Gallery of MOS transversals - Revision history

FloraC: Update navbox

2025-02-12T11:45:28Z

Update navbox

← Older revision		Revision as of 11:45, 12 February 2025
Line 53:		Line 53:
	* [[orwell13trans57ex]]		* [[orwell13trans57ex]]

	{{~~Scale~~ gallery}}		{{Navbox scale gallery}}

	[[Category:MOS transversals\| ]] <!-- Main article -->		[[Category:MOS transversals\| ]] <!-- Main article -->
	[[Category:Lists of scales\|MOS transversals]]		[[Category:Lists of scales\|MOS transversals]]

ArrowHead294: Clean up

2025-02-11T20:02:31Z

Clean up

← Older revision		Revision as of 20:02, 11 February 2025
Line 1:		Line 1:
	By giving a [[~~Transversal\|~~transversal]] for a [[~~MOSScales\|~~MOS]] for a particular rank two temperament, we can define the MOS as the tempering, in that temperament, of the scale. This is not very interesting in itself; what is more interesting is that since only three primes--2 and two odd primes--can be used for the transversal, we can put the result into [[~~Scala\|~~Scala]], and use its "Lattice and player" command under the Analyze pull-down menu to depict the MOS in terms of a lattice diagram. This can be used to better understand the chord relationships within the MOS. It should be noted that while only chords with two odd primes are depicted, larger chords are associated to them. When 3 and 5 are relatively complex as in miracle, for instance, 7 is likely to be brought along with them, and hence the lattice picture of the 5-limit triads can be used to understand relations between tetrads in miracle and other temperaments of a similar kind. Choosing two primes which bound a chord of interest often works: for instance 3 and 5 bound 7 in miracle, so that the 5-limit transversal shows 7-limit tetrads. On the other hand, in the 11-limit, 5 and 11 bound both 7 and 9, so that the complete 11-limit sextads are represented by the triads of the 2.5.11 transveral.		By giving a [[transversal]] for a [[MOS]] for a particular rank two temperament, we can define the MOS as the tempering, in that temperament, of the scale. This is not very interesting in itself; what is more interesting is that since only three primes--2 and two odd primes--can be used for the transversal, we can put the result into [[Scala]], and use its "Lattice and player" command under the Analyze pull-down menu to depict the MOS in terms of a lattice diagram. This can be used to better understand the chord relationships within the MOS. It should be noted that while only chords with two odd primes are depicted, larger chords are associated to them. When 3 and 5 are relatively complex as in miracle, for instance, 7 is likely to be brought along with them, and hence the lattice picture of the 5-limit triads can be used to understand relations between tetrads in miracle and other temperaments of a similar kind. Choosing two primes which bound a chord of interest often works: for instance 3 and 5 bound 7 in miracle, so that the 5-limit transversal shows 7-limit tetrads. On the other hand, in the 11-limit, 5 and 11 bound both 7 and 9, so that the complete 11-limit sextads are represented by the triads of the 2.5.11 transveral.

	A difficulty with the method is that the planar arrangement does not correspond precisely with the linear arrangement of MOS; the single comma between the three primes rolls up the plane into a cylinder, hence there may be chords not represented by the transveral lattice. Rather than attempting to roll any cylinders, one may take advantage of the fact that with only three generators there is just one comma on the subgroup temperament; multiplying by it, dividing by it, and taking the original scale one gets an extended transversal which reduces to the same MOS but which shows the chords within a larger lattice. These are the scales with "ex" postfixing the name of the scale.		A difficulty with the method is that the planar arrangement does not correspond precisely with the linear arrangement of MOS; the single comma between the three primes rolls up the plane into a cylinder, hence there may be chords not represented by the transveral lattice. Rather than attempting to roll any cylinders, one may take advantage of the fact that with only three generators there is just one comma on the subgroup temperament; multiplying by it, dividing by it, and taking the original scale one gets an extended transversal which reduces to the same MOS but which shows the chords within a larger lattice. These are the scales with "ex" postfixing the name of the scale.

	=[[Kleismic_family#Catakleismic\|Catakleismic]]=		= [[Kleismic_family#Catakleismic\|Catakleismic]] =
	* [[~~catakleismic34fok\|~~catakleismic34fok]]		* [[catakleismic34fok]]
	* [[~~kleismic34trans\|~~kleismic34trans]]		* [[kleismic34trans]]
	* [[~~catakleismic34trans\|~~catakleismic34trans]]		* [[catakleismic34trans]]
	* [[~~catakleismic34semitransversal\|~~catakleismic34semitransversal]]		* [[catakleismic34semitransversal]]
	* [[~~catakleismic34transex\|~~catakleismic34transex]]		* [[catakleismic34transex]]

	=[[Ragismic_microtemperaments#Ennealimmal\|Ennealimmal]]=		= [[Ragismic_microtemperaments#Ennealimmal\|Ennealimmal]] =
	* [[~~ennealimmal45trans\|~~ennealimmal45trans]]		* [[ennealimmal45trans]]

