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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 22:51:19 UTC</tt>.<br> | | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-09-30 22:56:19 UTC</tt>.<br> |
| : The original revision id was <tt>593744148</tt>.<br> | | : The original revision id was <tt>593744268</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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| ||= 50-tone ||= 3 ||= -1 ||= +19 ||= C^ = Bx ||= desc double-dim 2nd ||= ^dd2 || | | ||= 50-tone ||= 3 ||= -1 ||= +19 ||= C^ = Bx ||= desc double-dim 2nd ||= ^dd2 || |
| ||= 53-tone ||= 5 ||= -1 ||= +12 ||= C^ = B# ||= desc dim 2nd ||= vd2 || | | ||= 53-tone ||= 5 ||= -1 ||= +12 ||= C^ = B# ||= desc dim 2nd ||= vd2 || |
| The value of i equals the stepspan of the up interval. A look at the scale fragments reveals why 29-tone's up is a descending interval:
| | A look at the scale fragments reveals why 29-tone's up is a descending interval: |
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| 22-tone: C Db * C# D | | 22-tone: C Db * C# D |
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| 29-tone: C * Db C# * D | | 29-tone: C * Db C# * D |
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| The 22-tone and 27-tone frameworks all have Db adjacent to C, so that C^ equals Db. For 29-tone, Db = C^^. To find a D-something that is adjacent to C, we must use Dbb, which is one key __below__ C. Thus Cv = Dbb, and C^ = B#, ^ is a descending dim 2nd, and the unison is an up-dim 2nd, ^d2. 41-tone, 50-tone and 53-tone also have ups that are descending. This is not a problem: | | The 22-tone and 27-tone frameworks all have Db adjacent to C, so that C^ equals Db. For 29-tone, Db = C^^. To find a D-something that is adjacent to C, we must use Dbb, which is one key __below__ C. Thus Cv = Dbb, and C^ = B#, ^ is a descending dim 2nd, and the unison is an up-dim 2nd, ^d2. Descending ups are not a problem: |
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| The 29-tone genchain:
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| ||= genspan from C ||= keyspan from C || || || ||= || ||
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| ||= -13 ||= 11 || E#vv || Fv || Gbb ||= || ||
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| ||= -12 ||= 28 || B#vv || Cv || Dbb ||= || ||
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| ||= -11 ||= 16 || Fxvv || Gv || Abb ||= || ||
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| ||= -10 ||= 4 || Cxvv || Dv || Ebb ||= || ||
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| ||= -9 ||= 21 || Gxvv || Av || Bbb ||= || ||
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| ||= -8 ||= 9 || Dxvv || Ev ||= Fb ||= || ||
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| ||= -7 ||= 26 || Axvv || Bv ||= Cb ||= || ||
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| ||= -6 ||= 14 || Exvv || F#v ||= Gb ||= || ||
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| ||= -5 ||= 2 || Bxvv || C#v ||= Db ||= || ||
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| ||= -4 ||= 19 || || G#v ||= Ab ||= || ||
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| ||= -3 ||= 7 || || D#v ||= Eb ||= Fbb^ || ||
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| ||= -2 ||= 24 || || A#v ||= Bb ||= Cbb^ || ||
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| ||= -1 ||= 12 || || E#v ||= F ||= Gbb^ || ||
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| ||= 0 ||= 0 || || B#v ||= C ||= Dbb^ || ||
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| ||= 1 ||= 17 || || Fxv ||= G ||= Abb^ || ||
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| ||= 2 ||= 5 || || Cxv ||= D ||= Ebb^ || ||
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| ||= 3 ||= 22 || || Gxv ||= A ||= Bbb^ || ||
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| ||= 4 ||= 10 || || Dxv ||= E ||= Fb^ || ||
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| ||= 5 ||= 27 || || Axv ||= B ||= Cb^ || ||
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| ||= 6 ||= 15 || || Exv ||= F# ||= Gb^ || ||
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| ||= 7 ||= 3 || || Bxv ||= C# ||= Db^ || ||
