Comparison of mode notation systems: Difference between revisions
Wikispaces>TallKite **Imported revision 580762913 - Original comment: ** |
Wikispaces>TallKite **Imported revision 580763689 - 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 04: | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-04-21 04:47:21 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>580763689</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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|| 6th Meantone[7] || Phrygian || sLLL sLL || E F G A B C D E || F C G D A **E** B || | || 6th Meantone[7] || Phrygian || sLLL sLL || E F G A B C D E || F C G D A **E** B || | ||
|| 7th Meantone[7] || Locrian || sLLs LLL || B C D E F G A B || F C G D A E **B** || | || 7th Meantone[7] || Locrian || 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" or possibly "fourth meantone seven". The same 7 modes, all with C as the tonic: | 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" or possibly "fourth meantone seven". If in D, as above, it would be "D 4th Meantone heptatonic". The same 7 modes, all with C as the tonic: | ||
|| new scale name || old scale name || Ls pattern || example in C || ------------------- genchain --------------- || | || new scale name || old scale name || Ls pattern || example in C || ------------------- genchain --------------- || | ||
|| 1st Meantone[7] || Lydian || LLLs LLs || C D E F# G A B C ||> **C** G D A E B F# || | || 1st Meantone[7] || Lydian || LLLs LLs || C D E F# G A B C ||> **C** G D A E B F# || | ||
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==[[#How to name rank-2 scales-Fractional-octave periods]]**__Fractional-octave periods__**== | ==[[#How to name rank-2 scales-Fractional-octave periods]]**__Fractional-octave periods__**== | ||
Fractional-period rank-2 temperaments have multiple genchains running in parallel. For example, shrutal[10] might look like this: | Fractional-period rank-2 temperaments have multiple genchains running in parallel. For example, shrutal[10] might look like this: | ||
Eb | Eb -- Bb -- F --- C --- G | ||
A | A --- E --- B --- F# -- C# | ||
Or alternatively, using 16/15 not 3/2 as the generator: | Or alternatively, using 16/15 not 3/2 as the generator: | ||
Eb | Eb -- E --- F --- F# -- G | ||
A | A --- Bb -- B --- C --- C# | ||
Multiple genchains occur because rank-2 really is 2 dimensional, with a "genweb" running in octaves (or whatever the period is) vertically and fifths (or whatever the generator is) horizontally. When the period is an octave, this octave-reduces to a single horizontal genchain. But shrutal has a genweb with vertical half-octaves, which octave-reduces to two parallel genchains. Temperaments with third-octave periods reduce to a triple-genchain, and so forth. | Multiple genchains occur because rank-2 really is 2 dimensional, with a "genweb" running in octaves (or whatever the period is) vertically and fifths (or whatever the generator is) horizontally. When the period is an octave, this octave-reduces to a single horizontal genchain. But shrutal has a genweb with vertical half-octaves, which octave-reduces to two parallel genchains. Temperaments with third-octave periods reduce to a triple-genchain, and so forth. | ||
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==[[#How to name rank-2 scales-Non-MOS scales]]**__Non-MOS scales__**== | ==[[#How to name rank-2 scales-Non-MOS scales]]**__Non-MOS scales__**== | ||
These can be indicated with curly brackets | These can be indicated with curly brackets {}, because regular brackets [] are reserved for MOS scales. The same naming methods apply: | ||
An ungapped example: C D E F F# G A B C, which has a genchain F **C** G D A E B F#, and is named 2nd Meantone{8}. | |||
A gapped example: C D E F F# G A Bb C | A gapped example: C D E F F# G A Bb C, with genchain Bb F **C** G D A E * F#. Alter as few notes as possible to get if not a MOS, at least an unbroken genchain: F **C** G D A E B F#. The scale is 2nd Meantone[8] b7. | ||
Sort of a Fur Elise scale: A B C D D# E F G G# A | Sort of a Fur Elise scale: 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. | ||
