Kite's ups and downs notation: Difference between revisions
Wikispaces>TallKite **Imported revision 593739606 - Original comment: ** |
Wikispaces>TallKite **Imported revision 593740006 - 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>2016-09-30 19: | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-09-30 19:59:57 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>593740006</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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JI associations: Major = yellow or fifthward white, minor = green or fourthward white, upmajor = red, downminor = blue, downmajor = upminor = jade or amber. | JI associations: Major = yellow or fifthward white, minor = green or fourthward white, upmajor = red, downminor = blue, downmajor = upminor = jade or amber. | ||
24-EDO is an example of a multi-ring EDO. An EDO is multi-ring if the keyspan of the fifth | 24-EDO is an example of a **multi-ring** EDO. An EDO is multi-ring if the keyspan of the generator (usually the fifth) isn't coprime with the keyspan of the octave, and **single-ring** or 1-ring if it is. 24-EDO has a fifth of 14 steps, and is 2-ring because there are 2 unconnected circles of 12 fifths. They are notated as the mid one and the up one: | ||
Eb - Bb - F - C - G - D - A - E - B - F# - C# - G#/Ab - Eb | Eb - Bb - F - C - G - D - A - E - B - F# - C# - G#/Ab - Eb | ||
Eb^ - Bb^ - F^ - C^ - G^ - D^ - A^ - E^ - B^ - F#^ - C#^ - G#^/Ab^ - Eb^ | Eb^ - Bb^ - F^ - C^ - G^ - D^ - A^ - E^ - B^ - F#^ - C#^ - G#^/Ab^ - Eb^ | ||
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=__Rank-2 | =__Rank-2 Scales: 8ve Periods__= | ||
Ups and downs can be used to notate rank-2 scales. | Ups and downs can be used to notate rank-2 scales as well. Let's start with fifth-generated tunings. For large frameworks, we'll need a long genchain: | ||
Let's start with fifth-generated tunings. For large frameworks, we'll need a long genchain: | |||
...Fbb Cbb Gbb Dbb Abb Ebb Bbb Fb Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E# B# Fx Cx Gx Dx Ax Ex Bx... | ...Fbb Cbb Gbb Dbb Abb Ebb Bbb Fb Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E# B# Fx Cx Gx Dx Ax Ex Bx... | ||
Fifth-generated rank-2 tunings can be notated without ups and downs in any framework on either side of the 4\7 kite: | Fifth-generated rank-2 tunings can be notated without ups and downs in any framework on either side of the 4\7 kite: | ||
12-tone genchain Eb | 12-tone genchain Eb Bb F C G D A E B F# C# G# makes this scale: C C# D Eb E F F# G G# A Bb B C | ||
12-tone genchain | 12-tone genchain F C G D A E B F# C# G# D# A# makes this scale: C C# D D# E F F# G G# A A# B C | ||
For rank-2 scales to work with a given framework, the keyspans of the generator and the period must be coprime. These correspond to single-ring EDOs. Each node in the Stern-Brocot chart is formed by these two keyspans, thus this node must not be on the spine of a kite. For example, fifth-generated tunings like meantone and pythagorean are compatible with 12-tone, but not with 15-tone. Likewise a third-generated tuning like dicot or mohajira is incompatible with 12-tone (3 or 4 isn't coprime with 12), but compatible with 24-tone (7 is coprime with 24). | |||
For rank-2 scales to work with a given framework, the keyspans of the generator and the period must be coprime. These correspond to | |||
All fifthless frameworks are incompatible with fifth-generated heptatonic notation, since the minor 2nd becomes a descending interval. All perfect and pentatonic frameworks are incompatible with fifth-generated rank-2 tunings, except for 5-tone and 7-tone. These two are easily notated without ups and downs: | All fifthless frameworks are incompatible with fifth-generated heptatonic notation, since the minor 2nd becomes a descending interval. All perfect and pentatonic frameworks are incompatible with fifth-generated rank-2 tunings, except for 5-tone and 7-tone. These two are easily notated without ups and downs: | ||
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There is no variant of D adjacent to C, and there is no 2nd with keyspan 1 or -1. Some other method of notation must be used for rank-2 fifth-generated tunings in these two frameworks. | There is no variant of D adjacent to C, and there is no 2nd with keyspan 1 or -1. Some other method of notation must be used for rank-2 fifth-generated tunings in these two frameworks. | ||
