Comparison of mode notation systems: Difference between revisions
Wikispaces>TallKite **Imported revision 580767511 - Original comment: ** |
Wikispaces>TallKite **Imported revision 580768947 - 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 06: | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-04-21 06:26:35 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>580768947</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** || | ||
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". | 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 | 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. | ||
|| 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** || | ||
The octave inverse of a generator is also a generator. To avoid ambiguity in mode numbers, the smaller of the two | 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. | ||
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, | |||
Pentatonic meantone scales: | Pentatonic meantone scales: | ||
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==[[#How to name rank-2 scales-Generator choice]]** | ==[[#How to name rank-2 scales-Generator choice]]**__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. | 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 || | ||
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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, 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 | 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 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 || | ||
|| Melodic minor || A B C D E F# G# A || C * D **A** E B F# * G# || F C G D **A** E B || 5th Meantone[7] #6 #7 || | || Melodic minor || A B C D E F# G# A || C * D **A** E B F# * G# || F C G D **A** E B || 5th Meantone[7] #6 #7 || | ||
||= " ||= " ||= " || D **A** E B F# C# G# || 2nd Meantone[ | ||= " ||= " ||= " || D **A** E B F# C# G# || 2nd Meantone[7] b3 || | ||
|| Japanese pentatonic || A B C E F A || F C * * **A** E B || **A** E B F# C# || 1st Meantone[5] b3 | || Japanese pentatonic || A B C E F A || F C * * **A** E B || **A** E B F# C# || 1st Meantone[5] b3 b6 || | ||
|| (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 # | || (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 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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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 B to get 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 B 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 notation is used for the alteration (b7 not b8), because only 7 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. | ||
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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;. <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 /> | <br /> | ||
The same seven modes, all with C as the tonic, to illustrate the difference between modes | 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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</table> | </table> | ||
<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, | 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 /> | ||
<br /> | <br /> | ||
Pentatonic meantone scales:<br /> | Pentatonic meantone scales:<br /> | ||
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<br /> | <br /> | ||
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<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x- | <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-More examples"></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>More examples</u></strong></h2> | ||
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 /> | |||
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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<!-- 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> | <!-- 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 | 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 determine the mode number from the compacted genchain, then add the appropriate alterations.<br /> | ||
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<td>D <strong>A</strong> E B F# C# G#<br /> | <td>D <strong>A</strong> E B F# C# G#<br /> | ||
</td> | </td> | ||
<td>2nd Meantone[ | <td>2nd Meantone[7] b3<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td><strong>A</strong> E B F# C#<br /> | <td><strong>A</strong> E B F# C#<br /> | ||
</td> | </td> | ||
<td>1st Meantone[5] b3 | <td>1st Meantone[5] b3 b6<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>Ab Eb Bb <strong>F</strong> C<br /> | <td>Ab Eb Bb <strong>F</strong> C<br /> | ||
</td> | </td> | ||
<td>4th Meantone[5] #2 #3 # | <td>4th Meantone[5] #2 #3 #6<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
</table> | </table> | ||
<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 /> | |||
<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 /> | |||
<br /> | <br /> | ||
<br /> | <br /> | ||
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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{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 B to get an unbroken genchain: F <strong>C</strong> 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 <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. Even though the scale is octotonic, heptatonic notation is used for the alteration (b7 not b8), because only 7 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 /> | ||
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The rough draft at <!-- ws:start:WikiTextUrlRule: | The rough draft at <!-- ws:start:WikiTextUrlRule:1117: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:1117 --> can be deleted.</body></html></pre></div> | ||