42edo: Difference between revisions

Revision as of 03:39, 11 November 2017

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The //42 equal division// divides the octave into 42 equal parts of 28.571 [[cent]]s each. It has a 3 (the size of which being coprime to its cardinality, this being a first for a composite equal division of cardinality 7n) and a 5 both over 12 cents sharp, using the same 400 cent interval to represent 5/4 as does 12, which means it [[tempering out|tempers out]] 128/125. In the [[7-limit]], it tempers out 64/63 and 126/125, making it a tuning supporting [[Augmented family|augene temperament]].

While not an accurate tuning on the full 7-limit, it does an excellent job on the 2.9.15.7.33.39 [[k*N subgroups|2*42 subgroup]], having the same tuning on it as does [[84edo]]. On this subgroup 42 has the same [[comma]]s as 84.

42edo is a [[xenharmonic/Ups and Downs Notation#Other%20EDOs|regular]] edo because its 5th falls between 4\7 = 686¢ and 3\5 = 720¢. 42edo is one of the most difficult regular edos to notate, because no other regular edo's 5th is as sharp (see 47edo for the opposite extreme). Assuming the natural notes form a chain of fifths, the major 2nd is 8 edosteps and the minor 2nd is only one. The naturals create a roughly 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. The notation requires triple ups and downs, even more if chords are to be spelled correctly. For example, a 1/1 - 5/4 - 3/2 - 9/5 chord with a root on the key or fret midway between G and A would be written either as G#v<span style="font-size: 90%; vertical-align: super;">3</span> - B#v<span style="font-size: 90%; vertical-align: super;">5</span> - D#v<span style="font-size: 90%; vertical-align: super;">3</span> - F#v or as Ab^<span style="font-size: 90%; vertical-align: super;">3</span> - C^ - Eb^<span style="font-size: 90%; vertical-align: super;">3</span> - Gb^<span style="font-size: 90%; vertical-align: super;">5</span>. This is a dot-double-down double-up-seven chord, written either as G#v<span style="font-size: 90%; vertical-align: super;">3</span>.vv,^^7 or as Ab^<span style="font-size: 90%; vertical-align: super;">3</span>.vv,^^7.

==Intervals of 42edo== 

||~ Degree ||~ Size (Cents) ||||~ relative notation ||~ absolute notation ||
||= 0 ||= 0 ||= perfect unison ||= P1 ||= D ||
||= 1 ||= 29 ||= up 1sn, minor 2nd ||= ^1, m2 ||= D^, Eb ||
||= 2 ||= 57 ||= double-up 1sn, upminor 2nd ||= ^^1, ^m2 ||= D^^, Eb^ ||
||= 3 ||= 86 ||= double-up minor 2nd ||= ^^m2 ||= Eb^^ ||
||= 4 ||= 114 ||= downmid 2nd ||= v~2 ||= Eb^<span style="font-size: 90%; vertical-align: super;">3</span> ||
||= 5 ||= 143 ||= upmid 2nd ||= ^~2 ||= Ev<span style="font-size: 90%; vertical-align: super;">3</span> ||
||= 6 ||= 171 ||= double-down major 2nd ||= vvM2 ||= Evv ||
||= 7 ||= 200 ||= downmajor 2nd ||= vM2 ||= Ev ||
||= 8 ||= 229 ||= major 2nd ||= M2 ||= E ||
||= 9 ||= 257 ||= minor 3rd ||= m3 ||= F ||
||= 10 ||= 286 ||= upminor 3rd ||= ^m3 ||= F^ ||
||= 11 ||= 314 ||= double-up minor 3rd ||= ^^m3 ||= F^^ ||
||= 12 ||= 343 ||= downmid 3rd ||= v~3 ||= F^<span style="font-size: 90%; vertical-align: super;">3</span> ||
||= 13 ||= 371 ||= upmid 3rd ||= ^~3 ||= F#v<span style="font-size: 90%; vertical-align: super;">3</span> ||
||= 14 ||= 400 ||= double-down major 3rd ||= vvM3 ||= F#vv ||
||= 15 ||= 429 ||= downmajor 3rd ||= vM3 ||= F#v ||
||= 16 ||= 457 ||= major 3rd, down 4th ||= M3, v4 ||= F#, Gv ||
||= 17 ||= 486 ||= perfect 4th ||= P4 ||= G ||
||= 18 ||= 514 ||= up 4th ||= ^4 ||= G^ ||
||= 19 ||= 543 ||= double-up 4th ||= ^^4 ||= G^^ ||
||= 20 ||= 571 ||= triple-up 4th ||= ^<span style="font-size: 90%; vertical-align: super;">3</span>4 ||= G^<span style="font-size: 90%; vertical-align: super;">3</span> ||
||= 21 ||= 600 ||= triple-down aug 4th, triple-up dim 5th ||= v<span style="font-size: 90%; vertical-align: super;">3</span>A4, ^<span style="font-size: 90%; vertical-align: super;">3</span>d5 ||= G#v<span style="font-size: 90%; vertical-align: super;">3</span>, Ab^<span style="font-size: 90%; vertical-align: super;">3</span> ||
||= 22 ||= 629 ||= triple-down 5th ||= v<span style="font-size: 90%; vertical-align: super;">3</span>5 ||= Av<span style="font-size: 90%; vertical-align: super;">3</span> ||
||= 23 ||= 657 ||= double-down 5th ||= vv5 ||= Avv ||
||= 24 ||= 686 ||= down 5th ||= v5 ||= Av ||
||= 25 ||= 714 ||= perfect 5th ||= P5 ||= A ||
||= 26 ||= 743 ||= up 5th, minor 6th ||= ^5, m6 ||= A^, Bb ||
||= 27 ||= 771 ||= upminor 6th ||= ^m6 ||= Bb^ ||
||= 28 ||= 800 ||= double-up minor 6th ||= ^^m6 ||= Bb^^ ||
||= 29 ||= 829 ||= downmid 6th ||= v~6 ||= Bb^<span style="font-size: 90%; vertical-align: super;">3</span> ||
||= 30 ||= 857 ||= upmid 6th ||= ^~6 ||= Bv<span style="font-size: 90%; vertical-align: super;">3</span> ||
||= 31 ||= 886 ||= double-down major 6th ||= vvM6 ||= Bvv ||
||= 32 ||= 914 ||= downmajor 6th ||= vM6 ||= Bv ||
||= 33 ||= 943 ||= major 6th ||= M6 ||= B ||
||= 34 ||= 971 ||= minor 7th ||= m7 ||= C ||
||= 35 ||= 1000 ||= upminor 7th ||= ^m7 ||= C^ ||
||= 36 ||= 1029 ||= double-up minor 7th ||= ^^m7 ||= C^^ ||
