Pergen names: Difference between revisions
Wikispaces>TallKite **Imported revision 622065493 - Original comment: ** |
Wikispaces>TallKite **Imported revision 622073697 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-11-20 | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-11-20 23:50:27 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>622073697</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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Not all possible combinations of periods and generators are unique pergens. {P8/2, P5/2} is actually {P8/2, P4/2}. There is no {P8, M2/2}, and {P8/2, M2/2} is actually {P8/2, P5}. The following table lists all the rank-2 pergens that contain primes 2 and 3, grouped by the size of the larger splitting factor. | Not all possible combinations of periods and generators are unique pergens. {P8/2, P5/2} is actually {P8/2, P4/2}. There is no {P8, M2/2}, and {P8/2, M2/2} is actually {P8/2, P5}. The following table lists all the rank-2 pergens that contain primes 2 and 3, grouped by the size of the larger splitting factor. | ||
The enharmonic interval can be added to or subtracted from any note or interval, and it will be renamed, but unchanged. It's analogous to the dim 2nd in 12-edo, which equates A1 with m2, A4 with d5, etc. | |||
The genchain shown is a short section of the full genchain. C - G implies ...Eb Bb F C G D A E B F# C#... And C - Eb^=Ev - G implies ...F - Ab^=Av - C - Eb^=Ev - G - Bb^=Bv - D - F^=F#v - A - C^=C#v - E... If the octave is split, the genchain shows the octave: In C - F#v=Gb^ - C, the last C is an octave above the first one. | The genchain shown is a short section of the full genchain. C - G implies ...Eb Bb F C G D A E B F# C#... And C - Eb^=Ev - G implies ...F - Ab^=Av - C - Eb^=Ev - G - Bb^=Bv - D - F^=F#v - A - C^=C#v - E... If the octave is split, the genchain shows the octave: In C - F#v=Gb^ - C, the last C is an octave above the first one. | ||
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(table is under construction) | (table is under construction) | ||
||~ pergen set ||~ | ||~ pergen set ||~ split interval(s) ||~ enharmonic | ||
interval(s) ||~ equiva- | |||
lence(s) ||~ genchain(s) ||~ example | |||
temperament ||~ compatible edos | temperament ||~ compatible edos | ||
(12-31 only) || | (12-31 only) || | ||
||= {P8, P5} ||= | ||= {P8, P5} ||= none ||= P1 ||= none ||= C - G ||= meantone ||= 12, 13b, 14*, 15*, 16, | ||
17, 18b*, 19, 20*, 21*, | 17, 18b*, 19, 20*, 21*, | ||
22, 23, 24*, 25*, 26, | 22, 23, 24*, 25*, 26, | ||
27, 28*, 29, 30*, 31 || | 27, 28*, 29, 30*, 31 || | ||
||~ halves ||~ ||~ ||~ ||~ ||~ ||~ || | ||~ halves ||~ ||~ ||~ ||~ ||~ ||~ || | ||
||= {P8/2, P5} | ||= {P8/2, P5} ||= P8/2 = vA4 = ^d5 ||= ^^d2 ||= C^^ = B# ||= C - F#v=Gb^ - C ||= srutal, ^1 = 81/80 ||= 12, 20*, 22, 24*, 30* || | ||
||= " | ||= " ||= P8/2 = ^A4 = vd5 | ||
(if 5th < 700¢) ||= vvd2 ||= C^^ = Db ||= C - F#^=Gbv - C ||= large deep red, | |||
^1 = 64/63 ||= 12, 14, 16, 18b, | ^1 = 64/63 ||= 12, 14, 16, 18b, | ||
24*, 26, 28* || | 24*, 26, 28* || | ||
||= " | ||= " ||= P8/2 = ^P4 = vP5 ||= vvM2 ||= C^^ = D ||= C - F^=Gv - C ||= (is this needed?) ||= || | ||
||= {P8, P4/2} | ||= {P8, P4/2} ||= P4/2 = ^M2 = vm3 ||= vvm2 ||= C^^ = Db ||= C - D^=Ebv - F ||= semaphore ||= || | ||
||= " | ||= " ||= P4/2 = vA2 = ^d3 ||= ^^dd2 ||= C^^ = B## ||= C - D#v=Ebb^ - F ||= ||= || | ||
||= " | ||= " ||= P4/2 = ^A2 = vd3 ||= vvdd2 ||= C^^ = Db<span style="vertical-align: super;">3</span> ||= C - D#^=Ebv - F ||= ||= || | ||
||= {P8, P5/2} | ||= {P8, P5/2} ||= P5/2 = ^m3 = vM3 ||= vvA1 ||= C^^ = C# ||= C - Eb^=Ev - G ||= mohajira, | ||
^1 = j1 = 33/32 ||= 14*, 17, 20*, 21*, 24 | ^1 = j1 = 33/32 ||= 14*, 17, 18b, 20*, 21*, | ||