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| ||= 8 ||= 20 || || ||= G# ||= Ab^ || ||
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| ||= 9 ||= 8 || || ||= D# ||= Eb^ || Fbb^^ ||
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| ||= 10 ||= 25 || || ||= A# ||= Bb^ || Cbb^^ ||
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| ||= 11 ||= 13 || || ||= E# ||= F^ || Gbb^^ ||
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| ||= 12 ||= 1 || || ||= B# ||= C^ || Dbb^^ ||
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| ||= 13 ||= 18 || || ||= Fx ||= G^ || Abb^^ ||
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| ||= 14 ||= 6 || || ||= Cx ||= D^ || Ebb^^ ||
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| ||= 15 ||= 23 || || ||= Gx ||= A^ || Bbb^^ ||
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| ||= 16 ||= 11 || || ||= Dx ||= E^ || Fb^^ ||
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| ||= 17 ||= 28 || || ||= Ax ||= B^ || Cb^^ ||
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| ||= ||= || || || etc. ||= || ||
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| The 29-tone keyboard, with alternate tunings for the black keys: | | The 29-tone keyboard, with alternate tunings for the black keys: |
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| ||= 4 ||= -10 ||= Dv ||= +19 ||= C#^ = Db^^ || | | ||= 4 ||= -10 ||= Dv ||= +19 ||= C#^ = Db^^ || |
| ||= 5 ||= +2 ||= D ||= ||= || | | ||= 5 ||= +2 ||= D ||= ||= || |
| ||= 6 ||= -15 ||= Ebv = D#vv ||= +14 ||= D^ ||
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| ||= 7 ||= -3 ||= Eb = D#v ||= +26 ||= D^^ = Ebb^3 ||
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| ||= 8 ||= -20 ||= Evv = Dxv3 ||= +9 ||= D# = Eb^ ||
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| ||= 9 ||= -8 ||= Ev ||= +21 ||= D#^ = Eb^^ ||
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| ||= 10 ||= +4 ||= E ||= ||= ||
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| ||= 11 ||= -13 ||= Fv ||= +16 ||= E^ ||
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| ||= 12 ||= -1 ||= F ||= ||= ||
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| ||= 13 ||= -18 ||= Gbv = F#vv ||= +11 ||= F^ ||
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| ||= 14 ||= -6 ||= Gb = F#v ||= +23 ||= F^^ = Gbb^3 ||
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| ||= 15 ||= -23 ||= Gvv = Fxv3 ||= +6 ||= F# = Gb^ ||
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| ||= 16 ||= -11 ||= Gv ||= +18 ||= F#^ = Gb^^ ||
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| ||= 17 ||= +1 ||= G ||= ||= ||
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| ||= 18 ||= -16 ||= Abv = G#vv ||= +13 ||= G^ ||
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| ||= 19 ||= -4 ||= Ab = G#v ||= +25 ||= G^^ = Abb^3 ||
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| ||= 20 ||= -21 ||= Avv = Gxv3 ||= +8 ||= G# = Ab^ ||
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| ||= 21 ||= -9 ||= Av ||= +20 ||= G#^ = Ab^^ ||
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| ||= 22 ||= +3 ||= A ||= ||= ||
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| ||= 23 ||= -14 ||= Bbv = A#vv ||= +15 ||= A^ ||
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| ||= 24 ||= -2 ||= Bb = A#v ||= +27 ||= A^^ = Bbb^3 ||
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| ||= 25 ||= -19 ||= Bvv = Axv3 ||= +10 ||= A# = Bb^ ||
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| ||= 26 ||= -7 ||= Bv ||= +22 ||= A#^ = Bb^^ ||
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| ||= 27 ||= +5 ||= B ||= ||= ||
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| ||= 28 ||= -12 ||= Cv ||= +17 ||= B^ ||
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| ||= 29 ||= 0 ||= C ||= ||= ||
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| 39-tone and 49-tone are problematic: | | The value of i equals the stepspan of the up interval. 39-tone and 49-tone are problematic: |
| 39-tone: C * Db * * C# * D | | 39-tone: C * Db * * C# * D |
| 49-tone: C * Db * * * * C# * D | | 49-tone: C * Db * * * * C# * D |
