34edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:~~spt3125~~|~~spt3125~~]] and made on <tt>2013-06-30 17:11:45 UTC</tt>.

: This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2013-11-17 22:04:10 UTC</tt>.

: The original revision id was <tt>~~440066828~~</tt>.

: The original revision id was <tt>469917004</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Line 42:

|| degrees of 34edo || solfege || cents || approx. ratios of

[[tel/2.3.5.13.17|2.3.5.13.17]] [[xenharmonic/subgroup|subgroup]] || additional ratios

of the full [[xenharmonic/17-limit|17-limit]] ||

of the full [[xenharmonic/17-limit|17-limit]] || pseudo-traditional

|| 0 || do || 0.0 || 1/1 || ||

notation ||

|| 1 || di || 35.294 || || ||

|| 0 || do || 0.0 || 1/1 || || C ||

|| 2 || rih || 70.588 || || ||

|| 1 || di || 35.294 || || || C ^ ||

|| 3 || ra || 105.882 || 17/16, 18/17, 16/15 || 15/14 ||

|| 2 || rih || 70.588 || || || Db = C ^^ = B# ||

|| 4 || ru || 141.176 || 13/12 || 14/13, 12/11 ||

|| 3 || ra || 105.882 || 17/16, 18/17, 16/15 || 15/14 || C#v = Db^ ||

|| 5 || reh || 176.471 || 10/9 || 11/10 ||

|| 4 || ru || 141.176 || 13/12 || 14/13, 12/11 || C# ||

|| 6 || re || 211.765 || 9/8, 17/15 || 8/7 ||

|| 5 || reh || 176.471 || 10/9 || 11/10 || C#^ = Dv ||

|| 7 || raw || 247.059 || 15/13 || ||

|| 6 || re || 211.765 || 9/8, 17/15 || 8/7 || D ||

|| 8 || meh || 282.353 || 20/17, 75/64 || 7/6, 13/11 ||

|| 7 || raw || 247.059 || 15/13 || || D^ ||

|| 9 || me || 317.647 || 6/5 || 17/14 ||

|| 8 || meh || 282.353 || 20/17, 75/64 || 7/6, 13/11 || Eb ||

|| 10 || mu || 352.941 || 16/13 || 11/9 ||

|| 9 || me || 317.647 || 6/5 || 17/14 || D#v ||

|| 11 || mi || 388.235 || 5/4 || ||

|| 10 || mu || 352.941 || 16/13 || 11/9 || D# ||

|| 12 || maa || 423.529 || 51/40, 32/25 || 14/11, 9/7 ||

|| 11 || mi || 388.235 || 5/4 || || ||

|| 13 || maw || 458.823 || 13/10, 17/13 || 22/17 ||

|| 12 || maa || 423.529 || 51/40, 32/25 || 14/11, 9/7 || E ||

|| 14 || fa || 494.118 || 4/3 || ||

|| 13 || maw || 458.823 || 13/10, 17/13 || 22/17 || E^ = Fv ||

|| 15 || fih || 529.412 || || 15/11 ||

|| 14 || fa || 494.118 || 4/3 || || F ||

|| 16 || fu || 564.706 || 18/13 || 11/8 ||

|| 15 || fih || 529.412 || || 15/11 || F^ = E#v ||

|| 17 || fi/se || 600 || 17/12, 24/17 || 7/5, 10/7 ||

|| 16 || fu || 564.706 || 18/13 || 11/8 || Gb ||

|| 18 || su || 635.294 || 13/9 || 16/11 ||

|| 17 || fi/se || 600 || 17/12, 24/17 || 7/5, 10/7 || Gb^ ||

|| 19 || sih || 670.588 || || 22/15 ||

|| 18 || su || 635.294 || 13/9 || 16/11 || F# ||

|| 20 || sol || 705.882 || 3/2 || ||

|| 19 || sih || 670.588 || || 22/15 || F#^ ||

|| 21 || saw || 741.176 || 20/13, 26/17 || 17/11 ||

|| 20 || sol || 705.882 || 3/2 || || G ||

