47edo: Difference between revisions

Revision as of 03:57, 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 03:57:05 UTC.

The original revision id was 617184721.

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 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
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: 
D * * * * * * * * E F * * * * * * * * G * * * * * * * * A * * * * * * * * B C * * * * * * * * D
This notation requires quintuple, sextuple, and even septuple ups and downs.


==Intervals of 47edo== 

||~ Degree ||~ Size (Cents) ||~ relative notation ||
||= 0 ||> 0.0000 ||= P1 ||
||= 1 ||> 25.5319 || A1 ||
||= 2 ||> 51.0638 || AA1 ||
||= 3 ||> 76.5957 || A31, d32 ||
||= 4 ||> 102.1277 || dd2 ||
||= 5 ||> 127.6596 || d2 ||
||= 6 ||> 153.1915 || m2 ||
||= 7 ||> 178.7234 || M2 ||
||= 8 ||> 204.2553 ||   ||
||= 9 ||> 229.7872 ||   ||
||= 10 ||> 255.3191 ||   ||
||= 11 ||> 280.8511 ||   ||
||= 12 ||> 306.3830 ||   ||
||= 13 ||> 331.9149 ||   ||
||= 14 ||> 357.4468 || M3 ||
||= 15 ||> 382.9787 ||   ||
||= 16 ||> 408.5106 ||   ||
||= 17 ||> 434.0426 ||   ||
||= 18 ||> 459.5745 ||   ||
||= 19 ||> 485.1064 ||   ||
||= 20 ||> 510.6383 ||   ||
||= 21 ||> 536.1702 ||   ||
||= 22 ||> 561.7021 ||   ||
||= 23 ||> 587.2340 ||   ||
||= 24 ||> 612.7660 ||   ||
||= 25 ||> 638.2979 ||   ||
||= 26 ||> 663.8298 ||   ||
||= 27 ||> 689.3617 ||   ||
||= 28 ||> 714.8936 ||   ||
||= 29 ||> 740.4255 ||   ||
||= 30 ||> 765.9574 ||   ||
||= 31 ||> 791.4894 ||   ||
||= 32 ||> 817.0213 ||   ||
||= 33 ||> 842.5532 ||   ||
||= 34 ||> 868.0851 ||   ||
||= 35 ||> 893.6170 ||   ||
||= 36 ||> 919.1489 ||   ||
||= 37 ||> 944.6809 ||   ||
||= 38 ||> 970.2128 ||   ||
||= 39 ||> 995.7447 ||   ||
||= 40 ||> 1021.2766 ||   ||
||= 41 ||> 1046.8085 ||   ||
||= 42 ||> 1072.3404 ||   ||
||= 43 ||> 1097.8723 ||   ||
||= 44 ||> 1123.4043 ||   ||
||= 45 ||> 1148.9362 ||   ||
||= 46 ||> 1174.4681 ||   ||
||= 47 ||> 1200.0000 ||   ||

