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Comparison of mode notation systems: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
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<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;white-space: pre-wrap ! important" class="old-revision-html">=__How to name rank-2 scales__=  
<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;white-space: pre-wrap ! important" class="old-revision-html">=__How to name rank-2 scales__=  


Here's how to name MOS, MODMOS and even non-MOS rank-2 scales systematically. Like [[xenharmonic/Modal UDP notation|Modal UDP notation]], it starts with the convention of using //some-temperament-name//[//some-number//] to create a generator-chain, and adds a way to number each mode uniquely. Here are all the modes of Meantone[7], using ~3/2 as the generator:
Here's how to name MOS, MODMOS and even non-MOS rank-2 scales systematically. Like [[xenharmonic/Modal UDP notation|Modal UDP notation]], it starts with the convention of using //some-temperament-name//[//some-number//] to create a generator-chain, and adds a way to number each mode uniquely. For example, here are all the modes of Meantone[7], using ~3/2 as the generator:
|| old scale name || new scale name || Ls pattern || example on white keys || genchain ||
|| old scale name || new scale name || Ls pattern || example on white keys || genchain ||
|| Lydian || 1st Meantone[7] || LLLs LLs || F G A B C D E F || **F** C G D A E B ||
|| Lydian || 1st Meantone[7] || LLLs LLs || F G A B C D E F || **F** C G D A E B ||
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|| Phrygian || 6th Meantone[7] || sLLL sLL || E F G A B C D E || F C G D A **E** B ||
|| Phrygian || 6th Meantone[7] || sLLL sLL || E F G A B C D E || F C G D A **E** B ||
|| Locrian || 7th Meantone[7] || sLLs LLL || B C D E F G A B || F C G D A E **B** ||
|| Locrian || 7th Meantone[7] || sLLs LLL || B C D E F G A B || F C G D A E **B** ||
Scales are formed from a segment of the generator-chain, or genchain. The first note in the genchain is the tonic of mode #1, the 2nd note is the tonic of mode #2, etc. For example, Dorian is 4th Meantone[7], spoken as "fourth meantone heptatonic" or possibly "fourth meantone seven". If in D, as above, it would be "D 4th meantone heptatonic". The same 7 modes, all with C as the tonic:
 
Scales are formed from a segment of the generator-chain, or genchain. The first note in the genchain is the tonic of mode #1, the 2nd note is the tonic of mode #2, etc. For example, Dorian is 4th Meantone[7], spoken as "fourth meantone heptatonic". If in D, as above, it would be "D 4th meantone heptatonic". The same seven modes, all with C as the tonic, to illustrate the difference between modes:
|| old scale name || new scale name || Ls pattern || example in C || ------------------- genchain --------------- ||
|| old scale name || new scale name || Ls pattern || example in C || ------------------- genchain --------------- ||
|| Lydian || 1st Meantone[7] || LLLs LLs || C D E F# G A B C ||&gt; **C** G D A E B F# ||
|| Lydian || 1st Meantone[7] || LLLs LLs || C D E F# G A B C ||&gt; **C** G D A E B F# ||
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|| Locrian || 7th Meantone[7] || sLLs LLL || C Db Eb F Gb Ab Bb C || Gb Db Ab Eb Bb F **C** ||
|| Locrian || 7th Meantone[7] || sLLs LLL || C Db Eb F Gb Ab Bb C || Gb Db Ab Eb Bb F **C** ||
Similar modes are grouped together. The overall progression is from sharper to flatter. However for the 5 pentatonic modes, the overall progression is from flatter to sharper. Unlike modal UDP notation, the generator isn't always chroma-positive.
Similar modes are grouped together. The overall progression is from sharper to flatter. However for the 5 pentatonic modes, the overall progression is from flatter to sharper. Unlike modal UDP notation, the generator isn't always chroma-positive.
Pentatonic meantone scales:
|| old scale name || new scale name || Ls pattern || example in C || --------- genchain ------- ||
|| old scale name || new scale name || Ls pattern || example in C || --------- genchain ------- ||
|| major pentatonic || 1st Meantone[5] || ssL sL || C D E G A C ||&gt; **C** G D A E ||
|| major pentatonic || 1st Meantone[5] || ssL sL || C D E G A C ||&gt; **C** G D A E ||
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||= ??? || 5th Meantone[5] || LsL ss || C Eb F Ab Bb C || Ab Eb Bb F **C** ||
||= ??? || 5th Meantone[5] || LsL ss || C Eb F Ab Bb C || Ab Eb Bb F **C** ||


12-note meantone scales:
Chromatic meantone scales:
|| scale name || Ls pattern || example in C || genchain ||
|| scale name || Ls pattern || example in C || genchain ||
|| 1st Meantone[12] || sLsLsLL sLsLL || C C# D D# E E# F# G G# A A# B C || **C** G D A E B F# C# G# D# A# E# ||
|| 1st Meantone[12] || sLsLsLL sLsLL || C C# D D# E E# F# G G# A A# B C || **C** G D A E B F# C# G# D# A# E# ||
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C D E F F# G A B C, which has a genchain F **C** G D A E B F#, and is named C 2nd Meantone{8}.
C D E F F# G A B C, which has a genchain F **C** G D A E B F#, and is named C 2nd Meantone{8}.


C D E F F# G A Bb C, with genchain Bb F **C** G D A E * F#. Alter as few notes as possible to get if not a MOS, at least an unbroken genchain: F **C** G D A E B F#. The scale is C 2nd Meantone{8} b7.
C D E F F# G A Bb C, with genchain Bb F **C** G D A E * F#. Alter as few notes as possible to get an unbroken genchain:  
F **C** G D A E B F#. The scale is C 2nd Meantone{8} b7.