||= 37 ||= 1057 ||= downmid 7th ||= v~7 ||= C^<span style="font-size: 90%; vertical-align: super;">3</span> ||
||= 38 ||= 1086 ||= upmid 7th ||= ^~7 ||= C#v<span style="font-size: 90%; vertical-align: super;">3</span> ||
||= 39 ||= 1114 ||= double-down major 7th ||= vvM7 ||= C#vv ||
||= 40 ||= 1143 ||= downmajor 7th ||= vM7 ||= C#v ||
||= 41 ||= 1171 ||= major 7th, down 8ve ||= M7, v8 ||= C#, Dv ||
||= 42 ||= 1200 ||= perfect 8ve ||= P8 ||= D ||

Original HTML content:

<html><head><title>42edo</title></head><body>The <em>42 equal division</em> divides the octave into 42 equal parts of 28.571 <a class="wiki_link" href="/cent">cent</a>s each. It has a 3 (the size of which being coprime to its cardinality, this being a first for a composite equal division of cardinality 7n) and a 5 both over 12 cents sharp, using the same 400 cent interval to represent 5/4 as does 12, which means it <a class="wiki_link" href="/tempering%20out">tempers out</a> 128/125. In the <a class="wiki_link" href="/7-limit">7-limit</a>, it tempers out 64/63 and 126/125, making it a tuning supporting <a class="wiki_link" href="/Augmented%20family">augene temperament</a>.<br />
<br />
While not an accurate tuning on the full 7-limit, it does an excellent job on the 2.9.15.7.33.39 <a class="wiki_link" href="/k%2AN%20subgroups">2*42 subgroup</a>, having the same tuning on it as does <a class="wiki_link" href="/84edo">84edo</a>. On this subgroup 42 has the same <a class="wiki_link" href="/comma">comma</a>s as 84.<br />
<br />
42edo is a <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Other%20EDOs">regular</a> edo because its 5th falls between 4\7 = 686¢ and 3\5 = 720¢. 42edo is one of the most difficult regular edos to notate, because no other regular edo's 5th is as sharp (see 47edo for the opposite extreme). Assuming the natural notes form a chain of fifths, the major 2nd is 8 edosteps and the minor 2nd is only one. The naturals create a roughly 5edo-ish scale, with two of the notes inflected by a comma-sized edostep:<br />
<br />
D * * * * * * * * E F * * * * * * * * G * * * * * * * * A * * * * * * * * B C * * * * * * * * D<br />
<br />
D# is next to E. The notation requires triple ups and downs, even more if chords are to be spelled correctly. For example, a 1/1 - 5/4 - 3/2 - 9/5 chord with a root on the key or fret midway between G and A would be written either as G#v<span style="font-size: 90%; vertical-align: super;">3</span> - B#v<span style="font-size: 90%; vertical-align: super;">5</span> - D#v<span style="font-size: 90%; vertical-align: super;">3</span> - F#v or as Ab^<span style="font-size: 90%; vertical-align: super;">3</span> - C^ - Eb^<span style="font-size: 90%; vertical-align: super;">3</span> - Gb^<span style="font-size: 90%; vertical-align: super;">5</span>. This is a dot-double-down double-up-seven chord, written either as G#v<span style="font-size: 90%; vertical-align: super;">3</span>.vv,^^7 or as Ab^<span style="font-size: 90%; vertical-align: super;">3</span>.vv,^^7.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Intervals of 42edo"></a><!-- ws:end:WikiTextHeadingRule:0 -->Intervals of 42edo</h2>
 <br />


<table class="wiki_table">
    <tr>
        <th>Degree<br />
</th>
        <th>Size (Cents)<br />
</th>
        <th colspan="2">relative notation<br />
</th>
        <th>absolute notation<br />
</th>
    </tr>
    <tr>
        <td style="text-align: center;">0<br />
</td>
        <td style="text-align: center;">0<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: center;">29<br />
</td>
        <td style="text-align: center;">up 1sn, minor 2nd<br />
</td>
        <td style="text-align: center;">^1, m2<br />
</td>
        <td style="text-align: center;">D^, Eb<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">2<br />
</td>
        <td style="text-align: center;">57<br />
</td>
        <td style="text-align: center;">double-up 1sn, upminor 2nd<br />
</td>
        <td style="text-align: center;">^^1, ^m2<br />
</td>
        <td style="text-align: center;">D^^, Eb^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">3<br />
</td>
        <td style="text-align: center;">86<br />
</td>
        <td style="text-align: center;">double-up 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;">4<br />
</td>
        <td style="text-align: center;">114<br />
</td>
        <td style="text-align: center;">downmid 2nd<br />
</td>
        <td style="text-align: center;">v~2<br />
</td>
        <td style="text-align: center;">Eb^<span style="font-size: 90%; vertical-align: super;">3</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">5<br />
</td>
        <td style="text-align: center;">143<br />
</td>
        <td style="text-align: center;">upmid 2nd<br />
</td>
        <td style="text-align: center;">^~2<br />
</td>
        <td style="text-align: center;">Ev<span style="font-size: 90%; vertical-align: super;">3</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">6<br />
</td>
        <td style="text-align: center;">171<br />
</td>
        <td style="text-align: center;">double-down major 2nd<br />