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 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.<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 />
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 2 of the notes inflected by a comma: <br />
D * * * * * * * * E F * * * * * * * * G * * * * * * * * A * * * * * * * * B C * * * * * * * * D<br />
This notation requires quintuple, sextuple, and even septuple ups and downs.<br />
<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>
    </tr>
    <tr>
        <td style="text-align: center;">0<br />
</td>
        <td style="text-align: right;">0.0000<br />
</td>
        <td style="text-align: center;">P1<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1<br />
</td>
        <td style="text-align: right;">25.5319<br />
</td>
        <td>A1<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">2<br />
</td>
        <td style="text-align: right;">51.0638<br />
</td>
        <td>AA1<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">3<br />
</td>
        <td style="text-align: right;">76.5957<br />
</td>
        <td>A31, d32<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">4<br />
</td>
        <td style="text-align: right;">102.1277<br />
</td>
        <td>dd2<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">5<br />
</td>
        <td style="text-align: right;">127.6596<br />
</td>
        <td>d2<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">6<br />
</td>
        <td style="text-align: right;">153.1915<br />
</td>
        <td>m2<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">7<br />
</td>
        <td style="text-align: right;">178.7234<br />
</td>
        <td>M2<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">8<br />
</td>
        <td style="text-align: right;">204.2553<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">9<br />
</td>
        <td style="text-align: right;">229.7872<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">10<br />
</td>
        <td style="text-align: right;">255.3191<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">11<br />
</td>
        <td style="text-align: right;">280.8511<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">12<br />
</td>
        <td style="text-align: right;">306.3830<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">13<br />
</td>
        <td style="text-align: right;">331.9149<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">14<br />
</td>
        <td style="text-align: right;">357.4468<br />
</td>
        <td>M3<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">15<br />
</td>
        <td style="text-align: right;">382.9787<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">16<br />
</td>
        <td style="text-align: right;">408.5106<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">17<br />
</td>
        <td style="text-align: right;">434.0426<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">18<br />
</td>
        <td style="text-align: right;">459.5745<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">19<br />
</td>
        <td style="text-align: right;">485.1064<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">20<br />
</td>
        <td style="text-align: right;">510.6383<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">21<br />
</td>
        <td style="text-align: right;">536.1702<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">22<br />
</td>
        <td style="text-align: right;">561.7021<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">23<br />
</td>
        <td style="text-align: right;">587.2340<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">24<br />
</td>
        <td style="text-align: right;">612.7660<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">25<br />
</td>
        <td style="text-align: right;">638.2979<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">26<br />
</td>
        <td style="text-align: right;">663.8298<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">27<br />
</td>
        <td style="text-align: right;">689.3617<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">28<br />
</td>
        <td style="text-align: right;">714.8936<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">29<br />
</td>
        <td style="text-align: right;">740.4255<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">30<br />
</td>
        <td style="text-align: right;">765.9574<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">31<br />
</td>
        <td style="text-align: right;">791.4894<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">32<br />
</td>
        <td style="text-align: right;">817.0213<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">33<br />
</td>
        <td style="text-align: right;">842.5532<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">34<br />
</td>
        <td style="text-align: right;">868.0851<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">35<br />
</td>
        <td style="text-align: right;">893.6170<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">36<br />
</td>
        <td style="text-align: right;">919.1489<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">37<br />
</td>
        <td style="text-align: right;">944.6809<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">38<br />
</td>
        <td style="text-align: right;">970.2128<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">39<br />
</td>
        <td style="text-align: right;">995.7447<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">40<br />
</td>
        <td style="text-align: right;">1021.2766<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">41<br />
</td>
        <td style="text-align: right;">1046.8085<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">42<br />
</td>
        <td style="text-align: right;">1072.3404<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">43<br />
</td>
        <td style="text-align: right;">1097.8723<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">44<br />
</td>
        <td style="text-align: right;">1123.4043<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">45<br />
</td>
        <td style="text-align: right;">1148.9362<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">46<br />
</td>
        <td style="text-align: right;">1174.4681<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">47<br />
</td>
        <td style="text-align: right;">1200.0000<br />
</td>
        <td><br />
</td>
    </tr>
</table>

