&amp;gt;&#039;&#039;75.51&#039;&#039;+134.694&amp;lt;/span&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 37/196+44/196&lt;br /&gt;
&lt;br /&gt;
226.531+269.388&lt;br /&gt;
| &lt;br /&gt;
|-&lt;br /&gt;
| &lt;br /&gt;
| &lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 287.713+416.382&lt;br /&gt;
| {{val| 29 46 81 100 107 }} + {{val| 46 73 129 159 170 }}&amp;lt;/span&amp;gt;&amp;lt;span style=&amp;quot;background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small; line-height: 1.5;&amp;quot;&amp;gt;φ&amp;lt;/span&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 119.283+85.7795&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0); display: block; text-align: center;&amp;quot;&amp;gt;79.522+128.769&amp;lt;/span&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 238.566+257.3385&lt;br /&gt;
| &lt;br /&gt;
|-&lt;br /&gt;
| &lt;br /&gt;
| (29+42)\121&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 287.603+416.529&lt;br /&gt;
| {{val| 121 192 339~340 419 448 }}&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | &#039;&#039;23\242&#039;&#039;+9\121&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;114.05&#039;&#039;+89.256&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0);&amp;quot;&amp;gt;&#039;&#039;23\363+27\242&#039;&#039;&amp;lt;/span&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0);&amp;quot;&amp;gt;&#039;&#039;76.033+133.884&#039;&#039;&amp;lt;/span&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 23\121+27\121&lt;br /&gt;
&lt;br /&gt;
228.099+267.769&lt;br /&gt;
| &lt;br /&gt;
|-&lt;br /&gt;
| &lt;br /&gt;
| &lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 287.267+416.978&lt;br /&gt;
| {{val| 29 46 81 100 107 }} + {{val| 109 173 306 377 403 }}&amp;lt;span style=&amp;quot;background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;&amp;quot;&amp;gt;φ&amp;lt;/span&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 116.8205+87.323&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0); display: block; text-align: center;&amp;quot;&amp;gt;78.617+130.984&amp;lt;/span&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 235.85+261.969&lt;br /&gt;
| &lt;br /&gt;
|-&lt;br /&gt;
| (11+16)\46&lt;br /&gt;
| &lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 286.9565+417.391&lt;br /&gt;
| {{val| 46 73 129 159 170 }}&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | &#039;&#039;9\92+5\69&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;117.391+86.9565&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0);&amp;quot;&amp;gt;3\46+5\46&amp;lt;/span&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0);&amp;quot;&amp;gt;78.261+130.435&amp;lt;/span&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 9\46+5\23&lt;br /&gt;
&lt;br /&gt;
234.783+260.87&lt;br /&gt;
| &lt;br /&gt;
|-&lt;br /&gt;
| &lt;br /&gt;
| &lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 286.587+417.884&lt;br /&gt;
| {{val| 29 46 81 100 107 }} + {{val| 63 100 177 218 233 }}&amp;lt;span style=&amp;quot;background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;&amp;quot;&amp;gt;φ&amp;lt;/span&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 117.925+88.626&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0); display: block; text-align: center;&amp;quot;&amp;gt;77.635+132.9395&amp;lt;/span&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 232.936+265.879&lt;br /&gt;
| &lt;br /&gt;
|-&lt;br /&gt;
| &lt;br /&gt;
| (48+70)\201&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 286.567+417.91&lt;br /&gt;
| {{val| 201 319 564 695 703 }}&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | &#039;&#039;13\134+44\603&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;116.418+87.56&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0);&amp;quot;&amp;gt;13\201+22\201&amp;lt;/span&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0);&amp;quot;&amp;gt;77.612+131.343&amp;lt;/span&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 39\201+44\201&lt;br /&gt;
&lt;br /&gt;
232.836+262.687&lt;br /&gt;
| &lt;br /&gt;
|-&lt;br /&gt;
| &lt;br /&gt;
| (37+54)\155&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 286.452+418.0645&lt;br /&gt;
| {{val| 155 246 435 536 573 }}&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 3\31+&#039;&#039;34\465&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
116.129+&#039;&#039;87.742&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0);&amp;quot;&amp;gt;2\31+17\155&amp;lt;/span&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0);&amp;quot;&amp;gt;77.419+131.613&amp;lt;/span&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 30\155+34\155&lt;br /&gt;
&lt;br /&gt;
232.258+263.226&lt;br /&gt;
| &lt;br /&gt;
|-&lt;br /&gt;
| &lt;br /&gt;
| &lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 286.387+418.151&lt;br /&gt;
| {{val| 46 73 129 159 170 }} + {{val| 109 173 306 377 403 }}&amp;lt;span style=&amp;quot;background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;&amp;quot;&amp;gt;φ&amp;lt;/span&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 115.968+87.842&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0); display: block; text-align: center;&amp;quot;&amp;gt;77.312+131.7365&amp;lt;/span&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 231.935+263.527&lt;br /&gt;
| &lt;br /&gt;
|-&lt;br /&gt;
| &lt;br /&gt;
| (63+92)\264&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 286.364+418.182&lt;br /&gt;
| {{val| 264 419 741 913 976 }}&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | &#039;&#039;51\528+29\396&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;115.909+87.87&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0);&amp;quot;&amp;gt;17\264+29\264&amp;lt;/span&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0);&amp;quot;&amp;gt;77.273+131.818&amp;lt;/span&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 51\264+58\264&lt;br /&gt;
&lt;br /&gt;
231.818+263.636&lt;br /&gt;
| &lt;br /&gt;
|-&lt;br /&gt;
| (26+38)\109&lt;br /&gt;
| &lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 286.2385+418.349&lt;br /&gt;
| {{val| 109 173 306 377 403 }}&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | &#039;&#039;21\218&#039;&#039;+8\109&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;115.596&#039;&#039;+88.07&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0);&amp;quot;&amp;gt;7\109+12\109&amp;lt;/span&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0);&amp;quot;&amp;gt;77.064+132.11&amp;lt;/span&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 21\109+24\109&lt;br /&gt;
&lt;br /&gt;
231.192+264.22&lt;br /&gt;
| Boundary of smaller &amp;quot;gentle region&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
| &lt;br /&gt;
| (67+98)\281&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 286.121+418.505&lt;br /&gt;
| {{val| 281 446 789 972 1039 }}&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 27\281+&#039;&#039;62\843&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
115.3025+&#039;&#039;88.256&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0);&amp;quot;&amp;gt;18\281+31\281&amp;lt;/span&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0);&amp;quot;&amp;gt;76.868+132.384&amp;lt;/span&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 54\281+62\281&lt;br /&gt;
&lt;br /&gt;
230.605+264.769&lt;br /&gt;
| &lt;br /&gt;
|-&lt;br /&gt;
