Pergen names: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-11-20 04:57:28 UTC</tt>.

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-11-20 09:53:37 UTC</tt>.

: The original revision id was <tt>~~621999693~~</tt>.

: The original revision id was <tt>622022613</tt>.

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

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

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Analogous to 22-edo, sometimes additional accidentals aren't needed, but are desirable, to avoid misspelled chords. For example, schismic is fifth-based and can be notated conventionally. But this causes 4:5:6 to be spelled as C Fb G. With ^1 = 81/80, the chord can be spelled C Ev G.

Not all possible combinations of periods and generators are unique pergens~~. {P8, WWP5/2} is actually {P8, P5/2}~~. {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}.

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}.

This table lists all unique rank-2 pergens, assuming primes 2 and 3, grouped by the size of the larger splitting factor.

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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.

An edo is incompatible with a pergen if the split is impossible. For example, all odd-numbered edos are incompatible with half-octave pergens. An edo is somewhat incompatible with a pergen if the period and generator can only generate a subset of the edo. For example, 15-edo is somewhat incompatible with {P8, P5}, because any chain-of-5ths scale ~~would translate to~~ a 5-edo subset. Such edos are marked with asterisks. 13b is incompatible with {P8, P5/2}, but 13 isn't. However, 13 is incompatible with heptatonic notation.

An edo is incompatible with a pergen if the split is impossible. For example, all odd-numbered edos are incompatible with half-octave pergens. An edo is somewhat incompatible with a pergen if the period and generator can only generate a subset of the edo. For example, 15-edo is somewhat incompatible with {P8, P5}, because any chain-of-5ths scale could only make a 5-edo subset. Such edos are marked with asterisks. 13b is incompatible with {P8, P5/2}, but 13 isn't. However, 13 is incompatible with heptatonic notation.

(table is under construction)

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/1 = j1 = 33/32 ||= " ||

||~ thirds ||~ ||~ ||~ ||~ ||~ ||~ ||

||= {P8/3, P5} ||= ||= ||= ||= ||= ||= 12, 15, 18b*, 21, 24*,

||= {P8/3, P5} ||= ||= P8/3 = vM3 = ^^d4

(^/v may reverse) ||= ^3d2 ||= C - Ev - Ab^ - C ||= ||= 12, 15, 18b*, 21, 24*,

27, 30* ||

||= {P8, P4/3} ||= ||= ||= ||= ||= ||= 13b, 14*, 15, 21*,

||= {P8, P4/3} ||= ||= P4/3 = ^^m2 = vM2 ||= v3A1 ||= C - Dv - Eb^ - F ||= ||= 13b, 14*, 15, 21*,

22, 28*, 29, 30* ||

||= {P8, P5/3} ||= ||= ||= ||= ||= ||= 15*, 16, 20*, 21,

||= {P8, P5/3} ||= ||= P5/3 = ^M2 = vvm3 ||= v3m2 ||= C - D^ - Fv - G ||= ||= 15*, 16, 20*, 21,

25*, 26, 30*, 31 ||

||= {P8, P11/3} ||= ||= ||= ||= ||= ||= same as {P8, P4/3} ||

||= {P8, P11/3} ||= ||= P11/3 = vA4 = ^^dd5 ||= ^3dd2 ||= C - F#v - Cb^ - F ||= ||= same as {P8, P4/3} ||

||= " ||= ||= P11/3 = ^P4 = vvP5 ||= v3M2 ||= C F^ Cv F ||= ||= ||

||= {P8/3, P4/2} ||= ||= ||= ||= ||= ||= 15, 18b*, 24, 30 ||

||= {P8/3, P5/2} ||= ||= ||= ||= ||= ||= 18b, 24, 30 ||

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||= {P8/3, P4/3} ||= ||= ||= ||= ||= ||= 15, 21, 30* ||

||~ quarters ||~ ||~ ||~ ||~ ||~ ||~ ||

||= {P8/4, P5} ||= ||= ||= ||= ||= ||= 12, 16, 20, 24*, 28 ||

||= {P8/4, P5} ||= ||= P8/4 = vm3 = ^3d2

||= {P8, P4/4} ||= ||= ||= ||= ||= ||= ||

(^/v may reverse) ||= v4d2 ||= C Ebv Gbbvv A^ C ||= ||= 12, 16, 20, 24*, 28 ||

||= {P8, P5/4} ||= ||= ||= ||= ||= ||= ||

||= {P8, P4/4} ||= ||= P4/4 = ^m2 = v3AA1 ||= ^4dd2 ||= C Db^ Ebb^^ Ev F ||= ||= ||