</td>
        <td style="text-align: center;">vvM2<br />
</td>
        <td style="text-align: center;">Evv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">7<br />
</td>
        <td style="text-align: center;">200<br />
</td>
        <td style="text-align: center;">downmajor 2nd<br />
</td>
        <td style="text-align: center;">vM2<br />
</td>
        <td style="text-align: center;">Ev<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">8<br />
</td>
        <td style="text-align: center;">229<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;">9<br />
</td>
        <td style="text-align: center;">257<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;">10<br />
</td>
        <td style="text-align: center;">286<br />
</td>
        <td style="text-align: center;">upminor 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;">11<br />
</td>
        <td style="text-align: center;">314<br />
</td>
        <td style="text-align: center;">double-up 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;">12<br />
</td>
        <td style="text-align: center;">343<br />
</td>
        <td style="text-align: center;">downmid 3rd<br />
</td>
        <td style="text-align: center;">v~3<br />
</td>
        <td style="text-align: center;">F^<span style="font-size: 90%; vertical-align: super;">3</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">13<br />
</td>
        <td style="text-align: center;">371<br />
</td>
        <td style="text-align: center;">upmid 3rd<br />
</td>
        <td style="text-align: center;">^~3<br />
</td>
        <td style="text-align: center;">F#v<span style="font-size: 90%; vertical-align: super;">3</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">14<br />
</td>
        <td style="text-align: center;">400<br />
</td>
        <td style="text-align: center;">double-down major 3rd<br />
</td>
        <td style="text-align: center;">vvM3<br />
</td>
        <td style="text-align: center;">F#vv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">15<br />
</td>
        <td style="text-align: center;">429<br />
</td>
        <td style="text-align: center;">downmajor 3rd<br />
</td>
        <td style="text-align: center;">vM3<br />
</td>
        <td style="text-align: center;">F#v<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">16<br />
</td>
        <td style="text-align: center;">457<br />
</td>
        <td style="text-align: center;">major 3rd, down 4th<br />
</td>
        <td style="text-align: center;">M3, v4<br />
</td>
        <td style="text-align: center;">F#, Gv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">17<br />
</td>
        <td style="text-align: center;">486<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;">18<br />
</td>
        <td style="text-align: center;">514<br />
</td>
        <td style="text-align: center;">up 4th<br />
</td>
        <td style="text-align: center;">^4<br />
</td>
        <td style="text-align: center;">G^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">19<br />
</td>
        <td style="text-align: center;">543<br />
</td>
        <td style="text-align: center;">double-up 4th<br />
</td>
        <td style="text-align: center;">^^4<br />
</td>
        <td style="text-align: center;">G^^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">20<br />
</td>
        <td style="text-align: center;">571<br />
</td>
        <td style="text-align: center;">triple-up 4th<br />
</td>
        <td style="text-align: center;">^<span style="font-size: 90%; vertical-align: super;">3</span>4<br />
</td>
        <td style="text-align: center;">G^<span style="font-size: 90%; vertical-align: super;">3</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">21<br />
</td>
        <td style="text-align: center;">600<br />
</td>
        <td style="text-align: center;">triple-down aug 4th, triple-up dim 5th<br />
</td>
        <td style="text-align: center;">v<span style="font-size: 90%; vertical-align: super;">3</span>A4, ^<span style="font-size: 90%; vertical-align: super;">3</span>d5<br />
</td>
        <td style="text-align: center;">G#v<span style="font-size: 90%; vertical-align: super;">3</span>, Ab^<span style="font-size: 90%; vertical-align: super;">3</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">22<br />
</td>
        <td style="text-align: center;">629<br />
</td>
        <td style="text-align: center;">triple-down 5th<br />
</td>
        <td style="text-align: center;">v<span style="font-size: 90%; vertical-align: super;">3</span>5<br />
</td>
        <td style="text-align: center;">Av<span style="font-size: 90%; vertical-align: super;">3</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">23<br />
</td>
        <td style="text-align: center;">657<br />
</td>
        <td style="text-align: center;">double-down 5th<br />
</td>
        <td style="text-align: center;">vv5<br />
</td>
        <td style="text-align: center;">Avv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">24<br />
</td>
        <td style="text-align: center;">686<br />
</td>
        <td style="text-align: center;">down 5th<br />