| &lt;br /&gt;
| &lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 286.101+418.533&lt;br /&gt;
| {{val| 46 73 129 159 170 }} + {{val| 63 100 177 218 233 }}&amp;lt;span style=&amp;quot;background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;&amp;quot;&amp;gt;φ&amp;lt;/span&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 116.526+89.264&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0); display: block; text-align: center;&amp;quot;&amp;gt;77.684+133.8965&amp;lt;/span&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 233.052+267.793&lt;br /&gt;
| &lt;br /&gt;
|-&lt;br /&gt;
| &lt;br /&gt;
| (41+60)\172&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 286.0465+418.605&lt;br /&gt;
| {{val| 172 273 483 595 636 }}&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | &#039;&#039;33\344+19\258&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;115.116+88.372&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0);&amp;quot;&amp;gt;11\172+19\172&amp;lt;/span&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0);&amp;quot;&amp;gt;76.744+132.558&amp;lt;/span&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 33\172+38\172&lt;br /&gt;
&lt;br /&gt;
230.232+265.116&lt;br /&gt;
| &lt;br /&gt;
|-&lt;br /&gt;
| &lt;br /&gt;
| (56+82)\235&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 285.957+418.723&lt;br /&gt;
| {{val| 235 373 660 813 869 }}&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | &#039;&#039;9\94+52\705&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
114.894+81.511&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0);&amp;quot;&amp;gt;3\47+26\235&amp;lt;/span&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0);&amp;quot;&amp;gt;76.596+132.766&amp;lt;/span&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 9\47+52\235&lt;br /&gt;
&lt;br /&gt;
229.787+265.532&lt;br /&gt;
| &lt;br /&gt;
|-&lt;br /&gt;
| &lt;br /&gt;
| &lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 285.852+418.864&lt;br /&gt;
| {{val| 109 173 306 377 403 }} + {{val| 63 100 177 218 233 }}&amp;lt;span style=&amp;quot;background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;&amp;quot;&amp;gt;φ&amp;lt;/span&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 114.963+88.4675&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0); display: block; text-align: center;&amp;quot;&amp;gt;76.642+132.701&amp;lt;/span&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 229.926+265.402&lt;br /&gt;
| &lt;br /&gt;
|-&lt;br /&gt;
| &amp;lt;span style=&amp;quot;display: block; text-align: center;&amp;quot;&amp;gt;(15+22)\63&amp;lt;/span&amp;gt;&lt;br /&gt;
| &lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | &amp;lt;span style=&amp;quot;display: block; text-align: center;&amp;quot;&amp;gt;285.714+419.048&amp;lt;/span&amp;gt;&lt;br /&gt;
| {{val| 63 100 177 218 233 }}&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 2\21+&#039;&#039;2\27&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
114.286+&#039;&#039;88.889&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0);&amp;quot;&amp;gt;4\63+1\9&amp;lt;/span&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0); text-align: start;&amp;quot;&amp;gt;76.1905+133.333&amp;lt;/span&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 4\21+2\9&lt;br /&gt;
&lt;br /&gt;
228.571+266.667&lt;br /&gt;
| &lt;br /&gt;
|-&lt;br /&gt;
| &lt;br /&gt;
| &lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 285.513+419.316&lt;br /&gt;
| {{val| 46 73 129 159 170 }} + {{val| 80 127 225 277 296 }}&amp;lt;span style=&amp;quot;background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;&amp;quot;&amp;gt;φ&amp;lt;/span&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | &amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0); display: block; text-align: center;&amp;quot;&amp;gt;113.7825+89.20&amp;lt;/span&amp;gt;&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0); display: block; text-align: center;&amp;quot;&amp;gt;&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0);&amp;quot;&amp;gt;75.855+133.80&amp;lt;/span&amp;gt;&amp;lt;/span&amp;gt;&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0); display: block; text-align: center;&amp;quot;&amp;gt;&amp;lt;/span&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 227.565+267.606&lt;br /&gt;
| &lt;br /&gt;
|-&lt;br /&gt;
| &lt;br /&gt;
| &amp;lt;span style=&amp;quot;display: block; text-align: center;&amp;quot;&amp;gt;(49+72)\206&amp;lt;/span&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | &amp;lt;span style=&amp;quot;display: block; text-align: center;&amp;quot;&amp;gt;285.437+419.4175&amp;lt;/span&amp;gt;&lt;br /&gt;
| {{val| 206 327 578~579 713 762 }}&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 10\103+15\206&lt;br /&gt;
&lt;br /&gt;
116.505+87.37&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0);&amp;quot;&amp;gt;&#039;&#039;20\309+45\412&#039;&#039;&amp;lt;/span&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0);&amp;quot;&amp;gt;&#039;&#039;77.67+131.068&#039;&#039;&amp;lt;/span&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 20\103+45\206&lt;br /&gt;
&lt;br /&gt;
233.01+262.136&lt;br /&gt;
| &lt;br /&gt;
|-&lt;br /&gt;
| &amp;lt;span style=&amp;quot;display: block; text-align: center;&amp;quot;&amp;gt;(34+50)\143&amp;lt;/span&amp;gt;&lt;br /&gt;
| &lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | &amp;lt;span style=&amp;quot;display: block; text-align: center;&amp;quot;&amp;gt;285.315+419.58&amp;lt;/span&amp;gt;&lt;br /&gt;
| {{val| 143 227 401~402 495 529 }}&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | &#039;&#039;14\143+31\429&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
117.4825+86.71&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0);&amp;quot;&amp;gt;&#039;&#039;28\429+31\286&#039;&#039;&amp;lt;/span&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0);&amp;quot;&amp;gt;&#039;&#039;78.322+130.07&#039;&#039;&amp;lt;/span&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 28\143+31\143&lt;br /&gt;
&lt;br /&gt;
234.965+260.14&lt;br /&gt;
| &lt;br /&gt;
|-&lt;br /&gt;
| &lt;br /&gt;
| &lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 285.234+419.688&lt;br /&gt;
| {{val| 63 100 177 218 233 }} + {{val| 80 127 225 277 296 }}&amp;lt;span style=&amp;quot;background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;&amp;quot;&amp;gt;φ&amp;lt;/span&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 113.085+89.636&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0); display: block; text-align: center;&amp;quot;&amp;gt;75.39+134.454&amp;lt;/span&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 226.169+268.909&lt;br /&gt;
| &lt;br /&gt;
|-&lt;br /&gt;
| &amp;lt;span style=&amp;quot;display: block; text-align: center;&amp;quot;&amp;gt;(54+78)\223&amp;lt;/span&amp;gt;&lt;br /&gt;
| &lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | &lt;br /&gt;
&amp;lt;span style=&amp;quot;display: block; text-align: center;&amp;quot;&amp;gt;285.202+419.731&amp;lt;/span&amp;gt;&lt;br /&gt;
| {{val| 223 354 626~627 771 825 }}&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | &#039;&#039;43\446+49\669&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
