Comparison of mode notation systems: Difference between revisions

Wikispaces>TallKite
**Imported revision 580762913 - Original comment: **
Wikispaces>TallKite
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<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>
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: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-04-21 04:30:39 UTC</tt>.<br>
: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-04-21 04:47:21 UTC</tt>.<br>
: The original revision id was <tt>580762913</tt>.<br>
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|| 6th Meantone[7] || Phrygian || sLLL sLL || E F G A B C D E || F C G D A **E** B ||
|| 6th Meantone[7] || Phrygian || sLLL sLL || E F G A B C D E || F C G D A **E** B ||
|| 7th Meantone[7] || Locrian || sLLs LLL || B C D E F G A B || F C G D A E **B** ||
|| 7th Meantone[7] || Locrian || 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". 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" 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:
|| new scale name || old scale name || Ls pattern || example in C || ------------------- genchain --------------- ||
|| new scale name || old scale name || Ls pattern || example in C || ------------------- genchain --------------- ||
|| 1st Meantone[7] || Lydian || LLLs LLs || C D E F# G A B C ||&gt; **C** G D A E B F# ||
|| 1st Meantone[7] || Lydian || LLLs LLs || C D E F# G A B C ||&gt; **C** G D A E B F# ||
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==[[#How to name rank-2 scales-Fractional-octave periods]]**__Fractional-octave periods__**==  
==[[#How to name rank-2 scales-Fractional-octave periods]]**__Fractional-octave periods__**==  
Fractional-period rank-2 temperaments have multiple genchains running in parallel. For example, shrutal[10] might look like this:
Fractional-period rank-2 temperaments have multiple genchains running in parallel. For example, shrutal[10] might look like this:
Eb _ Bb _ F __ C __ G
Eb -- Bb -- F --- C --- G
A __ E __ B __ F# _ C#
A --- E --- B --- F# -- C#


Or alternatively, using 16/15 not 3/2 as the generator:
Or alternatively, using 16/15 not 3/2 as the generator:
Eb _ E __ F __ F# _ G
Eb -- E --- F --- F# -- G
A __ Bb _ B __ C __ C#
A --- Bb -- B --- C --- C#


Multiple genchains occur because rank-2 really is 2 dimensional, with a "genweb" running in octaves (or whatever the period is) vertically and fifths (or whatever the generator is) horizontally. When the period is an octave, this octave-reduces to a single horizontal genchain. But shrutal has a genweb with vertical half-octaves, which octave-reduces to two parallel genchains. Temperaments with third-octave periods reduce to a triple-genchain, and so forth.
Multiple genchains occur because rank-2 really is 2 dimensional, with a "genweb" running in octaves (or whatever the period is) vertically and fifths (or whatever the generator is) horizontally. When the period is an octave, this octave-reduces to a single horizontal genchain. But shrutal has a genweb with vertical half-octaves, which octave-reduces to two parallel genchains. Temperaments with third-octave periods reduce to a triple-genchain, and so forth.
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==[[#How to name rank-2 scales-Non-MOS scales]]**__Non-MOS scales__**==  
==[[#How to name rank-2 scales-Non-MOS scales]]**__Non-MOS scales__**==  
These can be indicated with curly brackets, as Meantone{8}. The same naming methods apply:
These can be indicated with curly brackets {}, because regular brackets [] are reserved for MOS scales. The same naming methods apply:


Then there's non-MOS rank-2 scales, gapped and ungapped. E.g. Meantone[8], perhaps C D E F F# G A B C which is F C G D A E B F#. The C scale would be Meantone[8] 2nd mode.
An ungapped example: C D E F F# G A B C, which has a genchain F **C** G D A E B F#, and is named 2nd Meantone{8}.


A gapped example: C D E F F# G A Bb C which is Bb F C G D A E (gap) F#. Move as few notes as possible to get not a MOS but at least an unbroken genchain: F C G D A E B F#. So the C scale is Meantone[8] 2nd mode b7.
A gapped example: 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 2nd Meantone[8] b7.


Sort of a Fur Elise scale: A B C D D# E F G G# A is F C G D A E B (gap of 2) G# D#. Sharpen F and C to get an unbroken genchain. Then we get Meantone[9] 3rd mode b3 b7.
Sort of a Fur Elise scale: 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.


Here's a tricky one: F G A C F, the genchain is F C G (gap) A, no way to make an unbroken chain. I would notate this Meantone[5] 1st mode, no 6. Or perhaps "no 5" since it's pentatonic.
Here's a tricky one: F G A C F, the genchain is F C G (gap) A, no way to make an unbroken chain. I would notate this Meantone[5] 1st mode, no 5.