	=[[Magic_family#Magic\|Magic]]=		= [[Magic_family#Magic\|Magic]] =
	* [[~~magic19trans37\|~~magic19trans37]]		* [[magic19trans37]]
	* [[~~magic22trans37\|~~magic22trans37]]		* [[magic22trans37]]
	* [[~~magic19trans37ex\|~~magic19trans37ex]]		* [[magic19trans37ex]]
	* [[~~magic22trans37ex\|~~magic22trans37ex]]		* [[magic22trans37ex]]

	=[[Meantone_family#Septimal meantone\|Meantone]]=		= [[Meantone_family#Septimal meantone\|Meantone]] =
	* [[~~meantone19trans37\|~~meantone19trans37]]		* [[meantone19trans37]]
	* [[~~meantone31trans37\|~~meantone31trans37]]		* [[meantone31trans37]]
	* [[~~meantone19trans37ex\|~~meantone19trans37ex]]		* [[meantone19trans37ex]]
	* [[~~meantone31trans37ex\|~~meantone31trans37ex]]		* [[meantone31trans37ex]]

	=[[Gamelismic_clan#Miracle\|Miracle]]=		= [[Gamelismic_clan#Miracle\|Miracle]] =
	* [[~~miracle21trans\|~~miracle21trans]]		* [[miracle21trans]]
	* [[~~miracle31trans\|~~miracle31trans]]		* [[miracle31trans]]
	* [[~~miracle21trans511\|~~miracle21trans511]]		* [[miracle21trans511]]
	* [[~~miracle31trans511\|~~miracle31trans511]]		* [[miracle31trans511]]

	=[[Würschmidt_family#Hemiwürschmidt\|Hemiwürschmidt]]=		= [[Würschmidt_family#Hemiwürschmidt\|Hemiwürschmidt]] =
	* [[~~hemiwuerschmidt19trans37\|~~hemiwuerschmidt19trans37]]		* [[hemiwuerschmidt19trans37]]
	* [[~~hemiwuerschmidt25trans37\|~~hemiwuerschmidt25trans37]]		* [[hemiwuerschmidt25trans37]]
	* [[~~hemiwuerschmidt31trans37\|~~hemiwuerschmidt31trans37]]		* [[hemiwuerschmidt31trans37]]

	=[[Starling_temperaments#Myna temperament\|Myna]]=		= [[Starling_temperaments#Myna temperament\|Myna]] =
	* [[~~myna19trans\|~~myna19trans]]		* [[myna19trans]]
	* [[~~myna23trans\|~~myna23trans]]		* [[myna23trans]]
	* [[~~myna27trans\|~~myna27trans]]		* [[myna27trans]]
	* [[~~myna19trans37\|~~myna19trans37]]		* [[myna19trans37]]
	* [[~~myna23trans37\|~~myna23trans37]]		* [[myna23trans37]]
	* [[~~myna27trans37\|~~myna27trans37]]		* [[myna27trans37]]

	=[[~~Semicomma_family\|~~Orwell]]=		= [[Orwell]] =
	* [[~~orwell13trans\|~~orwell13trans]]		* [[orwell13trans]]
	* [[~~orwell22trans\|~~orwell22trans]]		* [[orwell22trans]]
	* [[~~orwell31trans\|~~orwell31trans]]		* [[orwell31trans]]
	* [[~~orwell13trans57\|~~orwell13trans57]]		* [[orwell13trans57]]
	* [[~~orwell22trans57\|~~orwell22trans57]]		* [[orwell22trans57]]
	* [[~~orwell31trans57\|~~orwell31trans57]]		* [[orwell31trans57]]
	* [[~~orwell13trans57ex\|~~orwell13trans57ex]]		* [[orwell13trans57ex]]

	{{Scale gallery}}		{{Scale gallery}}

	[[Category:MOS transversals\| ]] <!-- ~~main~~ article -->		[[Category:MOS transversals\| ]] <!-- Main article -->
	[[Category:Lists of scales\|MOS transversals]]		[[Category:Lists of scales\|MOS transversals]]

BudjarnLambeth: {{Scale gallery}}

2024-12-02T04:40:41Z

← Older revision		Revision as of 04:40, 2 December 2024
Line 52:		Line 52:
	* [[orwell31trans57\|orwell31trans57]]		* [[orwell31trans57\|orwell31trans57]]
	* [[orwell13trans57ex\|orwell13trans57ex]]		* [[orwell13trans57ex\|orwell13trans57ex]]

			{{Scale gallery}}

	[[Category:MOS transversals\| ]] <!-- main article -->		[[Category:MOS transversals\| ]] <!-- main article -->
	[[Category:Lists of scales\|MOS transversals]]		[[Category:Lists of scales\|MOS transversals]]

Fredg999 category edits: Categories order

2023-04-26T02:07:37Z

Categories order

← Older revision		Revision as of 02:07, 26 April 2023
Line 53:		Line 53:
	* [[orwell13trans57ex\|orwell13trans57ex]]		* [[orwell13trans57ex\|orwell13trans57ex]]

			[[Category:MOS transversals\| ]] <!-- main article -->
	[[Category:Lists of scales\|MOS transversals]]		[[Category:Lists of scales\|MOS transversals]]
	~~[[Category:MOS transversals\| ]] <!-- main article -->~~

