47edo: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Wikispaces>TallKite
**Imported revision 617184721 - Original comment: **
Wikispaces>TallKite
**Imported revision 617218497 - Original comment: **
Line 1: Line 1:
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-09-05 03:57:05 UTC</tt>.<br>
: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-09-05 14:52:52 UTC</tt>.<br>
: The original revision id was <tt>617184721</tt>.<br>
: The original revision id was <tt>617218497</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>
Line 12: Line 12:
47edo is the 15th [[prime numbers|prime]] edo, following [[43edo]] and preceding [[53edo]].
47edo is the 15th [[prime numbers|prime]] edo, following [[43edo]] and preceding [[53edo]].


47edo is a regular edo because its 5th falls between 4\7 = 686¢ and 3\5 = 720¢. (Its alternate 5th does as well.) 47edo is the most difficult regular edo to notate, because no other regular edo's 5th is as far off from a just 3/2.
47edo is a [[Ups and Downs Notation#Other%20EDOs|regular]] edo because its 5th falls between 4\7 = 686¢ and 3\5 = 720¢. (Its alternate 5th does as well.) 47edo is the most difficult regular edo to notate, because no other regular edo's 5th is as far off from a just 3/2.


A notation using the best 5th has major and minor 2nds of 7 and 6 edosteps respectively, with the naturals creating a very 7edo-ish scale:  
A notation using the best 5th has major and minor 2nds of 7 and 6 edosteps respectively, with the naturals creating a very 7edo-ish scale:  
D * * * * * * E * * * * * F * * * * * * G * * * * * * A * * * * * * B * * * * * C * * * * * * D
D * * * * * * E * * * * * F * * * * * * G * * * * * * A * * * * * * B * * * * * C * * * * * * D
This notation requires triple, quadruple and even quintuple sharps and flats.
D# is next to D. This notation requires triple, quadruple and even quintuple sharps and flats.


Using the 2nd best 5th is even more awkward. The major 2nd is 9 edosteps and the minor is only one. The naturals create a very 5edo-ish scale, with 2 of the notes inflected by a comma:  
Using the 2nd best 5th is even more awkward. The major 2nd is 9 edosteps and the minor is only one. The naturals create a very 5edo-ish scale, with two of the notes inflected by a comma-sized edostep:  
D * * * * * * * * E F * * * * * * * * G * * * * * * * * A * * * * * * * * B C * * * * * * * * D
D * * * * * * * * E F * * * * * * * * G * * * * * * * * A * * * * * * * * B C * * * * * * * * D
This notation requires quintuple, sextuple, and even septuple ups and downs.
D# is next to E. This notation requires quadruple, quintuple, and even sextuple ups and downs, as well as single sharps and flats.
 