</td>
        <td style="text-align: center;">v5<br />
</td>
        <td style="text-align: center;">Av<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">25<br />
</td>
        <td style="text-align: center;">714<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;">26<br />
</td>
        <td style="text-align: center;">743<br />
</td>
        <td style="text-align: center;">up 5th, minor 6th<br />
</td>
        <td style="text-align: center;">^5, m6<br />
</td>
        <td style="text-align: center;">A^, Bb<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">27<br />
</td>
        <td style="text-align: center;">771<br />
</td>
        <td style="text-align: center;">upminor 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;">28<br />
</td>
        <td style="text-align: center;">800<br />
</td>
        <td style="text-align: center;">double-up 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;">29<br />
</td>
        <td style="text-align: center;">829<br />
</td>
        <td style="text-align: center;">downmid 6th<br />
</td>
        <td style="text-align: center;">v~6<br />
</td>
        <td style="text-align: center;">Bb^<span style="font-size: 90%; vertical-align: super;">3</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">30<br />
</td>
        <td style="text-align: center;">857<br />
</td>
        <td style="text-align: center;">upmid 6th<br />
</td>
        <td style="text-align: center;">^~6<br />
</td>
        <td style="text-align: center;">Bv<span style="font-size: 90%; vertical-align: super;">3</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">31<br />
</td>
        <td style="text-align: center;">886<br />
</td>
        <td style="text-align: center;">double-down major 6th<br />
</td>
        <td style="text-align: center;">vvM6<br />
</td>
        <td style="text-align: center;">Bvv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">32<br />
</td>
        <td style="text-align: center;">914<br />
</td>
        <td style="text-align: center;">downmajor 6th<br />
</td>
        <td style="text-align: center;">vM6<br />
</td>
        <td style="text-align: center;">Bv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">33<br />
</td>
        <td style="text-align: center;">943<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;">34<br />
</td>
        <td style="text-align: center;">971<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;">35<br />
</td>
        <td style="text-align: center;">1000<br />
</td>
        <td style="text-align: center;">upminor 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;">36<br />
</td>
        <td style="text-align: center;">1029<br />
</td>
        <td style="text-align: center;">double-up 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;">37<br />
</td>
        <td style="text-align: center;">1057<br />
</td>
        <td style="text-align: center;">downmid 7th<br />
</td>
        <td style="text-align: center;">v~7<br />
</td>
        <td style="text-align: center;">C^<span style="font-size: 90%; vertical-align: super;">3</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">38<br />
</td>
        <td style="text-align: center;">1086<br />
</td>
        <td style="text-align: center;">upmid 7th<br />
</td>
        <td style="text-align: center;">^~7<br />
</td>
        <td style="text-align: center;">C#v<span style="font-size: 90%; vertical-align: super;">3</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">39<br />
</td>
        <td style="text-align: center;">1114<br />
</td>
        <td style="text-align: center;">double-down major 7th<br />
</td>
        <td style="text-align: center;">vvM7<br />
</td>
        <td style="text-align: center;">C#vv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">40<br />
</td>
        <td style="text-align: center;">1143<br />
</td>
        <td style="text-align: center;">downmajor 7th<br />
</td>
        <td style="text-align: center;">vM7<br />
</td>
        <td style="text-align: center;">C#v<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">41<br />
</td>
        <td style="text-align: center;">1171<br />
</td>
        <td style="text-align: center;">major 7th, down 8ve<br />
</td>
        <td style="text-align: center;">M7, v8<br />
</td>
        <td style="text-align: center;">C#, Dv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">42<br />
</td>
        <td style="text-align: center;">1200<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>

@@ 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:TallKite|TallKite]] and made on <tt>2017-11-11 03:00:01 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-11-11 03:39:15 UTC</tt>.<br>
-: The original revision id was <tt>621434943</tt>.<br>
+: The original revision id was <tt>621435409</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 10: / Line 10: @@
 While not an accurate tuning on the full 7-limit, it does an excellent job on the 2.9.15.7.33.39 [[k*N subgroups|2*42 subgroup]], having the same tuning on it as does [[84edo]]. On this subgroup 42 has the same [[comma]]s as 84.