|| 22 || leh || 776.471 || 25/16, 80/51 || 14/9 ||

|| 21 || saw || 741.176 || 20/13, 26/17 || 17/11 || G^ ||

|| 23 || le || 811.765 || 8/5 || ||

|| 22 || leh || 776.471 || 25/16, 80/51 || 14/9 || Ab ||

|| 24 || lu || 847.059 || 13/8 || 18/11 ||

|| 23 || le || 811.765 || 8/5 || || Ab^ ||

|| 25 || la || 882.353 || 5/3 || 28/17 ||

|| 24 || lu || 847.059 || 13/8 || 18/11 || G# ||

|| 26 || laa || 917.647 || 17/10 || 12/7, 22/13 ||

|| 25 || la || 882.353 || 5/3 || 28/17 || Av ||

|| 27 || law || 952.941 || 26/15 || ||

|| 26 || laa || 917.647 || 17/10 || 12/7, 22/13 || A ||

|| 28 || teh || 988.235 || 16/9, 30/17 || 7/4 ||

|| 27 || law || 952.941 || 26/15 || || A^ = Bbv =G## ||

|| 29 || te || 1023.529 || 9/5 || 20/11 ||

|| 28 || teh || 988.235 || 16/9, 30/17 || 7/4 || Bb ||

|| 30 || tu || 1058.823 || 24/13 || 13/7, 11/6 ||

|| 29 || te || 1023.529 || 9/5 || 20/11 || Bb^ ||

|| 31 || ti || 1094.118 || 32/17, 17/9, 15/8 || 28/15 ||

|| 30 || tu || 1058.823 || 24/13 || 13/7, 11/6 || A# ||

|| 32 || taa || 1129.412 || || ||

|| 31 || ti || 1094.118 || 32/17, 17/9, 15/8 || 28/15 || A#^ = Bv ||

|| 33 || da || 1164.706 || || ||

|| 32 || taa || 1129.412 || || || B ||

|| 33 || da || 1164.706 || || || B^ = A##v ||

==Notations==

The chain of fifths gives you the seven naturals, and their sharps and flats. The sharp or flat of a note is (what is commonly called) a neutral second away - the double-sharp adds up to a minor third away. This has led certain complainers, aiming to notate 17 edo (which is relatively popular), to want an extra modifying mark to raise something a small step of which. The 34 tone equal temperament, however, can be constructed from two equally spaced 17-note scales: a symbol indicating an adjustment of 1/34 up or down can also serves the purpose of the previous sentence, by using two of it. This of course emphasizes certain aspects of 34-edo which may not be most efficient for some musical purposes. The reader can easily construct a notation. One concern is that a system with 15 nominals for example, instead of seven, might be waste - of paper, space, brainmemory etc. if they aren't used consecutively and frequently. The system spelled out here has familiarity as an advantage or disadvantage. Tangentially, while the table uses ^ and v for "up" and "down", Kosmorosky prefers using filled in triangles because that's what I decided on years ago, and he's one of a handful of people worldwide who uses the tuning extensively, as far as I know, but whatever, I can't hit you through a computer if you use alternate symbols!

==Commas==

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<td>additional ratios

of the full <a class="wiki_link" href="http://xenharmonic.wikispaces.com/17-limit">17-limit</a>