115.695+87.892&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0);&amp;quot;&amp;gt;&#039;&#039;43\669+49\446&#039;&#039;&amp;lt;/span&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0);&amp;quot;&amp;gt;&#039;&#039;77.13+131.839&#039;&#039;&amp;lt;/span&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 43\223+49\223&lt;br /&gt;
&lt;br /&gt;
231.39+263.677&lt;br /&gt;
| &lt;br /&gt;
|-&lt;br /&gt;
| &amp;lt;span style=&amp;quot;display: block; text-align: center;&amp;quot;&amp;gt;(19+28)\80&amp;lt;/span&amp;gt;&lt;br /&gt;
| &lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | &amp;lt;span style=&amp;quot;display: block; text-align: center;&amp;quot;&amp;gt;285+420&amp;lt;/span&amp;gt;&lt;br /&gt;
| {{val| 80 127 225 277 296 }}&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | &#039;&#039;3\32+3\40&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;112.5+90&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0);&amp;quot;&amp;gt;1\16+9\80&amp;lt;/span&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;background-color: rgba(255,255,255,0);&amp;quot;&amp;gt;75+135&amp;lt;/span&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 3\16+9\40&lt;br /&gt;
&lt;br /&gt;
225+270&lt;br /&gt;
| Boundary of larger &amp;quot;gentle region&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | (4+6)\17&lt;br /&gt;
|&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 282.353+423.529&lt;br /&gt;
|&amp;lt;nowiki&amp;gt;&amp;lt; 17 27 48 60 63|&amp;lt;/nowiki&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 1\17+&#039;&#039;4\51&#039;&#039;&lt;br /&gt;
70.588+&#039;&#039;93.1765&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;3\34&#039;&#039;+1\17&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;105.882&#039;&#039;+70.588&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot; | 3\17+4\17&lt;br /&gt;
211.765+282.353&lt;br /&gt;
|&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[Category:Gentle]]&lt;br /&gt;
[[Category:Interval regions]]&lt;br /&gt;
[[Category:Tables]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Functional_systems&amp;diff=209224</id>
		<title>Functional systems</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Functional_systems&amp;diff=209224"/>
		<updated>2025-09-03T21:08:31Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;The &#039;&#039;&#039;functional systems&#039;&#039;&#039; are defined by [[Osmium]] as a way to categorize [[interval]]s. The basic premise of the functional systems is defining [[interval class|interval classes]] that are ambiguous between more basic interval classes.&lt;br /&gt;
&lt;br /&gt;
== The 50-function system ==&lt;br /&gt;
&lt;br /&gt;
=== A starting point: The 12-form ===&lt;br /&gt;
Even outside of [[12edo]], the 12-form is a common harmonic structure, found in 3-limit and 5-limit chromatic scales, which influences the human perception of intervals.&lt;br /&gt;
&lt;br /&gt;
{{Todo|expand|inline=1|text=Add derivation of 50-function system}}&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|+&lt;br /&gt;
!Function&lt;br /&gt;
!Type&lt;br /&gt;
!Interval region&lt;br /&gt;
!Rough center&lt;br /&gt;
|-&lt;br /&gt;
|0.0&lt;br /&gt;
|integer&lt;br /&gt;
|unison&lt;br /&gt;
|0c&lt;br /&gt;
|-&lt;br /&gt;
|sp&lt;br /&gt;
| -&lt;br /&gt;
|comma&lt;br /&gt;
|10c&lt;br /&gt;
|-&lt;br /&gt;
|0.3&lt;br /&gt;
| -&lt;br /&gt;
|diesis&lt;br /&gt;
|33c&lt;br /&gt;
|-&lt;br /&gt;
|0.5&lt;br /&gt;
|ambitonal&lt;br /&gt;
|quarter-tone&lt;br /&gt;
|50c&lt;br /&gt;
|-&lt;br /&gt;
|0.7&lt;br /&gt;
|semiambitonal&lt;br /&gt;
|subminor second&lt;br /&gt;
|67c&lt;br /&gt;
|-&lt;br /&gt;
|1&lt;br /&gt;
|&#039;&#039;&#039;integer&#039;&#039;&#039;&lt;br /&gt;
|semitone&lt;br /&gt;
|100c&lt;br /&gt;
|-&lt;br /&gt;
|1.3&lt;br /&gt;
|semiambitonal&lt;br /&gt;
|supraminor second&lt;br /&gt;
|133c&lt;br /&gt;
|-&lt;br /&gt;
|1.5&lt;br /&gt;
|ambitonal&lt;br /&gt;
|neutral second&lt;br /&gt;
|150c&lt;br /&gt;
|-&lt;br /&gt;
|1.7&lt;br /&gt;
|semiambitonal&lt;br /&gt;
|submajor second&lt;br /&gt;
|167c&lt;br /&gt;
|-&lt;br /&gt;
|2&lt;br /&gt;
|&#039;&#039;&#039;integer&#039;&#039;&#039;&lt;br /&gt;
|major second&lt;br /&gt;
|200c&lt;br /&gt;
|-&lt;br /&gt;
|2.3&lt;br /&gt;
|semiambitonal&lt;br /&gt;
|supramajor second&lt;br /&gt;
|233c&lt;br /&gt;
|-&lt;br /&gt;
|2.5&lt;br /&gt;
|ambitonal&lt;br /&gt;
|second-third&lt;br /&gt;
|250c&lt;br /&gt;
|-&lt;br /&gt;
|2.7&lt;br /&gt;
|semiambitonal&lt;br /&gt;
|subminor third&lt;br /&gt;
|267c&lt;br /&gt;
|-&lt;br /&gt;
|3&lt;br /&gt;
|&#039;&#039;&#039;integer&#039;&#039;&#039;&lt;br /&gt;
|minor third&lt;br /&gt;
|300c&lt;br /&gt;
|-&lt;br /&gt;
|3.3&lt;br /&gt;
|semiambitonal&lt;br /&gt;
|supraminor third&lt;br /&gt;
|333c&lt;br /&gt;
|-&lt;br /&gt;
|3.5&lt;br /&gt;
|ambitonal&lt;br /&gt;
|neutral third&lt;br /&gt;
|350c&lt;br /&gt;
|-&lt;br /&gt;
|3.7&lt;br /&gt;
|semiambitonal&lt;br /&gt;
|submajor third&lt;br /&gt;
|367c&lt;br /&gt;
|-&lt;br /&gt;
|4&lt;br /&gt;
|&#039;&#039;&#039;integer&#039;&#039;&#039;&lt;br /&gt;
|major third&lt;br /&gt;
|400c&lt;br /&gt;
|-&lt;br /&gt;
|4.3&lt;br /&gt;
|semiambitonal&lt;br /&gt;
|supermajor third&lt;br /&gt;
|435c&lt;br /&gt;
|-&lt;br /&gt;
|4.5&lt;br /&gt;
|ambitonal&lt;br /&gt;
|third-fourth&lt;br /&gt;
|460c&lt;br /&gt;
|-&lt;br /&gt;
|4.7&lt;br /&gt;
|semiambitonal&lt;br /&gt;
|subfourth&lt;br /&gt;
|475c&lt;br /&gt;
|-&lt;br /&gt;
|5&lt;br /&gt;
|&#039;&#039;&#039;integer&#039;&#039;&#039;&lt;br /&gt;
|perfect fourth&lt;br /&gt;
|500c&lt;br /&gt;
|-&lt;br /&gt;
|5.3&lt;br /&gt;
|semiambitonal&lt;br /&gt;
|superfourth&lt;br /&gt;
|533c&lt;br /&gt;
|-&lt;br /&gt;
|5.5&lt;br /&gt;
|ambitonal&lt;br /&gt;
|neutral fourth&lt;br /&gt;
|550c&lt;br /&gt;
|-&lt;br /&gt;
|5.7&lt;br /&gt;
|semiambitonal&lt;br /&gt;
|subtritone&lt;br /&gt;
|567c&lt;br /&gt;
|-&lt;br /&gt;
|6&lt;br /&gt;
|&#039;&#039;&#039;integer&#039;&#039;&#039;&lt;br /&gt;
|tritone&lt;br /&gt;
|600c&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[Category:Interval regions]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Comma_(interval_region)&amp;diff=209223</id>
		<title>Comma (interval region)</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Comma_(interval_region)&amp;diff=209223"/>
		<updated>2025-09-03T21:08:31Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;Comma&#039;&#039;&#039; usually refers to intervals that are [[tempered out]] to transform some [[limit]] or [[subgroup]] of [[just intonation]] into a [[temperament]]. For that, more common definition of &#039;&#039;comma&#039;&#039;, see the page: &#039;&#039;&#039;[[Comma]]&#039;&#039;&#039;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;Comma&#039;&#039; can, less often, be used to refer to any interval bigger than 0 [[cents]], but smaller than around 30 cents. To distinguish this from the other definition of &#039;&#039;comma&#039;&#039;, this is usually called &#039;&#039;&#039;comma (interval region)&#039;&#039;&#039;. For &#039;&#039;comma (interval region)&#039;&#039;, see the page: &#039;&#039;&#039;[[Comma and diesis]]&#039;&#039;&#039;.&lt;br /&gt;
&lt;br /&gt;
[[Category:Interval regions]]&lt;br /&gt;
[[Category:Comma]][[Category:Smart redirect]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=2.3-equivalent_class_and_Pythagorean-commatic_interval_naming_system&amp;diff=209222</id>
		<title>2.3-equivalent class and Pythagorean-commatic interval naming system</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=2.3-equivalent_class_and_Pythagorean-commatic_interval_naming_system&amp;diff=209222"/>