Fredg999 category edits: Categories

2023-04-26T02:07:23Z

Fredg999: Recategorization, improved markup and layout

2021-08-06T21:28:40Z

Recategorization, improved markup and layout

← Older revision		Revision as of 21:28, 6 August 2021
Line 1:		Line 1:
	~~__FORCETOC__~~
	~~=Introduction=~~
	By giving a [[Transversal\|transversal]] for a [[MOSScales\|MOS]] for a particular rank two temperament, we can define the MOS as the tempering, in that temperament, of the scale. This is not very interesting in itself; what is more interesting is that since only three primes--2 and two odd primes--can be used for the transversal, we can put the result into [[Scala\|Scala]], and use its "Lattice and player" command under the Analyze pull-down menu to depict the MOS in terms of a lattice diagram. This can be used to better understand the chord relationships within the MOS. It should be noted that while only chords with two odd primes are depicted, larger chords are associated to them. When 3 and 5 are relatively complex as in miracle, for instance, 7 is likely to be brought along with them, and hence the lattice picture of the 5-limit triads can be used to understand relations between tetrads in miracle and other temperaments of a similar kind. Choosing two primes which bound a chord of interest often works: for instance 3 and 5 bound 7 in miracle, so that the 5-limit transversal shows 7-limit tetrads. On the other hand, in the 11-limit, 5 and 11 bound both 7 and 9, so that the complete 11-limit sextads are represented by the triads of the 2.5.11 transveral.		By giving a [[Transversal\|transversal]] for a [[MOSScales\|MOS]] for a particular rank two temperament, we can define the MOS as the tempering, in that temperament, of the scale. This is not very interesting in itself; what is more interesting is that since only three primes--2 and two odd primes--can be used for the transversal, we can put the result into [[Scala\|Scala]], and use its "Lattice and player" command under the Analyze pull-down menu to depict the MOS in terms of a lattice diagram. This can be used to better understand the chord relationships within the MOS. It should be noted that while only chords with two odd primes are depicted, larger chords are associated to them. When 3 and 5 are relatively complex as in miracle, for instance, 7 is likely to be brought along with them, and hence the lattice picture of the 5-limit triads can be used to understand relations between tetrads in miracle and other temperaments of a similar kind. Choosing two primes which bound a chord of interest often works: for instance 3 and 5 bound 7 in miracle, so that the 5-limit transversal shows 7-limit tetrads. On the other hand, in the 11-limit, 5 and 11 bound both 7 and 9, so that the complete 11-limit sextads are represented by the triads of the 2.5.11 transveral.

Line 6:		Line 4:

	=[[Kleismic_family#Catakleismic\|Catakleismic]]=		=[[Kleismic_family#Catakleismic\|Catakleismic]]=
	[[catakleismic34fok\|catakleismic34fok]]		* [[catakleismic34fok\|catakleismic34fok]]
			* [[kleismic34trans\|kleismic34trans]]
	[[kleismic34trans\|kleismic34trans]]		* [[catakleismic34trans\|catakleismic34trans]]
			* [[catakleismic34semitransversal\|catakleismic34semitransversal]]
	[[catakleismic34trans\|catakleismic34trans]]		* [[catakleismic34transex\|catakleismic34transex]]

	[[catakleismic34semitransversal\|catakleismic34semitransversal]]

	[[catakleismic34transex\|catakleismic34transex]]

	=[[Ragismic_microtemperaments#Ennealimmal\|Ennealimmal]]=		=[[Ragismic_microtemperaments#Ennealimmal\|Ennealimmal]]=
	[[ennealimmal45trans\|ennealimmal45trans]]		* [[ennealimmal45trans\|ennealimmal45trans]]

	=[[Magic_family#Magic\|Magic]]=		=[[Magic_family#Magic\|Magic]]=
	[[magic19trans37\|magic19trans37]]		* [[magic19trans37\|magic19trans37]]
			* [[magic22trans37\|magic22trans37]]
	[[magic22trans37\|magic22trans37]]		* [[magic19trans37ex\|magic19trans37ex]]
			* [[magic22trans37ex\|magic22trans37ex]]
	[[magic19trans37ex\|magic19trans37ex]]

	[[magic22trans37ex\|magic22trans37ex]]

	=[[Meantone_family#Septimal meantone\|Meantone]]=		=[[Meantone_family#Septimal meantone\|Meantone]]=
	[[meantone19trans37\|meantone19trans37]]		* [[meantone19trans37\|meantone19trans37]]
			* [[meantone31trans37\|meantone31trans37]]
	[[meantone31trans37\|meantone31trans37]]		* [[meantone19trans37ex\|meantone19trans37ex]]
			* [[meantone31trans37ex\|meantone31trans37ex]]
	[[meantone19trans37ex\|meantone19trans37ex]]

	[[meantone31trans37ex\|meantone31trans37ex]]

	=[[Gamelismic_clan#Miracle\|Miracle]]=		=[[Gamelismic_clan#Miracle\|Miracle]]=
	[[miracle21trans\|miracle21trans]]		* [[miracle21trans\|miracle21trans]]
			* [[miracle31trans\|miracle31trans]]
	[[miracle31trans\|miracle31trans]]		* [[miracle21trans511\|miracle21trans511]]
			* [[miracle31trans511\|miracle31trans511]]
	[[miracle21trans511\|miracle21trans511]]