==Intervals of 47edo==  
==Intervals of 47edo==  


||~ Degree ||~ Size (Cents) ||~ relative notation ||
||~ Degree ||~ Size (Cents) ||~ relative notation ||~  ||~ absolute notation ||
||= 0 ||&gt; 0.0000 ||= P1 ||
||= 0 ||&gt; 0.0000 ||= perfect unison ||= P1 ||= D ||
||= 1 ||&gt; 25.5319 || A1 ||
||= 1 ||&gt; 25.5319 ||= aug 1sn ||= A1 ||= D# ||
||= 2 ||&gt; 51.0638 || AA1 ||
||= 2 ||&gt; 51.0638 ||= double-aug 1sn ||= AA1 ||= Dx ||
||= 3 ||&gt; 76.5957 || A31, d32 ||
||= 3 ||&gt; 76.5957 ||= triple-aug 1sn, triple-dim 2nd ||= A31, d32 ||= D#3, Eb4 ||
||= 4 ||&gt; 102.1277 || dd2 ||
||= 4 ||&gt; 102.1277 ||= double-dim 2nd ||= dd2 ||= Eb3 ||
||= 5 ||&gt; 127.6596 || d2 ||
||= 5 ||&gt; 127.6596 ||= dim 2nd ||= d2 ||= Ebb ||
||= 6 ||&gt; 153.1915 || m2 ||
||= 6 ||&gt; 153.1915 ||= minor 2nd ||= m2 ||= Eb ||
||= 7 ||&gt; 178.7234 || M2 ||
||= 7 ||&gt; 178.7234 ||= major 2nd ||= M2 ||= E ||
||= 8 ||&gt; 204.2553 ||   ||
||= 8 ||&gt; 204.2553 ||= aug 2nd ||= A2 ||= E# ||
||= 9 ||&gt; 229.7872 ||   ||
||= 9 ||&gt; 229.7872 ||= double-aug 2nd ||= AA2 ||= Ex ||
||= 10 ||&gt; 255.3191 ||   ||
||= 10 ||&gt; 255.3191 ||= triple-aug 2nd, triple-dim 3rd ||= A32, d33 ||= E#3, Fb3 ||
||= 11 ||&gt; 280.8511 ||   ||
||= 11 ||&gt; 280.8511 ||= double-dim 3rd ||= dd3 ||= Fbb ||
||= 12 ||&gt; 306.3830 ||   ||
||= 12 ||&gt; 306.3830 ||= dim 3rd ||= d3 ||= Fb ||
||= 13 ||&gt; 331.9149 ||   ||
||= 13 ||&gt; 331.9149 ||= minor 3rd ||= m3 ||= F ||
||= 14 ||&gt; 357.4468 || M3 ||
||= 14 ||&gt; 357.4468 ||= major 3rd ||= M3 ||= F# ||
||= 15 ||&gt; 382.9787 ||   ||
||= 15 ||&gt; 382.9787 ||= aug 3rd ||= A3 ||= Fx ||
||= 16 ||&gt; 408.5106 ||   ||
||= 16 ||&gt; 408.5106 ||= double-aug 3rd ||= AA3 ||= F#3 ||
||= 17 ||&gt; 434.0426 ||   ||
||= 17 ||&gt; 434.0426 ||= triple-aug 3rd, triple-dim 4th ||= A33, d34 ||= F#4, Gb3 ||
||= 18 ||&gt; 459.5745 ||   ||
||= 18 ||&gt; 459.5745 ||= double-dim 4th ||= dd4 ||= Gbb ||
||= 19 ||&gt; 485.1064 ||   ||
||= 19 ||&gt; 485.1064 ||= dim 4th ||= d4 ||= Gb ||
||= 20 ||&gt; 510.6383 ||   ||
||= 20 ||&gt; 510.6383 ||= perfect 4th ||= P4 ||= G ||
||= 21 ||&gt; 536.1702 ||   ||
||= 21 ||&gt; 536.1702 ||= aug 4th ||= A4 ||= G# ||
||= 22 ||&gt; 561.7021 ||   ||
||= 22 ||&gt; 561.7021 ||= double-aug 4th ||= AA4 ||= Gx ||
||= 23 ||&gt; 587.2340 ||   ||
||= 23 ||&gt; 587.2340 ||= triple-aug 4th ||= A34 ||= G#3 ||
||= 24 ||&gt; 612.7660 ||   ||
||= 24 ||&gt; 612.7660 ||= triple-dim 5th ||= d35 ||= Ab3 ||
||= 25 ||&gt; 638.2979 ||   ||
||= 25 ||&gt; 638.2979 ||= double-dim 5th ||= dd5 ||= Abb ||
||= 26 ||&gt; 663.8298 ||   ||
||= 26 ||&gt; 663.8298 ||= dim 5th ||= d5 ||= Ab ||
||= 27 ||&gt; 689.3617 ||   ||
||= 27 ||&gt; 689.3617 ||= perfect 5th ||= P5 ||= A ||
||= 28 ||&gt; 714.8936 ||   ||
||= 28 ||&gt; 714.8936 ||= aug 5th ||= A5 ||= A# ||
||= 29 ||&gt; 740.4255 ||   ||
||= 29 ||&gt; 740.4255 ||= double-aug 5th ||= AA5 ||= Ax ||
||= 30 ||&gt; 765.9574 ||   ||
||= 30 ||&gt; 765.9574 ||= triple-aug 5th, triple-dim 6th ||= A35, d36 ||= A#3, Bb4 ||
||= 31 ||&gt; 791.4894 ||   ||
||= 31 ||&gt; 791.4894 ||= double-dim 6th ||= dd6 ||= Bb3 ||
||= 32 ||&gt; 817.0213 ||   ||
||= 32 ||&gt; 817.0213 ||= dim 6th ||= d6 ||= Bbb ||
||= 33 ||&gt; 842.5532 ||   ||
||= 33 ||&gt; 842.5532 ||= minor 6th ||= m6 ||= Bb ||
||= 34 ||&gt; 868.0851 ||   ||
||= 34 ||&gt; 868.0851 ||= major 6th ||= M6 ||= B ||
||= 35 ||&gt; 893.6170 ||   ||
||= 35 ||&gt; 893.6170 ||= aug 6th ||= A6 ||= B# ||
||= 36 ||&gt; 919.1489 ||   ||
||= 36 ||&gt; 919.1489 ||= double-aug 6th ||= AA6 ||= Bx ||
||= 37 ||&gt; 944.6809 ||   ||
||= 37 ||&gt; 944.6809 ||= triple-aug 6th, triple-dim 7th ||= A36, d37 ||= B#3, Cb3 ||
||= 38 ||&gt; 970.2128 ||   ||
||= 38 ||&gt; 970.2128 ||= double-dim 7th ||= dd7 ||= Cbb ||
||= 39 ||&gt; 995.7447 ||   ||
||= 39 ||&gt; 995.7447 ||= dim 7th ||= d7 ||= Cb ||
||= 40 ||&gt; 1021.2766 ||   ||
||= 40 ||&gt; 1021.2766 ||= minor 7th ||= m7 ||= C ||
||= 41 ||&gt; 1046.8085 ||   ||
||= 41 ||&gt; 1046.8085 ||= major 7th ||= M7 ||= C# ||
||= 42 ||&gt; 1072.3404 ||   ||
||= 42 ||&gt; 1072.3404 ||= aug 7th ||= A7 ||= Cx ||
||= 43 ||&gt; 1097.8723 ||   ||
||= 43 ||&gt; 1097.8723 ||= double-aug 7th ||= AA7 ||= C#3 ||
||= 44 ||&gt; 1123.4043 ||   ||
||= 44 ||&gt; 1123.4043 ||= triple-aug 7th, triple-dim 8ve ||= A37, d38 ||= C#4, Db3 ||
||= 45 ||&gt; 1148.9362 ||   ||
||= 45 ||&gt; 1148.9362 ||= double-dim 8ve ||= dd8 ||= Dbb ||
||= 46 ||&gt; 1174.4681 ||   ||
||= 46 ||&gt; 1174.4681 ||= dim 8ve ||= d8 ||= Db ||
||= 47 ||&gt; 1200.0000 ||   ||</pre></div>
||= 47 ||&gt; 1200.0000 ||= perfect 8ve ||= P8 ||= 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">&lt;html&gt;&lt;head&gt;&lt;title&gt;47edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x47 tone Equal Temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;span style="color: #616161; font-size: 99%;"&gt;47 tone Equal Temperament&lt;/span&gt;&lt;/h1&gt;
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;47edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x47 tone Equal Temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;span style="color: #616161; font-size: 99%;"&gt;47 tone Equal Temperament&lt;/span&gt;&lt;/h1&gt;
Line 81: Line 80:
47edo is the 15th &lt;a class="wiki_link" href="/prime%20numbers"&gt;prime&lt;/a&gt; edo, following &lt;a class="wiki_link" href="/43edo"&gt;43edo&lt;/a&gt; and preceding &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt;.&lt;br /&gt;
47edo is the 15th &lt;a class="wiki_link" href="/prime%20numbers"&gt;prime&lt;/a&gt; edo, following &lt;a class="wiki_link" href="/43edo"&gt;43edo&lt;/a&gt; and preceding &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
47edo is a regular edo because its 5th falls between 4\7 = 686¢ and 3\5 = 720¢. (Its alternate 5th does as well.) 47edo is the most difficult regular edo to notate, because no other regular edo's 5th is as far off from a just 3/2.&lt;br /&gt;
47edo is a &lt;a class="wiki_link" href="/Ups%20and%20Downs%20Notation#Other%20EDOs"&gt;regular&lt;/a&gt; edo because its 5th falls between 4\7 = 686¢ and 3\5 = 720¢. (Its alternate 5th does as well.) 47edo is the most difficult regular edo to notate, because no other regular edo's 5th is as far off from a just 3/2.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
A notation using the best 5th has major and minor 2nds of 7 and 6 edosteps respectively, with the naturals creating a very 7edo-ish scale: &lt;br /&gt;
A notation using the best 5th has major and minor 2nds of 7 and 6 edosteps respectively, with the naturals creating a very 7edo-ish scale: &lt;br /&gt;
D * * * * * * E * * * * * F * * * * * * G * * * * * * A * * * * * * B * * * * * C * * * * * * D&lt;br /&gt;
D * * * * * * E * * * * * F * * * * * * G * * * * * * A * * * * * * B * * * * * C * * * * * * D&lt;br /&gt;
This notation requires triple, quadruple and even quintuple sharps and flats.&lt;br /&gt;
D# is next to D. This notation requires triple, quadruple and even quintuple sharps and flats.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Using the 2nd best 5th is even more awkward. The major 2nd is 9 edosteps and the minor is only one. The naturals create a very 5edo-ish scale, with 2 of the notes inflected by a comma: &lt;br /&gt;
Using the 2nd best 5th is even more awkward. The major 2nd is 9 edosteps and the minor is only one. The naturals create a very 5edo-ish scale, with two of the notes inflected by a comma-sized edostep: &lt;br /&gt;
D * * * * * * * * E F * * * * * * * * G * * * * * * * * A * * * * * * * * B C * * * * * * * * D&lt;br /&gt;
D * * * * * * * * E F * * * * * * * * G * * * * * * * * A * * * * * * * * B C * * * * * * * * D&lt;br /&gt;
This notation requires quintuple, sextuple, and even septuple ups and downs.&lt;br /&gt;
D# is next to E. This notation requires quadruple, quintuple, and even sextuple ups and downs, as well as single sharps and flats.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x47 tone Equal Temperament-Intervals of 47edo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Intervals of 47edo&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x47 tone Equal Temperament-Intervals of 47edo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Intervals of 47edo&lt;/h2&gt;
Line 103: Line 101:
&lt;/th&gt;
&lt;/th&gt;
         &lt;th&gt;relative notation&lt;br /&gt;
         &lt;th&gt;relative notation&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;absolute notation&lt;br /&gt;
&lt;/th&gt;
&lt;/th&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 109: Line 111:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: right;"&gt;0.0000&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;0.0000&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;perfect unison&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;P1&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;P1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;D&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 118: Line 124:
         &lt;td style="text-align: right;"&gt;25.5319&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;25.5319&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;A1&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;aug 1sn&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;D#&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 126: Line 136:
         &lt;td style="text-align: right;"&gt;51.0638&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;51.0638&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;AA1&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;double-aug 1sn&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;AA1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Dx&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 134: Line 148:
         &lt;td style="text-align: right;"&gt;76.5957&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;76.5957&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;A31, d32&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;triple-aug 1sn, triple-dim 2nd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A31, d32&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;D#3, Eb4&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 142: Line 160:
         &lt;td style="text-align: right;"&gt;102.1277&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;102.1277&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;dd2&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;double-dim 2nd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;dd2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Eb3&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 150: Line 172:
         &lt;td style="text-align: right;"&gt;127.6596&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;127.6596&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;d2&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;dim 2nd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;d2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Ebb&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 158: Line 184:
         &lt;td style="text-align: right;"&gt;153.1915&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;153.1915&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;m2&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;minor 2nd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;m2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Eb&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 166: Line 196:
         &lt;td style="text-align: right;"&gt;178.7234&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;178.7234&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;M2&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;major 2nd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;M2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;E&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 174: Line 208:
         &lt;td style="text-align: right;"&gt;204.2553&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;204.2553&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;aug 2nd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;E#&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 182: Line 220:
         &lt;td style="text-align: right;"&gt;229.7872&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;229.7872&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;double-aug 2nd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;AA2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Ex&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 190: Line 232:
         &lt;td style="text-align: right;"&gt;255.3191&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;255.3191&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;triple-aug 2nd, triple-dim 3rd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A32, d33&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;E#3, Fb3&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 198: Line 244:
         &lt;td style="text-align: right;"&gt;280.8511&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;280.8511&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;double-dim 3rd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;dd3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Fbb&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 206: Line 256:
         &lt;td style="text-align: right;"&gt;306.3830&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;306.3830&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;dim 3rd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;d3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Fb&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 214: Line 268:
         &lt;td style="text-align: right;"&gt;331.9149&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;331.9149&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;minor 3rd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;m3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;F&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 222: Line 280:
         &lt;td style="text-align: right;"&gt;357.4468&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;357.4468&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;M3&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;major 3rd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;M3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;F#&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 230: Line 292:
         &lt;td style="text-align: right;"&gt;382.9787&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;382.9787&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;aug 3rd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Fx&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 238: Line 304:
         &lt;td style="text-align: right;"&gt;408.5106&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;408.5106&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;double-aug 3rd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;AA3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;F#3&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 246: Line 316:
         &lt;td style="text-align: right;"&gt;434.0426&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;434.0426&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;triple-aug 3rd, triple-dim 4th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A33, d34&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;F#4, Gb3&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 254: Line 328:
         &lt;td style="text-align: right;"&gt;459.5745&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;459.5745&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;double-dim 4th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;dd4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Gbb&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 262: Line 340:
         &lt;td style="text-align: right;"&gt;485.1064&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;485.1064&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;dim 4th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;d4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Gb&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 270: Line 352:
         &lt;td style="text-align: right;"&gt;510.6383&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;510.6383&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;perfect 4th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;P4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;G&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 278: Line 364:
         &lt;td style="text-align: right;"&gt;536.1702&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;536.1702&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;aug 4th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;G#&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 286: Line 376:
         &lt;td style="text-align: right;"&gt;561.7021&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;561.7021&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;double-aug 4th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;AA4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Gx&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 294: Line 388:
         &lt;td style="text-align: right;"&gt;587.2340&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;587.2340&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;triple-aug 4th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A34&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;G#3&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 302: Line 400:
         &lt;td style="text-align: right;"&gt;612.7660&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;612.7660&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;triple-dim 5th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;d35&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Ab3&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 310: Line 412:
         &lt;td style="text-align: right;"&gt;638.2979&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;638.2979&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;double-dim 5th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;dd5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Abb&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 318: Line 424:
         &lt;td style="text-align: right;"&gt;663.8298&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;663.8298&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;dim 5th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;d5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Ab&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 326: Line 436:
         &lt;td style="text-align: right;"&gt;689.3617&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;689.3617&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;perfect 5th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;P5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 334: Line 448:
         &lt;td style="text-align: right;"&gt;714.8936&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;714.8936&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;aug 5th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A#&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 342: Line 460:
         &lt;td style="text-align: right;"&gt;740.4255&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;740.4255&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;double-aug 5th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;AA5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Ax&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 350: Line 472:
         &lt;td style="text-align: right;"&gt;765.9574&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;765.9574&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;triple-aug 5th, triple-dim 6th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A35, d36&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A#3, Bb4&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 358: Line 484:
         &lt;td style="text-align: right;"&gt;791.4894&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;791.4894&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;double-dim 6th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;dd6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Bb3&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 366: Line 496:
         &lt;td style="text-align: right;"&gt;817.0213&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;817.0213&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;dim 6th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;d6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Bbb&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 374: Line 508:
         &lt;td style="text-align: right;"&gt;842.5532&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;842.5532&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;minor 6th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;m6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Bb&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 382: Line 520:
         &lt;td style="text-align: right;"&gt;868.0851&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;868.0851&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;major 6th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;M6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;B&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 390: Line 532:
         &lt;td style="text-align: right;"&gt;893.6170&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;893.6170&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;aug 6th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;B#&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 398: Line 544:
         &lt;td style="text-align: right;"&gt;919.1489&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;919.1489&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;double-aug 6th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;AA6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Bx&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 406: Line 556:
         &lt;td style="text-align: right;"&gt;944.6809&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;944.6809&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;triple-aug 6th, triple-dim 7th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A36, d37&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;B#3, Cb3&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 414: Line 568:
         &lt;td style="text-align: right;"&gt;970.2128&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;970.2128&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;double-dim 7th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;dd7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Cbb&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 422: Line 580:
         &lt;td style="text-align: right;"&gt;995.7447&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;995.7447&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;dim 7th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;d7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Cb&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 430: Line 592:
         &lt;td style="text-align: right;"&gt;1021.2766&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;1021.2766&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;minor 7th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;m7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 438: Line 604:
         &lt;td style="text-align: right;"&gt;1046.8085&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;1046.8085&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;major 7th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;M7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C#&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 446: Line 616:
         &lt;td style="text-align: right;"&gt;1072.3404&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;1072.3404&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;aug 7th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Cx&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 454: Line 628:
         &lt;td style="text-align: right;"&gt;1097.8723&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;1097.8723&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;double-aug 7th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;AA7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C#3&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 462: Line 640:
         &lt;td style="text-align: right;"&gt;1123.4043&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;1123.4043&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;triple-aug 7th, triple-dim 8ve&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A37, d38&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C#4, Db3&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 470: Line 652:
         &lt;td style="text-align: right;"&gt;1148.9362&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;1148.9362&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;double-dim 8ve&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;dd8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Dbb&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 478: Line 664:
         &lt;td style="text-align: right;"&gt;1174.4681&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;1174.4681&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;dim 8ve&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;d8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Db&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 486: Line 676:
         &lt;td style="text-align: right;"&gt;1200.0000&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;1200.0000&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;perfect 8ve&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;P8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;D&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;