</body></html>

@@ 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:xenwolf|xenwolf]] and made on <tt>2016-12-29 17:38:00 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-09-05 03:57:05 UTC</tt>.<br>
-: The original revision id was <tt>602901266</tt>.<br>
+: The original revision id was <tt>617184721</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 11: / Line 11: @@
 edo is the 15th [[prime numbers|prime]] edo, following [[43edo]] and preceding [[53edo]].
+edo 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.
+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
+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:
+D * * * * * * * * E F * * * * * * * * G * * * * * * * * A * * * * * * * * B C * * * * * * * * D
+This notation requires quintuple, sextuple, and even septuple ups and downs.
 ==Intervals of 47edo==
-||~ Degree ||~ Size (Cents) ||
+||~ Degree ||~ Size (Cents) ||~ relative notation ||
-||=  0 ||&gt;    0.0000 ||
+||= 0 ||&gt; 0.0000 ||= P1 ||
-||=  1 ||&gt;   25.5319 ||
+||= 1 ||&gt; 25.5319 || A1 ||
-||=  2 ||&gt;   51.0638 ||
+||= 2 ||&gt; 51.0638 || AA1 ||
-||=  3 ||&gt;   76.5957 ||
+||= 3 ||&gt; 76.5957 || A31, d32 ||
-||=  4 ||&gt;  102.1277 ||
+||= 4 ||&gt; 102.1277 || dd2 ||
-||=  5 ||&gt;  127.6596 ||
+||= 5 ||&gt; 127.6596 || d2 ||
-||=  6 ||&gt;  153.1915 ||
+||= 6 ||&gt; 153.1915 || m2 ||
-||=  7 ||&gt;  178.7234 ||
+||= 7 ||&gt; 178.7234 || M2 ||
-||=  8 ||&gt;  204.2553 ||
+||= 8 ||&gt; 204.2553 ||   ||
-||=  9 ||&gt;  229.7872 ||
+||= 9 ||&gt; 229.7872 ||   ||
-||= 10 ||&gt;  255.3191 ||
+||= 10 ||&gt; 255.3191 ||   ||
-||= 11 ||&gt;  280.8511 ||
+||= 11 ||&gt; 280.8511 ||   ||
-||= 12 ||&gt;  306.3830 ||
+||= 12 ||&gt; 306.3830 ||   ||
-||= 13 ||&gt;  331.9149 ||
+||= 13 ||&gt; 331.9149 ||   ||
-||= 14 ||&gt;  357.4468 ||
+||= 14 ||&gt; 357.4468 || M3 ||
-||= 15 ||&gt;  382.9787 ||
+||= 15 ||&gt; 382.9787 ||   ||
-||= 16 ||&gt;  408.5106 ||
+||= 16 ||&gt; 408.5106 ||   ||
-||= 17 ||&gt;  434.0426 ||
+||= 17 ||&gt; 434.0426 ||   ||
-||= 18 ||&gt;  459.5745 ||
+||= 18 ||&gt; 459.5745 ||   ||
-||= 19 ||&gt;  485.1064 ||
+||= 19 ||&gt; 485.1064 ||   ||
-||= 20 ||&gt;  510.6383 ||
+||= 20 ||&gt; 510.6383 ||   ||
-||= 21 ||&gt;  536.1702 ||
+||= 21 ||&gt; 536.1702 ||   ||
-||= 22 ||&gt;  561.7021 ||
+||= 22 ||&gt; 561.7021 ||   ||
-||= 23 ||&gt;  587.2340 ||
+||= 23 ||&gt; 587.2340 ||   ||
-||= 24 ||&gt;  612.7660 ||
+||= 24 ||&gt; 612.7660 ||   ||
-||= 25 ||&gt;  638.2979 ||
+||= 25 ||&gt; 638.2979 ||   ||
-||= 26 ||&gt;  663.8298 ||
+||= 26 ||&gt; 663.8298 ||   ||
-||= 27 ||&gt;  689.3617 ||
+||= 27 ||&gt; 689.3617 ||   ||
-||= 28 ||&gt;  714.8936 ||
+||= 28 ||&gt; 714.8936 ||   ||
-||= 29 ||&gt;  740.4255 ||
+||= 29 ||&gt; 740.4255 ||   ||
-||= 30 ||&gt;  765.9574 ||
+||= 30 ||&gt; 765.9574 ||   ||
-||= 31 ||&gt;  791.4894 ||
+||= 31 ||&gt; 791.4894 ||   ||
-||= 32 ||&gt;  817.0213 ||
+||= 32 ||&gt; 817.0213 ||   ||
-||= 33 ||&gt;  842.5532 ||
+||= 33 ||&gt; 842.5532 ||   ||
-||= 34 ||&gt;  868.0851 ||
+||= 34 ||&gt; 868.0851 ||   ||
-||= 35 ||&gt;  893.6170 ||
+||= 35 ||&gt; 893.6170 ||   ||
-||= 36 ||&gt;  919.1489 ||
+||= 36 ||&gt; 919.1489 ||   ||
-||= 37 ||&gt;  944.6809 ||
+||= 37 ||&gt; 944.6809 ||   ||
-||= 38 ||&gt;  970.2128 ||
+||= 38 ||&gt; 970.2128 ||   ||
-||= 39 ||&gt;  995.7447 ||
+||= 39 ||&gt; 995.7447 ||   ||
-||= 40 ||&gt; 1021.2766 ||
+||= 40 ||&gt; 1021.2766 ||   ||
-||= 41 ||&gt; 1046.8085 ||
+||= 41 ||&gt; 1046.8085 ||   ||
-||= 42 ||&gt; 1072.3404 ||
+||= 42 ||&gt; 1072.3404 ||   ||
-||= 43 ||&gt; 1097.8723 ||
+||= 43 ||&gt; 1097.8723 ||   ||
-||= 44 ||&gt; 1123.4043 ||
+||= 44 ||&gt; 1123.4043 ||   ||
-||= 45 ||&gt; 1148.9362 ||
+||= 45 ||&gt; 1148.9362 ||   ||
-||= 46 ||&gt; 1174.4681 ||
+||= 46 ||&gt; 1174.4681 ||   ||
-||= 47 ||&gt; 1200.0000 ||</pre></div>
+||= 47 ||&gt; 1200.0000 ||   ||</pre></div>
 <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;
@@ Line 69: / Line 80: @@
 &lt;br /&gt;
 edo 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;
+edo 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;
+&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;
+This notation requires triple, quadruple and even quintuple sharps and flats.&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;
+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;
+&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;
@@ Line 79: / Line 101: @@
 &lt;/th&gt;
          &lt;th&gt;Size (Cents)&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;relative notation&lt;br /&gt;
 &lt;/th&gt;
      &lt;/tr&gt;
@@ Line 85: / Line 109: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;0.0000&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;P1&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 91: / Line 117: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;25.5319&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;A1&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 97: / Line 125: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;51.0638&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;AA1&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 103: / Line 133: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;76.5957&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;A31, d32&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 109: / Line 141: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;102.1277&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;dd2&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 115: / Line 149: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;127.6596&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;d2&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 121: / Line 