=__Rank-2 Scales: Non-8ve Periods__= | |||
Ups and downs can also be used when naming fractional octave rank-2 tunings. These tunings have multiple genchains. Each genchain has a different "height"; one is up, another is down, etc. See [[xenharmonic/Naming Rank-2 Scales#Kite%20Giedraitis%20method-Fractional-octave%20periods|xenharmonic.wikispaces.com/Naming+Rank-2+Scales]] | Ups and downs can also be used when naming fractional octave rank-2 tunings. These tunings have multiple genchains. Each genchain has a different "height"; one is up, another is down, etc. See [[xenharmonic/Naming Rank-2 Scales#Kite%20Giedraitis%20method-Fractional-octave%20periods|xenharmonic.wikispaces.com/Naming+Rank-2+Scales]] | ||
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||= 22 ||= 0 ||= D ||= ||= ||</pre></div> | ||= 22 ||= 0 ||= D ||= ||= ||</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Ups and Downs Notation</title></head><body><!-- ws:start:WikiTextTocRule: | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Ups and Downs Notation</title></head><body><!-- ws:start:WikiTextTocRule:34:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --><div style="margin-left: 1em;"><a href="#x&quot;Ups and downs&quot; for 22edo">&quot;Ups and downs&quot; for 22edo</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><div style="margin-left: 1em;"><a href="#Other EDOs">Other EDOs</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><div style="margin-left: 1em;"><a href="#x22edo Chord Names">22edo Chord Names</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --><div style="margin-left: 2em;"><a href="#toc3"></a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><div style="margin-left: 1em;"><a href="#Chord names in other EDOs">Chord names in other EDOs</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --><div style="margin-left: 1em;"><a href="#Cross-EDO considerations">Cross-EDO considerations</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --><div style="margin-left: 1em;"><a href="#Scale Fragments">Scale Fragments</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --><div style="margin-left: 1em;"><a href="#Summary of EDO notation">Summary of EDO notation</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><div style="margin-left: 2em;"><a href="#Summary of EDO notation-&quot;Regular&quot; EDOs">&quot;Regular&quot; EDOs</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --><div style="margin-left: 2em;"><a href="#Summary of EDO notation-&quot;Perfect&quot; EDOs">&quot;Perfect&quot; EDOs</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --><div style="margin-left: 2em;"><a href="#Summary of EDO notation-&quot;Fourthward&quot; EDOs">&quot;Fourthward&quot; EDOs</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --><div style="margin-left: 2em;"><a href="#Summary of EDO notation-&quot;Pentatonic&quot; EDOs">&quot;Pentatonic&quot; EDOs</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --><div style="margin-left: 2em;"><a href="#Summary of EDO notation-&quot;Fifth-less&quot; EDOs">&quot;Fifth-less&quot; EDOs</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --><div style="margin-left: 1em;"><a href="#Ups and downs solfege">Ups and downs solfege</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --><div style="margin-left: 1em;"><a href="#Rank-2 Scales: 8ve Periods">Rank-2 Scales: 8ve Periods</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --><div style="margin-left: 1em;"><a href="#Rank-2 Scales: Non-8ve Periods">Rank-2 Scales: Non-8ve Periods</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --><div style="margin-left: 1em;"><a href="#Generators other than a fifth">Generators other than a fifth</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --></div> | ||
<!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x&quot;Ups and downs&quot; for 22edo"></a><!-- ws:end:WikiTextHeadingRule:0 --><u>&quot;Ups and downs&quot; for 22edo</u></h1> | |||
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Ups and Downs is a notation system developed by <a class="wiki_link" href="/KiteGiedraitis">Kite</a> that works with almost all EDOs and rank 2 tunings. It only adds 3 symbols to standard notation, so it's very easy to learn. The name comes from the up symbol &quot;^&quot; and the down symbol &quot;v&quot;.<br /> | Ups and Downs is a notation system developed by <a class="wiki_link" href="/KiteGiedraitis">Kite</a> that works with almost all EDOs and rank 2 tunings. It only adds 3 symbols to standard notation, so it's very easy to learn. The name comes from the up symbol &quot;^&quot; and the down symbol &quot;v&quot;.<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 /> | ||
