Comparison of mode notation systems: Difference between revisions
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==[[#How to name rank-2 scales-MODMOS scales]]**__MODMOS scales__**== | ==[[#How to name rank-2 scales-MODMOS scales]]**__MODMOS scales__**== | ||
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. For example, for harmonic minor, A is the 4th note of the uncompacted genchain, but the 5th note of the compacted one | 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. For example, for harmonic minor, A is the 4th note of the uncompacted genchain, but the 5th note of the compacted one. "+" and "-" are used to indicate the altered notes. For example, Meantone[7,+3,-6] means that the 3rd note in the compacted genchain is moved 7 steps to the right, and the 6th note is moved 7 steps to the left. "+" and "-" are preferred over "#" and "b" because in the case of a chroma-negative generator, "+" makes the note flatter. | ||
|| old scale name || example in A || genchain || compacted genchain || new scale name || | || old scale name || example in A || genchain || 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,+3] || | || 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,+3] || | ||
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|| Double harmonic minor || A B C D# E F G# A || F C * * __**A**__ E B * * G# D# || F C G D __**A**__ E B || 5th Meantone[7,+3,+4] || | || Double harmonic minor || A B C D# E F G# A || F C * * __**A**__ E B * * G# D# || F C G D __**A**__ E B || 5th Meantone[7,+3,+4] || | ||
|| || || || __**A**__ E B F# C# G# D# || 1st Meantone[7,-4,-5] || | || || || || __**A**__ E B F# C# G# D# || 1st Meantone[7,-4,-5] || | ||
|| Double harmonic major || A Bb C# D E F G# A || Bb F * * D A E * * C# G# || Bb F C G D __**A**__ E || 6th Meantone[7,+3,+4] || | || Double harmonic major || A Bb C# D E F G# A || Bb F * * D A E * * C# G# || Bb F C G D __**A**__ E || 6th Meantone[7,+3,+4] || | ||
|| || || || D __**A**__ E B F# C# G# || 2nd Meantone[7,-4,-5] || | |||
|| Japanese pentatonic || A B C E F A || F C * * __**A**__ E B || __**A**__ E B F# C# || 1st Meantone[5,-4,-5] || | || Japanese pentatonic || A B C E F A || F C * * __**A**__ E B || __**A**__ E B F# C# || 1st Meantone[5,-4,-5] || | ||
|| (a mode of the above) || F A B C E F || __**F**__ C * * A E B || Ab Eb Bb __**F**__ C || 4th Meantone[5,-4,-5] || | || (a mode of the above) || F A B C E F || __**F**__ C * * A E B || Ab Eb Bb __**F**__ C || 4th Meantone[5,-4,-5] || | ||
Use the compacted genchain to find the mode number so that harmonic minor and melodic minor are both the 5th mode, just as standard minor is. Also so that two notes a (possibly aug or dim) fifth apart will still have adjacent mode numbers. | |||
//Things to consider:// | //Things to consider:// | ||
The ambiguity of MODMOS names can be | The ambiguity of MODMOS names can be resolved by devising a rule to determine the one proper compacted genchain. For example, choose the one that moves as few notes as possible, breaking ties with a bias towards moving to the right. The disadvantage of ambiguity is that if the double harmonic minor is 1st Meantone[7,-4,-5] and the double harmonic major is 6th Meantone[7,+3,+4], one can't tell that they are modes of each other. The advantage is that if a piece changes from a MOS scale to a MODMOS scale, one can describe both scales with the same mode number. For example, a piece might change from minor = 5th Meantone[7] to melodic minor = 5th Meantone[7,+1,+3]. In other words, in this context, melodic minor is better described as 5th Meantone[7,+1,+3] than as 4th Meantone[7,+2]. | ||
//Perhaps use [7,^3] in place of [7,+3]?// | //Perhaps use [7,^3] in place of [7,+3]?// | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-MODMOS scales"></a><!-- ws:end:WikiTextHeadingRule:0 --><!-- ws:start:WikiTextAnchorRule:18:&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:18 --><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:18:&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:18 --><strong><u>MODMOS scales</u></strong></h2> | ||
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 <u>compacted</u> genchain. For example, for harmonic minor, A is the 4th note of the uncompacted genchain, but the 5th note of the compacted one | 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 <u>compacted</u> genchain. For example, for harmonic minor, A is the 4th note of the uncompacted genchain, but the 5th note of the compacted one. &quot;+&quot; and &quot;-&quot; are used to indicate the altered notes. For example, Meantone[7,+3,-6] means that the 3rd note in the compacted genchain is moved 7 steps to the right, and the 6th note is moved 7 steps to the left. &quot;+&quot; and &quot;-&quot; are preferred over &quot;#&quot; and &quot;b&quot; because in the case of a chroma-negative generator, &quot;+&quot; makes the note flatter.<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td>Double harmonic major<br /> | ||
</td> | </td> | ||
<td><br /> | <td>A Bb C# D E F G# A<br /> | ||
</td> | </td> | ||
<td><br /> | <td>Bb F * * D A E * * C# G#<br /> | ||
</td> | </td> | ||
<td><br /> | <td>Bb F C G D <u><strong>A</strong></u> E<br /> | ||
</td> | </td> | ||
<td><br /> | <td>6th Meantone[7,+3,+4]<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td><br /> | ||
</td> | </td> | ||
<td> | <td><br /> | ||
</td> | </td> | ||
<td> | <td><br /> | ||
</td> | </td> | ||
<td> | <td>D <u><strong>A</strong></u> E B F# C# G#<br /> | ||
</td> | </td> | ||
<td> | <td>2nd Meantone[7,-4,-5]<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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</table> | </table> | ||
Use the compacted genchain to find the mode number so that harmonic minor and melodic minor are both the 5th mode, just as standard minor is. Also so that two notes a (possibly aug or dim) fifth apart will still have adjacent mode numbers.<br /> | |||
<br /> | |||
<br /> | <br /> | ||
<em>Things to consider:</em><br /> | <em>Things to consider:</em><br /> | ||
<br /> | <br /> | ||
The ambiguity of MODMOS names can be | The ambiguity of MODMOS names can be resolved by devising a rule to determine the one proper compacted genchain. For example, choose the one that moves as few notes as possible, breaking ties with a bias towards moving to the right. The disadvantage of ambiguity is that if the double harmonic minor is 1st Meantone[7,-4,-5] and the double harmonic major is 6th Meantone[7,+3,+4], one can't tell that they are modes of each other. The advantage is that if a piece changes from a MOS scale to a MODMOS scale, one can describe both scales with the same mode number. For example, a piece might change from minor = 5th Meantone[7] to melodic minor = 5th Meantone[7,+1,+3]. In other words, in this context, melodic minor is better described as 5th Meantone[7,+1,+3] than as 4th Meantone[7,+2].<br /> | ||
<br /> | <br /> | ||
<em>Perhaps use [7,^3] in place of [7,+3]?</em><br /> | <em>Perhaps use [7,^3] in place of [7,+3]?</em><br /> | ||
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Admins: Please delete the blank page at <!-- ws:start:WikiTextUrlRule: | Admins: Please delete the blank page at <!-- ws:start:WikiTextUrlRule:1492: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:1492 --></body></html></pre></div> | ||