</td>

<td>pseudo-traditional

notation

</td>

</tr>

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</td>

<td>

</td>

<td>C

</td>

</tr>

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</td>

<td>

</td>

<td>C ^

</td>

</tr>

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</td>

<td>

</td>

<td>Db = C ^^ = B#

</td>

</tr>

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</td>

<td>15/14

</td>

<td>C#v = Db^

</td>

</tr>

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</td>

<td>14/13, 12/11

</td>

<td>C#

</td>

</tr>

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</td>

<td>11/10

</td>

<td>C#^ = Dv

</td>

</tr>

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</td>

<td>8/7

</td>

<td>D

</td>

</tr>

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</td>

<td>

</td>

<td>D^

</td>

</tr>

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</td>

<td>7/6, 13/11

</td>

<td>Eb

</td>

</tr>

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</td>

<td>17/14

</td>

<td>D#v

</td>

</tr>

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</td>

<td>11/9

</td>

<td>D#

</td>

</tr>

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</td>

<td>5/4

</td>

<td>

</td>

<td>

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</td>

<td>14/11, 9/7

</td>

<td>E

</td>

</tr>

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</td>

<td>22/17

</td>

<td>E^ = Fv

</td>

</tr>

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</td>

<td>

</td>

<td>F

</td>

</tr>

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Line 548:

</td>

<td>15/11

</td>

<td>F^ = E#v

</td>

</tr>

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Line 562:

</td>

<td>11/8

</td>

<td>Gb

</td>

</tr>

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Line 576:

</td>

<td>7/5, 10/7

</td>

<td>Gb^

</td>

</tr>

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</td>

<td>16/11

</td>

<td>F#

</td>

</tr>

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</td>

<td>22/15

</td>

<td>F#^

</td>

</tr>

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</td>

<td>

</td>

<td>G

</td>

</tr>

Line 584:

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</td>

<td>17/11

</td>

<td>G^

</td>

</tr>

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</td>

<td>14/9

</td>

<td>Ab

</td>

</tr>

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</td>

<td>

</td>

<td>Ab^

</td>

</tr>

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</td>

<td>18/11

</td>

<td>G#

</td>

</tr>

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</td>

<td>28/17

</td>

<td>Av

</td>

</tr>

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</td>

<td>12/7, 22/13

</td>

<td>A

</td>

</tr>

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</td>

<td>

</td>

<td>A^ = Bbv =G##

</td>

</tr>

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</td>

<td>7/4

</td>

<td>Bb

</td>

</tr>

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</td>

<td>20/11

</td>

<td>Bb^

</td>

</tr>

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</td>

<td>13/7, 11/6

</td>

<td>A#

</td>

</tr>

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</td>

<td>28/15

</td>

<td>A#^ = Bv

</td>

</tr>

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Line 786:

</td>

<td>

</td>

<td>B

</td>

</tr>

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</td>

<td>

</td>

<td>B^ = A##v

</td>

</tr>

</table>

<h2 id="toc5"><a name="x-Notations"></a>Notations</h2>

The chain of fifths gives you the seven naturals, and their sharps and flats. The sharp or flat of a note is (what is commonly called) a neutral second away - the double-sharp adds up to a minor third away. This has led certain complainers, aiming to notate 17 edo (which is relatively popular), to want an extra modifying mark to raise something a small step of which. The 34 tone equal temperament, however, can be constructed from two equally spaced 17-note scales: a symbol indicating an adjustment of 1/34 up or down can also serves the purpose of the previous sentence, by using two of it. This of course emphasizes certain aspects of 34-edo which may not be most efficient for some musical purposes. The reader can easily construct a notation. One concern is that a system with 15 nominals for example, instead of seven, might be waste - of paper, space, brainmemory etc. if they aren't used consecutively and frequently. The system spelled out here has familiarity as an advantage or disadvantage. Tangentially, while the table uses ^ and v for &quot;up&quot; and &quot;down&quot;, Kosmorosky prefers using filled in triangles because that's what I decided on years ago, and he's one of a handful of people worldwide who uses the tuning extensively, as far as I know, but whatever, I can't hit you through a computer if you use alternate symbols!

<h2 id="~~toc5~~"><a name="x-Commas"></a>Commas</h2>

<h2 id="toc6"><a name="x-Commas"></a>Commas</h2>

34-EDO <a class="wiki_link" href="http://xenharmonic.wikispaces.com/tempering%20out">tempers out</a> the following <a class="wiki_link" href="http://xenharmonic.wikispaces.com/comma">comma</a>s. (Note: This assumes the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/val">val</a> &lt; <a class="wiki_link" href="http://tel.wikispaces.com/34%2054%2079%2095%20118%20126">34 54 79 95 118 126</a> |.)