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| There is no variant of D adjacent to C, and there is no 2nd with keyspan 1 or -1. In theory, 39-tone's C^ could be an octuply-diminished 9th. 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. In theory, 39-tone's C^ could be an octuply-diminished 9th. Notating rank-2 fifth-generated tunings in these two frameworks requires out-of-order notes. |
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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:4293:&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:4293 --><br /> | | <!-- ws:start:WikiTextLocalImageRule:3475:&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:3475 --><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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| <br /> | | <br /> |
| <br /> | | <br /> |
| <!-- ws:start:WikiTextLocalImageRule:4294:&lt;img src=&quot;/file/view/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%201.jpg/570451171/800x1035/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%201.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 1035px; width: 800px;&quot; /&gt; --><img src="/file/view/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%201.jpg/570451171/800x1035/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%201.jpg" alt="Tibia in G with ^v, rygb 1.jpg" title="Tibia in G with ^v, rygb 1.jpg" style="height: 1035px; width: 800px;" /><!-- ws:end:WikiTextLocalImageRule:4294 --><br /> | | <!-- ws:start:WikiTextLocalImageRule:3476:&lt;img src=&quot;/file/view/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%201.jpg/570451171/800x1035/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%201.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 1035px; width: 800px;&quot; /&gt; --><img src="/file/view/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%201.jpg/570451171/800x1035/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%201.jpg" alt="Tibia in G with ^v, rygb 1.jpg" title="Tibia in G with ^v, rygb 1.jpg" style="height: 1035px; width: 800px;" /><!-- ws:end:WikiTextLocalImageRule:3476 --><br /> |
| <br /> | | <br /> |
| <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><!-- ws:end:WikiTextHeadingRule:6 --><!-- ws:start:WikiTextLocalImageRule:4295:&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:4295 --></h2> | | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><!-- ws:end:WikiTextHeadingRule:6 --><!-- ws:start:WikiTextLocalImageRule:3477:&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:3477 --></h2> |
| <br /> | | <br /> |
| <!-- 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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| </table> | | </table> |
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| The value of i equals the stepspan of the up interval. A look at the scale fragments reveals why 29-tone's up is a descending interval:<br />
| | A look at the scale fragments reveals why 29-tone's up is a descending interval:<br /> |
| <br /> | | <br /> |
| 22-tone: C Db * C# D<br /> | | 22-tone: C Db * C# D<br /> |
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| 29-tone: C * Db C# * D<br /> | | 29-tone: C * Db C# * D<br /> |
| <br /> | | <br /> |
| The 22-tone and 27-tone frameworks all have Db adjacent to C, so that C^ equals Db. For 29-tone, Db = C^^. To find a D-something that is adjacent to C, we must use Dbb, which is one key <u>below</u> C. Thus Cv = Dbb, and C^ = B#, ^ is a descending dim 2nd, and the unison is an up-dim 2nd, ^d2. 41-tone, 50-tone and 53-tone also have ups that are descending. This is not a problem:<br /> | | The 22-tone and 27-tone frameworks all have Db adjacent to C, so that C^ equals Db. For 29-tone, Db = C^^. To find a D-something that is adjacent to C, we must use Dbb, which is one key <u>below</u> C. Thus Cv = Dbb, and C^ = B#, ^ is a descending dim 2nd, and the unison is an up-dim 2nd, ^d2. Descending ups are not a problem:<br /> |
| <br /> | | <br /> |
| <br />
| | The 29-tone keyboard, with alternate tunings for the black keys:<br /> |
| <br />
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| The 29-tone genchain:<br /> | |
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| <table class="wiki_table"> | | <table class="wiki_table"> |
| <tr> | | <tr> |
| <td style="text-align: center;">genspan from C<br />