		<updated>2025-09-03T21:08:30Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;The &#039;&#039;&#039;2.3-equivalent class&#039;&#039;&#039; characterizes a [[just interval]] by its deviation from [[Pythagorean tuning]]. If the Pythagorean chain of fifths is used to derive an interval&#039;s harmonic function, then the 2.3-equivalent class, being orthogonal thereto, characterizes an interval&#039;s harmonic &amp;quot;color&amp;quot;. It is proposed as a replacement of [[Harmonic class|harmonic class (HC)]] since it has been criticized that each HC lacks a consistent psychoacoustic quality. &lt;br /&gt;
&lt;br /&gt;
This interval classification system takes full advantage of [[regular temperament theory]]. An interval&#039;s 2.3-equivalent class can be mathematically expressed as an interval&#039;s no-2 no-3 [[monzo]]. The notion finds applications in various [[musical notation|notation]] systems that use the [[diatonic]] [[nominal-accidental chain]] including but not limited to [[FJS]], [[HEJI]], and [[color notation]]. &lt;br /&gt;
&lt;br /&gt;
For example, [[15/8]], [[5/4]], [[5/3]] and [[10/9]] all have distinct harmonic functions, but it can be argued they have the same harmonic &amp;quot;color&amp;quot; of an otonal-5. In FJS they are denoted by the same superscript: M7&amp;lt;sup&amp;gt;5&amp;lt;/sup&amp;gt;, M3&amp;lt;sup&amp;gt;5&amp;lt;/sup&amp;gt;, M6&amp;lt;sup&amp;gt;5&amp;lt;/sup&amp;gt;, and M2&amp;lt;sup&amp;gt;5&amp;lt;/sup&amp;gt;, respectively. In HEJI they are notated by the same down-arrow on a certain root note; in color notation they share the same color name &amp;quot;yo&amp;quot;. &lt;br /&gt;
&lt;br /&gt;
From that basis we may derive the &#039;&#039;&#039;Pythagorean-commatic interval naming system&#039;&#039;&#039;, in which each interval&#039;s name consists of its abstract [[interval category]] prefixed by the commatic inflection from the Pythagorean reference point in that category. For example, [[7/4]] is the &#039;&#039;septimal minor seventh&#039;&#039;, since it is in the minor seventh category, and off from the [[16/9|Pythagorean minor seventh (16/9)]] by a [[64/63|septimal comma (64/63)]]. &lt;br /&gt;
&lt;br /&gt;
Intuitive as it is, these notes should be taken:&lt;br /&gt;
# Logically, there are two intervals for each name, residing on the opposite sides of the Pythagorean interval. The name should by default refer to the simpler one and the complex one should be further distinguished by &#039;&#039;retro&#039;&#039;. The &#039;&#039;septimal minor seventh&#039;&#039; refers to 7/4; &#039;&#039;retroseptimal minor seventh&#039;&#039; refers to 1024/567. &lt;br /&gt;
# The system does not state how one should conceive of the interval categories, so each interval may have multiple names. 7/4 is the septimal minor seventh as well as the garischismic double diminished octave, if one will call it. &lt;br /&gt;
&lt;br /&gt;
Most traditional interval names loosely follow the spirit of the system, with some exceptions:&lt;br /&gt;
# Subdivided usage in terms of commas and intervals, and of upward and downward inflections, such as &#039;&#039;acute&#039;&#039;/&#039;&#039;grave&#039;&#039; for &#039;&#039;syntonic&#039;&#039;. It is not an actual problem so long as one memorizes all the details. &lt;br /&gt;
# Inflection on a non-Pythagorean interval, such as [[55/32]] being the keenanismic supermajor sixth, where the supermajor sixth is [[12/7]]. It is not an actual problem since we can analyse the name in smaller parts. &lt;br /&gt;
# &#039;&#039;Septimal&#039;&#039;, &#039;&#039;undecimal&#039;&#039;, etc. These are not used to mean an inflection of the corresponding comma but the HC, and thus [[49/48]] is also marked septimal despite having a stack of two 7&#039;s in the numerator.&lt;br /&gt;
&lt;br /&gt;
5-limit intervals are a particular mess being a mix of above, largely due to their historical significance. The corresponding HC is marked by &#039;&#039;classic(al)&#039;&#039; or synonymously &#039;&#039;pental&#039;&#039;, entangled with a finite set of intervals denominated as &#039;&#039;just&#039;&#039;. So [[25/24]] is the &#039;&#039;classic(al)&#039;&#039;/&#039;&#039;pental&#039;&#039;/&#039;&#039;just chromatic semitone&#039;&#039;. Alternative terms have been proposed to address that. &#039;&#039;Ptolemaic&#039;&#039; is used for inflection by the syntonic comma, so 25/24 is the &#039;&#039;double ptolemaic&#039;&#039; or &#039;&#039;diptolemaic chromatic semitone&#039;&#039;. Similarly, &#039;&#039;archytas&#039;&#039; is proposed for inflection by the septimal comma. &lt;br /&gt;
&lt;br /&gt;
[[Category:Interval regions]]&lt;br /&gt;
[[Category:Notation]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=List_of_interval_regions&amp;diff=209221</id>
		<title>List of interval regions</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=List_of_interval_regions&amp;diff=209221"/>
		<updated>2025-09-03T21:08:30Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;This is a list of [[interval region]]s, to be used in planning the interval region pages for the wiki. &lt;br /&gt;
&lt;br /&gt;
* [[Unison (interval region)]] (0-6c)&lt;br /&gt;
** [[1/1|Perfect unison]]: redirect to 1/1&lt;br /&gt;
** [[Microcomma]] (0-6c)&lt;br /&gt;
* [[Comma and diesis]] (0-60c)&lt;br /&gt;
** [[Comma (interval region)]] (0-35c)&lt;br /&gt;
*** [[Microcomma]] (0-6c)&lt;br /&gt;
*** [[Kleisma (interval region)]] (6-9c)&lt;br /&gt;
*** [[Semicomma (interval region)]] (8-20c)&lt;br /&gt;
*** [[Full comma]] (20-35c)&lt;br /&gt;
** [[Diesis (interval region)]] (30-60c)&lt;br /&gt;
*** [[Shimmerstep]] (30-45c) &lt;br /&gt;
*** [[Quartertone (interval region)]] (40-60c)&lt;br /&gt;
* [[Semitone (interval region)]] (40-140c)&lt;br /&gt;
** [[Quartertone (interval region)]] (40-60c) (Inframinor second)&lt;br /&gt;
** [[Small semitone]] (55-90c) (Subminor second)&lt;br /&gt;
** [[Medium semitone]] (85-130c) (Minor second)&lt;br /&gt;
** [[Supraminor second]] (125-140c)&lt;br /&gt;
* [[Neutral second|Neutral second (generic interval region)]] (125-180c)&lt;br /&gt;
** [[Supraminor second]] (125-140c)&lt;br /&gt;
** [[Neutral second (specific interval region)]] (140-160c)&lt;br /&gt;
** [[Submajor second]] (160-180c) (Equable heptatonic second)&lt;br /&gt;
* [[Major second|Major second (generic interval region)]] (160-260c)&lt;br /&gt;
** [[Submajor second]] (160-180c) (Equable heptatonic second)&lt;br /&gt;
** [[Major second (specific interval region)]] (175-225c)&lt;br /&gt;
*** [[Pentamajor second]] (175-195c)&lt;br /&gt;
*** [[Trimajor second]] (190-215c) (Pymajor second, novamajor second)&lt;br /&gt;
*** [[Neomajor second]] (210-225c)&lt;br /&gt;
** [[Supermajor second]] (220-240c)&lt;br /&gt;
** [[Second-third]] (240-260c) (Chthonic/semifourth, ultramajor second)&lt;br /&gt;
* [[Minor third|Minor third (generic interval region)]] (240-340c)&lt;br /&gt;
**[[Second-third]] (240-260c) (Chthonic/semifourth, inframinor third)&lt;br /&gt;
** [[Subminor third]] (260-285c)&lt;br /&gt;
** [[Minor third (specific interval region)]] (275-325c)&lt;br /&gt;
*** Neominor third (275-290c)&lt;br /&gt;
*** Triminor third (285-305c) (Pyminor third, novaminor third)&lt;br /&gt;
*** Pentaminor third (300-325c)&lt;br /&gt;
** [[Supraminor third]] (320-340c)&lt;br /&gt;
&lt;br /&gt;