||= {P8, P5/4} ||= ||= P5/4 = vM2 = ^3m2 ||= v4A1 || C Dv Evv F^ G^ ||= ||= ||

||= {P8, P11/4} ||= ||= ||= ||= ||= ||= ||

||= {P8, P12/4} ||= ||= ||= ||= ||= ||= ||

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||= {P8/2, P5/4} ||= ||= ||= ||= ||= ||= ||

||= ||= ||= ||= ||= ||= ||= ||

||= etc. ||= ||= ||= ||= ||= ||= ||

||= ||= ||= ||= ||= ||= ||= ||

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Analogous to 22-edo, sometimes additional accidentals aren't needed, but are desirable, to avoid misspelled chords. For example, schismic is fifth-based and can be notated conventionally. But this causes 4:5:6 to be spelled as C Fb G. With ^1 = 81/80, the chord can be spelled C Ev G.

Not all possible combinations of periods and generators are unique pergens~~. {P8, WWP5/2} is actually {P8, P5/2}~~. {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}.

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}.

This table lists all unique rank-2 pergens, assuming primes 2 and 3, grouped by the size of the larger splitting factor.

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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.

An edo is incompatible with a pergen if the split is impossible. For example, all odd-numbered edos are incompatible with half-octave pergens. An edo is somewhat incompatible with a pergen if the period and generator can only generate a subset of the edo. For example, 15-edo is somewhat incompatible with {P8, P5}, because any chain-of-5ths scale ~~would translate to~~ a 5-edo subset. Such edos are marked with asterisks. 13b is incompatible with {P8, P5/2}, but 13 isn't. However, 13 is incompatible with heptatonic notation.

An edo is incompatible with a pergen if the split is impossible. For example, all odd-numbered edos are incompatible with half-octave pergens. An edo is somewhat incompatible with a pergen if the period and generator can only generate a subset of the edo. For example, 15-edo is somewhat incompatible with {P8, P5}, because any chain-of-5ths scale could only make a 5-edo subset. Such edos are marked with asterisks. 13b is incompatible with {P8, P5/2}, but 13 isn't. However, 13 is incompatible with heptatonic notation.

(table is under construction)

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</td>

<td style="text-align: center;">P8/3 = vM3 = ^^d4

(^/v may reverse)

</td>

<td style="text-align: center;">^3d2

</td>

<td style="text-align: center;">C - Ev - Ab^ - C

</td>

Line 1,031:

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</td>

<td style="text-align: center;">P4/3 = ^^m2 = vM2

</td>

<td style="text-align: center;">v3A1

</td>

<td style="text-align: center;">C - Dv - Eb^ - F

</td>

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</td>

<td style="text-align: center;">P5/3 = ^M2 = vvm3

</td>

<td style="text-align: center;">v3m2

</td>

<td style="text-align: center;">C - D^ - Fv - G

</td>

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</td>

</td>

<td style="text-align: center;">P11/3 = vA4 = ^^dd5

</td>

<td style="text-align: center;">^3dd2

</td>

<td style="text-align: center;">C - F#v - Cb^ - F

</td>

</td>

<td style="text-align: center;">same as {P8, P4/3}

</td>

</tr>

<tr>

<td style="text-align: center;">&quot;

</td>

</td>

<td style="text-align: center;">P11/3 = ^P4 = vvP5

</td>

<td style="text-align: center;">v3M2

</td>

<td style="text-align: center;">C F^ Cv F

</td>

</td>

~~</td>~~

~~<td style="text-align: center;">same as {P8, P4/3} ~~

</td>

</tr>

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</td>

<td style="text-align: center;">P8/4 = vm3 = ^3d2

(^/v may reverse)

</td>

<td style="text-align: center;">v4d2

</td>

<td style="text-align: center;">C Ebv Gbbvv A^ C

</td>

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</td>

<td style="text-align: center;">P4/4 = ^m2 = v3AA1

</td>

<td style="text-align: center;">^4dd2

</td>

<td style="text-align: center;">C Db^ Ebb^^ Ev F

</td>

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</td>

<td style="text-align: center;">P5/4 = vM2 = ^3m2

</td>

<td style="text-align: center;">v4A1

</td>

<td>C Dv Evv F^ G^

</td>

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</tr>

<tr>

<td style="text-align: center;">etc.