	[[miracle31trans511\|miracle31trans511]]

	=[[Würschmidt_family#Hemiwürschmidt\|Hemiwürschmidt]]=		=[[Würschmidt_family#Hemiwürschmidt\|Hemiwürschmidt]]=
	[[hemiwuerschmidt19trans37\|hemiwuerschmidt19trans37]]		* [[hemiwuerschmidt19trans37\|hemiwuerschmidt19trans37]]
			* [[hemiwuerschmidt25trans37\|hemiwuerschmidt25trans37]]
	[[hemiwuerschmidt25trans37\|hemiwuerschmidt25trans37]]		* [[hemiwuerschmidt31trans37\|hemiwuerschmidt31trans37]]

	[[hemiwuerschmidt31trans37\|hemiwuerschmidt31trans37]]

	=[[Starling_temperaments#Myna temperament\|Myna]]=		=[[Starling_temperaments#Myna temperament\|Myna]]=
	[[myna19trans\|myna19trans]]		* [[myna19trans\|myna19trans]]
			* [[myna23trans\|myna23trans]]
	[[myna23trans\|myna23trans]]		* [[myna27trans\|myna27trans]]
			* [[myna19trans37\|myna19trans37]]
	[[myna27trans\|myna27trans]]		* [[myna23trans37\|myna23trans37]]
			* [[myna27trans37\|myna27trans37]]
	[[myna19trans37\|myna19trans37]]

	[[myna23trans37\|myna23trans37]]

	[[myna27trans37\|myna27trans37]]

	=[[Semicomma_family\|Orwell]]=		=[[Semicomma_family\|Orwell]]=
	[[orwell13trans\|orwell13trans]]		* [[orwell13trans\|orwell13trans]]
			* [[orwell22trans\|orwell22trans]]
	[[orwell22trans\|orwell22trans]]		* [[orwell31trans\|orwell31trans]]
			* [[orwell13trans57\|orwell13trans57]]
	[[orwell31trans\|orwell31trans]]		* [[orwell22trans57\|orwell22trans57]]
			* [[orwell31trans57\|orwell31trans57]]
	[[orwell13trans57\|orwell13trans57]]		* [[orwell13trans57ex\|orwell13trans57ex]]

	[[orwell22trans57\|orwell22trans57]]

	[[orwell31trans57\|orwell31trans57]]

	[[~~orwell13trans57ex~~\|~~orwell13trans57ex~~]] [[Category:~~gallery~~]]		[[Category:Lists of scales\|MOS transversals]]
			[[Category:Just intonation scales\| ]]
			[[Category:Transversal scales\| ]]
	[[Category:MOS]]		[[Category:MOS]]
	~~[[Category:scale]]~~
	~~[[Category:Transversal scales]]~~

Keenan Pepper: Clean up categories

2021-04-24T19:35:31Z

Clean up categories

← Older revision		Revision as of 19:35, 24 April 2021
Line 80:		Line 80:

	[[orwell13trans57ex\|orwell13trans57ex]] [[Category:gallery]]		[[orwell13trans57ex\|orwell13trans57ex]] [[Category:gallery]]
	[[Category:~~mos~~]]		[[Category:MOS]]
	[[Category:scale]]		[[Category:scale]]
	[[Category:Transversal scales]]		[[Category:Transversal scales]]

Keenan Pepper category edits: Moving from Category:Transversal to Category:Transversal scales using Cat-a-lot

2020-12-04T22:57:15Z

Moving from Category:Transversal to Category:Transversal scales using Cat-a-lot

← Older revision		Revision as of 22:57, 4 December 2020
Line 82:		Line 82:
	[[Category:mos]]		[[Category:mos]]
	[[Category:scale]]		[[Category:scale]]
	[[Category:~~transversal~~]]		[[Category:Transversal scales]]

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

Show changes

Wikispaces>genewardsmith: Imported revision 288010000 - Original comment:

2011-12-21T15:46:29Z

**Imported revision 288010000 - Original comment: **

← Older revision		Revision as of 15:46, 21 December 2011
Line 1:		Line 1:
	<h2>IMPORTED REVISION FROM WIKISPACES</h2>		<h2>IMPORTED REVISION FROM WIKISPACES</h2>
	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
	: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2011-09-~~27 10~~:45:08 UTC</tt>.<br>		: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2011-12-21 15:46:29 UTC</tt>.<br>
	: The original revision id was <tt>~~258649332~~</tt>.<br>		: The original revision id was <tt>288010000</tt>.<br>
	: The revision comment was: <tt></tt><br>		: The revision comment was: <tt></tt><br>
	The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>		The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
Line 41:		Line 41:
	[[miracle31trans511]]		[[miracle31trans511]]