Revision as of 14:52, 5 September 2017

IMPORTED REVISION FROM WIKISPACES

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

This revision was by author TallKite and made on 2017-09-05 14:52:52 UTC.
The original revision id was 617218497.
The revision comment was:

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

Original Wikitext content:

=<span style="color: #616161; font-size: 99%;">47 tone Equal Temperament</span>= 

**//47-EDO//** divides the octave into 47 equal parts of 25.5319 cents each. It has a fifth which is 12.5933 cents flat, unless you use the alternative fifth which is 12.9386 cents sharp, similar to 35edo. It has therefore not aroused much interest, but its best approximation to 9/8 is actually quite good, one-third of a cent sharp. It does a good job of approximating the 2.9.5.7.33.13.17.57.69 23-limit [[k*N subgroups|2*47 subgroup]] of the [[23-limit]], on which it tempers out the same commas as [[94edo]]. It provides a good tuning for [[Chromatic pairs#Baldy|baldy]] and [[Chromatic pairs#Silver|silver]] temperaments and relatives.

47edo is the 15th [[prime numbers|prime]] edo, following [[43edo]] and preceding [[53edo]].

47edo is a [[Ups and Downs Notation#Other%20EDOs|regular]] edo because its 5th falls between 4\7 = 686¢ and 3\5 = 720¢. (Its alternate 5th does as well.) 47edo is the most difficult regular edo to notate, because no other regular edo's 5th is as far off from a just 3/2.

A notation using the best 5th has major and minor 2nds of 7 and 6 edosteps respectively, with the naturals creating a very 7edo-ish scale: 
D * * * * * * E * * * * * F * * * * * * G * * * * * * A * * * * * * B * * * * * C * * * * * * D
D# is next to D. This notation requires triple, quadruple and even quintuple sharps and flats.

Using the 2nd best 5th is even more awkward. The major 2nd is 9 edosteps and the minor is only one. The naturals create a very 5edo-ish scale, with two of the notes inflected by a comma-sized edostep: 
D * * * * * * * * E F * * * * * * * * G * * * * * * * * A * * * * * * * * B C * * * * * * * * D
D# is next to E. This notation requires quadruple, quintuple, and even sextuple ups and downs, as well as single sharps and flats.

==Intervals of 47edo== 

||~ Degree ||~ Size (Cents) ||~ relative notation ||~   ||~ absolute notation ||
||= 0 ||> 0.0000 ||= perfect unison ||= P1 ||= D ||
||= 1 ||> 25.5319 ||= aug 1sn ||= A1 ||= D# ||
||= 2 ||> 51.0638 ||= double-aug 1sn ||= AA1 ||= Dx ||
||= 3 ||> 76.5957 ||= triple-aug 1sn, triple-dim 2nd ||= A31, d32 ||= D#3, Eb4 ||
||= 4 ||> 102.1277 ||= double-dim 2nd ||= dd2 ||= Eb3 ||
||= 5 ||> 127.6596 ||= dim 2nd ||= d2 ||= Ebb ||
||= 6 ||> 153.1915 ||= minor 2nd ||= m2 ||= Eb ||
||= 7 ||> 178.7234 ||= major 2nd ||= M2 ||= E ||
||= 8 ||> 204.2553 ||= aug 2nd ||= A2 ||= E# ||
||= 9 ||> 229.7872 ||= double-aug 2nd ||= AA2 ||= Ex ||
||= 10 ||> 255.3191 ||= triple-aug 2nd, triple-dim 3rd ||= A32, d33 ||= E#3, Fb3 ||
||= 11 ||> 280.8511 ||= double-dim 3rd ||= dd3 ||= Fbb ||
||= 12 ||> 306.3830 ||= dim 3rd ||= d3 ||= Fb ||
||= 13 ||> 331.9149 ||= minor 3rd ||= m3 ||= F ||
||= 14 ||> 357.4468 ||= major 3rd ||= M3 ||= F# ||
||= 15 ||> 382.9787 ||= aug 3rd ||= A3 ||= Fx ||
||= 16 ||> 408.5106 ||= double-aug 3rd ||= AA3 ||= F#3 ||
||= 17 ||> 434.0426 ||= triple-aug 3rd, triple-dim 4th ||= A33, d34 ||= F#4, Gb3 ||
||= 18 ||> 459.5745 ||= double-dim 4th ||= dd4 ||= Gbb ||
||= 19 ||> 485.1064 ||= dim 4th ||= d4 ||= Gb ||
||= 20 ||> 510.6383 ||= perfect 4th ||= P4 ||= G ||
||= 21 ||> 536.1702 ||= aug 4th ||= A4 ||= G# ||
||= 22 ||> 561.7021 ||= double-aug 4th ||= AA4 ||= Gx ||
||= 23 ||> 587.2340 ||= triple-aug 4th ||= A34 ||= G#3 ||
||= 24 ||> 612.7660 ||= triple-dim 5th ||= d35 ||= Ab3 ||
||= 25 ||> 638.2979 ||= double-dim 5th ||= dd5 ||= Abb ||
||= 26 ||> 663.8298 ||= dim 5th ||= d5 ||= Ab ||
||= 27 ||> 689.3617 ||= perfect 5th ||= P5 ||= A ||
||= 28 ||> 714.8936 ||= aug 5th ||= A5 ||= A# ||
||= 29 ||> 740.4255 ||= double-aug 5th ||= AA5 ||= Ax ||
||= 30 ||> 765.9574 ||= triple-aug 5th, triple-dim 6th ||= A35, d36 ||= A#3, Bb4 ||
||= 31 ||> 791.4894 ||= double-dim 6th ||= dd6 ||= Bb3 ||
||= 32 ||> 817.0213 ||= dim 6th ||= d6 ||= Bbb ||
||= 33 ||> 842.5532 ||= minor 6th ||= m6 ||= Bb ||
||= 34 ||> 868.0851 ||= major 6th ||= M6 ||= B ||
||= 35 ||> 893.6170 ||= aug 6th ||= A6 ||= B# ||
||= 36 ||> 919.1489 ||= double-aug 6th ||= AA6 ||= Bx ||
||= 37 ||> 944.6809 ||= triple-aug 6th, triple-dim 7th ||= A36, d37 ||= B#3, Cb3 ||
||= 38 ||> 970.2128 ||= double-dim 7th ||= dd7 ||= Cbb ||
||= 39 ||> 995.7447 ||= dim 7th ||= d7 ||= Cb ||
||= 40 ||> 1021.2766 ||= minor 7th ||= m7 ||= C ||
||= 41 ||> 1046.8085 ||= major 7th ||= M7 ||= C# ||
||= 42 ||> 1072.3404 ||= aug 7th ||= A7 ||= Cx ||
||= 43 ||> 1097.8723 ||= double-aug 7th ||= AA7 ||= C#3 ||
||= 44 ||> 1123.4043 ||= triple-aug 7th, triple-dim 8ve ||= A37, d38 ||= C#4, Db3 ||
||= 45 ||> 1148.9362 ||= double-dim 8ve ||= dd8 ||= Dbb ||
||= 46 ||> 1174.4681 ||= dim 8ve ||= d8 ||= Db ||
||= 47 ||> 1200.0000 ||= perfect 8ve ||= P8 ||= D ||