27, 28*, 30*, 31 | 24, 27, 28*, 30*, 31 || | ||
||= {P8/2, P4/2} ||= P4/2 = /M2 = \m3, | |||
||= {P8/2, P4/2} | |||
P5/2 = ^m3 = vM3, | P5/2 = ^m3 = vM3, | ||
P8/2 = v/A4 = ^\d5 | P8/2 = v/A4 = ^\d5 | ||
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vvA1, | vvA1, | ||
^^\\d2, | ^^\\d2, | ||
vv\\M2 ||= C - D/=Eb\ - F, | vv\\M2 ||= C// = Db, | ||
C^^ = C#, | |||
C^^// = D ||= C - D/=Eb\ - F, | |||
C - Eb^=Ev - G, | C - Eb^=Ev - G, | ||
C - F#v/=Gb^\ - C, | C - F#v/=Gb^\ - C, | ||
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/1 = r1 = 64/63 ||= 14, 18b, 20*, | /1 = r1 = 64/63 ||= 14, 18b, 20*, | ||
24, 28*, 30* || | 24, 28*, 30* || | ||
||= " | ||= " ||= P8/2 = vA4 = ^d5, | ||
P4/2 = /M2 = \m3, | P4/2 = /M2 = \m3, | ||
P5/2 = ^/m3 = v\M3 ||= ^^d2, | P5/2 = ^/m3 = v\M3 ||= ^^d2, | ||
\\m2, | \\m2, | ||
vv\\A1 ||= C - F#v=Gb^ - C, | vv\\A1 ||= C^^ = B#, | ||
C// = Db, | |||
C^^// = C# ||= C - F#v=Gb^ - C, | |||
C - D/=Eb\ - F, | C - D/=Eb\ - F, | ||
C - Eb^/=Ev\ - G ||= sgg&bbT, | C - Eb^/=Ev\ - G ||= sgg&bbT, | ||
^1 = g1 = 81/80, | ^1 = g1 = 81/80, | ||
/1 = r1 = 64/63 ||= " || | /1 = r1 = 64/63 ||= " || | ||
||= " | ||= " ||= P8/2 = vA4 = ^d5, | ||
P5/2 = /m3 = \M3, | P5/2 = /m3 = \M3, | ||
P4/2 =v/M2 = ^\m3 ||= ^^d2, | P4/2 =v/M2 = ^\m3 ||= ^^d2, | ||
\\A1, | \\A1, | ||
^^\\m2 ||= C - F#v=Gb^ - C, | ^^\\m2 ||= C^^ = B#, | ||
C// = C# | |||
C^^// = B## ||= C - F#v=Gb^ - C, | |||
C - Eb/=E\ - G, | C - Eb/=E\ - G, | ||
C - Dv/=Eb^\ - F ||= sgg&aaT, | C - Dv/=Eb^\ - F ||= sgg&aaT, | ||
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/1 = j1 = 33/32 ||= " || | /1 = j1 = 33/32 ||= " || | ||
||~ thirds ||~ ||~ ||~ ||~ ||~ ||~ || | ||~ thirds ||~ ||~ ||~ ||~ ||~ ||~ || | ||
||= {P8/3, P5} | ||= {P8/3, P5} ||= P8/3 = vM3 = ^^d4 | ||
(^/v may reverse) ||= ^<span style="vertical-align: super;">3</span>d2 ||= <span style="font-family: Arial,Helvetica,sans-serif;">C - Ev - Ab^ - C</span> ||= ||= 12, 15, 18b*, 21, 24*, | (^/v may reverse) ||= ^<span style="vertical-align: super;">3</span>d2 ||= C^<span style="vertical-align: super;">3</span> = B# ||= <span style="font-family: Arial,Helvetica,sans-serif;">C - Ev - Ab^ - C</span> ||= ||= 12, 15, 18b*, 21, 24*, | ||
27, 30* || | 27, 30* || | ||
||= {P8, P4/3} | ||= {P8, P4/3} ||= P4/3 = ^^m2 = vM2 ||= v<span style="vertical-align: super;">3</span>A1 ||= C^<span style="vertical-align: super;">3</span> = C# ||= C - Dv - Eb^ - F ||= ||= 13b, 14*, 15, 21*, | ||
22, 28*, 29, 30* || | 22, 28*, 29, 30* || | ||
||= {P8, P5/3} | ||= {P8, P5/3} ||= P5/3 = ^M2 = vvm3 ||= v<span style="vertical-align: super;">3</span>m2 ||= C^<span style="vertical-align: super;">3</span> = Db ||= C - D^ - Fv - G ||= ||= 15*, 16, 20*, 21, | ||
25*, 26, 30*, 31 || | 25*, 26, 30*, 31 || | ||
||= {P8, P11/3} | ||= {P8, P11/3} ||= P11/3 = vA4 = ^^dd5 ||= ^<span style="vertical-align: super;">3</span>dd2 ||= C^<span style="vertical-align: super;">3</span> = B## ||= C - F#v - Cb^ - F ||= ||= same as {P8, P4/3} || | ||
||= " | ||= " ||= P11/3 = ^P4 = vvP5 ||= v<span style="vertical-align: super;">3</span>M2 ||= C^<span style="vertical-align: super;">3</span> = D ||= C F^ Cv F ||= ||= " || | ||
||= {P8/3, P4/2} ||= ||= ||= ||= ||= ||= 15, 18b*, 24, 30 || | ||= {P8/3, P4/2} ||= ||= ||= ||= ||= ||= 15, 18b*, 24, 30 || | ||
||= {P8/3, P5/2} ||= ||= ||= ||= ||= ||= 18b, 24, 30 || | ||= {P8/3, P5/2} ||= ||= ||= ||= ||= ||= 18b, 24, 30 || | ||
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||= {P8/3, P4/3} ||= ||= ||= ||= ||= ||= 15, 21, 30* || | ||= {P8/3, P4/3} ||= ||= ||= ||= ||= ||= 15, 21, 30* || | ||
||~ quarters ||~ ||~ ||~ ||~ ||~ ||~ || | ||~ quarters ||~ ||~ ||~ ||~ ||~ ||~ || | ||
||= {P8/4, P5} | ||= {P8/4, P5} ||= P8/4 = vm3 = ^<span style="vertical-align: super;">3</span>A2 | ||