	=[[~~Wuerschmidt~~ family#~~Hemiwuerschmidt~~\|~~Hemiwuerschmidt~~]]=		=[[Würschmidt family#Hemiwürschmidt\|Hemiwürschmidt]]=
	[[hemiwuerschmidt19trans37]]		[[hemiwuerschmidt19trans37]]
	[[hemiwuerschmidt25trans37]]		[[hemiwuerschmidt25trans37]]
Line 63:		Line 63:
	[[orwell13trans57ex]]</pre></div>		[[orwell13trans57ex]]</pre></div>
	<h4>Original HTML content:</h4>		<h4>Original HTML content:</h4>
	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Gallery of MOS transversals</title></head><body><!-- ws:start:WikiTextTocRule:18:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --><a href="#Introduction">Introduction</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --> \| <a href="#Catakleismic">Catakleismic</a><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --> \| <a href="#Ennealimmal">Ennealimmal</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> \| <a href="#Magic">Magic</a><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --> \| <a href="#Meantone">Meantone</a><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --> \| <a href="#Miracle">Miracle</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --> \| <a href="#~~Hemiwuerschmidt~~">~~Hemiwuerschmidt~~</a><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --> \| <a href="#Myna">Myna</a><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --> \| <a href="#Orwell">Orwell</a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: -->		<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Gallery of MOS transversals</title></head><body><!-- ws:start:WikiTextTocRule:18:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --><a href="#Introduction">Introduction</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --> \| <a href="#Catakleismic">Catakleismic</a><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --> \| <a href="#Ennealimmal">Ennealimmal</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> \| <a href="#Magic">Magic</a><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --> \| <a href="#Meantone">Meantone</a><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --> \| <a href="#Miracle">Miracle</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --> \| <a href="#Hemiwürschmidt">Hemiwürschmidt</a><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --> \| <a href="#Myna">Myna</a><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --> \| <a href="#Orwell">Orwell</a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: -->
	<!-- ws:end:WikiTextTocRule:28 --><br />		<!-- ws:end:WikiTextTocRule:28 --><br />
	<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Introduction"></a><!-- ws:end:WikiTextHeadingRule:0 -->Introduction</h1>		<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Introduction"></a><!-- ws:end:WikiTextHeadingRule:0 -->Introduction</h1>
Line 98:		Line 98:
	<a class="wiki_link" href="/miracle31trans511">miracle31trans511</a><br />		<a class="wiki_link" href="/miracle31trans511">miracle31trans511</a><br />
	<br />		<br />
	<!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="~~Hemiwuerschmidt~~"></a><!-- ws:end:WikiTextHeadingRule:12 --><a class="wiki_link" href="/~~Wuerschmidt~~%20family#~~Hemiwuerschmidt~~">~~Hemiwuerschmidt~~</a></h1>		<!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Hemiwürschmidt"></a><!-- ws:end:WikiTextHeadingRule:12 --><a class="wiki_link" href="/W%C3%BCrschmidt%20family#Hemiwürschmidt">Hemiwürschmidt</a></h1>
	<a class="wiki_link" href="/hemiwuerschmidt19trans37">hemiwuerschmidt19trans37</a><br />		<a class="wiki_link" href="/hemiwuerschmidt19trans37">hemiwuerschmidt19trans37</a><br />
	<a class="wiki_link" href="/hemiwuerschmidt25trans37">hemiwuerschmidt25trans37</a><br />		<a class="wiki_link" href="/hemiwuerschmidt25trans37">hemiwuerschmidt25trans37</a><br />

← Older revision		Revision as of 20:02, 11 February 2025
Line 1:		Line 1:
	By giving a [[~~Transversal\|~~transversal]] for a [[~~MOSScales\|~~MOS]] for a particular rank two temperament, we can define the MOS as the tempering, in that temperament, of the scale. This is not very interesting in itself; what is more interesting is that since only three primes--2 and two odd primes--can be used for the transversal, we can put the result into [[~~Scala\|~~Scala]], and use its "Lattice and player" command under the Analyze pull-down menu to depict the MOS in terms of a lattice diagram. This can be used to better understand the chord relationships within the MOS. It should be noted that while only chords with two odd primes are depicted, larger chords are associated to them. When 3 and 5 are relatively complex as in miracle, for instance, 7 is likely to be brought along with them, and hence the lattice picture of the 5-limit triads can be used to understand relations between tetrads in miracle and other temperaments of a similar kind. Choosing two primes which bound a chord of interest often works: for instance 3 and 5 bound 7 in miracle, so that the 5-limit transversal shows 7-limit tetrads. On the other hand, in the 11-limit, 5 and 11 bound both 7 and 9, so that the complete 11-limit sextads are represented by the triads of the 2.5.11 transveral.		By giving a [[transversal]] for a [[MOS]] for a particular rank two temperament, we can define the MOS as the tempering, in that temperament, of the scale. This is not very interesting in itself; what is more interesting is that since only three primes--2 and two odd primes--can be used for the transversal, we can put the result into [[Scala]], and use its "Lattice and player" command under the Analyze pull-down menu to depict the MOS in terms of a lattice diagram. This can be used to better understand the chord relationships within the MOS. It should be noted that while only chords with two odd primes are depicted, larger chords are associated to them. When 3 and 5 are relatively complex as in miracle, for instance, 7 is likely to be brought along with them, and hence the lattice picture of the 5-limit triads can be used to understand relations between tetrads in miracle and other temperaments of a similar kind. Choosing two primes which bound a chord of interest often works: for instance 3 and 5 bound 7 in miracle, so that the 5-limit transversal shows 7-limit tetrads. On the other hand, in the 11-limit, 5 and 11 bound both 7 and 9, so that the complete 11-limit sextads are represented by the triads of the 2.5.11 transveral.