-edo is a [[xenharmonic/Ups and Downs Notation#Other%20EDOs|regular]] edo because its 5th falls between 4\7 = 686¢ and 3\5 = 720¢. 42edo is one of the most difficult regular edos to notate, because no other regular edo's 5th is as sharp (see 47edo for the opposite extreme). The major 2nd is 8 edosteps and the minor is only one. The naturals create a roughly 5edo-ish scale, with two of the notes inflected by a comma-sized edostep:
+edo is a [[xenharmonic/Ups and Downs Notation#Other%20EDOs|regular]] edo because its 5th falls between 4\7 = 686¢ and 3\5 = 720¢. 42edo is one of the most difficult regular edos to notate, because no other regular edo's 5th is as sharp (see 47edo for the opposite extreme). Assuming the natural notes form a chain of fifths, the major 2nd is 8 edosteps and the minor 2nd is only one. The naturals create a roughly 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. The notation requires quadruple ups and downs, even more if chortds are to be spelled properly. For example, a 4:5:6:7 chord with a root on the key or fret midway between G and A would be written either
+D# is next to E. The notation requires triple ups and downs, even more if chords are to be spelled correctly. For example, a 1/1 - 5/4 - 3/2 - 9/5 chord with a root on the key or fret midway between G and A would be written either as G#v&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt; - B#v&lt;span style="font-size: 90%; vertical-align: super;"&gt;5&lt;/span&gt; - D#v&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt; - F#v or as Ab^&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt; - C^ - Eb^&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt; - Gb^&lt;span style="font-size: 90%; vertical-align: super;"&gt;5&lt;/span&gt;. This is a dot-double-down double-up-seven chord, written either as G#v&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;.vv,^^7 or as Ab^&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;.vv,^^7.
 ==Intervals of 42edo==
@@ Line 20: / Line 20: @@
 ||~ Degree ||~ Size (Cents) ||||~ relative notation ||~ absolute notation ||
 ||= 0 ||= 0 ||= perfect unison ||= P1 ||= D ||
-||= 1 ||= 29 ||= up 1sn, minor 2nd ||= ^1, m2 ||= D# ||
+||= 1 ||= 29 ||= up 1sn, minor 2nd ||= ^1, m2 ||= D^, Eb ||
-||= 2 ||= 57 ||= double-up 1sn, upminor 2nd ||= ^^1, ^m2 ||= Dx ||
+||= 2 ||= 57 ||= double-up 1sn, upminor 2nd ||= ^^1, ^m2 ||= D^^, Eb^ ||
-||= 3 ||= 86 ||= triple-up 1sn, double-up minor 2nd ||= ^&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;1, ^^m2 ||= D#&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;, Eb&lt;span style="font-size: 90%; vertical-align: super;"&gt;4&lt;/span&gt; ||
+||= 3 ||= 86 ||= double-up minor 2nd ||= ^^m2 ||= Eb^^ ||
-||= 4 ||= 114 ||= downmid 2nd ||= v~2 ||= Eb&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt; ||
+||= 4 ||= 114 ||= downmid 2nd ||= v~2 ||= Eb^&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt; ||
-||= 5 ||= 143 ||= upmid 2nd ||= ^~2 ||= Ebb ||
+||= 5 ||= 143 ||= upmid 2nd ||= ^~2 ||= Ev&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt; ||
-||= 6 ||= 171 ||= double-down major 2nd ||= vvM2 ||= Eb ||
+||= 6 ||= 171 ||= double-down major 2nd ||= vvM2 ||= Evv ||
-||= 7 ||= 200 ||= downmajor 2nd ||= vM2 ||= E ||
+||= 7 ||= 200 ||= downmajor 2nd ||= vM2 ||= Ev ||
-||= 8 ||= 229 ||= major 2nd ||= M2 ||= E# ||
+||= 8 ||= 229 ||= major 2nd ||= M2 ||= E ||
-||= 9 ||= 257 ||= minor 3rd ||= m3 ||= Ex ||
+||= 9 ||= 257 ||= minor 3rd ||= m3 ||= F ||
-||= 10 ||= 286 ||= upminor 3rd ||= ^m3 ||= E#&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;, Fb&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt; ||
+||= 10 ||= 286 ||= upminor 3rd ||= ^m3 ||= F^ ||
-||= 11 ||= 314 ||= double-up minor 3rd ||= ^^m3 ||= Fbb ||
+||= 11 ||= 314 ||= double-up minor 3rd ||= ^^m3 ||= F^^ ||
-||= 12 ||= 343 ||= downmid 3rd ||= v~3 ||= Fb ||
+||= 12 ||= 343 ||= downmid 3rd ||= v~3 ||= F^&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt; ||
-||= 13 ||= 371 ||= upmid 3rd ||= ^~3 ||= F ||
+||= 13 ||= 371 ||= upmid 3rd ||= ^~3 ||= F#v&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt; ||
-||= 14 ||= 400 ||= double-down major 3rd ||= vvM3 ||= F# ||
+||= 14 ||= 400 ||= double-down major 3rd ||= vvM3 ||= F#vv ||
-||= 15 ||= 429 ||= downmajor 3rd ||= vM3 ||= Fx ||
+||= 15 ||= 429 ||= downmajor 3rd ||= vM3 ||= F#v ||
-||= 16 ||= 457 ||= major 3rd, down 4th ||= M3, v4 ||= F#&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt; ||
+||= 16 ||= 457 ||= major 3rd, down 4th ||= M3, v4 ||= F#, Gv ||
-||= 17 ||= 486 ||= perfect 4th ||= P4 ||= F#&lt;span style="font-size: 90%; vertical-align: super;"&gt;4&lt;/span&gt;, Gb&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt; ||
+||= 17 ||= 486 ||= perfect 4th ||= P4 ||= G ||
-||= 18 ||= 514 ||= up 4th ||= ^4 ||= Gbb ||
+||= 18 ||= 514 ||= up 4th ||= ^4 ||= G^ ||
-||= 19 ||= 543 ||= double-up 4th ||= ^^4 ||= Gb ||
+||= 19 ||= 543 ||= double-up 4th ||= ^^4 ||= G^^ ||
-||= 20 ||= 571 ||= triple-up 4th ||= ^&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;4 ||= G ||
+||= 20 ||= 571 ||= triple-up 4th ||= ^&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;4 ||= G^&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt; ||
-||= 21 ||= 600 ||= triple-down aug 4th, triple-up dim 5th ||= v&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;A4, ^&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;d5 ||= G# ||
+||= 21 ||= 600 ||= triple-down aug 4th, triple-up dim 5th ||= v&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;A4, ^&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;d5 ||= G#v&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;, Ab^&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt; ||
-||= 22 ||= 629 ||= triple-down 5th ||= v&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;5 ||= Gx ||
+||= 22 ||= 629 ||= triple-down 5th ||= v&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;5 ||= Av&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt; ||