Original HTML content:

<html><head><title>47edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x47 tone Equal Temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #616161; font-size: 99%;">47 tone Equal Temperament</span></h1>
 <br />
<strong><em>47-EDO</em></strong> divides the octave into 47 equal parts of 25.5319 cents each. It has a fifth which is 12.5933 cents flat, unless you use the alternative fifth which is 12.9386 cents sharp, similar to 35edo. It has therefore not aroused much interest, but its best approximation to 9/8 is actually quite good, one-third of a cent sharp. It does a good job of approximating the 2.9.5.7.33.13.17.57.69 23-limit <a class="wiki_link" href="/k%2AN%20subgroups">2*47 subgroup</a> of the <a class="wiki_link" href="/23-limit">23-limit</a>, on which it tempers out the same commas as <a class="wiki_link" href="/94edo">94edo</a>. It provides a good tuning for <a class="wiki_link" href="/Chromatic%20pairs#Baldy">baldy</a> and <a class="wiki_link" href="/Chromatic%20pairs#Silver">silver</a> temperaments and relatives.<br />
<br />
47edo is the 15th <a class="wiki_link" href="/prime%20numbers">prime</a> edo, following <a class="wiki_link" href="/43edo">43edo</a> and preceding <a class="wiki_link" href="/53edo">53edo</a>.<br />
<br />
47edo is a <a class="wiki_link" href="/Ups%20and%20Downs%20Notation#Other%20EDOs">regular</a> edo because its 5th falls between 4\7 = 686¢ and 3\5 = 720¢. (Its alternate 5th does as well.) 47edo is the most difficult regular edo to notate, because no other regular edo's 5th is as far off from a just 3/2.<br />
<br />
A notation using the best 5th has major and minor 2nds of 7 and 6 edosteps respectively, with the naturals creating a very 7edo-ish scale: <br />
D * * * * * * E * * * * * F * * * * * * G * * * * * * A * * * * * * B * * * * * C * * * * * * D<br />
D# is next to D. This notation requires triple, quadruple and even quintuple sharps and flats.<br />
<br />
Using the 2nd best 5th is even more awkward. The major 2nd is 9 edosteps and the minor is only one. The naturals create a very 5edo-ish scale, with two of the notes inflected by a comma-sized edostep: <br />
D * * * * * * * * E F * * * * * * * * G * * * * * * * * A * * * * * * * * B C * * * * * * * * D<br />
D# is next to E. This notation requires quadruple, quintuple, and even sextuple ups and downs, as well as single sharps and flats.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x47 tone Equal Temperament-Intervals of 47edo"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals of 47edo</h2>
 <br />