* [[Neutral third|Neutral third (generic interval region)]] (320-380c)&lt;br /&gt;
** [[Supraminor third]] (320-340c)&lt;br /&gt;
** [[Neutral third (specific interval region)]] (340-360c)&lt;br /&gt;
** [[Submajor third]] (360-380c)&lt;br /&gt;
&lt;br /&gt;
* [[Major third|Major third (generic interval region)]]&lt;br /&gt;
** [[Submajor third]] (360-380c)&lt;br /&gt;
** [[Major third (specific interval region)]] (375-425c)&lt;br /&gt;
*** [[Pentamajor third]] (375-400c)&lt;br /&gt;
*** [[Trimajor third]] (395-415c)&lt;br /&gt;
*** [[Neomajor third]] (410-425c)&lt;br /&gt;
** [[Supermajor third]] (420-440c)&lt;br /&gt;
** [[Third-fourth]] (440-460c) (Naiadic/semisixth, ultramajor third)&lt;br /&gt;
&lt;br /&gt;
* [[Perfect fourth|Perfect fourth (generic interval region)]] (440-560c)&lt;br /&gt;
** [[Third-fourth]] (440-460c) (Naiadic/semisixth, infrafourth)&lt;br /&gt;
** [[Subfourth (interval region)]] (460-485c)&lt;br /&gt;
** [[Perfect fourth (specific interval region)]] (480c-515c)&lt;br /&gt;
&lt;br /&gt;
* [[Superfourth (generic interval region)]] (510-560c) (semiaugmented fourth)&lt;br /&gt;
** [[Superfourth (specific interval region)]] (510-540c)&lt;br /&gt;
** [[Neutral fourth]] (540-560c)&lt;br /&gt;
&lt;br /&gt;
* [[Tritone|Tritone (interval region)]] (540-660c) (augmented fourth, diminished fifth)&lt;br /&gt;
** [[Neutral fourth]] (540-560c)&lt;br /&gt;
** [[Narrow tritone]] (560-590c)&lt;br /&gt;
** [[Medium tritone]] (585-615c)&lt;br /&gt;
... (octave complements)&lt;br /&gt;
&lt;br /&gt;
* [[Octave|Octave (generic interval region)]] (1140-1200c)&lt;br /&gt;
** [[Octave less diesis]] (1140-1170c)&lt;br /&gt;
** [[Octave less comma|Octave less comma (generic interval region)]] (1170-1200c)&lt;br /&gt;
*** [[Octave less comma (specific interval region)]] (1170-1194c)&lt;br /&gt;
*** [[Octave less microcomma]] (1194-1200c)&lt;br /&gt;
** [[Octave (specific interval region)]] (1194-1200c)&lt;br /&gt;
*** [[Octave less microcomma]] (1194-1200c)&lt;br /&gt;
*** [[Perfect octave]] - redirect to [[2/1]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{todo|WIP|inline=1}}&lt;br /&gt;
&lt;br /&gt;
[[Category:Interval regions|*]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Interval_region&amp;diff=209220</id>
		<title>Interval region</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Interval_region&amp;diff=209220"/>
		<updated>2025-09-03T21:08:30Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;There are infinite possible intervals (both tempered and just), even within a single [[2/1|octave]]. It can be helpful to group these intervals into a finite number of &#039;&#039;&#039;interval regions&#039;&#039;&#039; or &#039;&#039;&#039;interval categories&#039;&#039;&#039;. &lt;br /&gt;
&lt;br /&gt;
== Concrete regions vs abstract categories ==&lt;br /&gt;
An &#039;&#039;interval region&#039;&#039; usually implies it is concrete, defined by concrete boundaries of interval sizes. The boundaries are usually fuzzy to allow some vagueness, in line with how we perceive them. Which region an interval falls into solely depends on the interval&#039;s size. &lt;br /&gt;
&lt;br /&gt;
An &#039;&#039;interval category&#039;&#039; is usually meant to be abstract. It uses some [[mapping]] to determine which category an interval falls into, short-circuiting the question of where exactly to place the boundaries. It also takes account of an interval&#039;s [[prime factorization|prime components]], allowing us to find a composite interval&#039;s category through [[interval arithmetic]]. &lt;br /&gt;
&lt;br /&gt;
The [[5L 2s|diatonic]] interval category system commonly used to categorize JI intervals consists of a [[interval quality|quality]] and a diatonic scale degree. &lt;br /&gt;
&lt;br /&gt;
== Extended-diatonic interval names ==&lt;br /&gt;
{{Main|Extended-diatonic interval names}}&lt;br /&gt;
Many interval naming systems extend the diatonic interval names by adding new [[interval qualities]] to the usual set. While some systems preserve the fifth-based structure entirely, other systems define regions based on the proximity to the intervals associated with the diatonic intervals, which are then divided into finer subregions.&lt;br /&gt;
&lt;br /&gt;
== Latitude ==&lt;br /&gt;
When describing interval regions in terms of size relative to a (possibly tempered) fifth, it leads to the system of [[Latitude|latitude and medial intervals]].&lt;br /&gt;
&lt;br /&gt;
== Schulter system ==&lt;br /&gt;
[[Margo Schulter]] describes her system for categorizing intervals in &#039;&#039;[http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum]&#039;&#039;, which begins:&lt;br /&gt;
&lt;br /&gt;
: In naming categories of intervals, or regions of the spectrum in which they are found, there may be many valid and desirable schemes reflecting the diversity of viewpoints and styles to be found in world musics. What I describe here is merely one possible solution, and one influenced by my own musicmaking experience and philosophy which seeks an equitable and inclusive balance between intervals at or near simple integer ratios, and those having a more complex or active nature.&lt;br /&gt;
&lt;br /&gt;
Schulter proposes the following categories and gives a tentative range of cents values for intervals that fall within those categories. In &#039;&#039;Regions&#039;&#039;, she points out, &amp;quot;A main caution is that the borders are inevitably &#039;fuzzy,&#039; so that one region shades into another and suggested values in cents are more illustrative than definitive.&amp;quot;&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
! | Interval Category&lt;br /&gt;
! | Approx. Cents Ranges&lt;br /&gt;
! colspan=&amp;quot;2&amp;quot; |sub-category&lt;br /&gt;
|-&lt;br /&gt;
| | [[Unison|Pure Unison]] (1:1)&lt;br /&gt;
| | 0&lt;br /&gt;
|&lt;br /&gt;
|&lt;br /&gt;
|-&lt;br /&gt;
| | [[Comma]]s&lt;br /&gt;
| | 0-30&lt;br /&gt;
|&lt;br /&gt;
|&lt;br /&gt;
|-&lt;br /&gt;
| | [[Diesis|Dieses]]&lt;br /&gt;
| | 30-60&lt;br /&gt;
|&lt;br /&gt;
|&lt;br /&gt;
|-&lt;br /&gt;
|  rowspan=&amp;quot;3&amp;quot;| [[Minor second|Minor Second]]s&lt;br /&gt;
|  rowspan=&amp;quot;3&amp;quot;| 60-125&lt;br /&gt;
|small&lt;br /&gt;
|60-80&lt;br /&gt;
|-&lt;br /&gt;
|middle&lt;br /&gt;
|80-100&lt;br /&gt;
|-&lt;br /&gt;
|large&lt;br /&gt;
|100-125&lt;br /&gt;
|-&lt;br /&gt;
|  rowspan=&amp;quot;3&amp;quot;|[[Neutral second|Neutral Second]]s&lt;br /&gt;
|  rowspan=&amp;quot;3&amp;quot;| 125-170&lt;br /&gt;
|small&lt;br /&gt;
|125-135&lt;br /&gt;
|-&lt;br /&gt;
|middle&lt;br /&gt;
|135-160&lt;br /&gt;
|-&lt;br /&gt;
|large&lt;br /&gt;
|160-170&lt;br /&gt;
|-&lt;br /&gt;
| |[[Equable heptatonic|Equable Heptatonic]]&lt;br /&gt;
| | 160-182&lt;br /&gt;
|&lt;br /&gt;
|&lt;br /&gt;
|-&lt;br /&gt;
|  rowspan=&amp;quot;3&amp;quot;|[[Major second|Major Second]]s&lt;br /&gt;
|  rowspan=&amp;quot;3&amp;quot;| 180-240&lt;br /&gt;
|small&lt;br /&gt;
|180-200&lt;br /&gt;
|-&lt;br /&gt;
|middle&lt;br /&gt;
|200-220&lt;br /&gt;
|-&lt;br /&gt;
|large&lt;br /&gt;
|220-240&lt;br /&gt;
|-&lt;br /&gt;
| |[[Interseptimal interval|Interseptimal]] (Maj2-min3)&lt;br /&gt;
| | 240-260&lt;br /&gt;
|&lt;br /&gt;
|&lt;br /&gt;
|-&lt;br /&gt;
|  rowspan=&amp;quot;3&amp;quot;|[[Minor third|Minor Third]]s&lt;br /&gt;
|  rowspan=&amp;quot;3&amp;quot;| 260-330&lt;br /&gt;
|small&lt;br /&gt;
|260-280&lt;br /&gt;
|-&lt;br /&gt;
