Comparison of mode notation systems: Difference between revisions
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===**__2nd method for MODMOS scales__**=== | ===**__2nd method for MODMOS scales__**=== | ||
Another approach applies chromatic alterations not to the genchain but to the resulting scale, using scale degrees, not genchain positions, similar to UDP notation. There is still ambiguity. | Another approach applies chromatic alterations not to the genchain but to the resulting scale, using scale degrees, not genchain positions, similar to UDP notation. "#" means raised by L-s, and for //some-temperament-name//[N], "#" means moved N steps on the genchain, either forwards or backwards. There is still ambiguity. | ||
Harmonic minor A B C D E F G# A is 5th Meantone [7] #7, not 5th Meantone [7,+3] | Harmonic minor A B C D E F G# A is 5th Meantone [7] #7, not 5th Meantone [7,+3] | ||
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The advantage of the 1st method is that the modes of a MODMOS differ only by mode number. Thus it's easier to tell if two scales are modes of each other. However, if ambiguity is allowed, this won't always be true. | The advantage of the 1st method is that the modes of a MODMOS differ only by mode number. Thus it's easier to tell if two scales are modes of each other. However, if ambiguity is allowed, this won't always be true. | ||
The advantage of the 2nd method is that it's closer to how musicians describe scales, and thus more intuitive. | The advantage of the 2nd method is that it's closer to how musicians describe scales, and thus more intuitive. Also less computation. | ||
==[[#How to name rank-2 scales-Fractional-octave periods]]**__Fractional-octave periods__**== | ==[[#How to name rank-2 scales-Fractional-octave periods]]**__Fractional-octave periods__**== | ||
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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__**== | ||
**__1st method__:** | |||
Compact the genchain to remove any gaps via alterations. The mode number is derived from the compacted genchain. Examples: | Compact the genchain to remove any gaps via alterations. The mode number is derived from the compacted genchain. Examples: | ||
C D E F F# G A B C has the 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 has the 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[8,-7]. | 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,-7]. | ||
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,-6,-7]. | 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,-6,-7]. | ||
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,no4]. | 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,no4]. | ||
A B C E F A, a japanese pentatonic scale, with genchain F C * * __**A**__ E B. The F and C can't be sharpened to F# and C# to make an unbroken Meantone[5] genchain, because pentatonic alterations move notes by 5 steps, not 7. No amount of __pentatonic__ altering will make an unbroken genchain, so the scale must be named as a heptatonic scale with missing degrees: A 5th Meantone[7,no3,no4]. | A B C E F A, a japanese pentatonic scale, with genchain F C * * __**A**__ E B. The F and C can't be sharpened to F# and C# to make an unbroken Meantone[5] genchain, because pentatonic alterations move notes by 5 steps, not 7. No amount of __pentatonic__ altering will make an unbroken genchain, so the scale must be named as a heptatonic scale with missing degrees: A 5th Meantone [7,no3,no4]. | ||
//[Problem: The 2nd and 3rd examples use heptatonic alterations even though the scales aren't heptatonic.]// | //[Problem: The 2nd and 3rd examples use heptatonic alterations even though the scales aren't heptatonic.]// | ||
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//[Possible solution: non-MOS scales can't have chromatic alterations, only missing notes. 2nd example is 3rd Meantone[9,no8]. 3rd example is 5th Meantone[11,no8,no9].// | //[Possible solution: non-MOS scales can't have chromatic alterations, only missing notes. 2nd example is 3rd Meantone[9,no8]. 3rd example is 5th Meantone[11,no8,no9].// | ||