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| </td>
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| <td style="text-align: center;">keyspan from C<br /> | | <td style="text-align: center;">keyspan from C<br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;">genspan from C<br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;">note<br /> |
| </td> | | </td> |
| <td><br /> | | <td style="text-align: center;">genspan from C<br /> |
| </td> | | </td> |
| <td style="text-align: center;"><br /> | | <td style="text-align: center;">note<br /> |
| </td>
| |
| <td><br />
| |
| </td> | | </td> |
| </tr> | | </tr> |
| <tr> | | <tr> |
| <td style="text-align: center;">-13<br /> | | <td style="text-align: center;">0<br /> |
| </td> | | </td> |
| <td style="text-align: center;">11<br /> | | <td style="text-align: center;">0<br /> |
| </td> | | </td> |
| <td>E#vv<br /> | | <td style="text-align: center;">C<br /> |
| </td> | | </td> |
| <td>Fv<br /> | | <td style="text-align: center;"><br /> |
| </td>
| |
| <td>Gbb<br />
| |
| </td> | | </td> |
| <td style="text-align: center;"><br /> | | <td style="text-align: center;"><br /> |
| </td>
| |
| <td><br />
| |
| </td> | | </td> |
| </tr> | | </tr> |
| <tr> | | <tr> |
| <td style="text-align: center;">-12<br /> | | <td style="text-align: center;">1<br /> |
| </td> | | </td> |
| <td style="text-align: center;">28<br /> | | <td style="text-align: center;">-17<br /> |
| </td> | | </td> |
| <td>B#vv<br /> | | <td style="text-align: center;">Dbv = C#vv<br /> |
| </td> | | </td> |
| <td>Cv<br /> | | <td style="text-align: center;">+12<br /> |
| </td> | | </td> |
| <td>Dbb<br />
| | <td style="text-align: center;">C^<br /> |
| </td>
| |
| <td style="text-align: center;"><br /> | |
| </td>
| |
| <td><br />
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| </td> | | </td> |
| </tr> | | </tr> |
| <tr> | | <tr> |
| <td style="text-align: center;">-11<br /> | | <td style="text-align: center;">2<br /> |
| </td> | | </td> |
| <td style="text-align: center;">16<br /> | | <td style="text-align: center;">-5<br /> |
| </td> | | </td> |
| <td>Fxvv<br /> | | <td style="text-align: center;">Db = C#v<br /> |
| </td> | | </td> |
| <td>Gv<br /> | | <td style="text-align: center;">+24<br /> |
| </td> | | </td> |
| <td>Abb<br />
| | <td style="text-align: center;">C^^ = Dbb^<span style="vertical-align: super;">3</span><br /> |
| </td>
| |
| <td style="text-align: center;"><br /> | |
| </td> | |
| <td><br />
| |
| </td> | | </td> |
| </tr> | | </tr> |
| <tr> | | <tr> |
| <td style="text-align: center;">-10<br /> | | <td style="text-align: center;">3<br /> |
| </td> | | </td> |
| <td style="text-align: center;">4<br /> | | <td style="text-align: center;">-22<br /> |
| </td> | | </td> |
| <td>Cxvv<br /> | | <td style="text-align: center;">Dvv = Cxv<span style="vertical-align: super;">3</span><br /> |
| </td> | | </td> |
| <td>Dv<br /> | | <td style="text-align: center;">+7<br /> |
| </td> | | </td> |
| <td>Ebb<br />
| | <td style="text-align: center;">C# = Db^<br /> |
| </td>
| |
| <td style="text-align: center;"><br /> | |
| </td>
| |
| <td><br />
| |
| </td> | | </td> |
| </tr> | | </tr> |
| <tr> | | <tr> |
| <td style="text-align: center;">-9<br /> | | <td style="text-align: center;">4<br /> |
| </td> | | </td> |
| <td style="text-align: center;">21<br /> | | <td style="text-align: center;">-10<br /> |
| </td> | | </td> |
| <td>Gxvv<br /> | | <td style="text-align: center;">Dv<br /> |
| </td> | | </td> |
| <td>Av<br /> | | <td style="text-align: center;">+19<br /> |
| </td> | | </td> |
| <td>Bbb<br />
| | <td style="text-align: center;">C#^ = Db^^<br /> |
| </td>
| |
| <td style="text-align: center;"><br /> | |
| </td>
| |
| <td><br />
| |
| </td> | | </td> |
| </tr> | | </tr> |
| <tr> | | <tr> |
| <td style="text-align: center;">-8<br /> | | <td style="text-align: center;">5<br /> |
| </td> | | </td> |
| <td style="text-align: center;">9<br /> | | <td style="text-align: center;">+2<br /> |
| </td> | | </td> |
| <td>Dxvv<br />
| | <td style="text-align: center;">D<br /> |
| </td>
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| <td>Ev<br />
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| </td>
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| <td style="text-align: center;">Fb<br />