|middle&lt;br /&gt;
|280-300&lt;br /&gt;
|-&lt;br /&gt;
|large&lt;br /&gt;
|300-330&lt;br /&gt;
|-&lt;br /&gt;
|  rowspan=&amp;quot;3&amp;quot;| [[Neutral third|Neutral Third]]s&lt;br /&gt;
|  rowspan=&amp;quot;3&amp;quot;| 330-372&lt;br /&gt;
|small&lt;br /&gt;
|330-342&lt;br /&gt;
|-&lt;br /&gt;
|middle&lt;br /&gt;
|342-360&lt;br /&gt;
|-&lt;br /&gt;
|large&lt;br /&gt;
|360-372&lt;br /&gt;
|-&lt;br /&gt;
|  rowspan=&amp;quot;3&amp;quot;|[[Major third|Major Third]]s&lt;br /&gt;
|  rowspan=&amp;quot;3&amp;quot;| 372-440&lt;br /&gt;
|small&lt;br /&gt;
|372-400&lt;br /&gt;
|-&lt;br /&gt;
|middle&lt;br /&gt;
|400-423&lt;br /&gt;
|-&lt;br /&gt;
|large&lt;br /&gt;
|423-440&lt;br /&gt;
|-&lt;br /&gt;
| |[[Interseptimal interval|Interseptimal]] (Maj3-4)&lt;br /&gt;
| | 440-468&lt;br /&gt;
|&lt;br /&gt;
|&lt;br /&gt;
|-&lt;br /&gt;
|  rowspan=&amp;quot;3&amp;quot;|[[Perfect fourth|Perfect Fourth]]s&lt;br /&gt;
|  rowspan=&amp;quot;3&amp;quot;| 468-528&lt;br /&gt;
|small&lt;br /&gt;
|468-491&lt;br /&gt;
|-&lt;br /&gt;
|middle&lt;br /&gt;
|491-505&lt;br /&gt;
|-&lt;br /&gt;
|large&lt;br /&gt;
|505-528&lt;br /&gt;
|-&lt;br /&gt;
| |[[Superfourth]]s&lt;br /&gt;
| | 528-560&lt;br /&gt;
|&lt;br /&gt;
|&lt;br /&gt;
|-&lt;br /&gt;
|  rowspan=&amp;quot;3&amp;quot;|[[Tritone|Tritonic Region]]&lt;br /&gt;
|  rowspan=&amp;quot;3&amp;quot;| 560-640&lt;br /&gt;
|small&lt;br /&gt;
|560-577&lt;br /&gt;
|-&lt;br /&gt;
|middle&lt;br /&gt;
|577-623&lt;br /&gt;
|-&lt;br /&gt;
|large&lt;br /&gt;
|623-640&lt;br /&gt;
|-&lt;br /&gt;
| |[[Subfifth]]s&lt;br /&gt;
| | 640-672&lt;br /&gt;
|&lt;br /&gt;
|&lt;br /&gt;
|-&lt;br /&gt;
|  rowspan=&amp;quot;3&amp;quot;|[[Perfect fifth|Perfect Fifth]]s&lt;br /&gt;
|  rowspan=&amp;quot;3&amp;quot;| 672-732&lt;br /&gt;
|small&lt;br /&gt;
|672-695&lt;br /&gt;
|-&lt;br /&gt;
|middle&lt;br /&gt;
|695-709&lt;br /&gt;
|-&lt;br /&gt;
|large&lt;br /&gt;
|709-732&lt;br /&gt;
|-&lt;br /&gt;
| | [[Interseptimal interval|Interseptimal]] (5-min6)&lt;br /&gt;
| | 732-760&lt;br /&gt;
|&lt;br /&gt;
|&lt;br /&gt;
|-&lt;br /&gt;
|  rowspan=&amp;quot;3&amp;quot;|[[Minor sixth|Minor Sixth]]s&lt;br /&gt;
|  rowspan=&amp;quot;3&amp;quot;| 760-828&lt;br /&gt;
|small&lt;br /&gt;
|760-777&lt;br /&gt;
|-&lt;br /&gt;
|middle&lt;br /&gt;
|777-800&lt;br /&gt;
|-&lt;br /&gt;
|large&lt;br /&gt;
|800-828&lt;br /&gt;
|-&lt;br /&gt;
|  rowspan=&amp;quot;3&amp;quot;|[[Neutral sixth|Neutral Sixth]]s&lt;br /&gt;
|  rowspan=&amp;quot;3&amp;quot;| 828-870&lt;br /&gt;
|small&lt;br /&gt;
|828-840&lt;br /&gt;
|-&lt;br /&gt;
|middle&lt;br /&gt;
|840-858&lt;br /&gt;
|-&lt;br /&gt;
|large&lt;br /&gt;
|858-870&lt;br /&gt;
|-&lt;br /&gt;
|  rowspan=&amp;quot;3&amp;quot;|[[Major sixth|Major Sixth]]s&lt;br /&gt;
|  rowspan=&amp;quot;3&amp;quot;| 870-940&lt;br /&gt;
|small&lt;br /&gt;
|870-900&lt;br /&gt;
|-&lt;br /&gt;
|middle&lt;br /&gt;
|900-920&lt;br /&gt;
|-&lt;br /&gt;
|large&lt;br /&gt;
|920-940&lt;br /&gt;
|-&lt;br /&gt;
| | [[Interseptimal interval|Interseptimal]] (Maj6-min7)&lt;br /&gt;
| | 940-960&lt;br /&gt;
|&lt;br /&gt;
|&lt;br /&gt;
|-&lt;br /&gt;
|  rowspan=&amp;quot;3&amp;quot;|[[Minor seventh|Minor Seventh]]s&lt;br /&gt;
|  rowspan=&amp;quot;3&amp;quot;| 960-1025&lt;br /&gt;
|small&lt;br /&gt;
|960-987&lt;br /&gt;
|-&lt;br /&gt;
|middle&lt;br /&gt;
|987-1000&lt;br /&gt;
|-&lt;br /&gt;
|large&lt;br /&gt;
|1000-1025&lt;br /&gt;
|-&lt;br /&gt;
| | [[Equable heptatonic|Equable Heptatonic]]&lt;br /&gt;
| | 1018-1040&lt;br /&gt;
|&lt;br /&gt;
|&lt;br /&gt;
|-&lt;br /&gt;
|  rowspan=&amp;quot;3&amp;quot;|[[Neutral seventh|Neutral Seventh]]s&lt;br /&gt;
|  rowspan=&amp;quot;3&amp;quot;| 1030-1075&lt;br /&gt;
|small&lt;br /&gt;
|1030-1043&lt;br /&gt;
|-&lt;br /&gt;
|middle&lt;br /&gt;
|1043-1065&lt;br /&gt;
|-&lt;br /&gt;
|large&lt;br /&gt;
|1065-1075&lt;br /&gt;
|-&lt;br /&gt;
|  rowspan=&amp;quot;3&amp;quot;| [[Major seventh|Major Seventh]]s&lt;br /&gt;
|  rowspan=&amp;quot;3&amp;quot;| 1075-1140&lt;br /&gt;
|small&lt;br /&gt;
|1075-1100&lt;br /&gt;
|-&lt;br /&gt;
|middle&lt;br /&gt;
|1100-1120&lt;br /&gt;
|-&lt;br /&gt;
|large&lt;br /&gt;
|1120-1140&lt;br /&gt;
|-&lt;br /&gt;
| | Octave less diesis&lt;br /&gt;
| | 1140-1170&lt;br /&gt;
|&lt;br /&gt;
|&lt;br /&gt;
|-&lt;br /&gt;
| | Octave less comma&lt;br /&gt;
| | 1170-1200&lt;br /&gt;
|&lt;br /&gt;
|&lt;br /&gt;
|-&lt;br /&gt;
| | [[Octave|Pure Octave]] (2:1)&lt;br /&gt;
| | 1200&lt;br /&gt;
|&lt;br /&gt;
|&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;pre&amp;gt;Pure unison (1:1)           0 cents&lt;br /&gt;
 &lt;br /&gt;
Commas                   0-30 cents        (Section 11)&lt;br /&gt;
 &lt;br /&gt;
Dieses                  30-60 cents        (Section 11)&lt;br /&gt;
 &lt;br /&gt;
Minor seconds          60-125 cents        (Section 5)&lt;br /&gt;
        small              60-80 cents&lt;br /&gt;
        middle             80-100 cents&lt;br /&gt;
        large             100-125 cents&lt;br /&gt;
 &lt;br /&gt;
Neutral seconds       125-170 cents        (Section 6)&lt;br /&gt;
        small              125-135 cents&lt;br /&gt;
        middle             135-160 cents&lt;br /&gt;
        large              160-170 cents&lt;br /&gt;
 &lt;br /&gt;
Equable heptatonic&lt;br /&gt;
(heartland range)     160-182 cents        (Section 12)&lt;br /&gt;
 &lt;br /&gt;
Major seconds&lt;br /&gt;
(or tones)            180-240 cents        (Section 4)&lt;br /&gt;
        small              180-200 cents&lt;br /&gt;
        middle             200-220 cents&lt;br /&gt;
        large              220-240 cents&lt;br /&gt;
 &lt;br /&gt;
Interseptimal&lt;br /&gt;
(Maj2-min3)           240-260 cents        (Section 9)&lt;br /&gt;
 &lt;br /&gt;
Minor thirds          260-330 cents        (Section 2)&lt;br /&gt;
        small              260-280 cents&lt;br /&gt;
        middle             280-300 cents&lt;br /&gt;
        large              300-330 cents&lt;br /&gt;
 &lt;br /&gt;
Neutral thirds        330-372 cents        (Section 3)&lt;br /&gt;
        small              330-342 cents&lt;br /&gt;
        middle             342-360 cents&lt;br /&gt;
        large              360-372 cents&lt;br /&gt;
 &lt;br /&gt;
Major thirds          372-440 cents        (Section 2)&lt;br /&gt;
        small              372-400 cents&lt;br /&gt;
        middle             400-423 cents&lt;br /&gt;
        large              423-440 cents&lt;br /&gt;
 &lt;br /&gt;
Interseptimal         440-468 cents        (Section 9)&lt;br /&gt;
(Maj3-4)&lt;br /&gt;
 &lt;br /&gt;
Perfect fourths       468-528 cents        (Section 7)&lt;br /&gt;
        small              468-491 cents&lt;br /&gt;
        middle             491-505 cents&lt;br /&gt;
        large              505-523 cents&lt;br /&gt;
 &lt;br /&gt;
Superfourths          528-560 cents        (Section 10)&lt;br /&gt;
 &lt;br /&gt;
Tritonic region       560-640 cents        (Section 8)&lt;br /&gt;
        small              560-577 cents&lt;br /&gt;
        middle             577-623 cents&lt;br /&gt;
        large              623-640 cents&lt;br /&gt;
 &lt;br /&gt;
Subfifths             640-672 cents        (Section 10)&lt;br /&gt;
 &lt;br /&gt;
Perfect fifths        672-732 cents        (Section 7)&lt;br /&gt;
        small              672-695 cents&lt;br /&gt;
        middle             695-709 cents&lt;br /&gt;
        large              709-732 cents&lt;br /&gt;
 &lt;br /&gt;