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Line 1,029:

<h2 id="~~toc6~~"><a name="x-Listen"></a>Listen</h2>

<h2 id="toc7"><a name="x-Listen"></a>Listen</h2>

<ul><li><a class="wiki_link_ext" href="http://www.archive.org/details/Ascension_105" rel="nofollow" target="_blank">Ascension</a> (drums, bass, and 34-tone guitar)</li><li><a class="wiki_link_ext" href="https://www.youtube.com/watch?v=FXTM0HeuExk" rel="nofollow" target="_blank">Uncomfortable In Crowds (extended)</a> by Robin Perry</li></ul><h2 id="~~toc7~~"><a name="x-Links"></a>Links</h2>

<ul><li><a class="wiki_link_ext" href="http://www.archive.org/details/Ascension_105" rel="nofollow" target="_blank">Ascension</a> (drums, bass, and 34-tone guitar)</li><li><a class="wiki_link_ext" href="https://www.youtube.com/watch?v=FXTM0HeuExk" rel="nofollow" target="_blank">Uncomfortable In Crowds (extended)</a> by Robin Perry</li></ul><h2 id="toc8"><a name="x-Links"></a>Links</h2>

<ul><li><a class="wiki_link_ext" href="http://www.microstick.net/34guitararticle.htm" rel="nofollow">34 Equal Guitar</a> by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Larry%20Hanson">Larry Hanson</a></li></ul></body></html></pre></div>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2013-06-30 17:11:45 UTC</tt>.<br>
+: This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2013-11-17 22:04:10 UTC</tt>.<br>
-: The original revision id was <tt>440066828</tt>.<br>
+: The original revision id was <tt>469917004</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>
@@ Line 42: / Line 42: @@
 || degrees of 34edo || solfege || cents || approx. ratios of
 [[tel/2.3.5.13.17|2.3.5.13.17]] [[xenharmonic/subgroup|subgroup]] || additional ratios
-of the full [[xenharmonic/17-limit|17-limit]] ||
+of the full [[xenharmonic/17-limit|17-limit]] || pseudo-traditional
-|| 0 || do || 0.0 || 1/1 ||   ||
+notation ||
-|| 1 || di || 35.294 ||   ||   ||
+|| 0 || do || 0.0 || 1/1 ||   || C ||
-|| 2 || rih || 70.588 ||   ||   ||
+|| 1 || di || 35.294 ||   ||   || C ^ ||
-|| 3 || ra || 105.882 || 17/16, 18/17, 16/15 || 15/14 ||
+|| 2 || rih || 70.588 ||   ||   || Db = C ^^ = B# ||
-|| 4 || ru || 141.176 || 13/12 || 14/13, 12/11 ||
+|| 3 || ra || 105.882 || 17/16, 18/17, 16/15 || 15/14 || C#v = Db^ ||
-|| 5 || reh || 176.471 || 10/9 || 11/10 ||
+|| 4 || ru || 141.176 || 13/12 || 14/13, 12/11 || C# ||
-|| 6 || re || 211.765 || 9/8, 17/15 || 8/7 ||
+|| 5 || reh || 176.471 || 10/9 || 11/10 || C#^ = Dv ||
-|| 7 || raw || 247.059 || 15/13 ||   ||
+|| 6 || re || 211.765 || 9/8, 17/15 || 8/7 || D ||
-|| 8 || meh || 282.353 || 20/17, 75/64 || 7/6, 13/11 ||
+|| 7 || raw || 247.059 || 15/13 ||   || D^ ||
-|| 9 || me || 317.647 || 6/5 || 17/14 ||
+|| 8 || meh || 282.353 || 20/17, 75/64 || 7/6, 13/11 || Eb ||
-|| 10 || mu || 352.941 || 16/13 || 11/9 ||
+|| 9 || me || 317.647 || 6/5 || 17/14 || D#v ||
-|| 11 || mi || 388.235 || 5/4 ||   ||
+|| 10 || mu || 352.941 || 16/13 || 11/9 || D# ||
-|| 12 || maa || 423.529 || 51/40, 32/25 || 14/11, 9/7 ||
+|| 11 || mi || 388.235 || 5/4 ||   ||   ||
-|| 13 || maw || 458.823 || 13/10, 17/13 || 22/17 ||
+|| 12 || maa || 423.529 || 51/40, 32/25 || 14/11, 9/7 || E ||
-|| 14 || fa || 494.118 || 4/3 ||   ||
+|| 13 || maw || 458.823 || 13/10, 17/13 || 22/17 || E^ = Fv ||
-|| 15 || fih || 529.412 ||   || 15/11 ||
+|| 14 || fa || 494.118 || 4/3 ||   || F ||
-|| 16 || fu || 564.706 || 18/13 || 11/8 ||
+|| 15 || fih || 529.412 ||   || 15/11 || F^ = E#v ||
-|| 17 || fi/se || 600 || 17/12, 24/17 || 7/5, 10/7 ||
+|| 16 || fu || 564.706 || 18/13 || 11/8 || Gb ||
-|| 18 || su || 635.294 || 13/9 || 16/11 ||
+|| 17 || fi/se || 600 || 17/12, 24/17 || 7/5, 10/7 || Gb^ ||
-|| 19 || sih || 670.588 ||   || 22/15 ||
+|| 18 || su || 635.294 || 13/9 || 16/11 || F# ||
-|| 20 || sol || 705.882 || 3/2 ||   ||
+|| 19 || sih || 670.588 ||   || 22/15 || F#^ ||
-|| 21 || saw || 741.176 || 20/13, 26/17 || 17/11 ||
+|| 20 || sol || 705.882 || 3/2 ||   || G ||
-|| 22 || leh || 776.471 || 25/16, 80/51 || 14/9 ||
+|| 21 || saw || 741.176 || 20/13, 26/17 || 17/11 || G^ ||
-|| 23 || le || 811.765 || 8/5 ||   ||