	A difficulty with the method is that the planar arrangement does not correspond precisely with the linear arrangement of MOS; the single comma between the three primes rolls up the plane into a cylinder, hence there may be chords not represented by the transveral lattice. Rather than attempting to roll any cylinders, one may take advantage of the fact that with only three generators there is just one comma on the subgroup temperament; multiplying by it, dividing by it, and taking the original scale one gets an extended transversal which reduces to the same MOS but which shows the chords within a larger lattice. These are the scales with "ex" postfixing the name of the scale.		A difficulty with the method is that the planar arrangement does not correspond precisely with the linear arrangement of MOS; the single comma between the three primes rolls up the plane into a cylinder, hence there may be chords not represented by the transveral lattice. Rather than attempting to roll any cylinders, one may take advantage of the fact that with only three generators there is just one comma on the subgroup temperament; multiplying by it, dividing by it, and taking the original scale one gets an extended transversal which reduces to the same MOS but which shows the chords within a larger lattice. These are the scales with "ex" postfixing the name of the scale.

	=[[Kleismic_family#Catakleismic\|Catakleismic]]=		= [[Kleismic_family#Catakleismic\|Catakleismic]] =
	* [[~~catakleismic34fok\|~~catakleismic34fok]]		* [[catakleismic34fok]]
	* [[~~kleismic34trans\|~~kleismic34trans]]		* [[kleismic34trans]]
	* [[~~catakleismic34trans\|~~catakleismic34trans]]		* [[catakleismic34trans]]
	* [[~~catakleismic34semitransversal\|~~catakleismic34semitransversal]]		* [[catakleismic34semitransversal]]
	* [[~~catakleismic34transex\|~~catakleismic34transex]]		* [[catakleismic34transex]]

	=[[Ragismic_microtemperaments#Ennealimmal\|Ennealimmal]]=		= [[Ragismic_microtemperaments#Ennealimmal\|Ennealimmal]] =
	* [[~~ennealimmal45trans\|~~ennealimmal45trans]]		* [[ennealimmal45trans]]

	=[[Magic_family#Magic\|Magic]]=		= [[Magic_family#Magic\|Magic]] =
	* [[~~magic19trans37\|~~magic19trans37]]		* [[magic19trans37]]
	* [[~~magic22trans37\|~~magic22trans37]]		* [[magic22trans37]]
	* [[~~magic19trans37ex\|~~magic19trans37ex]]		* [[magic19trans37ex]]
	* [[~~magic22trans37ex\|~~magic22trans37ex]]		* [[magic22trans37ex]]

	=[[Meantone_family#Septimal meantone\|Meantone]]=		= [[Meantone_family#Septimal meantone\|Meantone]] =
	* [[~~meantone19trans37\|~~meantone19trans37]]		* [[meantone19trans37]]
	* [[~~meantone31trans37\|~~meantone31trans37]]		* [[meantone31trans37]]
	* [[~~meantone19trans37ex\|~~meantone19trans37ex]]		* [[meantone19trans37ex]]
	* [[~~meantone31trans37ex\|~~meantone31trans37ex]]		* [[meantone31trans37ex]]

	=[[Gamelismic_clan#Miracle\|Miracle]]=		= [[Gamelismic_clan#Miracle\|Miracle]] =
	* [[~~miracle21trans\|~~miracle21trans]]		* [[miracle21trans]]
	* [[~~miracle31trans\|~~miracle31trans]]		* [[miracle31trans]]
	* [[~~miracle21trans511\|~~miracle21trans511]]		* [[miracle21trans511]]
	* [[~~miracle31trans511\|~~miracle31trans511]]		* [[miracle31trans511]]

	=[[Würschmidt_family#Hemiwürschmidt\|Hemiwürschmidt]]=		= [[Würschmidt_family#Hemiwürschmidt\|Hemiwürschmidt]] =
	* [[~~hemiwuerschmidt19trans37\|~~hemiwuerschmidt19trans37]]		* [[hemiwuerschmidt19trans37]]
	* [[~~hemiwuerschmidt25trans37\|~~hemiwuerschmidt25trans37]]		* [[hemiwuerschmidt25trans37]]
	* [[~~hemiwuerschmidt31trans37\|~~hemiwuerschmidt31trans37]]		* [[hemiwuerschmidt31trans37]]

	=[[Starling_temperaments#Myna temperament\|Myna]]=		= [[Starling_temperaments#Myna temperament\|Myna]] =
	* [[~~myna19trans\|~~myna19trans]]		* [[myna19trans]]
	* [[~~myna23trans\|~~myna23trans]]		* [[myna23trans]]
	* [[~~myna27trans\|~~myna27trans]]		* [[myna27trans]]
	* [[~~myna19trans37\|~~myna19trans37]]		* [[myna19trans37]]
	* [[~~myna23trans37\|~~myna23trans37]]		* [[myna23trans37]]
	* [[~~myna27trans37\|~~myna27trans37]]		* [[myna27trans37]]