-||= 23 ||= 657 ||= double-down 5th ||= vv5 ||= G#&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt; ||
+||= 23 ||= 657 ||= double-down 5th ||= vv5 ||= Avv ||
-||= 24 ||= 686 ||= down 5th ||= v5 ||= Ab&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt; ||
+||= 24 ||= 686 ||= down 5th ||= v5 ||= Av ||
-||= 25 ||= 714 ||= perfect 5th ||= P5 ||= Abb ||
+||= 25 ||= 714 ||= perfect 5th ||= P5 ||= A ||
-||= 26 ||= 743 ||= up 5th, minor 6th ||= ^5, m6 ||= Ab ||
+||= 26 ||= 743 ||= up 5th, minor 6th ||= ^5, m6 ||= A^, Bb ||
-||= 27 ||= 771 ||= upminor 6th ||= ^m6 ||= A ||
+||= 27 ||= 771 ||= upminor 6th ||= ^m6 ||= Bb^ ||
-||= 28 ||= 800 ||= double-up minor 5th ||= ^^m6 ||= A# ||
+||= 28 ||= 800 ||= double-up minor 6th ||= ^^m6 ||= Bb^^ ||
-||= 29 ||= 829 ||= downmid 5th ||= v~6 ||= Ax ||
+||= 29 ||= 829 ||= downmid 6th ||= v~6 ||= Bb^&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt; ||
-||= 30 ||= 857 ||= upmid 6th ||= ^~6 ||= A#&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;, Bb&lt;span style="font-size: 90%; vertical-align: super;"&gt;4&lt;/span&gt; ||
+||= 30 ||= 857 ||= upmid 6th ||= ^~6 ||= Bv&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt; ||
-||= 31 ||= 886 ||= double-down major 6th ||= vvM6 ||= Bb&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt; ||
+||= 31 ||= 886 ||= double-down major 6th ||= vvM6 ||= Bvv ||
-||= 32 ||= 914 ||= downmajor 6th ||= vM6 ||= Bbb ||
+||= 32 ||= 914 ||= downmajor 6th ||= vM6 ||= Bv ||
-||= 33 ||= 943 ||= major 6th ||= M6 ||= Bb ||
+||= 33 ||= 943 ||= major 6th ||= M6 ||= B ||
-||= 34 ||= 971 ||= minor 7th ||= m7 ||= B ||
+||= 34 ||= 971 ||= minor 7th ||= m7 ||= C ||
-||= 35 ||= 1000 ||= upminor 7th ||= ^m7 ||= B# ||
+||= 35 ||= 1000 ||= upminor 7th ||= ^m7 ||= C^ ||
-||= 36 ||= 1029 ||= double-up minor 7th ||= ^^m7 ||= Bx ||
+||= 36 ||= 1029 ||= double-up minor 7th ||= ^^m7 ||= C^^ ||
-||= 37 ||= 1057 ||= downmid 7th ||= v~7 ||= B#&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;, Cb&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt; ||
+||= 37 ||= 1057 ||= downmid 7th ||= v~7 ||= C^&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt; ||
-||= 38 ||= 1086 ||= upmid 7th ||= ^~7 ||= Cbb ||
+||= 38 ||= 1086 ||= upmid 7th ||= ^~7 ||= C#v&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt; ||
-||= 39 ||= 1114 ||= double-down major 7th ||= vvM7 ||= Cb ||
+||= 39 ||= 1114 ||= double-down major 7th ||= vvM7 ||= C#vv ||
-||= 40 ||= 1143 ||= downmajor 7th ||= vM7 ||= C ||
+||= 40 ||= 1143 ||= downmajor 7th ||= vM7 ||= C#v ||
-||= 41 ||= 1171 ||= major 7th ||= M7 ||= C# ||
+||= 41 ||= 1171 ||= major 7th, down 8ve ||= M7, v8 ||= C#, Dv ||
-||= 42 ||= 1200 ||= perfect 8ve ||= P8 ||= Cx ||</pre></div>
+||= 42 ||= 1200 ||= perfect 8ve ||= P8 ||= D ||</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;42edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;42 equal division&lt;/em&gt; divides the octave into 42 equal parts of 28.571 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s each. It has a 3 (the size of which being coprime to its cardinality, this being a first for a composite equal division of cardinality 7n) and a 5 both over 12 cents sharp, using the same 400 cent interval to represent 5/4 as does 12, which means it &lt;a class="wiki_link" href="/tempering%20out"&gt;tempers out&lt;/a&gt; 128/125. In the &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt;, it tempers out 64/63 and 126/125, making it a tuning supporting &lt;a class="wiki_link" href="/Augmented%20family"&gt;augene temperament&lt;/a&gt;.&lt;br /&gt;
@@ Line 67: / Line 67: @@
 While not an accurate tuning on the full 7-limit, it does an excellent job on the 2.9.15.7.33.39 &lt;a class="wiki_link" href="/k%2AN%20subgroups"&gt;2*42 subgroup&lt;/a&gt;, having the same tuning on it as does &lt;a class="wiki_link" href="/84edo"&gt;84edo&lt;/a&gt;. On this subgroup 42 has the same &lt;a class="wiki_link" href="/comma"&gt;comma&lt;/a&gt;s as 84.&lt;br /&gt;
 &lt;br /&gt;
-edo is a &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Other%20EDOs"&gt;regular&lt;/a&gt; edo because its 5th falls between 4\7 = 686¢ and 3\5 = 720¢. 42edo is one of the most difficult regular edos to notate, because no other regular edo's 5th is as sharp (see 47edo for the opposite extreme). The major 2nd is 8 edosteps and the minor is only one. The naturals create a roughly 5edo-ish scale, with two of the notes inflected by a comma-sized edostep:&lt;br /&gt;
+edo is a &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Other%20EDOs"&gt;regular&lt;/a&gt; edo because its 5th falls between 4\7 = 686¢ and 3\5 = 720¢. 42edo is one of the most difficult regular edos to notate, because no other regular edo's 5th is as sharp (see 47edo for the opposite extreme). Assuming the natural notes form a chain of fifths, the major 2nd is 8 edosteps and the minor 2nd is only one. The naturals create a roughly 5edo-ish scale, with two of the notes inflected by a comma-sized edostep:&lt;br /&gt;
 &lt;br /&gt;
 D * * * * * * * * E F * * * * * * * * G * * * * * * * * A * * * * * * * * B C * * * * * * * * D&lt;br /&gt;
 &lt;br /&gt;
-D# is next to E. The notation requires quadruple ups and downs, even more if chortds are to be spelled properly. For example, a 4:5:6:7 chord with a root on the key or fret midway between G and A would be written either&lt;br /&gt;
+D# is next to E. The notation requires triple ups and downs, even more if chords are to be spelled correctly. For example, a 1/1 - 5/4 - 3/2 - 9/5 chord with a root on the key or fret midway between G and A would be written either as G#v&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt; - B#v&lt;span style="font-size: 90%; vertical-align: super;"&gt;5&lt;/span&gt; - D#v&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt; - F#v or as Ab^&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt; - C^ - Eb^&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt; - Gb^&lt;span style="font-size: 90%; vertical-align: super;"&gt;5&lt;/span&gt;. This is a dot-double-down double-up-seven chord, written either as G#v&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;.vv,^^7 or as Ab^&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;.vv,^^7.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Intervals of 42edo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Intervals of 42edo&lt;/h2&gt;