(^/v may reverse) ||= v<span style="vertical-align: super;">4</span>d2 ||= C Ebv Gbvv A^ C ||= diminished, | (^/v may reverse) ||= v<span style="vertical-align: super;">4</span>d2 ||= C^<span style="vertical-align: super;">4</span> = Dbb ||= C Ebv Gbvv A^ C ||= diminished, | ||
^1 = 81/80 ||= 12, 16, 20, 24*, 28 || | ^1 = 81/80 ||= 12, 16, 20, 24*, 28 || | ||
||= {P8, P4/4} | ||= {P8, P4/4} ||= P4/4 = ^m2 = v<span style="vertical-align: super;">3</span>AA1 ||= ^<span style="vertical-align: super;">4</span>dd2 ||= C^<span style="vertical-align: super;">4</span> = B## ||= C Db^ Ebb^^ Ev F ||= ||= || | ||
||= {P8, P5/4} | ||= {P8, P5/4} ||= P5/4 = vM2 = ^<span style="vertical-align: super;">3</span>m2 ||= v<span style="vertical-align: super;">4</span>A1 ||= C^<span style="vertical-align: super;">4</span> = C# ||= C Dv Evv F^ G^ ||= ||= || | ||
||= {P8, P11/4} ||= | ||= {P8, P11/4} ||= P11/4 = ^M3 = v<span style="vertical-align: super;">3</span>dd5 ||= v<span style="vertical-align: super;">4</span>dd3 ||= C^<span style="vertical-align: super;">4</span> = Eb<span style="vertical-align: super;">3</span> ||= C E^ G#^^ Dbv F ||= ||= || | ||
||= {P8, P12/4} ||= | ||= {P8, P12/4} ||= P12/4 = vP4 = ^<span style="vertical-align: super;">3</span>M3 ||= v<span style="vertical-align: super;">4</span>m2 ||= C^<span style="vertical-align: super;">4</span> = Db ||= C Fv Bbvv D^ G ||= ||= || | ||
||= {P8/4, P4/2} ||= ||= ||= ||= ||= ||= || | ||= {P8/4, P4/2} ||= ||= ||= ||= ||= ||= || | ||
||= {P8/2, P4/4} ||= ||= ||= ||= ||= ||= || | ||= {P8/2, P4/4} ||= ||= ||= ||= ||= ||= || | ||
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(to be continued)</pre></div> | (to be continued)</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"><html><head><title>pergen names</title></head><body><!-- ws:start:WikiTextTocRule: | <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"><html><head><title>pergen names</title></head><body><!-- ws:start:WikiTextTocRule:28:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><a href="#Definition">Definition</a><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --> | <a href="#Derivation">Derivation</a><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --> | <a href="#Applications">Applications</a><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --> | <a href="#x^/P4"> ^/P4 </a><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --> | <a href="#B# ||"> B# ||</a><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --> | <a href="#C# ||"> C# ||</a><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --> | <a href="#Db ||"> Db ||</a><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --> | <a href="#B## ||"> B## ||</a><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --> | <a href="#D ||"> D ||</a><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --> | <a href="#Dbb ||"> Dbb ||</a><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --> | <a href="#B## ||"> B## ||</a><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --> | <a href="#C# ||"> C# ||</a><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --> | <a href="#Eb3 ||"> Eb3 ||</a><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --> | <a href="#Db ||"> Db ||</a><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Definition"></a><!-- ws:end:WikiTextHeadingRule:0 --><u><strong>Definition</strong></u></h1> | ||
<br /> | <br /> | ||