Interseptimal         732-760 cents        (Section 9)&lt;br /&gt;
(5-min6)&lt;br /&gt;
 &lt;br /&gt;
Minor sixths          760-828 cents        (Section 2)&lt;br /&gt;
        small              760-777 cents&lt;br /&gt;
        middle             777-800 cents&lt;br /&gt;
        large              800-828 cents&lt;br /&gt;
 &lt;br /&gt;
Neutral sixths        828-870 cents        (Section 3)&lt;br /&gt;
        small              828-840 cents&lt;br /&gt;
        middle             840-858 cents&lt;br /&gt;
        large              858-870 cents&lt;br /&gt;
 &lt;br /&gt;
Major sixths          870-940 cents        (Section 2)&lt;br /&gt;
        small              870-900 cents&lt;br /&gt;
        middle             900-920 cents&lt;br /&gt;
        large              920-940 cents&lt;br /&gt;
 &lt;br /&gt;
Interseptimal         940-960 cents        (Section 9)&lt;br /&gt;
(Maj6-min7)&lt;br /&gt;
 &lt;br /&gt;
Minor sevenths       960-1025 cents        (Section 4)&lt;br /&gt;
        small              960-987 cents&lt;br /&gt;
        middle            987-1000 cents&lt;br /&gt;
        large            1000-1025 cents&lt;br /&gt;
 &lt;br /&gt;
Equable heptatonic  1018-1040 cents        (Section 12)&lt;br /&gt;
(heartland range)&lt;br /&gt;
 &lt;br /&gt;
Neutral sevenths    1030-1075 cents        (Section 6)&lt;br /&gt;
        small            1030-1043 cents&lt;br /&gt;
        middle           1043-1065 cents&lt;br /&gt;
        large            1065-1075 cents&lt;br /&gt;
 &lt;br /&gt;
Major sevenths      1075-1140 cents        (Section 5)&lt;br /&gt;
        small            1075-1100 cents&lt;br /&gt;
        middle           1100-1120 cents&lt;br /&gt;
        large            1120-1140 cents&lt;br /&gt;
 &lt;br /&gt;
Octave less diesis  1140-1170 cents        (Section 11)&lt;br /&gt;
 &lt;br /&gt;
Octave less comma   1170-1200 cents        (Section 11)&lt;br /&gt;
 &lt;br /&gt;
Pure octave (2:1)        1200 cents&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
* [[Mike Sheiman&#039;s Alternative Interval Categorizations]]&lt;br /&gt;
* [[SKULO interval names]]&lt;br /&gt;
* [[5L 2s/Interval categories]]&lt;br /&gt;
* [[Supermajor and subminor]]&lt;br /&gt;
* [[Interval size measure]]&lt;br /&gt;
* [[Table of MOSes]]&lt;br /&gt;
* [[Gallery of just intervals]]&lt;br /&gt;
* [[Universal solfege]] - [[solfege]] based on the Schulter system&lt;br /&gt;
&lt;br /&gt;
[[Category:Interval regions| ]]&lt;br /&gt;
&amp;lt;!-- main article --&amp;gt;&lt;br /&gt;
[[Category:Classification]]&lt;br /&gt;
[[Category:Distance measure]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Whole_tone&amp;diff=209219</id>
		<title>Category:Whole tone</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Whole_tone&amp;diff=209219"/>
		<updated>2025-09-03T21:08:30Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[Category:Interval regions]]&lt;br /&gt;
[[Category:Second]]&lt;br /&gt;
[[Category:Major interval]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Unison&amp;diff=209218</id>
		<title>Category:Unison</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Unison&amp;diff=209218"/>
		<updated>2025-09-03T21:08:30Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{Cat main}}&lt;br /&gt;
{{See also|:Category:Commas}}&lt;br /&gt;
&lt;br /&gt;
[[Category:Interval regions]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Third_tone&amp;diff=209217</id>
		<title>Category:Third tone</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Third_tone&amp;diff=209217"/>
		<updated>2025-09-03T21:08:29Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[Category:Interval regions]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Tritone&amp;diff=209216</id>
		<title>Category:Tritone</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Tritone&amp;diff=209216"/>
		<updated>2025-09-03T21:08:29Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;Main article: [[Tritone]]&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[Category:Interval regions]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Tritave&amp;diff=209215</id>
		<title>Category:Tritave</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Tritave&amp;diff=209215"/>
		<updated>2025-09-03T21:08:29Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;Main article: [[Tritave]]&#039;&#039;&#039;&lt;br /&gt;
[[Category:Interval regions]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Third&amp;diff=209214</id>
		<title>Category:Third</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Third&amp;diff=209214"/>
		<updated>2025-09-03T21:08:29Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[Category:Interval regions]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Tenth&amp;diff=209213</id>
		<title>Category:Tenth</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Tenth&amp;diff=209213"/>
		<updated>2025-09-03T21:08:29Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[Category:Interval regions]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Supraminor_third&amp;diff=209212</id>
		<title>Category:Supraminor third</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Supraminor_third&amp;diff=209212"/>
		<updated>2025-09-03T21:08:29Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[Category:Third]]&lt;br /&gt;
[[Category:Interval regions]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Supraminor_sixth&amp;diff=209211</id>
		<title>Category:Supraminor sixth</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Supraminor_sixth&amp;diff=209211"/>
		<updated>2025-09-03T21:08:29Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[Category:Sixth]]&lt;br /&gt;
[[Category:Interval regions]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Supraminor_second&amp;diff=209210</id>
		<title>Category:Supraminor second</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Supraminor_second&amp;diff=209210"/>
		<updated>2025-09-03T21:08:28Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;The following intervals are seconds in the [[supraminor]] quality range.&lt;br /&gt;
&lt;br /&gt;
[[Category:Interval regions]]&lt;br /&gt;
[[Category:Second]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Supermajor_third&amp;diff=209209</id>
		<title>Category:Supermajor third</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Supermajor_third&amp;diff=209209"/>
		<updated>2025-09-03T21:08:28Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[Category:Third]]&lt;br /&gt;
[[Category:Interval regions]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Supermajor_sixth&amp;diff=209208</id>
		<title>Category:Supermajor sixth</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Supermajor_sixth&amp;diff=209208"/>
		<updated>2025-09-03T21:08:28Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[Category:Interval regions]]&lt;br /&gt;
[[Category:Sixth]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Supermajor_seventh&amp;diff=209207</id>
		<title>Category:Supermajor seventh</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Supermajor_seventh&amp;diff=209207"/>
		<updated>2025-09-03T21:08:28Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[Category:Seventh]]&lt;br /&gt;
[[Category:Interval regions]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Supermajor_second&amp;diff=209206</id>