@@ Line 109: / Line 109: @@
          &lt;td style="text-align: center;"&gt;^1, m2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;D#&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;D^, Eb&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 121: / Line 121: @@
          &lt;td style="text-align: center;"&gt;^^1, ^m2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Dx&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;D^^, Eb^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 129: / Line 129: @@
          &lt;td style="text-align: center;"&gt;86&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;triple-up 1sn, double-up minor 2nd&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;double-up minor 2nd&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;^&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;1, ^^m2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^^m2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;D#&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;, Eb&lt;span style="font-size: 90%; vertical-align: super;"&gt;4&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Eb^^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 145: / Line 145: @@
          &lt;td style="text-align: center;"&gt;v~2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Eb&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Eb^&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 157: / Line 157: @@
          &lt;td style="text-align: center;"&gt;^~2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Ebb&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Ev&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 169: / Line 169: @@
          &lt;td style="text-align: center;"&gt;vvM2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Eb&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Evv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 181: / Line 181: @@
          &lt;td style="text-align: center;"&gt;vM2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;E&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Ev&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 193: / Line 193: @@
          &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 style="text-align: center;"&gt;E&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 205: / Line 205: @@
          &lt;td style="text-align: center;"&gt;m3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Ex&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;F&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 217: / Line 217: @@
          &lt;td style="text-align: center;"&gt;^m3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;E#&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;, Fb&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;F^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 229: / Line 229: @@
          &lt;td style="text-align: center;"&gt;^^m3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Fbb&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;F^^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 241: / Line 241: @@
          &lt;td style="text-align: center;"&gt;v~3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Fb&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;F^&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 253: / Line 253: @@
          &lt;td style="text-align: center;"&gt;^~3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;F&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;F#v&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 265: / Line 265: @@
          &lt;td style="text-align: center;"&gt;vvM3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;F#&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;F#vv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 277: / Line 277: @@
          &lt;td style="text-align: center;"&gt;vM3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Fx&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;F#v&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 289: / Line 289: @@
          &lt;td style="text-align: center;"&gt;M3, v4&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;F#&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;F#, Gv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 301: / Line 301: @@
          &lt;td style="text-align: center;"&gt;P4&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;F#&lt;span style="font-size: 90%; vertical-align: super;"&gt;4&lt;/span&gt;, Gb&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;G&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 313: / Line 313: @@
          &lt;td style="text-align: center;"&gt;^4&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Gbb&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;G^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 325: / Line 325: @@
          &lt;td style="text-align: center;"&gt;^^4&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Gb&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;G^^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 337: / Line 337: @@
          &lt;td style="text-align: center;"&gt;^&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;4&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;G&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;G^&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 349: / Line 349: @@
          &lt;td style="text-align: center;"&gt;v&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;A4, ^&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;d5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;G#&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;G#v&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;, Ab^&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 361: / Line 361: @@