+|| 22 || leh || 776.471 || 25/16, 80/51 || 14/9 || Ab ||
-|| 24 || lu || 847.059 || 13/8 || 18/11 ||
+|| 23 || le || 811.765 || 8/5 ||   || Ab^ ||
-|| 25 || la || 882.353 || 5/3 || 28/17 ||
+|| 24 || lu || 847.059 || 13/8 || 18/11 || G# ||
-|| 26 || laa || 917.647 || 17/10 || 12/7, 22/13 ||
+|| 25 || la || 882.353 || 5/3 || 28/17 || Av ||
-|| 27 || law || 952.941 || 26/15 ||   ||
+|| 26 || laa || 917.647 || 17/10 || 12/7, 22/13 || A ||
-|| 28 || teh || 988.235 || 16/9, 30/17 || 7/4 ||
+|| 27 || law || 952.941 || 26/15 ||   || A^ = Bbv =G## ||
-|| 29 || te || 1023.529 || 9/5 || 20/11 ||
+|| 28 || teh || 988.235 || 16/9, 30/17 || 7/4 || Bb ||
-|| 30 || tu || 1058.823 || 24/13 || 13/7, 11/6 ||
+|| 29 || te || 1023.529 || 9/5 || 20/11 || Bb^ ||
-|| 31 || ti || 1094.118 || 32/17, 17/9, 15/8 || 28/15 ||
+|| 30 || tu || 1058.823 || 24/13 || 13/7, 11/6 || A# ||
-|| 32 || taa || 1129.412 ||   ||   ||
+|| 31 || ti || 1094.118 || 32/17, 17/9, 15/8 || 28/15 || A#^ = Bv ||
-|| 33 || da || 1164.706 ||   ||   ||
+|| 32 || taa || 1129.412 ||   ||   || B ||
+|| 33 || da || 1164.706 ||   ||   || B^ = A##v ||
+==&lt;span style="background-color: #ffffff;"&gt;Notations&lt;/span&gt;==
+The chain of fifths gives you the seven naturals, and their sharps and flats. The sharp or flat of a note is (what is commonly called) a neutral second away - the double-sharp adds up to a minor third away. This has led certain complainers, aiming to notate 17 edo (which is relatively popular), to want an extra modifying mark to raise something a small step of which. The 34 tone equal temperament, however, can be constructed from two equally spaced 17-note scales: a symbol indicating an adjustment of 1/34 up or down can also serves the purpose of the previous sentence, by using two of it. This of course emphasizes certain aspects of 34-edo which may not be most efficient for some musical purposes. The reader can easily construct a notation. One concern is that a system with 15 nominals for example, instead of seven, might be waste - of paper, space, brainmemory etc. if they aren't used consecutively and frequently. The system spelled out here has familiarity as an advantage or disadvantage. Tangentially, while the table uses ^ and v for "up" and "down", Kosmorosky prefers using filled in triangles because that's what I decided on years ago, and he's one of a handful of people worldwide who uses the tuning extensively, as far as I know, but whatever, I can't hit you through a computer if you use alternate symbols!
 ==&lt;span style="background-color: #ffffff;"&gt;Commas&lt;/span&gt;==
@@ Line 320: / Line 323: @@
          &lt;td&gt;additional ratios&lt;br /&gt;
 of the full &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/17-limit"&gt;17-limit&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;pseudo-traditional&lt;br /&gt;
+notation&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 332: / Line 338: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;C&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 344: / Line 352: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;C ^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 356: / Line 366: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Db = C ^^ = B#&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 368: / Line 380: @@
 &lt;/td&gt;
          &lt;td&gt;15/14&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;C#v = Db^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 380: / Line 394: @@
 &lt;/td&gt;
          &lt;td&gt;14/13, 12/11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;C#&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 392: / Line 408: @@
 &lt;/td&gt;
          &lt;td&gt;11/10&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;C#^ = Dv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 404: / Line 422: @@
 &lt;/td&gt;
          &lt;td&gt;8/7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;D&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 416: / Line 436: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;D^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 428: / Line 450: @@