A <strong>pergen</strong> set (pronounced &quot;peer-gen&quot;) is a way of identifying a rank-2 or rank-3 regular temperament solely by its period and generator(s). For any temperament, there are many possible periods and generators. The pergen set is chosen to use the fewest, and smallest, prime factors possible. Fractions are allowed, e.g. half-octave, but avoided if possible.<br /> | A <strong>pergen</strong> set (pronounced &quot;peer-gen&quot;) is a way of identifying a rank-2 or rank-3 regular temperament solely by its period and generator(s). For any temperament, there are many possible periods and generators. The pergen set is chosen to use the fewest, and smallest, prime factors possible. Fractions are allowed, e.g. half-octave, but avoided if possible.<br /> | ||
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<br /> | <br /> | ||
Not all possible combinations of periods and generators are unique pergens. {P8/2, P5/2} is actually {P8/2, P4/2}. There is no {P8, M2/2}, and {P8/2, M2/2} is actually {P8/2, P5}. The following table lists all the rank-2 pergens that contain primes 2 and 3, grouped by the size of the larger splitting factor.<br /> | Not all possible combinations of periods and generators are unique pergens. {P8/2, P5/2} is actually {P8/2, P4/2}. There is no {P8, M2/2}, and {P8/2, M2/2} is actually {P8/2, P5}. The following table lists all the rank-2 pergens that contain primes 2 and 3, grouped by the size of the larger splitting factor.<br /> | ||
<br /> | |||
The enharmonic interval can be added to or subtracted from any note or interval, and it will be renamed, but unchanged. It's analogous to the dim 2nd in 12-edo, which equates A1 with m2, A4 with d5, etc.<br /> | |||
<br /> | <br /> | ||
The genchain shown is a short section of the full genchain. C - G implies ...Eb Bb F C G D A E B F# C#... And C - Eb^=Ev - G implies ...F - Ab^=Av - C - Eb^=Ev - G - Bb^=Bv - D - F^=F#v - A - C^=C#v - E... If the octave is split, the genchain shows the octave: In C - F#v=Gb^ - C, the last C is an octave above the first one.<br /> | The genchain shown is a short section of the full genchain. C - G implies ...Eb Bb F C G D A E B F# C#... And C - Eb^=Ev - G implies ...F - Ab^=Av - C - Eb^=Ev - G - Bb^=Bv - D - F^=F#v - A - C^=C#v - E... If the octave is split, the genchain shows the octave: In C - F#v=Gb^ - C, the last C is an octave above the first one.<br /> | ||
| Line 732: | Line 742: | ||
<tr> | <tr> | ||
<th>pergen set<br /> | <th>pergen set<br /> | ||
</th> | </th> | ||
<th>split interval(s)<br /> | <th>split interval(s)<br /> | ||
| Line 740: | Line 747: | ||
<th>enharmonic<br /> | <th>enharmonic<br /> | ||
interval(s)<br /> | interval(s)<br /> | ||
</th> | |||
<th>equiva-<br /> | |||
lence(s)<br /> | |||
</th> | </th> | ||
<th>genchain(s)<br /> | <th>genchain(s)<br /> | ||
| Line 746: | Line 756: | ||
temperament<br /> | temperament<br /> | ||
</th> | </th> | ||
<th>compatible edos <br /> | <th>compatible edos<br /> | ||
(12-31 only)<br /> | (12-31 only)<br /> | ||
</th> | </th> | ||
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<td style="text-align: center;">{P8, P5}<br /> | <td style="text-align: center;">{P8, P5}<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">none<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">P1<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">none<br /> | <td style="text-align: center;">none<br /> | ||
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<tr> | <tr> | ||
<td style="text-align: center;">{P8/2, P5}<br /> | <td style="text-align: center;">{P8/2, P5}<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">P8/2 = vA4 = ^d5<br /> | <td style="text-align: center;">P8/2 = vA4 = ^d5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">^^d2<br /> | <td style="text-align: center;">^^d2<br /> | ||
</td> | |||
<td style="text-align: center;">C^^ = B#<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">C - F#v=Gb^ - C<br /> | <td style="text-align: center;">C - F#v=Gb^ - C<br /> | ||