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| </td>
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| <td style="text-align: center;"><br />
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| </td>
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| <td><br />
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| </td>
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| </tr>
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| <tr>
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| <td style="text-align: center;">-7<br />
| |
| </td>
| |
| <td style="text-align: center;">26<br />
| |
| </td>
| |
| <td>Axvv<br />
| |
| </td>
| |
| <td>Bv<br />
| |
| </td>
| |
| <td style="text-align: center;">Cb<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">-6<br />
| |
| </td>
| |
| <td style="text-align: center;">14<br />
| |
| </td>
| |
| <td>Exvv<br />
| |
| </td>
| |
| <td>F#v<br />
| |
| </td>
| |
| <td style="text-align: center;">Gb<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">-5<br />
| |
| </td>
| |
| <td style="text-align: center;">2<br />
| |
| </td>
| |
| <td>Bxvv<br />
| |
| </td>
| |
| <td>C#v<br />
| |
| </td>
| |
| <td style="text-align: center;">Db<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">-4<br />
| |
| </td>
| |
| <td style="text-align: center;">19<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>G#v<br />
| |
| </td>
| |
| <td style="text-align: center;">Ab<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">-3<br />
| |
| </td>
| |
| <td style="text-align: center;">7<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>D#v<br />
| |
| </td>
| |
| <td style="text-align: center;">Eb<br />
| |
| </td>
| |
| <td style="text-align: center;">Fbb^<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">-2<br />
| |
| </td>
| |
| <td style="text-align: center;">24<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>A#v<br />
| |
| </td>
| |
| <td style="text-align: center;">Bb<br />
| |
| </td>
| |
| <td style="text-align: center;">Cbb^<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">-1<br />
| |
| </td>
| |
| <td style="text-align: center;">12<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>E#v<br />
| |
| </td>
| |
| <td style="text-align: center;">F<br />
| |
| </td>
| |
| <td style="text-align: center;">Gbb^<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">0<br />
| |
| </td>
| |
| <td style="text-align: center;">0<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>B#v<br />
| |
| </td>
| |
| <td style="text-align: center;">C<br />
| |
| </td>
| |
| <td style="text-align: center;">Dbb^<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">1<br />
| |
| </td>
| |
| <td style="text-align: center;">17<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>Fxv<br />
| |
| </td>
| |
| <td style="text-align: center;">G<br />
| |
| </td>
| |
| <td style="text-align: center;">Abb^<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">2<br />
| |
| </td>
| |
| <td style="text-align: center;">5<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>Cxv<br />
| |
| </td>
| |
| <td style="text-align: center;">D<br />
| |
| </td>
| |
| <td style="text-align: center;">Ebb^<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">3<br />
| |
| </td>
| |
| <td style="text-align: center;">22<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>Gxv<br />
| |
| </td>
| |
| <td style="text-align: center;">A<br />
| |
| </td>
| |
| <td style="text-align: center;">Bbb^<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">4<br />
| |
| </td>
| |
| <td style="text-align: center;">10<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>Dxv<br />
| |
| </td>
| |
| <td style="text-align: center;">E<br />
| |
| </td>
| |
| <td style="text-align: center;">Fb^<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">5<br />
| |
| </td>
| |
| <td style="text-align: center;">27<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>Axv<br />
| |
| </td>
| |
| <td style="text-align: center;">B<br />
| |
| </td>
| |
| <td style="text-align: center;">Cb^<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">6<br />
| |
| </td>
| |