 &lt;/td&gt;
          &lt;td&gt;7/6, 13/11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Eb&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 440: / Line 464: @@
 &lt;/td&gt;
          &lt;td&gt;17/14&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;D#v&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 452: / Line 478: @@
 &lt;/td&gt;
          &lt;td&gt;11/9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;D#&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 462: / Line 490: @@
 &lt;/td&gt;
          &lt;td&gt;5/4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 476: / Line 506: @@
 &lt;/td&gt;
          &lt;td&gt;14/11, 9/7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;E&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 488: / Line 520: @@
 &lt;/td&gt;
          &lt;td&gt;22/17&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;E^ = Fv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 500: / Line 534: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;F&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 512: / Line 548: @@
 &lt;/td&gt;
          &lt;td&gt;15/11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;F^ = E#v&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 524: / Line 562: @@
 &lt;/td&gt;
          &lt;td&gt;11/8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Gb&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 536: / Line 576: @@
 &lt;/td&gt;
          &lt;td&gt;7/5, 10/7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Gb^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 548: / Line 590: @@
 &lt;/td&gt;
          &lt;td&gt;16/11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;F#&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 560: / Line 604: @@
 &lt;/td&gt;
          &lt;td&gt;22/15&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;F#^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 572: / Line 618: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;G&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 584: / Line 632: @@
 &lt;/td&gt;
          &lt;td&gt;17/11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;G^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 596: / Line 646: @@
 &lt;/td&gt;
          &lt;td&gt;14/9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Ab&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 608: / Line 660: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Ab^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 620: / Line 674: @@
 &lt;/td&gt;
          &lt;td&gt;18/11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;G#&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 632: / Line 688: @@
 &lt;/td&gt;
          &lt;td&gt;28/17&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Av&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 644: / Line 702: @@
 &lt;/td&gt;
          &lt;td&gt;12/7, 22/13&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;A&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 656: / Line 716: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;A^ = Bbv =G##&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 668: / Line 730: @@
 &lt;/td&gt;
          &lt;td&gt;7/4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Bb&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 680: / Line 744: @@
 &lt;/td&gt;
          &lt;td&gt;20/11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Bb^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 692: / Line 758: @@
 &lt;/td&gt;
          &lt;td&gt;13/7, 11/6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;A#&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 704: / Line 772: @@
 &lt;/td&gt;
          &lt;td&gt;28/15&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;A#^ = Bv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 716: / Line 786: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;B&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 728: / Line 800: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;B^ = A##v&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
