Kite's ups and downs notation: Difference between revisions
Wikispaces>TallKite **Imported revision 623289903 - Original comment: ** |
Wikispaces>TallKite **Imported revision 623953573 - 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>2017-12- | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-12-17 14:37:34 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>623953573</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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=__**Other EDOs**__= | =__**Other EDOs**__= | ||
The up symbol means "sharpened by one EDO-step" in any EDO that uses them. The size in cents of the up changes greatly depending on the edo, from 120¢ in 10-edo to ~17¢ in 72-edo. The sharp symbol's cents size also depends on the edo, ranging from 240¢ in 5-edo to ~26¢ in | The up symbol means "sharpened by one EDO-step" in any EDO that uses them. The size in cents of the up changes greatly depending on the edo, from 120¢ in 10-edo to ~17¢ in 72-edo. The sharp symbol's cents size also depends on the edo, ranging from 240¢ in 5-edo to ~26¢ in 47edo. | ||
EDOs come in 5 categories, based on the size of the fifth. From widest to narrowest: | EDOs come in 5 categories, based on the size of the fifth. From widest to narrowest: | ||
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This is in addition to the trivial EDOs, 2, 3, 4 and 6, which can be notated with standard notation as a subset of 12-EDO. The fifth is defined as the nearest approximation to 3/2. There is a little leeway to this in certain EDOs like 18 which have two possible fifths with nearly equal accuracy. | This is in addition to the trivial EDOs, 2, 3, 4 and 6, which can be notated with standard notation as a subset of 12-EDO. The fifth is defined as the nearest approximation to 3/2. There is a little leeway to this in certain EDOs like 18 which have two possible fifths with nearly equal accuracy. | ||
[[image:The Scale Tree.png width="800" height=" | [[image:The Scale Tree.png width="800" height="1023"]] | ||
The above diagram is actually a section of the Stern-Brocot tree. The tree usually has ratios, not octave fractions (i.e. 4/7, not 4\7 as above). Also it's usually arranged vertically with nodes of the same "generation" occurring at the same height. For example, 5\9 and 7\12 are both children of 4\7, and would usually be level with each other. Here the nodes are arranged vertically by denominator, i.e., the EDO itself. This version of the Stern-Brocot tree is the scale tree. The colored regions of the tree are what I call **kites**, and The heptatonic kite is blue and the pentatonic kite is orange. Every kite has a head (4\7 for the blue kite), a central spine (8\14, 12\21, etc.), a fifthward side on the right (7\12, 11\19, etc.) and a fourthward side on the left (5\9, 9\16, etc.). Every node on a spine is a **spinal** node. Every non-spinal node is part of three kites. It's the head of one kite and on the side of two others. | The above diagram is actually a section of the Stern-Brocot tree. The tree usually has ratios, not octave fractions (i.e. 4/7, not 4\7 as above). Also it's usually arranged vertically with nodes of the same "generation" occurring at the same height. For example, 5\9 and 7\12 are both children of 4\7, and would usually be level with each other. Here the nodes are arranged vertically by denominator, i.e., the EDO itself. This version of the Stern-Brocot tree is the scale tree. The colored regions of the tree are what I call **kites**, and The heptatonic kite is blue and the pentatonic kite is orange. Every kite has a head (4\7 for the blue kite), a central spine (8\14, 12\21, etc.), a fifthward side on the right (7\12, 11\19, etc.) and a fourthward side on the left (5\9, 9\16, etc.). Every node on a spine is a **spinal** node. Every non-spinal node is part of three kites. It's the head of one kite and on the side of two others. | ||
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<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Other EDOs"></a><!-- ws:end:WikiTextHeadingRule:2 --><u><strong>Other EDOs</strong></u></h1> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Other EDOs"></a><!-- ws:end:WikiTextHeadingRule:2 --><u><strong>Other EDOs</strong></u></h1> | ||