| <td style="text-align: center;">15<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>Exv<br />
| |
| </td>
| |
| <td style="text-align: center;">F#<br />
| |
| </td>
| |
| <td style="text-align: center;">Gb^<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">7<br />
| |
| </td>
| |
| <td style="text-align: center;">3<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>Bxv<br />
| |
| </td>
| |
| <td style="text-align: center;">C#<br />
| |
| </td>
| |
| <td style="text-align: center;">Db^<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">8<br />
| |
| </td>
| |
| <td style="text-align: center;">20<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">G#<br />
| |
| </td>
| |
| <td style="text-align: center;">Ab^<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">9<br />
| |
| </td>
| |
| <td style="text-align: center;">8<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">D#<br />
| |
| </td>
| |
| <td style="text-align: center;">Eb^<br />
| |
| </td>
| |
| <td>Fbb^^<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">10<br />
| |
| </td>
| |
| <td style="text-align: center;">25<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">A#<br />
| |
| </td>
| |
| <td style="text-align: center;">Bb^<br />
| |
| </td>
| |
| <td>Cbb^^<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">11<br />
| |
| </td>
| |
| <td style="text-align: center;">13<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">E#<br />
| |
| </td>
| |
| <td style="text-align: center;">F^<br />
| |
| </td>
| |
| <td>Gbb^^<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">12<br />
| |
| </td>
| |
| <td style="text-align: center;">1<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">B#<br />
| |
| </td>
| |
| <td style="text-align: center;">C^<br />
| |
| </td>
| |
| <td>Dbb^^<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">13<br />
| |
| </td>
| |
| <td style="text-align: center;">18<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">Fx<br />
| |
| </td>
| |
| <td style="text-align: center;">G^<br />
| |
| </td>
| |
| <td>Abb^^<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">14<br />
| |
| </td>
| |
| <td style="text-align: center;">6<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">Cx<br />
| |
| </td>
| |
| <td style="text-align: center;">D^<br />
| |
| </td>
| |
| <td>Ebb^^<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">15<br />
| |
| </td>
| |
| <td style="text-align: center;">23<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">Gx<br />
| |
| </td>
| |
| <td style="text-align: center;">A^<br />
| |
| </td>
| |
| <td>Bbb^^<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">16<br />
| |
| </td>
| |
| <td style="text-align: center;">11<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">Dx<br />
| |
| </td>
| |
| <td style="text-align: center;">E^<br />
| |
| </td>
| |
| <td>Fb^^<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">17<br />
| |
| </td>
| |
| <td style="text-align: center;">28<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">Ax<br />
| |
| </td>
| |
| <td style="text-align: center;">B^<br />
| |
| </td>
| |
| <td>Cb^^<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>etc.<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| The 29-tone keyboard, with alternate tunings for the black keys:<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <td style="text-align: center;">keyspan from C<br />
| |
| </td>
| |
| <td style="text-align: center;">genspan from C<br />
| |
| </td>
| |
| <td style="text-align: center;">note<br />
| |
| </td>
| |
| <td style="text-align: center;">genspan from C<br />
| |
| </td>
| |
| <td style="text-align: center;">note<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">0<br />
| |
| </td>
| |
| <td style="text-align: center;">0<br />
| |
| </td>
| |
| <td style="text-align: center;">C<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">1<br />
| |
| </td>
| |
| <td style="text-align: center;">-17<br />
| |
| </td>
| |
| <td style="text-align: center;">Dbv = C#vv<br />
| |
| </td>
| |
| <td style="text-align: center;">+12<br />
| |
| </td>
| |
| <td style="text-align: center;">C^<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">2<br />
| |
| </td>
| |
| <td style="text-align: center;">-5<br />
| |
| </td>