</td>

@@ 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>2017-11-20 04:57:28 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-11-20 09:53:37 UTC</tt>.<br>
-: The original revision id was <tt>621999693</tt>.<br>
+: The original revision id was <tt>622022613</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 105: / Line 105: @@
 Analogous to 22-edo, sometimes additional accidentals aren't needed, but are desirable, to avoid misspelled chords. For example, schismic is fifth-based and can be notated conventionally. But this causes 4:5:6 to be spelled as C Fb G. With ^1 = 81/80, the chord can be spelled C Ev G.
-Not all possible combinations of periods and generators are unique pergens. {P8, WWP5/2} is actually {P8, P5/2}. {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}.
+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}.
 This table lists all unique rank-2 pergens, assuming primes 2 and 3, grouped by the size of the larger splitting factor.
@@ Line 111: / Line 111: @@
 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.
-An edo is incompatible with a pergen if the split is impossible. For example, all odd-numbered edos are incompatible with half-octave pergens. An edo is somewhat incompatible with a pergen if the period and generator can only generate a subset of the edo. For example, 15-edo is somewhat incompatible with {P8, P5}, because any chain-of-5ths scale would translate to a 5-edo subset. Such edos are marked with asterisks. 13b is incompatible with {P8, P5/2}, but 13 isn't. However, 13 is incompatible with heptatonic notation.
+An edo is incompatible with a pergen if the split is impossible. For example, all odd-numbered edos are incompatible with half-octave pergens. An edo is somewhat incompatible with a pergen if the period and generator can only generate a subset of the edo. For example, 15-edo is somewhat incompatible with {P8, P5}, because any chain-of-5ths scale could only make a 5-edo subset. Such edos are marked with asterisks. 13b is incompatible with {P8, P5/2}, but 13 isn't. However, 13 is incompatible with heptatonic notation.
 (table is under construction)
@@ Line 169: / Line 169: @@
 /1 = j1 = 33/32 ||= " ||
 ||~ thirds ||~   ||~   ||~   ||~   ||~   ||~   ||
-||= {P8/3, P5} ||=   ||=   ||=   ||=   ||=   ||= 12, 15, 18b*, 21, 24*,
+||= {P8/3, P5} ||=   ||= P8/3 = vM3 = ^^d4
+(^/v may reverse) ||= ^&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;d2 ||= &lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;C - Ev - Ab^ - C&lt;/span&gt; ||=   ||= 12, 15, 18b*, 21, 24*,
 , 30* ||
-||= {P8, P4/3} ||=   ||=   ||=   ||=   ||=   ||= 13b, 14*, 15, 21*,
+||= {P8, P4/3} ||=   ||= P4/3 = ^^m2 = vM2 ||= v&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;A1 ||= C - Dv - Eb^ - F ||=   ||= 13b, 14*, 15, 21*,
 , 28*, 29, 30* ||
-||= {P8, P5/3} ||=   ||=   ||=   ||=   ||=   ||= 15*, 16, 20*, 21,
+||= {P8, P5/3} ||=   ||= P5/3 = ^M2 = vvm3 ||= v&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;m2 ||= C - D^ - Fv - G ||=   ||= 15*, 16, 20*, 21,
 *, 26, 30*, 31 ||
-||= {P8, P11/3} ||=   ||=   ||=   ||=   ||=   ||= same as {P8, P4/3} ||
+||= {P8, P11/3} ||=   ||= P11/3 = vA4 = ^^dd5 ||= ^&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;dd2 ||= C - F#v - Cb^ - F ||=   ||= same as {P8, P4/3} ||
+||= " ||=   ||= P11/3 = ^P4 = vvP5 ||= v&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;M2 ||= C F^ Cv F ||=   ||=   ||
 ||= {P8/3, P4/2} ||=   ||=   ||=   ||=   ||=   ||= 15, 18b*, 24, 30 ||
 ||= {P8/3, P5/2} ||=   ||=   ||=   ||=   ||=   ||= 18b, 24, 30 ||
@@ Line 183: / Line 185: @@
 ||= {P8/3, P4/3} ||=   ||=   ||=   ||=   ||=   ||= 15, 21, 30* ||
 ||~ quarters ||~   ||~   ||~   ||~   ||~   ||~   ||
-||= {P8/4, P5} ||=   ||=   ||=   ||=   ||=   ||= 12, 16, 20, 24*, 28 ||
+||= {P8/4, P5} ||=   ||= P8/4 = vm3 = ^&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;d2
-||= {P8, P4/4} ||=   ||=   ||=   ||=   ||=   ||=   ||
+(^/v may reverse) ||= v&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;d2 ||= C Ebv Gbbvv A^ C ||=   ||= 12, 16, 20, 24*, 28 ||
-||= {P8, P5/4} ||=   ||=   ||=   ||=   ||=   ||=   ||
+||= {P8, P4/4} ||=   ||= P4/4 = ^m2 = v&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;AA1 ||= ^&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;dd2 ||= C Db^ Ebb^^ Ev F ||=   ||=   ||
+||= {P8, P5/4} ||=   ||= P5/4 = vM2 = ^&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;m2 ||= v&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;A1 || C Dv Evv F^ G^ ||=   ||=   ||
 ||= {P8, P11/4} ||=   ||=   ||=   ||=   ||=   ||=   ||
 ||= {P8, P12/4} ||=   ||=   ||=   ||=   ||=   ||=   ||
@@ Line 192: / Line 195: @@
 ||= {P8/2, P5/4} ||=   ||=   ||=   ||=   ||=   ||=   ||
 ||=   ||=   ||=   ||=   ||=   ||=   ||=   ||
-||=   ||=   ||=   ||=   ||=   ||=   ||=   ||
+||= etc. ||=   ||=   ||=   ||=   ||=   ||=   ||
 ||=   ||=   ||=   ||=   ||=   ||=   ||=   ||
 ||=   ||=   ||=   ||=   ||=   ||=   ||=   ||
@@ Line 717: / Line 720: @@
