Comparison of mode notation systems: Difference between revisions
Wikispaces>TallKite **Imported revision 580769145 - Original comment: ** |
Wikispaces>TallKite **Imported revision 580772155 - 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 07:21:49 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>580772155</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> | ||
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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** || | ||
These [[MOSScales|MOS scales]] are formed from a segment of the [[periods and generators|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., somewhat analogous to harmonica positions. 4th Meantone[7] is spoken as "fourth meantone heptatonic". If in D, as above, it would be "D fourth meantone heptatonic". | |||
The same seven modes, all with C as the tonic, to illustrate the difference between modes. Similar modes are grouped together. The overall progression is from sharper to flatter. | The same seven modes, all with C as the tonic, to illustrate the difference between modes. Similar modes are grouped together. The overall progression is from sharper to flatter. | ||
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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** || | ||
The octave inverse of a generator is also a generator. To avoid ambiguity in mode numbers, the smaller of the two generators 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, which guarantees that the smaller MOS will always be a subset of the larger MOS. For example Meantone[5] is a subset of Meantone[7], and for Meantone[5] modes, the overall progression is from flatter to sharper, because the 3/2 generator is chroma-negative. | The octave inverse of a generator is also a generator. To avoid ambiguity in mode numbers, the smaller of the two generators 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 [[Regular Temperaments|temperament]], which guarantees that the smaller MOS will always be a subset of the larger MOS. For example, Meantone[5] is a subset of Meantone[7], and for Meantone[5] modes, the overall progression is from flatter to sharper, because the 3/2 generator is chroma-negative. | ||
Pentatonic meantone scales: | Pentatonic meantone scales: | ||
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==[[#How to name rank-2 scales-MODMOS scales]]**__MODMOS scales__**== | ==[[#How to name rank-2 scales-MODMOS scales]]**__MODMOS scales__**== | ||
As in modal UDP notation, these are written as MOS scales with chromatic alterations. To find the scale's name, | 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. | ||
|| old scale name || example in A || genchain (* marks a gap) || compacted genchain || new scale name || | || old scale name || example in A || genchain (* marks a gap) || compacted genchain || new scale name || | ||
|| Harmonic minor || A B C D E F G# A || F C * D **A** E B * * G# || F C G D **A** E B || 5th Meantone[7] #7 || | || Harmonic minor || A B C D E F G# A || F C * D **A** E B * * G# || F C G D **A** E B || 5th Meantone[7] #7 || | ||
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|| (a mode of the above) || F A B C E F || **F** C * * A E B || Ab Eb Bb **F** C || 4th Meantone[5] #2 #3 #6 || | || (a mode of the above) || F A B C E F || **F** C * * A E B || Ab Eb Bb **F** C || 4th Meantone[5] #2 #3 #6 || | ||
The Japanese pentatonic has b6, not b5, because heptatonic scale degrees are used, even though the scale is pentatonic. The rationale for this is that the notation uses 7 letters, so the notation is still essentially heptatonic. In other words, F is the 5th note of the scale, but F is the 6th letter counting from the tonic A. If the notation used only 5 letters, perhaps H J K L M, the alteration would be written "b5". | The Japanese pentatonic has b6, not b5, because heptatonic scale degrees are used, even though the scale is pentatonic. The rationale for this is that the notation uses 7 letters, so the notation is still essentially heptatonic. In other words, F is the 5th note of the scale, but F is the 6th letter counting from the tonic A. If the notation used only 5 letters, perhaps H J K L M, the alteration would be written "b5". | ||
The F mode of Japanese pentatonic alters three notes, not two, to avoid "b1 b5". Unfortunately, it's not apparent from the scale names that the last two examples are modes of each other. | The F mode of Japanese pentatonic alters three notes, not two, to avoid "b1 b5". Unfortunately, it's not apparent from the scale names that the last two examples are modes of each other. | ||
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|| 5th Shrutal[10] || Lssss-Lssss || C D Eb E F F# Ab A Bb B C || Ab Eb Bb F **C** || D A E B F# || | || 5th Shrutal[10] || Lssss-Lssss || C D Eb E F F# Ab A Bb B C || Ab Eb Bb F **C** || D A E B F# || | ||
There are only two Blackwood[10] modes. The period is a fifth-octave = 240¢. The generator is 5/4. There are five genchains. Ups and downs are used to avoid duplicate note names. | There are only two Blackwood[10] modes. The period is a fifth-octave = 240¢. The generator is 5/4. L = 146¢ and s = 94¢. There are five genchains. Ups and downs are used to avoid duplicate note names. | ||
|| scale name || Ls pattern || example in C || 1st genchain || 2nd chain || 3rd chain || 4th chain || 5th chain || | || scale name || Ls pattern || example in C || 1st genchain || 2nd chain || 3rd chain || 4th chain || 5th chain || | ||
|| 1st Blackwood[10] || LsLsLs LsLs || C C# D Ev E F# G G# A B C ||= **C** Ev || D F# || E G# || G B || A C# || | || 1st Blackwood[10] || LsLsLs LsLs || C C# D Ev E F# G G# A B C ||= **C** Ev || D F# || E G# || G B || A C# || | ||
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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__**== | ||
These can be indicated with curly brackets {}, because regular brackets [] are reserved for MOS scales | These can be indicated with curly brackets {}, because regular brackets [] are reserved for MOS scales. Examples: | ||
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 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{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. | ||
F G A C F, with genchain **F** C G * A. No amount of altering will make an unbroken | 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. | ||
==[[#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 [[ | This method of scale naming can be combined with [[Kite's color notation|color notation]], as in "2nd green heptatonic" for 2nd Meantone[7]. | ||