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<tr> | <tr> | ||
<td style="text-align: center;">&quot;<br /> | <td style="text-align: center;">&quot;<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">P8/2 = ^A4 = vd5<br /> | <td style="text-align: center;">P8/2 = ^A4 = vd5<br /> | ||
(if 5th &lt; 700¢)<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">vvd2<br /> | <td style="text-align: center;">vvd2<br /> | ||
</td> | |||
<td style="text-align: center;">C^^ = Db<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">C - F#^=Gbv - C<br /> | <td style="text-align: center;">C - F#^=Gbv - C<br /> | ||
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<tr> | <tr> | ||
<td style="text-align: center;">&quot;<br /> | <td style="text-align: center;">&quot;<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">P8/2 = ^P4 = vP5<br /> | <td style="text-align: center;">P8/2 = ^P4 = vP5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">vvM2<br /> | <td style="text-align: center;">vvM2<br /> | ||
</td> | |||
<td style="text-align: center;">C^^ = D<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">C - F^=Gv - C<br /> | <td style="text-align: center;">C - F^=Gv - C<br /> | ||
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<tr> | <tr> | ||
<td style="text-align: center;">{P8, P4/2}<br /> | <td style="text-align: center;">{P8, P4/2}<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">P4/2 = ^M2 = vm3<br /> | <td style="text-align: center;">P4/2 = ^M2 = vm3<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">vvm2<br /> | <td style="text-align: center;">vvm2<br /> | ||
</td> | |||
<td style="text-align: center;">C^^ = Db<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">C - D^=Ebv - F<br /> | <td style="text-align: center;">C - D^=Ebv - F<br /> | ||
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<tr> | <tr> | ||
<td style="text-align: center;">&quot;<br /> | <td style="text-align: center;">&quot;<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">P4/2 = vA2 = ^d3<br /> | <td style="text-align: center;">P4/2 = vA2 = ^d3<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">^^dd2<br /> | <td style="text-align: center;">^^dd2<br /> | ||
</td> | |||
<td style="text-align: center;">C^^ = B##<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">C - D#v=Ebb^ - F<br /> | <td style="text-align: center;">C - D#v=Ebb^ - F<br /> | ||
| Line 869: | Line 880: | ||
<tr> | <tr> | ||
<td style="text-align: center;">&quot;<br /> | <td style="text-align: center;">&quot;<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">P4/2 = ^A2 = vd3<br /> | <td style="text-align: center;">P4/2 = ^A2 = vd3<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">vvdd2<br /> | <td style="text-align: center;">vvdd2<br /> | ||
</td> | |||
<td style="text-align: center;">C^^ = Db<span style="vertical-align: super;">3</span><br /> | |||
</td> | </td> | ||
<td style="text-align: center;">C - D#^=Ebv - F<br /> | <td style="text-align: center;">C - D#^=Ebv - F<br /> | ||
| Line 885: | Line 896: | ||
<tr> | <tr> | ||
<td style="text-align: center;">{P8, P5/2}<br /> | <td style="text-align: center;">{P8, P5/2}<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">P5/2 = ^m3 = vM3<br /> | <td style="text-align: center;">P5/2 = ^m3 = vM3<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">vvA1<br /> | <td style="text-align: center;">vvA1<br /> | ||
</td> | |||
<td style="text-align: center;">C^^ = C#<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">C - Eb^=Ev - G<br /> | <td style="text-align: center;">C - Eb^=Ev - G<br /> | ||
| Line 897: | Line 908: | ||
^1 = j1 = 33/32<br /> | ^1 = j1 = 33/32<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">14*, 17, 20*, 21*, | <td style="text-align: center;">14*, 17, 18b, 20*, 21*,<br /> | ||