 Analogous to 22-edo, sometimes additional accidentals aren't needed, but are desirable, to avoid misspelled chords. For example, schismic is fifth-based and can be notated conventionally. But this causes 4:5:6 to be spelled as C Fb G. With ^1 = 81/80, the chord can be spelled C Ev G.&lt;br /&gt;
 &lt;br /&gt;
-Not all possible combinations of periods and generators are unique pergens. {P8, WWP5/2} is actually {P8, P5/2}. {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}. &lt;br /&gt;
+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}. &lt;br /&gt;
 &lt;br /&gt;
 This table lists all unique rank-2 pergens, assuming primes 2 and 3, grouped by the size of the larger splitting factor.&lt;br /&gt;
@@ Line 723: / Line 726: @@
 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.&lt;br /&gt;
 &lt;br /&gt;
-An edo is incompatible with a pergen if the split is impossible. For example, all odd-numbered edos are incompatible with half-octave pergens. An edo is somewhat incompatible with a pergen if the period and generator can only generate a subset of the edo. For example, 15-edo is somewhat incompatible with {P8, P5}, because any chain-of-5ths scale would translate to a 5-edo subset. Such edos are marked with asterisks. 13b is incompatible with {P8, P5/2}, but 13 isn't. However, 13 is incompatible with heptatonic notation.&lt;br /&gt;
+An edo is incompatible with a pergen if the split is impossible. For example, all odd-numbered edos are incompatible with half-octave pergens. An edo is somewhat incompatible with a pergen if the period and generator can only generate a subset of the edo. For example, 15-edo is somewhat incompatible with {P8, P5}, because any chain-of-5ths scale could only make a 5-edo subset. Such edos are marked with asterisks. 13b is incompatible with {P8, P5/2}, but 13 isn't. However, 13 is incompatible with heptatonic notation.&lt;br /&gt;
 &lt;br /&gt;
 (table is under construction)&lt;br /&gt;
@@ Line 1,014: / Line 1,017: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;P8/3 = vM3 = ^^d4&lt;br /&gt;
+(^/v may reverse)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;d2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;span style="font-family: Arial,Helvetica,sans-serif;"&gt;C - Ev - Ab^ - C&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 1,031: / Line 1,035: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;P4/3 = ^^m2 = vM2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;v&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;A1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;C - Dv - Eb^ - F&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 1,048: / Line 1,052: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;P5/3 = ^M2 = vvm3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;v&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;m2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;C - D^ - Fv - G&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 1,064: / Line 1,068: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;P11/3 = vA4 = ^^dd5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;^&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;dd2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;C - F#v - Cb^ - F&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;same as {P8, P4/3}&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;P11/3 = ^P4 = vvP5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;v&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;M2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;C F^ Cv F&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;same as {P8, P4/3}&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 1,193: / Line 1,213: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;P8/4 = vm3 = ^&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;d2&lt;br /&gt;
+(^/v may reverse)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;v&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;d2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;C Ebv Gbbvv A^ C&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 1,209: / Line 1,230: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;P4/4 = ^m2 = v&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;AA1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;dd2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;C Db^ Ebb^^ Ev F&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 1,225: / Line 1,246: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;P5/4 = vM2 = ^&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;m2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;v&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;A1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td&gt;C Dv Evv F^ G^&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 1,333: / Line 1,354: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;etc.&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;