Comparison of mode notation systems: Difference between revisions
Wikispaces>TallKite **Imported revision 580765591 - Original comment: ** |
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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> | 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 | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-04-21 06:00:40 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>580767511</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html"> | <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">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: | ||
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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|| 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". 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: | 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 ||> **C** G D A E B F# || | || Lydian || 1st Meantone[7] || LLLs LLs || C D E F# G A B C ||> **C** G D A E B F# || | ||
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|| Phrygian || 6th Meantone[7] || sLLL sLL || C Db Eb F G Ab Bb C || ---- Db Ab Eb Bb F **C** G || | || Phrygian || 6th Meantone[7] || sLLL sLL || C Db Eb F G Ab Bb C || ---- Db Ab Eb Bb F **C** G || | ||
|| 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. | Similar modes are grouped together. The overall progression is from sharper to flatter. | ||
The octave inverse of a generator is also a generator. To avoid ambiguity in mode numbers, the smaller of the two options is chosen. An exception is made for 3/2, which is preferred over 4/3 for historical reasons. | |||
Unlike modal UDP notation, the generator isn't always chroma-positive. This is necessary to keep the same generator for different MOS's of the same temperament, to guarantee that Meantone[5] will be a subset of Meantone[7] .However for the 5 pentatonic modes, the overall progression is from flatter to sharper. | |||
Pentatonic meantone scales: | Pentatonic meantone scales: | ||
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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** || | ||
Chromatic meantone scales | |||
==[[#How to name rank-2 scales-Generator choice]]**__Generator choice__**== | |||
The octave inverse of a generator is also a generator. To avoid ambiguity, the smaller of the two options is chosen. An exception is made for 3/2, which is preferred over 4/3 for historical reasons. More examples: | |||
Chromatic meantone scales. If the fifth were larger than 700¢, which would be the case for Superpyth[12], L and s would be interchanged. | |||
|| 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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|| 7th Meantone[12] || LsLsLLs LsLsL || C Db D Eb E F Gb G Ab A Bb B C || Gb Db Ab Eb Bb F **C** G D A E B || | || 7th Meantone[12] || LsLsLLs LsLsL || C Db D Eb E F Gb G Ab A Bb B C || Gb Db Ab Eb Bb F **C** G D A E B || | ||
||= etc. || || || || | ||= etc. || || || || | ||
Sensi[8] modes in 19edo (generator = 3rd = ~9/7 = 7\19, L = 3\19, s = 2\19) | Sensi[8] modes in 19edo (generator = 3rd = ~9/7 = 7\19, L = 3\19, s = 2\19) | ||
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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 | C D E F F# G A Bb C, with genchain Bb F **C** G D A E * F#. Alter B to get an unbroken genchain: F **C** G D A E B F#. The scale is C 2nd Meantone{8} b7. The scale is octotonic, but heptatonic notation is used for the alteration, b7 not b8, because only 7 note names are used. | ||
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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==[[#How to name rank-2 scales-Color notation]]__Color notation__== | ==[[#How to name rank-2 scales-Color notation]]__Color notation__== | ||
This method of scale naming can be combined with [[xenharmonic/Kite's color notation|Kite's color notation]], as in "2nd green heptatonic" for 2nd Meantone[7].</pre></div> | This method of scale naming can be combined with [[xenharmonic/Kite's color notation|Kite's color notation]], as in "2nd green heptatonic" for 2nd Meantone[7]. | ||
The rough draft at http://xenharmonic.wikispaces.com/Modal+Notation+by+Genchain+Position can be deleted.</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>Naming Rank-2 Scales</title></head><body> | <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 /> | ||
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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<br /> | <br /> | ||
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 &quot;fourth meantone heptatonic&quot;. If in D, as above, it would be &quot;D 4th meantone heptatonic&quot;. The same seven modes, all with C as the tonic, to illustrate the difference between modes:<br /> | 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 &quot;fourth meantone heptatonic&quot;. If in D, as above, it would be &quot;D 4th meantone heptatonic&quot;. <br /> | ||
<br /> | |||
The same seven modes, all with C as the tonic, to illustrate the difference between modes:<br /> | |||
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</table> | </table> | ||
Similar modes are grouped together. The overall progression is from sharper to flatter. | Similar modes are grouped together. The overall progression is from sharper to flatter.<br /> | ||
<br /> | |||
The octave inverse of a generator is also a generator. To avoid ambiguity in mode numbers, the smaller of the two options is chosen. An exception is made for 3/2, which is preferred over 4/3 for historical reasons.<br /> | |||