<table class="wiki_table">
    <tr>
        <th>Degree<br />
</th>
        <th>Size (Cents)<br />
</th>
        <th>relative notation<br />
</th>
        <th><br />
</th>
        <th>absolute notation<br />
</th>
    </tr>
    <tr>
        <td style="text-align: center;">0<br />
</td>
        <td style="text-align: right;">0.0000<br />
</td>
        <td style="text-align: center;">perfect unison<br />
</td>
        <td style="text-align: center;">P1<br />
</td>
        <td style="text-align: center;">D<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1<br />
</td>
        <td style="text-align: right;">25.5319<br />
</td>
        <td style="text-align: center;">aug 1sn<br />
</td>
        <td style="text-align: center;">A1<br />
</td>
        <td style="text-align: center;">D#<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">2<br />
</td>
        <td style="text-align: right;">51.0638<br />
</td>
        <td style="text-align: center;">double-aug 1sn<br />
</td>
        <td style="text-align: center;">AA1<br />
</td>
        <td style="text-align: center;">Dx<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">3<br />
</td>
        <td style="text-align: right;">76.5957<br />
</td>
        <td style="text-align: center;">triple-aug 1sn, triple-dim 2nd<br />
</td>
        <td style="text-align: center;">A31, d32<br />
</td>
        <td style="text-align: center;">D#3, Eb4<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">4<br />
</td>
        <td style="text-align: right;">102.1277<br />
</td>
        <td style="text-align: center;">double-dim 2nd<br />
</td>
        <td style="text-align: center;">dd2<br />
</td>
        <td style="text-align: center;">Eb3<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">5<br />
</td>
        <td style="text-align: right;">127.6596<br />
</td>
        <td style="text-align: center;">dim 2nd<br />
</td>
        <td style="text-align: center;">d2<br />
</td>
        <td style="text-align: center;">Ebb<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">6<br />
</td>
        <td style="text-align: right;">153.1915<br />
</td>
        <td style="text-align: center;">minor 2nd<br />
</td>
        <td style="text-align: center;">m2<br />
</td>
        <td style="text-align: center;">Eb<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">7<br />
</td>
        <td style="text-align: right;">178.7234<br />
</td>
        <td style="text-align: center;">major 2nd<br />
</td>
        <td style="text-align: center;">M2<br />
</td>
        <td style="text-align: center;">E<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">8<br />
</td>
        <td style="text-align: right;">204.2553<br />
</td>
        <td style="text-align: center;">aug 2nd<br />
</td>
        <td style="text-align: center;">A2<br />
</td>
        <td style="text-align: center;">E#<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">9<br />
</td>
        <td style="text-align: right;">229.7872<br />
</td>
        <td style="text-align: center;">double-aug 2nd<br />
</td>
        <td style="text-align: center;">AA2<br />
</td>
        <td style="text-align: center;">Ex<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">10<br />
</td>
        <td style="text-align: right;">255.3191<br />
</td>
        <td style="text-align: center;">triple-aug 2nd, triple-dim 3rd<br />
</td>
        <td style="text-align: center;">A32, d33<br />
</td>
        <td style="text-align: center;">E#3, Fb3<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">11<br />
</td>
        <td style="text-align: right;">280.8511<br />
</td>
        <td style="text-align: center;">double-dim 3rd<br />
</td>
        <td style="text-align: center;">dd3<br />
</td>
        <td style="text-align: center;">Fbb<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">12<br />
</td>
        <td style="text-align: right;">306.3830<br />
</td>
        <td style="text-align: center;">dim 3rd<br />
</td>
        <td style="text-align: center;">d3<br />
</td>
        <td style="text-align: center;">Fb<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">13<br />
</td>
        <td style="text-align: right;">331.9149<br />
</td>
        <td style="text-align: center;">minor 3rd<br />
</td>
        <td style="text-align: center;">m3<br />
</td>
        <td style="text-align: center;">F<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">14<br />
</td>
        <td style="text-align: right;">357.4468<br />
</td>
        <td style="text-align: center;">major 3rd<br />
</td>
        <td style="text-align: center;">M3<br />
</td>
        <td style="text-align: center;">F#<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">15<br />
</td>
        <td style="text-align: right;">382.9787<br />
</td>
        <td style="text-align: center;">aug 3rd<br />
</td>
        <td style="text-align: center;">A3<br />
</td>
        <td style="text-align: center;">Fx<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">16<br />
</td>
        <td style="text-align: right;">408.5106<br />
</td>
        <td style="text-align: center;">double-aug 3rd<br />
</td>
        <td style="text-align: center;">AA3<br />
</td>
        <td style="text-align: center;">F#3<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">17<br />
</td>
        <td style="text-align: right;">434.0426<br />
</td>
        <td style="text-align: center;">triple-aug 3rd, triple-dim 4th<br />
</td>
        <td style="text-align: center;">A33, d34<br />
</td>
        <td style="text-align: center;">F#4, Gb3<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">18<br />
</td>
        <td style="text-align: right;">459.5745<br />
</td>
        <td style="text-align: center;">double-dim 4th<br />
</td>
        <td style="text-align: center;">dd4<br />
</td>
        <td style="text-align: center;">Gbb<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">19<br />
</td>
        <td style="text-align: right;">485.1064<br />
</td>
        <td style="text-align: center;">dim 4th<br />
</td>
        <td style="text-align: center;">d4<br />
</td>
        <td style="text-align: center;">Gb<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">20<br />
</td>
        <td style="text-align: right;">510.6383<br />
</td>
        <td style="text-align: center;">perfect 4th<br />
</td>
        <td style="text-align: center;">P4<br />
</td>
        <td style="text-align: center;">G<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">21<br />
</td>
        <td style="text-align: right;">536.1702<br />
</td>
        <td style="text-align: center;">aug 4th<br />
</td>
        <td style="text-align: center;">A4<br />
</td>
        <td style="text-align: center;">G#<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">22<br />
</td>
        <td style="text-align: right;">561.7021<br />
</td>
        <td style="text-align: center;">double-aug 4th<br />
</td>
        <td style="text-align: center;">AA4<br />
</td>
        <td style="text-align: center;">Gx<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">23<br />
</td>
        <td style="text-align: right;">587.2340<br />
</td>
        <td style="text-align: center;">triple-aug 4th<br />
</td>
        <td style="text-align: center;">A34<br />