<br /> | <br /> | ||
The up symbol means &quot;sharpened by one EDO-step&quot; in any EDO that uses them. The size in cents of the up changes greatly depending on the edo, from 120¢ in 10-edo to ~17¢ in 72-edo. The sharp symbol's cents size also depends on the edo, ranging from 240¢ in 5-edo to ~26¢ in | The up symbol means &quot;sharpened by one EDO-step&quot; in any EDO that uses them. The size in cents of the up changes greatly depending on the edo, from 120¢ in 10-edo to ~17¢ in 72-edo. The sharp symbol's cents size also depends on the edo, ranging from 240¢ in 5-edo to ~26¢ in 47edo.<br /> | ||
<br /> | <br /> | ||
EDOs come in 5 categories, based on the size of the fifth. From widest to narrowest:<br /> | EDOs come in 5 categories, based on the size of the fifth. From widest to narrowest:<br /> | ||
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This is in addition to the trivial EDOs, 2, 3, 4 and 6, which can be notated with standard notation as a subset of 12-EDO. The fifth is defined as the nearest approximation to 3/2. There is a little leeway to this in certain EDOs like 18 which have two possible fifths with nearly equal accuracy.<br /> | This is in addition to the trivial EDOs, 2, 3, 4 and 6, which can be notated with standard notation as a subset of 12-EDO. The fifth is defined as the nearest approximation to 3/2. There is a little leeway to this in certain EDOs like 18 which have two possible fifths with nearly equal accuracy.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule:3467:&lt;img src=&quot;/file/view/The%20Scale%20Tree.png/623953169/ | <!-- ws:start:WikiTextLocalImageRule:3467:&lt;img src=&quot;/file/view/The%20Scale%20Tree.png/623953169/800x1023/The%20Scale%20Tree.png&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 1023px; width: 800px;&quot; /&gt; --><img src="/file/view/The%20Scale%20Tree.png/623953169/800x1023/The%20Scale%20Tree.png" alt="The Scale Tree.png" title="The Scale Tree.png" style="height: 1023px; width: 800px;" /><!-- ws:end:WikiTextLocalImageRule:3467 --><br /> | ||
<br /> | |||
The above diagram is actually a section of the Stern-Brocot tree. The tree usually has ratios, not octave fractions (i.e. 4/7, not 4\7 as above). Also it's usually arranged vertically with nodes of the same &quot;generation&quot; occurring at the same height. For example, 5\9 and 7\12 are both children of 4\7, and would usually be level with each other. Here the nodes are arranged vertically by denominator, i.e., the EDO itself. This version of the Stern-Brocot tree is the scale tree. The colored regions of the tree are what I call <strong>kites</strong>, and The heptatonic kite is blue and the pentatonic kite is orange. Every kite has a head (4\7 for the blue kite), a central spine (8\14, 12\21, etc.), a fifthward side on the right (7\12, 11\19, etc.) and a fourthward side on the left (5\9, 9\16, etc.). Every node on a spine is a <strong>spinal</strong> node. Every non-spinal node is part of three kites. It's the head of one kite and on the side of two others.<br /> | The above diagram is actually a section of the Stern-Brocot tree. The tree usually has ratios, not octave fractions (i.e. 4/7, not 4\7 as above). Also it's usually arranged vertically with nodes of the same &quot;generation&quot; occurring at the same height. For example, 5\9 and 7\12 are both children of 4\7, and would usually be level with each other. Here the nodes are arranged vertically by denominator, i.e., the EDO itself. This version of the Stern-Brocot tree is the scale tree. The colored regions of the tree are what I call <strong>kites</strong>, and The heptatonic kite is blue and the pentatonic kite is orange. Every kite has a head (4\7 for the blue kite), a central spine (8\14, 12\21, etc.), a fifthward side on the right (7\12, 11\19, etc.) and a fourthward side on the left (5\9, 9\16, etc.). Every node on a spine is a <strong>spinal</strong> node. Every non-spinal node is part of three kites. It's the head of one kite and on the side of two others.<br /> | ||
<br /> | <br /> | ||