Comparison of mode notation systems: Difference between revisions
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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:TallKite|TallKite]] and made on <tt>2016-04-21 16: | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-04-21 16:35:50 UTC</tt>.<br> | ||
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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> | ||
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==[[#How to name rank-2 scales-Non-MOS scales]]**__Non-MOS non-MODMOS scales__**== | ==[[#How to name rank-2 scales-Non-MOS scales]]**__Non-MOS non-MODMOS scales__**== | ||
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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 | 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 Bb to get an unbroken genchain: F **C** G D A E B F#. The scale is C 2nd Meantone | C D E F F# G A Bb C, with genchain Bb F **C** G D A E * F#. Alter Bb to get an unbroken genchain: F **C** G D A E B F#. The scale is C 2nd Meantone[8] b7. Even though the scale is octotonic, heptatonic scale degrees are used for the alteration (b7 not b8), because only seven note names are used. | ||
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 | 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. | ||
F G A C E F, with genchain **F** C G * A E. No amount of altering will make an unbroken genchain, so the name is F 1st Meantone[6] no 6. | F G A C E F, with genchain **F** C G * A E. No amount of altering will make an unbroken genchain, so the name is F 1st Meantone[6] no 6. | ||
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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"><html><head><title>Naming Rank-2 Scales</title></head><body>Here's how to name MOS, MODMOS and even non-MOS rank-2 scales systematically. Like <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Modal%20UDP%20notation">Modal UDP notation</a>, it starts with the convention of using <em>some-temperament-name</em>[<em>some-number</em>] 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:<br /> | <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>Naming Rank-2 Scales</title></head><body>Here's how to name MOS, MODMOS and even non-MOS rank-2 scales systematically. Like <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Modal%20UDP%20notation">Modal UDP notation</a>, it starts with the convention of using <em>some-temperament-name</em>[<em>some-number</em>] 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:<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-MODMOS scales"></a><!-- ws:end:WikiTextHeadingRule:0 --><!-- ws:start:WikiTextAnchorRule: | <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-MODMOS scales"></a><!-- ws:end:WikiTextHeadingRule:0 --><!-- ws:start:WikiTextAnchorRule:6:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@How to name rank-2 scales-MODMOS scales&quot; title=&quot;Anchor: How to name rank-2 scales-MODMOS scales&quot;/&gt; --><a name="How to name rank-2 scales-MODMOS scales"></a><!-- ws:end:WikiTextAnchorRule:6 --><strong><u>MODMOS scales</u></strong></h2> | ||
As in modal UDP notation, these are written as MOS scales with chromatic alterations. To find the scale's name, start with the genchain for the scale, which will always have gaps. Compact it into a chain without gaps by altering one or more notes. If there is more than one way to do this, the way that alters as few notes as possible is generally preferable. Determine the mode number from the compacted genchain, then add the appropriate alterations.<br /> | As in modal UDP notation, these are written as MOS scales with chromatic alterations. To find the scale's name, start with the genchain for the scale, which will always have gaps. Compact it into a chain without gaps by altering one or more notes. If there is more than one way to do this, the way that alters as few notes as possible is generally preferable. Determine the mode number from the compacted genchain, then add the appropriate alterations.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-Fractional-octave periods"></a><!-- ws:end:WikiTextHeadingRule:2 --><!-- ws:start:WikiTextAnchorRule: | <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-Fractional-octave periods"></a><!-- ws:end:WikiTextHeadingRule:2 --><!-- ws:start:WikiTextAnchorRule:7:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@How to name rank-2 scales-Fractional-octave periods&quot; title=&quot;Anchor: How to name rank-2 scales-Fractional-octave periods&quot;/&gt; --><a name="How to name rank-2 scales-Fractional-octave periods"></a><!-- ws:end:WikiTextAnchorRule:7 --><strong><u>Fractional-octave periods</u></strong></h2> | ||
Fractional-period rank-2 temperaments have multiple genchains running in parallel. For example, shrutal[10] might look like this:<br /> | Fractional-period rank-2 temperaments have multiple genchains running in parallel. For example, shrutal[10] might look like this:<br /> | ||
Eb -- Bb -- F --- C --- G<br /> | Eb -- Bb -- F --- C --- G<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x-Non-MOS non-MODMOS scales"></a><!-- ws:end:WikiTextHeadingRule:4 --><!-- ws:start:WikiTextAnchorRule: | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x-Non-MOS non-MODMOS scales"></a><!-- ws:end:WikiTextHeadingRule:4 --><!-- ws:start:WikiTextAnchorRule:8:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@How to name rank-2 scales-Non-MOS scales&quot; title=&quot;Anchor: How to name rank-2 scales-Non-MOS scales&quot;/&gt; --><a name="How to name rank-2 scales-Non-MOS scales"></a><!-- ws:end:WikiTextAnchorRule:8 --><strong><u>Non-MOS non-MODMOS scales</u></strong></h2> | ||
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C D E F F# G A B C, which has a genchain F <strong>C</strong> G D A E B F#, and is named C 2nd Meantone | C D E F F# G A B C, which has a genchain F <strong>C</strong> G D A E B F#, and is named C 2nd Meantone[8].<br /> | ||
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C D E F F# G A Bb C, with genchain Bb F <strong>C</strong> G D A E * F#. Alter Bb to get an unbroken genchain: F <strong>C</strong> G D A E B F#. The scale is C 2nd Meantone | C D E F F# G A Bb C, with genchain Bb F <strong>C</strong> G D A E * F#. Alter Bb to get an unbroken genchain: F <strong>C</strong> G D A E B F#. The scale is C 2nd Meantone[8] b7. Even though the scale is octotonic, heptatonic scale degrees are used for the alteration (b7 not b8), because only seven note names are used.<br /> | ||
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A B C D D# E F G G# A, with genchain F C G D <strong>A</strong> E B * * G# D#. Sharpen F and C to get an unbroken genchain: G D <strong>A</strong> E B F# C# G# D#, giving the name A 3rd Meantone | A B C D D# E F G G# A, with genchain F C G D <strong>A</strong> E B * * G# D#. Sharpen F and C to get an unbroken genchain: G D <strong>A</strong> E B F# C# G# D#, giving the name A 3rd Meantone[9] b3 b7.<br /> | ||
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F G A C E F, with genchain <strong>F</strong> C G * A E. No amount of altering will make an unbroken genchain, so the name is F 1st Meantone[6] no 6.<br /> | F G A C E F, with genchain <strong>F</strong> C G * A E. No amount of altering will make an unbroken genchain, so the name is F 1st Meantone[6] no 6.<br /> | ||
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