A B C D D# E F G G# A, with genchain F C G D **A** E B * * G# D#. Sharpen F and C to get an unbroken genchain: G D **A** E B F# C# G# D#, giving the name A 3rd Meantone{9} b3 b7.
A B C D D# E F G G# A, with genchain F C G D **A** E B * * G# D#. Sharpen F and C to get an unbroken genchain: G D **A** E B F# C# G# D#, giving the name A 3rd Meantone{9} b3 b7.
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<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Naming Rank-2 Scales&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="How to name rank-2 scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;u&gt;How to name rank-2 scales&lt;/u&gt;&lt;/h1&gt;
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Naming Rank-2 Scales&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="How to name rank-2 scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;u&gt;How to name rank-2 scales&lt;/u&gt;&lt;/h1&gt;
  &lt;br /&gt;
  &lt;br /&gt;
Here's how to name MOS, MODMOS and even non-MOS rank-2 scales systematically. Like &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Modal%20UDP%20notation"&gt;Modal UDP notation&lt;/a&gt;, it starts with the convention of using &lt;em&gt;some-temperament-name&lt;/em&gt;[&lt;em&gt;some-number&lt;/em&gt;] to create a generator-chain, and adds a way to number each mode uniquely. Here are all the modes of Meantone[7], using ~3/2 as the generator:&lt;br /&gt;
Here's how to name MOS, MODMOS and even non-MOS rank-2 scales systematically. Like &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Modal%20UDP%20notation"&gt;Modal UDP notation&lt;/a&gt;, it starts with the convention of using &lt;em&gt;some-temperament-name&lt;/em&gt;[&lt;em&gt;some-number&lt;/em&gt;] to create a generator-chain, and adds a way to number each mode uniquely. For example, here are all the modes of Meantone[7], using ~3/2 as the generator:&lt;br /&gt;




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&lt;/table&gt;
&lt;/table&gt;


Scales are formed from a segment of the generator-chain, or genchain. The first note in the genchain is the tonic of mode #1, the 2nd note is the tonic of mode #2, etc. For example, Dorian is 4th Meantone[7], spoken as &amp;quot;fourth meantone heptatonic&amp;quot; or possibly &amp;quot;fourth meantone seven&amp;quot;. If in D, as above, it would be &amp;quot;D 4th meantone heptatonic&amp;quot;. The same 7 modes, all with C as the tonic:&lt;br /&gt;
&lt;br /&gt;
Scales are formed from a segment of the generator-chain, or genchain. The first note in the genchain is the tonic of mode #1, the 2nd note is the tonic of mode #2, etc. For example, Dorian is 4th Meantone[7], spoken as &amp;quot;fourth meantone heptatonic&amp;quot;. If in D, as above, it would be &amp;quot;D 4th meantone heptatonic&amp;quot;. The same seven modes, all with C as the tonic, to illustrate the difference between modes:&lt;br /&gt;




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Similar modes are grouped together. The overall progression is from sharper to flatter. However for the 5 pentatonic modes, the overall progression is from flatter to sharper. Unlike modal UDP notation, the generator isn't always chroma-positive.&lt;br /&gt;
Similar modes are grouped together. The overall progression is from sharper to flatter. However for the 5 pentatonic modes, the overall progression is from flatter to sharper. Unlike modal UDP notation, the generator isn't always chroma-positive.&lt;br /&gt;
&lt;br /&gt;
Pentatonic meantone scales:&lt;br /&gt;




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&lt;br /&gt;
&lt;br /&gt;
12-note meantone scales:&lt;br /&gt;
Chromatic meantone scales:&lt;br /&gt;




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C D E F F# G A B C, which has a genchain F &lt;strong&gt;C&lt;/strong&gt; G D A E B F#, and is named C 2nd Meantone{8}.&lt;br /&gt;
C D E F F# G A B C, which has a genchain F &lt;strong&gt;C&lt;/strong&gt; G D A E B F#, and is named C 2nd Meantone{8}.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
C D E F F# G A Bb C, with genchain Bb F &lt;strong&gt;C&lt;/strong&gt; G D A E * F#. Alter as few notes as possible to get if not a MOS, at least an unbroken genchain: F &lt;strong&gt;C&lt;/strong&gt; G D A E B F#. The scale is C 2nd Meantone{8} b7.&lt;br /&gt;
C D E F F# G A Bb C, with genchain Bb F &lt;strong&gt;C&lt;/strong&gt; G D A E * F#. Alter as few notes as possible to get an unbroken genchain: &lt;br /&gt;
F &lt;strong&gt;C&lt;/strong&gt; G D A E B F#. The scale is C 2nd Meantone{8} b7.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A B C D D# E F G G# A, with genchain F C G D &lt;strong&gt;A&lt;/strong&gt; E B * * G# D#. Sharpen F and C to get an unbroken genchain: G D &lt;strong&gt;A&lt;/strong&gt; E B F# C# G# D#, giving the name A 3rd Meantone{9} b3 b7.&lt;br /&gt;
A B C D D# E F G G# A, with genchain F C G D &lt;strong&gt;A&lt;/strong&gt; E B * * G# D#. Sharpen F and C to get an unbroken genchain: G D &lt;strong&gt;A&lt;/strong&gt; E B F# C# G# D#, giving the name A 3rd Meantone{9} b3 b7.&lt;br /&gt;
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