| |
| <td style="text-align: center;">Db = C#v<br />
| |
| </td>
| |
| <td style="text-align: center;">+24<br />
| |
| </td>
| |
| <td style="text-align: center;">C^^ = Dbb^<span style="vertical-align: super;">3</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">3<br />
| |
| </td>
| |
| <td style="text-align: center;">-22<br />
| |
| </td>
| |
| <td style="text-align: center;">Dvv = Cxv<span style="vertical-align: super;">3</span><br />
| |
| </td>
| |
| <td style="text-align: center;">+7<br />
| |
| </td>
| |
| <td style="text-align: center;">C# = Db^<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">4<br />
| |
| </td>
| |
| <td style="text-align: center;">-10<br />
| |
| </td>
| |
| <td style="text-align: center;">Dv<br />
| |
| </td>
| |
| <td style="text-align: center;">+19<br />
| |
| </td>
| |
| <td style="text-align: center;">C#^ = Db^^<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">5<br />
| |
| </td>
| |
| <td style="text-align: center;">+2<br />
| |
| </td>
| |
| <td style="text-align: center;">D<br /> | |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">6<br />
| |
| </td>
| |
| <td style="text-align: center;">-15<br />
| |
| </td>
| |
| <td style="text-align: center;">Ebv = D#vv<br />
| |
| </td>
| |
| <td style="text-align: center;">+14<br />
| |
| </td>
| |
| <td style="text-align: center;">D^<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">7<br />
| |
| </td>
| |
| <td style="text-align: center;">-3<br />
| |
| </td>
| |
| <td style="text-align: center;">Eb = D#v<br />
| |
| </td>
| |
| <td style="text-align: center;">+26<br />
| |
| </td>
| |
| <td style="text-align: center;">D^^ = Ebb^3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">8<br />
| |
| </td>
| |
| <td style="text-align: center;">-20<br />
| |
| </td>
| |
| <td style="text-align: center;">Evv = Dxv3<br />
| |
| </td>
| |
| <td style="text-align: center;">+9<br />
| |
| </td>
| |
| <td style="text-align: center;">D# = Eb^<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">9<br />
| |
| </td>
| |
| <td style="text-align: center;">-8<br />
| |
| </td>
| |
| <td style="text-align: center;">Ev<br />
| |
| </td>
| |
| <td style="text-align: center;">+21<br />
| |
| </td>
| |
| <td style="text-align: center;">D#^ = Eb^^<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">10<br />
| |
| </td>
| |
| <td style="text-align: center;">+4<br />
| |
| </td>
| |
| <td style="text-align: center;">E<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">11<br />
| |
| </td>
| |
| <td style="text-align: center;">-13<br />
| |
| </td>
| |
| <td style="text-align: center;">Fv<br />
| |
| </td>
| |
| <td style="text-align: center;">+16<br />
| |
| </td>
| |
| <td style="text-align: center;">E^<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">12<br />
| |
| </td>
| |
| <td style="text-align: center;">-1<br />
| |
| </td>
| |
| <td style="text-align: center;">F<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">13<br />
| |
| </td>
| |
| <td style="text-align: center;">-18<br />
| |
| </td>
| |
| <td style="text-align: center;">Gbv = F#vv<br />
| |
| </td>
| |
| <td style="text-align: center;">+11<br />
| |
| </td>
| |
| <td style="text-align: center;">F^<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">14<br />
| |
| </td>
| |
| <td style="text-align: center;">-6<br />
| |
| </td>
| |
| <td style="text-align: center;">Gb = F#v<br />
| |
| </td>
| |
| <td style="text-align: center;">+23<br />
| |
| </td>
| |
| <td style="text-align: center;">F^^ = Gbb^3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">15<br />
| |
| </td>
| |
| <td style="text-align: center;">-23<br />
| |
| </td>
| |
| <td style="text-align: center;">Gvv = Fxv3<br />
| |
| </td>
| |
| <td style="text-align: center;">+6<br />
| |
| </td>
| |
| <td style="text-align: center;">F# = Gb^<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">16<br />
| |
| </td>
| |
| <td style="text-align: center;">-11<br />
| |
| </td>
| |
| <td style="text-align: center;">Gv<br />
| |
| </td>
| |
| <td style="text-align: center;">+18<br />
| |
| </td>
| |
| <td style="text-align: center;">F#^ = Gb^^<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">17<br />
| |
| </td>
| |
| <td style="text-align: center;">+1<br />