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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;. The same 7 modes, all with C as the tonic:&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; 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;




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&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="How to name rank-2 scales-Fractional-octave periods"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:14:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@How to name rank-2 scales-Fractional-octave periods&amp;quot; title=&amp;quot;Anchor: How to name rank-2 scales-Fractional-octave periods&amp;quot;/&amp;gt; --&gt;&lt;a name="How to name rank-2 scales-Fractional-octave periods"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:14 --&gt;&lt;strong&gt;&lt;u&gt;Fractional-octave periods&lt;/u&gt;&lt;/strong&gt;&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="How to name rank-2 scales-Fractional-octave periods"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:14:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@How to name rank-2 scales-Fractional-octave periods&amp;quot; title=&amp;quot;Anchor: How to name rank-2 scales-Fractional-octave periods&amp;quot;/&amp;gt; --&gt;&lt;a name="How to name rank-2 scales-Fractional-octave periods"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:14 --&gt;&lt;strong&gt;&lt;u&gt;Fractional-octave periods&lt;/u&gt;&lt;/strong&gt;&lt;/h2&gt;
  Fractional-period rank-2 temperaments have multiple genchains running in parallel. For example, shrutal[10] might look like this:&lt;br /&gt;
  Fractional-period rank-2 temperaments have multiple genchains running in parallel. For example, shrutal[10] might look like this:&lt;br /&gt;
Eb _ Bb _ F &lt;u&gt; C &lt;/u&gt; G&lt;br /&gt;
Eb -- Bb -- F --- C --- G&lt;br /&gt;
A &lt;u&gt; E &lt;/u&gt; B &lt;u&gt; F# _ C#&lt;br /&gt;
A --- E --- B --- F# -- C#&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Or alternatively, using 16/15 not 3/2 as the generator:&lt;br /&gt;
Or alternatively, using 16/15 not 3/2 as the generator:&lt;br /&gt;
Eb _ E &lt;/u&gt; F &lt;u&gt; F# _ G&lt;br /&gt;
Eb -- E --- F --- F# -- G&lt;br /&gt;
A &lt;/u&gt; Bb _ B &lt;u&gt; C &lt;/u&gt; C#&lt;br /&gt;
A --- Bb -- B --- C --- C#&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Multiple genchains occur because rank-2 really is 2 dimensional, with a &amp;quot;genweb&amp;quot; running in octaves (or whatever the period is) vertically and fifths (or whatever the generator is) horizontally. When the period is an octave, this octave-reduces to a single horizontal genchain. But shrutal has a genweb with vertical half-octaves, which octave-reduces to two parallel genchains. Temperaments with third-octave periods reduce to a triple-genchain, and so forth.&lt;br /&gt;
Multiple genchains occur because rank-2 really is 2 dimensional, with a &amp;quot;genweb&amp;quot; running in octaves (or whatever the period is) vertically and fifths (or whatever the generator is) horizontally. When the period is an octave, this octave-reduces to a single horizontal genchain. But shrutal has a genweb with vertical half-octaves, which octave-reduces to two parallel genchains. Temperaments with third-octave periods reduce to a triple-genchain, and so forth.&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="How to name rank-2 scales-Non-MOS scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:15:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@How to name rank-2 scales-Non-MOS scales&amp;quot; title=&amp;quot;Anchor: How to name rank-2 scales-Non-MOS scales&amp;quot;/&amp;gt; --&gt;&lt;a name="How to name rank-2 scales-Non-MOS scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:15 --&gt;&lt;strong&gt;&lt;u&gt;Non-MOS scales&lt;/u&gt;&lt;/strong&gt;&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="How to name rank-2 scales-Non-MOS scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:15:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@How to name rank-2 scales-Non-MOS scales&amp;quot; title=&amp;quot;Anchor: How to name rank-2 scales-Non-MOS scales&amp;quot;/&amp;gt; --&gt;&lt;a name="How to name rank-2 scales-Non-MOS scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:15 --&gt;&lt;strong&gt;&lt;u&gt;Non-MOS scales&lt;/u&gt;&lt;/strong&gt;&lt;/h2&gt;
  These can be indicated with curly brackets, as Meantone{8}. The same naming methods apply:&lt;br /&gt;
  These can be indicated with curly brackets {}, because regular brackets [] are reserved for MOS scales. The same naming methods apply:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Then there's non-MOS rank-2 scales, gapped and ungapped. E.g. Meantone[8], perhaps C D E F F# G A B C which is F C G D A E B F#. The C scale would be Meantone[8] 2nd mode.&lt;br /&gt;
An ungapped example: 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 2nd Meantone{8}.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A gapped example: C D E F F# G A Bb C which is Bb F C G D A E (gap) F#. Move as few notes as possible to get not a MOS but at least an unbroken genchain: F C G D A E B F#. So the C scale is Meantone[8] 2nd mode b7.&lt;br /&gt;
A gapped example: 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 2nd Meantone[8] b7.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Sort of a Fur Elise scale: A B C D D# E F G G# A is F C G D A E B (gap of 2) G# D#. Sharpen F and C to get an unbroken genchain. Then we get Meantone[9] 3rd mode b3 b7.&lt;br /&gt;
Sort of a Fur Elise scale: 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;
&lt;br /&gt;
&lt;br /&gt;
Here's a tricky one: F G A C F, the genchain is F C G (gap) A, no way to make an unbroken chain. I would notate this Meantone[5] 1st mode, no 6. Or perhaps &amp;quot;no 5&amp;quot; since it's pentatonic.&lt;br /&gt;
Here's a tricky one: F G A C F, the genchain is F C G (gap) A, no way to make an unbroken chain. I would notate this Meantone[5] 1st mode, no 5.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;