 &lt;/table&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="x-Notations"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;&lt;span style="background-color: #ffffff;"&gt;Notations&lt;/span&gt;&lt;/h2&gt;
+ The chain of fifths gives you the seven naturals, and their sharps and flats. The sharp or flat of a note is (what is commonly called) a neutral second away - the double-sharp adds up to a minor third away. This has led certain complainers, aiming to notate 17 edo (which is relatively popular), to want an extra modifying mark to raise something a small step of which. The 34 tone equal temperament, however, can be constructed from two equally spaced 17-note scales: a symbol indicating an adjustment of 1/34 up or down can also serves the purpose of the previous sentence, by using two of it. This of course emphasizes certain aspects of 34-edo which may not be most efficient for some musical purposes. The reader can easily construct a notation. One concern is that a system with 15 nominals for example, instead of seven, might be waste - of paper, space, brainmemory etc. if they aren't used consecutively and frequently. The system spelled out here has familiarity as an advantage or disadvantage. Tangentially, while the table uses ^ and v for &amp;quot;up&amp;quot; and &amp;quot;down&amp;quot;, Kosmorosky prefers using filled in triangles because that's what I decided on years ago, and he's one of a handful of people worldwide who uses the tuning extensively, as far as I know, but whatever, I can't hit you through a computer if you use alternate symbols!&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="x-Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;&lt;span style="background-color: #ffffff;"&gt;Commas&lt;/span&gt;&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="x-Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;&lt;span style="background-color: #ffffff;"&gt;Commas&lt;/span&gt;&lt;/h2&gt;
   &lt;span style="background-color: #ffffff;"&gt;34-EDO &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/tempering%20out"&gt;tempers out&lt;/a&gt; the following &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/comma"&gt;comma&lt;/a&gt;s. (Note: This assumes the &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/val"&gt;val&lt;/a&gt; &amp;lt; &lt;a class="wiki_link" href="http://tel.wikispaces.com/34%2054%2079%2095%20118%20126"&gt;34 54 79 95 118 126&lt;/a&gt; |.)&lt;/span&gt;&lt;br /&gt;
@@ Line 953: / Line 1,029: @@
 &lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="x-Listen"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Listen&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="x-Listen"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Listen&lt;/h2&gt;
-  &lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.archive.org/details/Ascension_105" rel="nofollow" target="_blank"&gt;Ascension&lt;/a&gt; (drums, bass, and 34-tone guitar)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="https://www.youtube.com/watch?v=FXTM0HeuExk" rel="nofollow" target="_blank"&gt;Uncomfortable In Crowds (extended)&lt;/a&gt; by Robin Perry&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="x-Links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Links&lt;/h2&gt;
+  &lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.archive.org/details/Ascension_105" rel="nofollow" target="_blank"&gt;Ascension&lt;/a&gt; (drums, bass, and 34-tone guitar)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="https://www.youtube.com/watch?v=FXTM0HeuExk" rel="nofollow" target="_blank"&gt;Uncomfortable In Crowds (extended)&lt;/a&gt; by Robin Perry&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="x-Links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Links&lt;/h2&gt;
   &lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.microstick.net/34guitararticle.htm" rel="nofollow"&gt;34 Equal Guitar&lt;/a&gt; by &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Larry%20Hanson"&gt;Larry Hanson&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>