27, 28*, 30*, 31 | 24, 27, 28*, 30*, 31<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;">{P8/2, P4/2}<br /> | <td style="text-align: center;">{P8/2, P4/2}<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">P4/2 = /M2 = \m3,<br /> | <td style="text-align: center;">P4/2 = /M2 = \m3,<br /> | ||
| Line 931: | Line 924: | ||
^^\\d2,<br /> | ^^\\d2,<br /> | ||
vv\\M2<br /> | vv\\M2<br /> | ||
</td> | |||
<td style="text-align: center;">C<em> = Db,<br /> | |||
C^^ = C#,<br /> | |||
C^^</em> = D<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">C - D/=Eb\ - F,<br /> | <td style="text-align: center;">C - D/=Eb\ - F,<br /> | ||
| Line 947: | Line 944: | ||
<tr> | <tr> | ||
<td style="text-align: center;">&quot;<br /> | <td style="text-align: center;">&quot;<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">P8/2 = vA4 = ^d5,<br /> | <td style="text-align: center;">P8/2 = vA4 = ^d5,<br /> | ||
| Line 957: | Line 952: | ||
\\m2,<br /> | \\m2,<br /> | ||
vv\\A1<br /> | vv\\A1<br /> | ||
</td> | |||
<td style="text-align: center;">C^^ = B#,<br /> | |||
C<em> = Db,<br /> | |||
C^^</em> = C#<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">C - F#v=Gb^ - C,<br /> | <td style="text-align: center;">C - F#v=Gb^ - C,<br /> | ||
| Line 971: | Line 970: | ||
<tr> | <tr> | ||
<td style="text-align: center;">&quot;<br /> | <td style="text-align: center;">&quot;<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">P8/2 = vA4 = ^d5,<br /> | <td style="text-align: center;">P8/2 = vA4 = ^d5,<br /> | ||
| Line 981: | Line 978: | ||
\\A1,<br /> | \\A1,<br /> | ||
^^\\m2<br /> | ^^\\m2<br /> | ||
</td> | |||
<td style="text-align: center;">C^^ = B#,<br /> | |||
C<em> = C#<br /> | |||
C^^</em> = B##<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">C - F#v=Gb^ - C,<br /> | <td style="text-align: center;">C - F#v=Gb^ - C,<br /> | ||
| Line 1,011: | Line 1,012: | ||
<tr> | <tr> | ||
<td style="text-align: center;">{P8/3, P5}<br /> | <td style="text-align: center;">{P8/3, P5}<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">P8/3 = vM3 = ^^d4<br /> | <td style="text-align: center;">P8/3 = vM3 = ^^d4<br /> | ||
| Line 1,019: | Line 1,018: | ||
<td style="text-align: center;">^<span style="vertical-align: super;">3</span>d2<br /> | <td style="text-align: center;">^<span style="vertical-align: super;">3</span>d2<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><span style=" | <td style="text-align: center;">C^<span style="vertical-align: super;">3</span> <!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="B# ||"></a><!-- ws:end:WikiTextHeadingRule:8 --> B#<br /> | ||
</td> | </td> | ||
<td></h1> | |||
<span style="font-family: Arial,Helvetica,sans-serif;">C - Ev - Ab^ - C</span></td> | |||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">12, 15, 18b*, 21, 24*, <br /> | <td style="text-align: center;">12, 15, 18b*, 21, 24*,<br /> | ||
27, 30*<br /> | 27, 30*<br /> | ||
</td> | </td> | ||
| Line 1,029: | Line 1,030: | ||
<tr> | <tr> | ||
<td style="text-align: center;">{P8, P4/3}<br /> | <td style="text-align: center;">{P8, P4/3}<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">P4/3 = ^^m2 = vM2<br /> | <td style="text-align: center;">P4/3 = ^^m2 = vM2<br /> | ||
| Line 1,036: | Line 1,035: | ||
<td style="text-align: center;">v<span style="vertical-align: super;">3</span>A1<br /> | <td style="text-align: center;">v<span style="vertical-align: super;">3</span>A1<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">C - | <td style="text-align: center;">C^<span style="vertical-align: super;">3</span> <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="C# ||"></a><!-- ws:end:WikiTextHeadingRule:10 --> C#<br /> | ||