//[Possible solution: | //[Possible solution: alterations must be heptatonic because . 2nd example is 3rd Meantone[7] add #4. 3rd example is 5th Meantone[11,no8,no9].// | ||
**__2nd method__:** | |||
As with MODMOS scales. | |||
C 2nd Meantone [8] | |||
C 2nd Meantone [8] b7 | |||
A 3rd Meantone [9] b3 b6 | |||
Alterations are heptatonic because Meantone [7] is the largest MOS contained in Meantone [8] or Meantone [9]. | |||
F 1st Meantone [6] no6 | |||
A 5th Meantone [7] no4 no7 | |||
G A B D E F# G, with genchain __**G**__ D A E B F# = G 1st Meantone [6] | |||
G A C D E F# G, with genchain C __**G**__ D A E * F# = G Meantone [6] #3 | |||
==[[#How to name rank-2 scales-Non-MOS scales]]__Explanation / Rationale__== | ==[[#How to name rank-2 scales-Non-MOS scales]]__Explanation / Rationale__== | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="Kite Giedraitis method-MODMOS scales-2nd method for MODMOS scales"></a><!-- ws:end:WikiTextHeadingRule:8 --><strong><u>2nd method for MODMOS scales</u></strong></h3> | <!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="Kite Giedraitis method-MODMOS scales-2nd method for MODMOS scales"></a><!-- ws:end:WikiTextHeadingRule:8 --><strong><u>2nd method for MODMOS scales</u></strong></h3> | ||
Another approach applies chromatic alterations not to the genchain but to the resulting scale, using scale degrees, not genchain positions, similar to UDP notation. There is still ambiguity.<br /> | Another approach applies chromatic alterations not to the genchain but to the resulting scale, using scale degrees, not genchain positions, similar to UDP notation. &quot;#&quot; means raised by L-s, and for <em>some-temperament-name</em>[N], &quot;#&quot; means moved N steps on the genchain, either forwards or backwards. There is still ambiguity.<br /> | ||
<br /> | <br /> | ||
Harmonic minor A B C D E F G# A is 5th Meantone [7] #7, not 5th Meantone [7,+3]<br /> | Harmonic minor A B C D E F G# A is 5th Meantone [7] #7, not 5th Meantone [7,+3]<br /> | ||
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The advantage of the 1st method is that the modes of a MODMOS differ only by mode number. Thus it's easier to tell if two scales are modes of each other. However, if ambiguity is allowed, this won't always be true.<br /> | The advantage of the 1st method is that the modes of a MODMOS differ only by mode number. Thus it's easier to tell if two scales are modes of each other. However, if ambiguity is allowed, this won't always be true.<br /> | ||
<br /> | <br /> | ||
The advantage of the 2nd method is that it's closer to how musicians describe scales, and thus more intuitive.<br /> | The advantage of the 2nd method is that it's closer to how musicians describe scales, and thus more intuitive. Also less computation.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Kite Giedraitis method-Fractional-octave periods"></a><!-- ws:end:WikiTextHeadingRule:10 --><!-- ws:start:WikiTextAnchorRule:51:&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:51 --><strong><u>Fractional-octave periods</u></strong></h2> | <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Kite Giedraitis method-Fractional-octave periods"></a><!-- ws:end:WikiTextHeadingRule:10 --><!-- ws:start:WikiTextAnchorRule:51:&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:51 --><strong><u>Fractional-octave periods</u></strong></h2> | ||
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<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Kite Giedraitis method-Non-MOS non-MODMOS scales"></a><!-- ws:end:WikiTextHeadingRule:12 --><!-- ws:start:WikiTextAnchorRule:52:&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:52 --><strong><u>Non-MOS non-MODMOS scales</u></strong></h2> | <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Kite Giedraitis method-Non-MOS non-MODMOS scales"></a><!-- ws:end:WikiTextHeadingRule:12 --><!-- ws:start:WikiTextAnchorRule:52:&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:52 --><strong><u>Non-MOS non-MODMOS scales</u></strong></h2> | ||
Compact the genchain to remove any gaps via alterations. The mode number is derived from the compacted genchain. Examples:<br /> | <br /> | ||