          &lt;td style="text-align: center;"&gt;v&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Gx&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Av&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 373: / Line 373: @@
          &lt;td style="text-align: center;"&gt;vv5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;G#&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Avv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 385: / Line 385: @@
          &lt;td style="text-align: center;"&gt;v5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Ab&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Av&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 397: / Line 397: @@
          &lt;td style="text-align: center;"&gt;P5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Abb&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;A&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 409: / Line 409: @@
          &lt;td style="text-align: center;"&gt;^5, m6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Ab&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;A^, Bb&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 421: / Line 421: @@
          &lt;td style="text-align: center;"&gt;^m6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;A&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Bb^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 429: / Line 429: @@
          &lt;td style="text-align: center;"&gt;800&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;double-up minor 5th&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;double-up 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;A#&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Bb^^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 441: / Line 441: @@
          &lt;td style="text-align: center;"&gt;829&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;downmid 5th&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;downmid 6th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;v~6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Ax&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Bb^&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 457: / Line 457: @@
          &lt;td style="text-align: center;"&gt;^~6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;A#&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;, Bb&lt;span style="font-size: 90%; vertical-align: super;"&gt;4&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Bv&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 469: / Line 469: @@
          &lt;td style="text-align: center;"&gt;vvM6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Bb&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Bvv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 481: / Line 481: @@
          &lt;td style="text-align: center;"&gt;vM6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Bbb&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Bv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 493: / Line 493: @@
          &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 style="text-align: center;"&gt;B&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 505: / Line 505: @@
          &lt;td style="text-align: center;"&gt;m7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;B&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;C&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 517: / Line 517: @@
          &lt;td style="text-align: center;"&gt;^m7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;B#&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;C^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 529: / Line 529: @@
          &lt;td style="text-align: center;"&gt;^^m7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Bx&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;C^^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 541: / Line 541: @@
          &lt;td style="text-align: center;"&gt;v~7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;B#&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;, Cb&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;C^&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 553: / Line 553: @@
          &lt;td style="text-align: center;"&gt;^~7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Cbb&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;C#v&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 565: / Line 565: @@
          &lt;td style="text-align: center;"&gt;vvM7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Cb&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;C#vv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 577: / Line 577: @@
          &lt;td style="text-align: center;"&gt;vM7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;C&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;C#v&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 585: / Line 585: @@
          &lt;td style="text-align: center;"&gt;1171&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;major 7th&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;major 7th, down 8ve&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;M7&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;M7, v8&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;C#&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;C#, Dv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 601: / Line 601: @@
          &lt;td style="text-align: center;"&gt;P8&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Cx&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;D&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;

42edo: Difference between revisions

Revision as of 03:39, 11 November 2017

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