	=[[~~Semicomma_family\|~~Orwell]]=		= [[Orwell]] =
	* [[~~orwell13trans\|~~orwell13trans]]		* [[orwell13trans]]
	* [[~~orwell22trans\|~~orwell22trans]]		* [[orwell22trans]]
	* [[~~orwell31trans\|~~orwell31trans]]		* [[orwell31trans]]
	* [[~~orwell13trans57\|~~orwell13trans57]]		* [[orwell13trans57]]
	* [[~~orwell22trans57\|~~orwell22trans57]]		* [[orwell22trans57]]
	* [[~~orwell31trans57\|~~orwell31trans57]]		* [[orwell31trans57]]
	* [[~~orwell13trans57ex\|~~orwell13trans57ex]]		* [[orwell13trans57ex]]

	{{Scale gallery}}		{{Scale gallery}}

	[[Category:MOS transversals\| ]] <!-- ~~main~~ article -->		[[Category:MOS transversals\| ]] <!-- Main article -->
	[[Category:Lists of scales\|MOS transversals]]		[[Category:Lists of scales\|MOS transversals]]

← Older revision		Revision as of 04:40, 2 December 2024
Line 52:		Line 52:
	* [[orwell31trans57\|orwell31trans57]]		* [[orwell31trans57\|orwell31trans57]]
	* [[orwell13trans57ex\|orwell13trans57ex]]		* [[orwell13trans57ex\|orwell13trans57ex]]

			{{Scale gallery}}

	[[Category:MOS transversals\| ]] <!-- main article -->		[[Category:MOS transversals\| ]] <!-- main article -->
	[[Category:Lists of scales\|MOS transversals]]		[[Category:Lists of scales\|MOS transversals]]

← Older revision		Revision as of 02:07, 26 April 2023
Line 53:		Line 53:
	* [[orwell13trans57ex\|orwell13trans57ex]]		* [[orwell13trans57ex\|orwell13trans57ex]]

			[[Category:MOS transversals\| ]] <!-- main article -->
	[[Category:Lists of scales\|MOS transversals]]		[[Category:Lists of scales\|MOS transversals]]
	~~[[Category:MOS transversals\| ]] <!-- main article -->~~

← Older revision		Revision as of 02:07, 26 April 2023
Line 54:		Line 54:

	[[Category:Lists of scales\|MOS transversals]]		[[Category:Lists of scales\|MOS transversals]]
	[[Category:~~Just intonation scales\| ]]~~		[[Category:MOS transversals\| ]] <!-- main article -->
	~~[[Category:Transversal scales~~\| ]]
	~~[[Category:MOS]]~~

← Older revision		Revision as of 21:28, 6 August 2021
Line 1:		Line 1:
	~~__FORCETOC__~~
	~~=Introduction=~~
	By giving a [[Transversal\|transversal]] for a [[MOSScales\|MOS]] for a particular rank two temperament, we can define the MOS as the tempering, in that temperament, of the scale. This is not very interesting in itself; what is more interesting is that since only three primes--2 and two odd primes--can be used for the transversal, we can put the result into [[Scala\|Scala]], and use its "Lattice and player" command under the Analyze pull-down menu to depict the MOS in terms of a lattice diagram. This can be used to better understand the chord relationships within the MOS. It should be noted that while only chords with two odd primes are depicted, larger chords are associated to them. When 3 and 5 are relatively complex as in miracle, for instance, 7 is likely to be brought along with them, and hence the lattice picture of the 5-limit triads can be used to understand relations between tetrads in miracle and other temperaments of a similar kind. Choosing two primes which bound a chord of interest often works: for instance 3 and 5 bound 7 in miracle, so that the 5-limit transversal shows 7-limit tetrads. On the other hand, in the 11-limit, 5 and 11 bound both 7 and 9, so that the complete 11-limit sextads are represented by the triads of the 2.5.11 transveral.		By giving a [[Transversal\|transversal]] for a [[MOSScales\|MOS]] for a particular rank two temperament, we can define the MOS as the tempering, in that temperament, of the scale. This is not very interesting in itself; what is more interesting is that since only three primes--2 and two odd primes--can be used for the transversal, we can put the result into [[Scala\|Scala]], and use its "Lattice and player" command under the Analyze pull-down menu to depict the MOS in terms of a lattice diagram. This can be used to better understand the chord relationships within the MOS. It should be noted that while only chords with two odd primes are depicted, larger chords are associated to them. When 3 and 5 are relatively complex as in miracle, for instance, 7 is likely to be brought along with them, and hence the lattice picture of the 5-limit triads can be used to understand relations between tetrads in miracle and other temperaments of a similar kind. Choosing two primes which bound a chord of interest often works: for instance 3 and 5 bound 7 in miracle, so that the 5-limit transversal shows 7-limit tetrads. On the other hand, in the 11-limit, 5 and 11 bound both 7 and 9, so that the complete 11-limit sextads are represented by the triads of the 2.5.11 transveral.