| |
| </td>
| |
| <td style="text-align: center;">G<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">18<br />
| |
| </td>
| |
| <td style="text-align: center;">-16<br />
| |
| </td>
| |
| <td style="text-align: center;">Abv = G#vv<br />
| |
| </td>
| |
| <td style="text-align: center;">+13<br />
| |
| </td>
| |
| <td style="text-align: center;">G^<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">19<br />
| |
| </td>
| |
| <td style="text-align: center;">-4<br />
| |
| </td>
| |
| <td style="text-align: center;">Ab = G#v<br />
| |
| </td>
| |
| <td style="text-align: center;">+25<br />
| |
| </td>
| |
| <td style="text-align: center;">G^^ = Abb^3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">20<br />
| |
| </td>
| |
| <td style="text-align: center;">-21<br />
| |
| </td>
| |
| <td style="text-align: center;">Avv = Gxv3<br />
| |
| </td>
| |
| <td style="text-align: center;">+8<br />
| |
| </td>
| |
| <td style="text-align: center;">G# = Ab^<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">21<br />
| |
| </td>
| |
| <td style="text-align: center;">-9<br />
| |
| </td>
| |
| <td style="text-align: center;">Av<br />
| |
| </td>
| |
| <td style="text-align: center;">+20<br />
| |
| </td>
| |
| <td style="text-align: center;">G#^ = Ab^^<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">22<br />
| |
| </td>
| |
| <td style="text-align: center;">+3<br />
| |
| </td>
| |
| <td style="text-align: center;">A<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">23<br />
| |
| </td>
| |
| <td style="text-align: center;">-14<br />
| |
| </td>
| |
| <td style="text-align: center;">Bbv = A#vv<br />
| |
| </td>
| |
| <td style="text-align: center;">+15<br />
| |
| </td>
| |
| <td style="text-align: center;">A^<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">24<br />
| |
| </td>
| |
| <td style="text-align: center;">-2<br />
| |
| </td>
| |
| <td style="text-align: center;">Bb = A#v<br />
| |
| </td>
| |
| <td style="text-align: center;">+27<br />
| |
| </td>
| |
| <td style="text-align: center;">A^^ = Bbb^3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">25<br />
| |
| </td>
| |
| <td style="text-align: center;">-19<br />
| |
| </td>
| |
| <td style="text-align: center;">Bvv = Axv3<br />
| |
| </td>
| |
| <td style="text-align: center;">+10<br />
| |
| </td>
| |
| <td style="text-align: center;">A# = Bb^<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">26<br />
| |
| </td>
| |
| <td style="text-align: center;">-7<br />
| |
| </td>
| |
| <td style="text-align: center;">Bv<br />
| |
| </td>
| |
| <td style="text-align: center;">+22<br />
| |
| </td>
| |
| <td style="text-align: center;">A#^ = Bb^^<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">27<br />
| |
| </td>
| |
| <td style="text-align: center;">+5<br />
| |
| </td>
| |
| <td style="text-align: center;">B<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">28<br />
| |
| </td>
| |
| <td style="text-align: center;">-12<br />
| |
| </td>
| |
| <td style="text-align: center;">Cv<br />
| |
| </td>
| |
| <td style="text-align: center;">+17<br />
| |
| </td>
| |
| <td style="text-align: center;">B^<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">29<br />
| |
| </td>
| |
| <td style="text-align: center;">0<br />
| |
| </td>
| |
| <td style="text-align: center;">C<br />
| |
| </td> | | </td> |
| <td style="text-align: center;"><br /> | | <td style="text-align: center;"><br /> |
| Line 5,950: |
Line 5,064: |
| <br /> | | <br /> |
| <br /> | | <br /> |
| 39-tone and 49-tone are problematic:<br /> | | The value of i equals the stepspan of the up interval. 39-tone and 49-tone are problematic:<br /> |
| 39-tone: C * Db * * C# * D<br /> | | 39-tone: C * Db * * C# * D<br /> |
| 49-tone: C * Db * * * * C# * D<br /> | | 49-tone: C * Db * * * * C# * D<br /> |
| <br /> | | <br /> |
| There is no variant of D adjacent to C, and there is no 2nd with keyspan 1 or -1. In theory, 39-tone's C^ could be an octuply-diminished 9th. 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. In theory, 39-tone's C^ could be an octuply-diminished 9th. Notating rank-2 fifth-generated tunings in these two frameworks requires out-of-order notes.<br /> |
| <br /> | | <br /> |
| <br /> | | <br /> |