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<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:4257:&lt;img src=&quot;/file/view/The%20Scale%20Tree.png/623953169/800x1002/The%20Scale%20Tree.png&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 1002px; width: 800px;&quot; /&gt; --><img src="/file/view/The%20Scale%20Tree.png/623953169/800x1002/The%20Scale%20Tree.png" alt="The Scale Tree.png" title="The Scale Tree.png" style="height: 1002px; width: 800px;" /><!-- ws:end:WikiTextLocalImageRule:4257 --><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 /> | ||
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JI associations: Major = yellow or fifthward white, minor = green or fourthward white, upmajor = red, downminor = blue, downmajor = upminor = jade or amber.<br /> | JI associations: Major = yellow or fifthward white, minor = green or fourthward white, upmajor = red, downminor = blue, downmajor = upminor = jade or amber.<br /> | ||
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24-EDO is an example of a multi-ring EDO. An EDO is multi-ring if the keyspan of the fifth | 24-EDO is an example of a <strong>multi-ring</strong> EDO. An EDO is multi-ring if the keyspan of the generator (usually the fifth) isn't coprime with the keyspan of the octave, and <strong>single-ring</strong> or 1-ring if it is. 24-EDO has a fifth of 14 steps, and is 2-ring because there are 2 unconnected circles of 12 fifths. They are notated as the mid one and the up one:<br /> | ||
Eb - Bb - F - C - G - D - A - E - B - F# - C# - G#/Ab - Eb<br /> | Eb - Bb - F - C - G - D - A - E - B - F# - C# - G#/Ab - Eb<br /> | ||
Eb^ - Bb^ - F^ - C^ - G^ - D^ - A^ - E^ - B^ - F#^ - C#^ - G#^/Ab^ - Eb^<br /> | Eb^ - Bb^ - F^ - C^ - G^ - D^ - A^ - E^ - B^ - F#^ - C#^ - G#^/Ab^ - Eb^<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><!-- ws:end:WikiTextHeadingRule:6 --><!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><!-- ws:end:WikiTextHeadingRule:6 --><!-- ws:start:WikiTextLocalImageRule:4259:&lt;img src=&quot;/file/view/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%202.jpg/570451199/800x957/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%202.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 957px; width: 800px;&quot; /&gt; --><img src="/file/view/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%202.jpg/570451199/800x957/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%202.jpg" alt="Tibia in G with ^v, rygb 2.jpg" title="Tibia in G with ^v, rygb 2.jpg" style="height: 957px; width: 800px;" /><!-- ws:end:WikiTextLocalImageRule:4259 --></h2> | ||
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<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Chord names in other EDOs"></a><!-- ws:end:WikiTextHeadingRule:8 --><u>Chord names in other EDOs</u></h1> | <!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Chord names in other EDOs"></a><!-- ws:end:WikiTextHeadingRule:8 --><u>Chord names in other EDOs</u></h1> | ||
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<!-- ws:start:WikiTextHeadingRule:28:&lt;h1&gt; --><h1 id="toc14"><a name="Rank-2 | <!-- ws:start:WikiTextHeadingRule:28:&lt;h1&gt; --><h1 id="toc14"><a name="Rank-2 Scales: 8ve Periods"></a><!-- ws:end:WikiTextHeadingRule:28 --><u>Rank-2 Scales: 8ve Periods</u></h1> | ||
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Ups and downs can be used to notate rank-2 scales. | Ups and downs can be used to notate rank-2 scales as well. Let's start with fifth-generated tunings. For large frameworks, we'll need a long genchain:<br /> | ||
Let's start with fifth-generated tunings. For large frameworks, we'll need a long genchain:<br /> | |||
...Fbb Cbb Gbb Dbb Abb Ebb Bbb Fb Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E# B# Fx Cx Gx Dx Ax Ex Bx...<br /> | ...Fbb Cbb Gbb Dbb Abb Ebb Bbb Fb Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E# B# Fx Cx Gx Dx Ax Ex Bx...<br /> | ||
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Fifth-generated rank-2 tunings can be notated without ups and downs in any framework on either side of the 4\7 kite:<br /> | Fifth-generated rank-2 tunings can be notated without ups and downs in any framework on either side of the 4\7 kite:<br /> | ||