</td>
        <td style="text-align: center;">G#3<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">24<br />
</td>
        <td style="text-align: right;">612.7660<br />
</td>
        <td style="text-align: center;">triple-dim 5th<br />
</td>
        <td style="text-align: center;">d35<br />
</td>
        <td style="text-align: center;">Ab3<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">25<br />
</td>
        <td style="text-align: right;">638.2979<br />
</td>
        <td style="text-align: center;">double-dim 5th<br />
</td>
        <td style="text-align: center;">dd5<br />
</td>
        <td style="text-align: center;">Abb<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">26<br />
</td>
        <td style="text-align: right;">663.8298<br />
</td>
        <td style="text-align: center;">dim 5th<br />
</td>
        <td style="text-align: center;">d5<br />
</td>
        <td style="text-align: center;">Ab<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">27<br />
</td>
        <td style="text-align: right;">689.3617<br />
</td>
        <td style="text-align: center;">perfect 5th<br />
</td>
        <td style="text-align: center;">P5<br />
</td>
        <td style="text-align: center;">A<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">28<br />
</td>
        <td style="text-align: right;">714.8936<br />
</td>
        <td style="text-align: center;">aug 5th<br />
</td>
        <td style="text-align: center;">A5<br />
</td>
        <td style="text-align: center;">A#<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">29<br />
</td>
        <td style="text-align: right;">740.4255<br />
</td>
        <td style="text-align: center;">double-aug 5th<br />
</td>
        <td style="text-align: center;">AA5<br />
</td>
        <td style="text-align: center;">Ax<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">30<br />
</td>
        <td style="text-align: right;">765.9574<br />
</td>
        <td style="text-align: center;">triple-aug 5th, triple-dim 6th<br />
</td>
        <td style="text-align: center;">A35, d36<br />
</td>
        <td style="text-align: center;">A#3, Bb4<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">31<br />
</td>
        <td style="text-align: right;">791.4894<br />
</td>
        <td style="text-align: center;">double-dim 6th<br />
</td>
        <td style="text-align: center;">dd6<br />
</td>
        <td style="text-align: center;">Bb3<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">32<br />
</td>
        <td style="text-align: right;">817.0213<br />
</td>
        <td style="text-align: center;">dim 6th<br />
</td>
        <td style="text-align: center;">d6<br />
</td>
        <td style="text-align: center;">Bbb<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">33<br />
</td>
        <td style="text-align: right;">842.5532<br />
</td>
        <td style="text-align: center;">minor 6th<br />
</td>
        <td style="text-align: center;">m6<br />
</td>
        <td style="text-align: center;">Bb<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">34<br />
</td>
        <td style="text-align: right;">868.0851<br />
</td>
        <td style="text-align: center;">major 6th<br />
</td>
        <td style="text-align: center;">M6<br />
</td>
        <td style="text-align: center;">B<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">35<br />
</td>
        <td style="text-align: right;">893.6170<br />
</td>
        <td style="text-align: center;">aug 6th<br />
</td>
        <td style="text-align: center;">A6<br />
</td>
        <td style="text-align: center;">B#<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">36<br />
</td>
        <td style="text-align: right;">919.1489<br />
</td>
        <td style="text-align: center;">double-aug 6th<br />
</td>
        <td style="text-align: center;">AA6<br />
</td>
        <td style="text-align: center;">Bx<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">37<br />
</td>
        <td style="text-align: right;">944.6809<br />
</td>
        <td style="text-align: center;">triple-aug 6th, triple-dim 7th<br />
</td>
        <td style="text-align: center;">A36, d37<br />
</td>
        <td style="text-align: center;">B#3, Cb3<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">38<br />
</td>
        <td style="text-align: right;">970.2128<br />
</td>
        <td style="text-align: center;">double-dim 7th<br />
</td>
        <td style="text-align: center;">dd7<br />
</td>
        <td style="text-align: center;">Cbb<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">39<br />
</td>
        <td style="text-align: right;">995.7447<br />
</td>
        <td style="text-align: center;">dim 7th<br />
</td>
        <td style="text-align: center;">d7<br />
</td>
        <td style="text-align: center;">Cb<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">40<br />
</td>
        <td style="text-align: right;">1021.2766<br />
</td>
        <td style="text-align: center;">minor 7th<br />
</td>
        <td style="text-align: center;">m7<br />
</td>
        <td style="text-align: center;">C<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">41<br />
</td>
        <td style="text-align: right;">1046.8085<br />
</td>
        <td style="text-align: center;">major 7th<br />
</td>
        <td style="text-align: center;">M7<br />
</td>
        <td style="text-align: center;">C#<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">42<br />
</td>
        <td style="text-align: right;">1072.3404<br />
</td>
        <td style="text-align: center;">aug 7th<br />
</td>
        <td style="text-align: center;">A7<br />
</td>
        <td style="text-align: center;">Cx<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">43<br />
</td>
        <td style="text-align: right;">1097.8723<br />
</td>
        <td style="text-align: center;">double-aug 7th<br />
</td>
        <td style="text-align: center;">AA7<br />
</td>
        <td style="text-align: center;">C#3<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">44<br />
</td>
        <td style="text-align: right;">1123.4043<br />
</td>
        <td style="text-align: center;">triple-aug 7th, triple-dim 8ve<br />
</td>
        <td style="text-align: center;">A37, d38<br />
</td>
        <td style="text-align: center;">C#4, Db3<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">45<br />
</td>
        <td style="text-align: right;">1148.9362<br />
</td>
        <td style="text-align: center;">double-dim 8ve<br />
</td>
        <td style="text-align: center;">dd8<br />
</td>
        <td style="text-align: center;">Dbb<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">46<br />
</td>
        <td style="text-align: right;">1174.4681<br />
</td>
        <td style="text-align: center;">dim 8ve<br />
</td>
        <td style="text-align: center;">d8<br />
</td>
        <td style="text-align: center;">Db<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">47<br />
</td>
        <td style="text-align: right;">1200.0000<br />
</td>
        <td style="text-align: center;">perfect 8ve<br />
</td>
        <td style="text-align: center;">P8<br />
</td>
        <td style="text-align: center;">D<br />
</td>
    </tr>
</table>

</body></html>