Here's a tricky one: F G A C F, the genchain is F C G (gap) A, no way to make an unbroken chain. I would notate this Meantone[5] 1st mode, | Here's a tricky one: F G A C F, the genchain is F C G (gap) A, no way to make an unbroken chain. I would notate this Meantone[5] 1st mode, no 5. | ||
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</table> | </table> | ||
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; or possibly &quot;fourth meantone seven&quot;. The same 7 modes, all with C as the tonic:<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; or possibly &quot;fourth meantone seven&quot;. If in D, as above, it would be &quot;D 4th Meantone heptatonic&quot;. The same 7 modes, all with C as the tonic:<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="How to name rank-2 scales-Fractional-octave periods"></a><!-- ws:end:WikiTextHeadingRule:6 --><!-- 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-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:14 --><strong><u>Fractional-octave periods</u></strong></h2> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="How to name rank-2 scales-Fractional-octave periods"></a><!-- ws:end:WikiTextHeadingRule:6 --><!-- 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-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:14 --><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 | Eb -- Bb -- F --- C --- G<br /> | ||
A | A --- E --- B --- F# -- C#<br /> | ||
<br /> | <br /> | ||
Or alternatively, using 16/15 not 3/2 as the generator:<br /> | Or alternatively, using 16/15 not 3/2 as the generator:<br /> | ||
Eb | Eb -- E --- F --- F# -- G<br /> | ||
A | A --- Bb -- B --- C --- C#<br /> | ||
<br /> | <br /> | ||
Multiple genchains occur because rank-2 really is 2 dimensional, with a &quot;genweb&quot; running in octaves (or whatever the period is) vertically and fifths (or whatever the generator is) horizontally. When the period is an octave, this octave-reduces to a single horizontal genchain. But shrutal has a genweb with vertical half-octaves, which octave-reduces to two parallel genchains. Temperaments with third-octave periods reduce to a triple-genchain, and so forth.<br /> | Multiple genchains occur because rank-2 really is 2 dimensional, with a &quot;genweb&quot; running in octaves (or whatever the period is) vertically and fifths (or whatever the generator is) horizontally. When the period is an octave, this octave-reduces to a single horizontal genchain. But shrutal has a genweb with vertical half-octaves, which octave-reduces to two parallel genchains. Temperaments with third-octave periods reduce to a triple-genchain, and so forth.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="How to name rank-2 scales-Non-MOS scales"></a><!-- ws:end:WikiTextHeadingRule:8 --><!-- ws:start:WikiTextAnchorRule:15:&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:15 --><strong><u>Non-MOS scales</u></strong></h2> | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="How to name rank-2 scales-Non-MOS scales"></a><!-- ws:end:WikiTextHeadingRule:8 --><!-- ws:start:WikiTextAnchorRule:15:&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:15 --><strong><u>Non-MOS scales</u></strong></h2> | ||
These can be indicated with curly brackets | These can be indicated with curly brackets {}, because regular brackets [] are reserved for MOS scales. The same naming methods apply:<br /> | ||
<br /> | <br /> | ||
An ungapped example: 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 2nd Meantone{8}.<br /> | |||
<br /> | <br /> | ||
A gapped example: C D E F F# G A Bb C | A gapped example: C D E F F# G A Bb C, with genchain Bb F <strong>C</strong> G D A E * F#. Alter as few notes as possible to get if not a MOS, at least an unbroken genchain: F <strong>C</strong> G D A E B F#. The scale is 2nd Meantone[8] b7.<br /> | ||
<br /> | <br /> | ||
Sort of a Fur Elise scale: A B C D D# E F G G# A | Sort of a Fur Elise scale: 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 /> | ||
Here's a tricky one: F G A C F, the genchain is F C G (gap) A, no way to make an unbroken chain. I would notate this Meantone[5] 1st mode, | Here's a tricky one: F G A C F, the genchain is F C G (gap) A, no way to make an unbroken chain. I would notate this Meantone[5] 1st mode, no 5.<br /> | ||
<br /> | <br /> | ||
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