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12-tone genchain Eb | 12-tone genchain Eb Bb F C G D A E B F# C# G# makes this scale: C C# D Eb E F F# G G# A Bb B C<br /> | ||
12-tone genchain | 12-tone genchain F C G D A E B F# C# G# D# A# makes this scale: C C# D D# E F F# G G# A A# B C<br /> | ||
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For rank-2 scales to work with a given framework, the keyspans of the generator and the period must be coprime. These correspond to single-ring EDOs. Each node in the Stern-Brocot chart is formed by these two keyspans, thus this node must not be on the spine of a kite. For example, fifth-generated tunings like meantone and pythagorean are compatible with 12-tone, but not with 15-tone. Likewise a third-generated tuning like dicot or mohajira is incompatible with 12-tone (3 or 4 isn't coprime with 12), but compatible with 24-tone (7 is coprime with 24).<br /> | |||
For rank-2 scales to work with a given framework, the keyspans of the generator and the period must be coprime. These correspond to | |||
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All fifthless frameworks are incompatible with fifth-generated heptatonic notation, since the minor 2nd becomes a descending interval. All perfect and pentatonic frameworks are incompatible with fifth-generated rank-2 tunings, except for 5-tone and 7-tone. These two are easily notated without ups and downs:<br /> | All fifthless frameworks are incompatible with fifth-generated heptatonic notation, since the minor 2nd becomes a descending interval. All perfect and pentatonic frameworks are incompatible with fifth-generated rank-2 tunings, except for 5-tone and 7-tone. These two are easily notated without ups and downs:<br /> | ||
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There is no variant of D adjacent to C, and there is no 2nd with keyspan 1 or -1. Some other method of notation must be used for rank-2 fifth-generated tunings in these two frameworks.<br /> | There is no variant of D adjacent to C, and there is no 2nd with keyspan 1 or -1. Some other method of notation must be used for rank-2 fifth-generated tunings in these two frameworks.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:30:&lt;h1&gt; --><h1 id="toc15"><a name="Rank-2 Scales: Non-8ve Periods"></a><!-- ws:end:WikiTextHeadingRule:30 --><u>Rank-2 Scales: Non-8ve Periods</u></h1> | |||
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Ups and downs can also be used when naming fractional octave rank-2 tunings. These tunings have multiple genchains. Each genchain has a different &quot;height&quot;; one is up, another is down, etc. See <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Naming%20Rank-2%20Scales#Kite%20Giedraitis%20method-Fractional-octave%20periods">xenharmonic.wikispaces.com/Naming+Rank-2+Scales</a><br /> | Ups and downs can also be used when naming fractional octave rank-2 tunings. These tunings have multiple genchains. Each genchain has a different &quot;height&quot;; one is up, another is down, etc. See <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Naming%20Rank-2%20Scales#Kite%20Giedraitis%20method-Fractional-octave%20periods">xenharmonic.wikispaces.com/Naming+Rank-2+Scales</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:32:&lt;h1&gt; --><h1 id="toc16"><a name="Generators other than a fifth"></a><!-- ws:end:WikiTextHeadingRule:32 --><u>Generators other than a fifth</u></h1> | ||
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The main reason to use ups and downs is to allow fifth-generated heptatonic notation in frameworks and EDOs that aren't fully compatible with such a notation, i.e. those not on the sides of the 4\7 kite. The main reason to use a generator other than a fifth is to use a notation more compatible with one's chosen framework or EDO. Thus there is little reason to use ups and downs in such a situation.<br /> | The main reason to use ups and downs is to allow fifth-generated heptatonic notation in frameworks and EDOs that aren't fully compatible with such a notation, i.e. those not on the sides of the 4\7 kite. The main reason to use a generator other than a fifth is to use a notation more compatible with one's chosen framework or EDO. Thus there is little reason to use ups and downs in such a situation.<br /> | ||