</td> | </td> | ||
<td></h1> | |||
C - Dv - Eb^ - F</td> | |||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
| Line 1,046: | Line 1,047: | ||
<tr> | <tr> | ||
<td style="text-align: center;">{P8, P5/3}<br /> | <td style="text-align: center;">{P8, P5/3}<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">P5/3 = ^M2 = vvm3<br /> | <td style="text-align: center;">P5/3 = ^M2 = vvm3<br /> | ||
| Line 1,053: | Line 1,052: | ||
<td style="text-align: center;">v<span style="vertical-align: super;">3</span>m2<br /> | <td style="text-align: center;">v<span style="vertical-align: super;">3</span>m2<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">C - | <td style="text-align: center;">C^<span style="vertical-align: super;">3</span> <!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Db ||"></a><!-- ws:end:WikiTextHeadingRule:12 --> Db<br /> | ||
</td> | </td> | ||
<td></h1> | |||
C - D^ - Fv - G</td> | |||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
| Line 1,063: | Line 1,064: | ||
<tr> | <tr> | ||
<td style="text-align: center;">{P8, P11/3}<br /> | <td style="text-align: center;">{P8, P11/3}<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">P11/3 = vA4 = ^^dd5<br /> | <td style="text-align: center;">P11/3 = vA4 = ^^dd5<br /> | ||
| Line 1,070: | Line 1,069: | ||
<td style="text-align: center;">^<span style="vertical-align: super;">3</span>dd2<br /> | <td style="text-align: center;">^<span style="vertical-align: super;">3</span>dd2<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">C - | <td style="text-align: center;">C^<span style="vertical-align: super;">3</span> <!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="B## ||"></a><!-- ws:end:WikiTextHeadingRule:14 --> B##<br /> | ||
</td> | </td> | ||
<td></h1> | |||
C - F#v - Cb^ - F</td> | |||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
| Line 1,079: | Line 1,080: | ||
<tr> | <tr> | ||
<td style="text-align: center;">&quot;<br /> | <td style="text-align: center;">&quot;<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">P11/3 = ^P4 = vvP5<br /> | <td style="text-align: center;">P11/3 = ^P4 = vvP5<br /> | ||
| Line 1,086: | Line 1,085: | ||
<td style="text-align: center;">v<span style="vertical-align: super;">3</span>M2<br /> | <td style="text-align: center;">v<span style="vertical-align: super;">3</span>M2<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">C | <td style="text-align: center;">C^<span style="vertical-align: super;">3</span> <!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="D ||"></a><!-- ws:end:WikiTextHeadingRule:16 --> D<br /> | ||
</td> | </td> | ||
<td></h1> | |||
C F^ Cv F</td> | |||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">&quot;<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,207: | Line 1,208: | ||
<tr> | <tr> | ||
<td style="text-align: center;">{P8/4, P5}<br /> | <td style="text-align: center;">{P8/4, P5}<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">P8/4 = vm3 = ^<span style="vertical-align: super;">3</span>A2<br /> | <td style="text-align: center;">P8/4 = vm3 = ^<span style="vertical-align: super;">3</span>A2<br /> | ||
| Line 1,215: | Line 1,214: | ||
<td style="text-align: center;">v<span style="vertical-align: super;">4</span>d2<br /> | <td style="text-align: center;">v<span style="vertical-align: super;">4</span>d2<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">C | <td style="text-align: center;">C^<span style="vertical-align: super;">4</span> <!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="Dbb ||"></a><!-- ws:end:WikiTextHeadingRule:18 --> Dbb<br /> | ||
</td> | </td> | ||
<td></h1> | |||
C Ebv Gbvv A^ C</td> | |||
<td style="text-align: center;">diminished,<br /> | <td style="text-align: center;">diminished,<br /> | ||