157: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;153.1915&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;m2&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 127: / Line 165: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;178.7234&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;M2&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 133: / Line 173: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;204.2553&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 139: / Line 181: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;229.7872&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 145: / Line 189: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;255.3191&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 151: / Line 197: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;280.8511&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 157: / Line 205: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;306.3830&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 163: / Line 213: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;331.9149&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 169: / Line 221: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;357.4468&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;M3&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 175: / Line 229: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;382.9787&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 181: / Line 237: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;408.5106&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 187: / Line 245: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;434.0426&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 193: / Line 253: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;459.5745&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 199: / Line 261: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;485.1064&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 205: / Line 269: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;510.6383&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 211: / Line 277: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;536.1702&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 217: / Line 285: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;561.7021&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 223: / Line 293: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;587.2340&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 229: / Line 301: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;612.7660&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 235: / Line 309: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;638.2979&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 241: / Line 317: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;663.8298&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 247: / Line 325: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;689.3617&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 253: / Line 333: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;714.8936&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 259: / Line 341: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;740.4255&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 265: / Line 349: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;765.9574&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 271: / Line 357: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;791.4894&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 277: / Line 365: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;817.0213&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 283: / Line 373: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;842.5532&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 289: / Line 381: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;868.0851&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 295: / Line 389: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;893.6170&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 301: / Line 397: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;919.1489&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 307: / Line 405: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;944.6809&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 313: / Line 413: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;970.2128&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 319: / Line 421: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;995.7447&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 325: / Line 429: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;1021.2766&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 331: / Line 437: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;1046.8085&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 337: / Line 445: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;1072.3404&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 343: / Line 453: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;1097.8723&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 349: / Line 461: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;1123.4043&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 355: / Line 469: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;1148.9362&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 361: / Line 477: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;1174.4681&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 367: / Line 485: @@
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;1200.0000&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;

47edo: Difference between revisions

Revision as of 03:57, 5 September 2017

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