Line 6:		Line 4:

	=[[Kleismic_family#Catakleismic\|Catakleismic]]=		=[[Kleismic_family#Catakleismic\|Catakleismic]]=
	[[catakleismic34fok\|catakleismic34fok]]		* [[catakleismic34fok\|catakleismic34fok]]
			* [[kleismic34trans\|kleismic34trans]]
	[[kleismic34trans\|kleismic34trans]]		* [[catakleismic34trans\|catakleismic34trans]]
			* [[catakleismic34semitransversal\|catakleismic34semitransversal]]
	[[catakleismic34trans\|catakleismic34trans]]		* [[catakleismic34transex\|catakleismic34transex]]

	[[catakleismic34semitransversal\|catakleismic34semitransversal]]

	[[catakleismic34transex\|catakleismic34transex]]

	=[[Ragismic_microtemperaments#Ennealimmal\|Ennealimmal]]=		=[[Ragismic_microtemperaments#Ennealimmal\|Ennealimmal]]=
	[[ennealimmal45trans\|ennealimmal45trans]]		* [[ennealimmal45trans\|ennealimmal45trans]]

	=[[Magic_family#Magic\|Magic]]=		=[[Magic_family#Magic\|Magic]]=
	[[magic19trans37\|magic19trans37]]		* [[magic19trans37\|magic19trans37]]
			* [[magic22trans37\|magic22trans37]]
	[[magic22trans37\|magic22trans37]]		* [[magic19trans37ex\|magic19trans37ex]]
			* [[magic22trans37ex\|magic22trans37ex]]
	[[magic19trans37ex\|magic19trans37ex]]

	[[magic22trans37ex\|magic22trans37ex]]

	=[[Meantone_family#Septimal meantone\|Meantone]]=		=[[Meantone_family#Septimal meantone\|Meantone]]=
	[[meantone19trans37\|meantone19trans37]]		* [[meantone19trans37\|meantone19trans37]]
			* [[meantone31trans37\|meantone31trans37]]
	[[meantone31trans37\|meantone31trans37]]		* [[meantone19trans37ex\|meantone19trans37ex]]
			* [[meantone31trans37ex\|meantone31trans37ex]]
	[[meantone19trans37ex\|meantone19trans37ex]]

	[[meantone31trans37ex\|meantone31trans37ex]]

	=[[Gamelismic_clan#Miracle\|Miracle]]=		=[[Gamelismic_clan#Miracle\|Miracle]]=
	[[miracle21trans\|miracle21trans]]		* [[miracle21trans\|miracle21trans]]
			* [[miracle31trans\|miracle31trans]]
	[[miracle31trans\|miracle31trans]]		* [[miracle21trans511\|miracle21trans511]]
			* [[miracle31trans511\|miracle31trans511]]
	[[miracle21trans511\|miracle21trans511]]

	[[miracle31trans511\|miracle31trans511]]

	=[[Würschmidt_family#Hemiwürschmidt\|Hemiwürschmidt]]=		=[[Würschmidt_family#Hemiwürschmidt\|Hemiwürschmidt]]=
	[[hemiwuerschmidt19trans37\|hemiwuerschmidt19trans37]]		* [[hemiwuerschmidt19trans37\|hemiwuerschmidt19trans37]]
			* [[hemiwuerschmidt25trans37\|hemiwuerschmidt25trans37]]
	[[hemiwuerschmidt25trans37\|hemiwuerschmidt25trans37]]		* [[hemiwuerschmidt31trans37\|hemiwuerschmidt31trans37]]

	[[hemiwuerschmidt31trans37\|hemiwuerschmidt31trans37]]

	=[[Starling_temperaments#Myna temperament\|Myna]]=		=[[Starling_temperaments#Myna temperament\|Myna]]=
	[[myna19trans\|myna19trans]]		* [[myna19trans\|myna19trans]]
			* [[myna23trans\|myna23trans]]
	[[myna23trans\|myna23trans]]		* [[myna27trans\|myna27trans]]
			* [[myna19trans37\|myna19trans37]]
	[[myna27trans\|myna27trans]]		* [[myna23trans37\|myna23trans37]]
			* [[myna27trans37\|myna27trans37]]
	[[myna19trans37\|myna19trans37]]

	[[myna23trans37\|myna23trans37]]

	[[myna27trans37\|myna27trans37]]

	=[[Semicomma_family\|Orwell]]=		=[[Semicomma_family\|Orwell]]=
	[[orwell13trans\|orwell13trans]]		* [[orwell13trans\|orwell13trans]]
			* [[orwell22trans\|orwell22trans]]
	[[orwell22trans\|orwell22trans]]		* [[orwell31trans\|orwell31trans]]
			* [[orwell13trans57\|orwell13trans57]]
	[[orwell31trans\|orwell31trans]]		* [[orwell22trans57\|orwell22trans57]]
			* [[orwell31trans57\|orwell31trans57]]
	[[orwell13trans57\|orwell13trans57]]		* [[orwell13trans57ex\|orwell13trans57ex]]

	[[orwell22trans57\|orwell22trans57]]

	[[orwell31trans57\|orwell31trans57]]

	[[~~orwell13trans57ex~~\|~~orwell13trans57ex~~]] [[Category:~~gallery~~]]		[[Category:Lists of scales\|MOS transversals]]
			[[Category:Just intonation scales\| ]]
			[[Category:Transversal scales\| ]]
	[[Category:MOS]]		[[Category:MOS]]
	~~[[Category:scale]]~~
	~~[[Category:Transversal scales]]~~