^1 = 81/80<br /> | ^1 = 81/80<br /> | ||
| Line 1,225: | Line 1,226: | ||
<tr> | <tr> | ||
<td style="text-align: center;">{P8, P4/4}<br /> | <td style="text-align: center;">{P8, P4/4}<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">P4/4 = ^m2 = v<span style="vertical-align: super;">3</span>AA1<br /> | <td style="text-align: center;">P4/4 = ^m2 = v<span style="vertical-align: super;">3</span>AA1<br /> | ||
| Line 1,232: | Line 1,231: | ||
<td style="text-align: center;">^<span style="vertical-align: super;">4</span>dd2<br /> | <td style="text-align: center;">^<span style="vertical-align: super;">4</span>dd2<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">C | <td style="text-align: center;">C^<span style="vertical-align: super;">4</span> <!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="B## ||"></a><!-- ws:end:WikiTextHeadingRule:20 --> B##<br /> | ||
</td> | </td> | ||
<td></h1> | |||
C Db^ Ebb^^ Ev F</td> | |||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
| Line 1,241: | Line 1,242: | ||
<tr> | <tr> | ||
<td style="text-align: center;">{P8, P5/4}<br /> | <td style="text-align: center;">{P8, P5/4}<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">P5/4 = vM2 = ^<span style="vertical-align: super;">3</span>m2<br /> | <td style="text-align: center;">P5/4 = vM2 = ^<span style="vertical-align: super;">3</span>m2<br /> | ||
| Line 1,248: | Line 1,247: | ||
<td style="text-align: center;">v<span style="vertical-align: super;">4</span>A1<br /> | <td style="text-align: center;">v<span style="vertical-align: super;">4</span>A1<br /> | ||
</td> | </td> | ||
<td>C | <td style="text-align: center;">C^<span style="vertical-align: super;">4</span> <!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="C# ||"></a><!-- ws:end:WikiTextHeadingRule:22 --> C#<br /> | ||
</td> | </td> | ||
<td></h1> | |||
C Dv Evv F^ G^</td> | |||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
| Line 1,258: | Line 1,259: | ||
<td style="text-align: center;">{P8, P11/4}<br /> | <td style="text-align: center;">{P8, P11/4}<br /> | ||
</td> | </td> | ||
<td style="text-align: center;" | <td style="text-align: center;">P11/4 = ^M3 = v<span style="vertical-align: super;">3</span>dd5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">v<span style="vertical-align: super;">4</span>dd3<br /> | <td style="text-align: center;">v<span style="vertical-align: super;">4</span>dd3<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">C | <td style="text-align: center;">C^<span style="vertical-align: super;">4</span> <!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc12"><a name="Eb3 ||"></a><!-- ws:end:WikiTextHeadingRule:24 --> Eb<span style="vertical-align: super;">3</span><br /> | ||
</td> | </td> | ||
<td></h1> | |||
C E^ G#^^ Dbv F</td> | |||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
| Line 1,274: | Line 1,275: | ||
<td style="text-align: center;">{P8, P12/4}<br /> | <td style="text-align: center;">{P8, P12/4}<br /> | ||
</td> | </td> | ||
<td style="text-align: center;" | <td style="text-align: center;">P12/4 = vP4 = ^<span style="vertical-align: super;">3</span>M3<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">v<span style="vertical-align: super;">4</span>m2<br /> | <td style="text-align: center;">v<span style="vertical-align: super;">4</span>m2<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">C | <td style="text-align: center;">C^<span style="vertical-align: super;">4</span> <!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc13"><a name="Db ||"></a><!-- ws:end:WikiTextHeadingRule:26 --> Db<br /> | ||
</td> | </td> | ||
<td></h1> | |||
C Fv Bbvv D^ G</td> | |||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||