		<title>Category:Supermajor second</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Supermajor_second&amp;diff=209206"/>
		<updated>2025-09-03T21:08:28Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[Category:Second]]&lt;br /&gt;
[[Category:Interval regions]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Superfourth&amp;diff=209202</id>
		<title>Category:Superfourth</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Superfourth&amp;diff=209202"/>
		<updated>2025-09-03T21:07:27Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;Main article: [[Superfourth]]&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[Category:Fourth]]&lt;br /&gt;
[[Category:Interval regions]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Superfifth&amp;diff=209201</id>
		<title>Category:Superfifth</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Superfifth&amp;diff=209201"/>
		<updated>2025-09-03T21:07:27Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[Category:Fifth]]&lt;br /&gt;
[[Category:Interval regions]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Subminor_third&amp;diff=209200</id>
		<title>Category:Subminor third</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Subminor_third&amp;diff=209200"/>
		<updated>2025-09-03T21:07:27Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[Category:Interval regions]]&lt;br /&gt;
[[Category:Third]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Submajor_sixth&amp;diff=209199</id>
		<title>Category:Submajor sixth</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Submajor_sixth&amp;diff=209199"/>
		<updated>2025-09-03T21:07:27Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[Category:Interval regions]]&lt;br /&gt;
[[Category:Sixth]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Subminor_sixth&amp;diff=209198</id>
		<title>Category:Subminor sixth</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Subminor_sixth&amp;diff=209198"/>
		<updated>2025-09-03T21:07:27Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[Category:Sixth]]&lt;br /&gt;
[[Category:Interval regions]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Subminor_seventh&amp;diff=209197</id>
		<title>Category:Subminor seventh</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Subminor_seventh&amp;diff=209197"/>
		<updated>2025-09-03T21:07:26Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[Category:Seventh]]&lt;br /&gt;
[[Category:Interval regions]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Submajor_third&amp;diff=209196</id>
		<title>Category:Submajor third</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Submajor_third&amp;diff=209196"/>
		<updated>2025-09-03T21:07:26Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[Category:Third]]&lt;br /&gt;
[[Category:Interval regions]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Sixth&amp;diff=209195</id>
		<title>Category:Sixth</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Sixth&amp;diff=209195"/>
		<updated>2025-09-03T21:07:26Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[Category:Interval regions]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Seventh&amp;diff=209194</id>
		<title>Category:Seventh</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Seventh&amp;diff=209194"/>
		<updated>2025-09-03T21:07:26Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[Category:Interval regions]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Subfourth&amp;diff=209193</id>
		<title>Category:Subfourth</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Subfourth&amp;diff=209193"/>
		<updated>2025-09-03T21:07:26Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[Category:Fourth]]&lt;br /&gt;
[[Category:Interval regions]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Subfifth&amp;diff=209192</id>
		<title>Category:Subfifth</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Subfifth&amp;diff=209192"/>
		<updated>2025-09-03T21:07:26Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;Main article: [[Subfifth]]&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[Category:Fifth]]&lt;br /&gt;
[[Category:Interval regions]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Semitwelfth&amp;diff=209191</id>
		<title>Category:Semitwelfth</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Semitwelfth&amp;diff=209191"/>
		<updated>2025-09-03T21:07:26Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{cat main}}&lt;br /&gt;
[[Category:Interval regions]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Semitone&amp;diff=209190</id>
		<title>Category:Semitone</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Semitone&amp;diff=209190"/>
		<updated>2025-09-03T21:07:25Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[Category:Interval regions]]&lt;br /&gt;
[[Category:Second]]&lt;br /&gt;
[[Category:Minor interval]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Semifourth&amp;diff=209189</id>
		<title>Category:Semifourth</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Semifourth&amp;diff=209189"/>
		<updated>2025-09-03T21:07:25Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{Cat main|Semifourth}}&lt;br /&gt;
[[Category:Interval regions]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Second&amp;diff=209188</id>
		<title>Category:Second</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Second&amp;diff=209188"/>
		<updated>2025-09-03T21:07:25Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[Category:Interval regions]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Quartertone&amp;diff=209187</id>
		<title>Category:Quartertone</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Quartertone&amp;diff=209187"/>
		<updated>2025-09-03T21:07:25Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[Category:Interval regions]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Pentave&amp;diff=209186</id>
		<title>Category:Pentave</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Pentave&amp;diff=209186"/>
		<updated>2025-09-03T21:07:25Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{Cat main}}&lt;br /&gt;
[[Category:Interval regions]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Octave&amp;diff=209185</id>
		<title>Category:Octave</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Octave&amp;diff=209185"/>
		<updated>2025-09-03T21:07:25Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;Main article: [[Octave]]&#039;&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
[[Category:Interval regions]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Nonet&amp;diff=209184</id>
		<title>Category:Nonet</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Nonet&amp;diff=209184"/>
		<updated>2025-09-03T21:07:24Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[Category:Interval regions]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Category:Neutral_third&amp;diff=209183</id>
		<title>Category:Neutral third</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Category:Neutral_third&amp;diff=209183"/>
		<updated>2025-09-03T21:07:24Z</updated>

		<summary type="html">&lt;p&gt;Fredg999 category edits: Moving from Category:Interval region to Category:Interval regions using Cat-a-lot&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[Category:Interval regions]]&lt;br /&gt;
[[Category:Third]]&lt;br /&gt;
[[Category:Neutral interval]]&lt;/div&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
</feed>