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<br /> | <br /> | ||
These <a class="wiki_link" href="/MOSScales">MOS scales</a> are formed from a segment of the <a class="wiki_link" href="/periods%20and%20generators">generator-chain</a>, or genchain. The first note in the genchain is the tonic of mode #1, the 2nd note is the tonic of mode #2, etc., somewhat analogous to harmonica positions. 4th Meantone[7] is spoken as &quot;fourth meantone heptatonic&quot;. If in D, as above, it would be &quot;D fourth meantone heptatonic&quot;.<br /> | |||
<br /> | <br /> | ||
The same seven modes, all with C as the tonic, to illustrate the difference between modes. Similar modes are grouped together. The overall progression is from sharper to flatter.<br /> | The same seven modes, all with C as the tonic, to illustrate the difference between modes. Similar modes are grouped together. The overall progression is from sharper to flatter.<br /> | ||
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<br /> | <br /> | ||
The octave inverse of a generator is also a generator. To avoid ambiguity in mode numbers, the smaller of the two generators 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, which guarantees that the smaller MOS will always be a subset of the larger MOS. For example Meantone[5] is a subset of Meantone[7], and for Meantone[5] modes, the overall progression is from flatter to sharper, because the 3/2 generator is chroma-negative.<br /> | The octave inverse of a generator is also a generator. To avoid ambiguity in mode numbers, the smaller of the two generators 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 <a class="wiki_link" href="/Regular%20Temperaments">temperament</a>, which guarantees that the smaller MOS will always be a subset of the larger MOS. For example, Meantone[5] is a subset of Meantone[7], and for Meantone[5] modes, the overall progression is from flatter to sharper, because the 3/2 generator is chroma-negative.<br /> | ||
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Pentatonic meantone scales:<br /> | Pentatonic meantone scales:<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: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-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:8 --><strong><u>MODMOS scales</u></strong></h2> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-MODMOS scales"></a><!-- ws:end:WikiTextHeadingRule:0 --><!-- 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-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:8 --><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, | 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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<br /> | <br /> | ||
The Japanese pentatonic has b6, not b5, because heptatonic scale degrees are used, even though the scale is pentatonic. The rationale for this is that the notation uses 7 letters, so the notation is still essentially heptatonic. In other words, F is the 5th note of the scale, but F is the 6th letter counting from the tonic A. If the notation used only 5 letters, perhaps H J K L M, the alteration would be written &quot;b5&quot;. <br /> | The Japanese pentatonic has b6, not b5, because heptatonic scale degrees are used, even though the scale is pentatonic. The rationale for this is that the notation uses 7 letters, so the notation is still essentially heptatonic. In other words, F is the 5th note of the scale, but F is the 6th letter counting from the tonic A. If the notation used only 5 letters, perhaps H J K L M, the alteration would be written &quot;b5&quot;.<br /> | ||
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The F mode of Japanese pentatonic alters three notes, not two, to avoid &quot;b1 b5&quot;. Unfortunately, it's not apparent from the scale names that the last two examples are modes of each other.<br /> | The F mode of Japanese pentatonic alters three notes, not two, to avoid &quot;b1 b5&quot;. Unfortunately, it's not apparent from the scale names that the last two examples are modes of each other.<br /> | ||
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There are only two Blackwood[10] modes. The period is a fifth-octave = 240¢. The generator is 5/4. There are five genchains. Ups and downs are used to avoid duplicate note names.<br /> | There are only two Blackwood[10] modes. The period is a fifth-octave = 240¢. The generator is 5/4. L = 146¢ and s = 94¢. There are five genchains. Ups and downs are used to avoid duplicate note names.<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: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-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:10 --><strong><u>Non-MOS non-MODMOS scales</u></strong></h2> | <!-- 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: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-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:10 --><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 | These can be indicated with curly brackets {}, because regular brackets [] are reserved for MOS scales. 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 /> | ||
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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 | 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 /> | ||
<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 /> | ||
<br /> | <br /> | ||
F G A C F, with genchain <strong>F</strong> C G * A. No amount of altering will make an unbroken | 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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<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x-Color notation"></a><!-- ws:end:WikiTextHeadingRule:6 --><!-- 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-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:11 --><u>Color notation</u></h2> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x-Color notation"></a><!-- ws:end:WikiTextHeadingRule:6 --><!-- 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-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:11 --><u>Color notation</u></h2> | ||
This method of scale naming can be combined with <a class="wiki_link" href=" | This method of scale naming can be combined with <a class="wiki_link" href="/Kite%27s%20color%20notation">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: | The rough draft at <!-- ws:start:WikiTextUrlRule:1116: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:1116 --> can be deleted.</body></html></pre></div> | ||