<strong><u>1st method</u>:</strong><br /> | |||
Compact the genchain to remove any gaps via alterations. The mode number is derived from the compacted genchain. Examples:<br /> | |||
<br /> | <br /> | ||
C D E F F# G A B C has the genchain F <u><strong>C</strong></u> G D A E B F#, and is named C 2nd Meantone[8].<br /> | C D E F F# G A B C has the genchain F <u><strong>C</strong></u> 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 <u><strong>C</strong></u> G D A E * F#. Alter Bb to get an unbroken genchain: F <u><strong>C</strong></u> G D A E B F#. The scale is C 2nd Meantone[8,-7].<br /> | C D E F F# G A Bb C, with genchain Bb F <u><strong>C</strong></u> G D A E * F#. Alter Bb to get an unbroken genchain: F <u><strong>C</strong></u> G D A E B F#. The scale is C 2nd Meantone[ 8,-7].<br /> | ||
<br /> | <br /> | ||
A B C D D# E F G G# A, with genchain F C G D <u><strong>A</strong></u> E B * * G# D#. Sharpen F and C to get an unbroken genchain: G D <u><strong>A</strong></u> E B F# C# G# D#, giving the name A 3rd Meantone[9,-6,-7].<br /> | A B C D D# E F G G# A, with genchain F C G D <u><strong>A</strong></u> E B * * G# D#. Sharpen F and C to get an unbroken genchain: G D <u><strong>A</strong></u> E B F# C# G# D#, giving the name A 3rd Meantone [9,-6,-7].<br /> | ||
<br /> | <br /> | ||
F G A C E F, with genchain <u><strong>F</strong></u> C G * A E. No amount of altering will make an unbroken genchain, so the name is F 1st Meantone[6,no4].<br /> | F G A C E F, with genchain <u><strong>F</strong></u> C G * A E. No amount of altering will make an unbroken genchain, so the name is F 1st Meantone [6,no4].<br /> | ||
<br /> | <br /> | ||
A B C E F A, a japanese pentatonic scale, with genchain F C * * <u><strong>A</strong></u> E B. The F and C can't be sharpened to F# and C# to make an unbroken Meantone[5] genchain, because pentatonic alterations move notes by 5 steps, not 7. No amount of <u>pentatonic</u> altering will make an unbroken genchain, so the scale must be named as a heptatonic scale with missing degrees: A 5th Meantone[7,no3,no4].<br /> | A B C E F A, a japanese pentatonic scale, with genchain F C * * <u><strong>A</strong></u> E B. The F and C can't be sharpened to F# and C# to make an unbroken Meantone[5] genchain, because pentatonic alterations move notes by 5 steps, not 7. No amount of <u>pentatonic</u> altering will make an unbroken genchain, so the scale must be named as a heptatonic scale with missing degrees: A 5th Meantone [7,no3,no4].<br /> | ||
<br /> | <br /> | ||
<em>[Problem: The 2nd and 3rd examples use heptatonic alterations even though the scales aren't heptatonic.]</em><br /> | <em>[Problem: The 2nd and 3rd examples use heptatonic alterations even though the scales aren't heptatonic.]</em><br /> | ||
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<em>[Possible solution: non-MOS scales can't have chromatic alterations, only missing notes. 2nd example is 3rd Meantone[9,no8]. 3rd example is 5th Meantone[11,no8,no9].</em><br /> | <em>[Possible solution: non-MOS scales can't have chromatic alterations, only missing notes. 2nd example is 3rd Meantone[9,no8]. 3rd example is 5th Meantone[11,no8,no9].</em><br /> | ||
<br /> | <br /> | ||
<em>[Possible solution: | <em>[Possible solution: alterations must be heptatonic because . 2nd example is 3rd Meantone[7] add #4. 3rd example is 5th Meantone[11,no8,no9].</em><br /> | ||
<br /> | |||
<strong><u>2nd method</u>:</strong><br /> | |||
As with MODMOS scales.<br /> | |||
C 2nd Meantone [8]<br /> | |||
C 2nd Meantone [8] b7<br /> | |||
A 3rd Meantone [9] b3 b6<br /> | |||
Alterations are heptatonic because Meantone [7] is the largest MOS contained in Meantone [8] or Meantone [9].<br /> | |||
<br /> | |||
F 1st Meantone [6] no6<br /> | |||
A 5th Meantone [7] no4 no7<br /> | |||
<br /> | <br /> | ||
G A B D E F# G, with genchain <u><strong>G</strong></u> D A E B F# = G 1st Meantone [6]<br /> | |||
G A C D E F# G, with genchain C <u><strong>G</strong></u> D A E * F# = G Meantone [6] #3<br /> | |||
<br /> | <br /> | ||
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