<br /> | |||
Unlike modal UDP notation, the generator isn't always chroma-positive. This is necessary to keep the same generator for different MOS's of the same temperament, to guarantee that Meantone[5] will be a subset of Meantone[7] .However for the 5 pentatonic modes, the overall progression is from flatter to sharper. <br /> | |||
<br /> | <br /> | ||
Pentatonic meantone scales:<br /> | Pentatonic meantone scales:<br /> | ||
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<br /> | <br /> | ||
Chromatic meantone scales | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Generator choice"></a><!-- ws:end:WikiTextHeadingRule:0 --><!-- ws:start:WikiTextAnchorRule:10:&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-Generator choice&quot; title=&quot;Anchor: How to name rank-2 scales-Generator choice&quot;/&gt; --><a name="How to name rank-2 scales-Generator choice"></a><!-- ws:end:WikiTextAnchorRule:10 --><strong><u>Generator choice</u></strong></h2> | |||
The octave inverse of a generator is also a generator. To avoid ambiguity, the smaller of the two options is chosen. An exception is made for 3/2, which is preferred over 4/3 for historical reasons. More examples:<br /> | |||
<br /> | |||
Chromatic meantone scales. If the fifth were larger than 700¢, which would be the case for Superpyth[12], L and s would be interchanged.<br /> | |||
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</table> | </table> | ||
<br /> | <br /> | ||
Sensi[8] modes in 19edo (generator = 3rd = ~9/7 = 7\19, L = 3\19, s = 2\19)<br /> | Sensi[8] modes in 19edo (generator = 3rd = ~9/7 = 7\19, L = 3\19, s = 2\19)<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-MODMOS scales"></a><!-- ws:end:WikiTextHeadingRule:2 --><!-- ws:start:WikiTextAnchorRule:11:&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:11 --><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, first write out the genchain for the scale, which will always have gaps. Then compact it into a chain without gaps by altering one or more notes. There may be more than one way to do this, usually choose the way that alters as few notes as possible. Then find the name of the mode, 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, first write out the genchain for the scale, which will always have gaps. Then compact it into a chain without gaps by altering one or more notes. There may be more than one way to do this, usually choose the way that alters as few notes as possible. Then find the name of the mode, then add the appropriate alterations.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x-Fractional-octave periods"></a><!-- ws:end:WikiTextHeadingRule:4 --><!-- ws:start:WikiTextAnchorRule:12:&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:12 --><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: | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x-Non-MOS non-MODMOS scales"></a><!-- ws:end:WikiTextHeadingRule:6 --><!-- ws:start:WikiTextAnchorRule:13:&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:13 --><strong><u>Non-MOS non-MODMOS scales</u></strong></h2> | ||
These can be indicated with curly brackets {}, because regular brackets [] are reserved for MOS scales. The same naming methods apply. Examples:<br /> | These can be indicated with curly brackets {}, because regular brackets [] are reserved for MOS scales. The same naming methods apply. Examples:<br /> | ||
<br /> | <br /> | ||
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 /> | 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 /> | ||
<br /> | <br /> | ||
C D E F F# G A Bb C, with genchain Bb F <strong>C</strong> G D A E * F#. Alter | C D E F F# G A Bb C, with genchain Bb F <strong>C</strong> G D A E * F#. Alter B to get an unbroken genchain: F <strong>C</strong> G D A E B F#. The scale is C 2nd Meantone{8} b7. The scale is octotonic, but heptatonic notation is used for the alteration, b7 not b8, because only 7 note names are used.<br /> | ||
F <strong>C</strong> G D A E B F#. The scale is C 2nd Meantone{8} b7.<br /> | |||
<br /> | <br /> | ||
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 /> | 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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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="x-Color notation"></a><!-- ws:end:WikiTextHeadingRule:8 --><!-- ws:start:WikiTextAnchorRule:14:&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-Color notation&quot; title=&quot;Anchor: How to name rank-2 scales-Color notation&quot;/&gt; --><a name="How to name rank-2 scales-Color notation"></a><!-- ws:end:WikiTextAnchorRule:14 --><u>Color notation</u></h2> | ||
This method of scale naming can be combined with <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Kite%27s%20color%20notation">Kite's color notation</a>, as in &quot;2nd green heptatonic&quot; for 2nd Meantone[7].</body></html></pre></div> | This method of scale naming can be combined with <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Kite%27s%20color%20notation">Kite's color notation</a>, as in &quot;2nd green heptatonic&quot; for 2nd Meantone[7].<br /> | ||
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The rough draft at <!-- ws:start:WikiTextUrlRule:1119:http://xenharmonic.wikispaces.com/Modal+Notation+by+Genchain+Position --><a href="http://xenharmonic.wikispaces.com/Modal+Notation+by+Genchain+Position">http://xenharmonic.wikispaces.com/Modal+Notation+by+Genchain+Position</a><!-- ws:end:WikiTextUrlRule:1119 --> can be deleted.</body></html></pre></div> | |||