21edo: 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>2016-12-~~07 21~~:23:55 UTC</tt>.

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-22 04:46:43 UTC</tt>.

: The original revision id was <tt>~~601671926~~</tt>.

: The original revision id was <tt>602739102</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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The patent val for 21edo tempers out 128/125 and 2187/2000 in the 5-limit, and supplies the optimal patent val for the 5-limit [[Laconic Family|laconic]] temperament tempering out 2187/2000, and also the optimal patent val for 7-limit, 11-limit and 13-limit laconic, spartan and gorgo temperaments. These temperaments lead to some "interesting" mappings, where 10/9 is larger than 9/8, 11/9 is larger than 16/13, and 8/7 maps to the same interval as 10/9, for instance.

|| **Degree** || **Cents ~~coarse/fine, DMS Value~~** ||||= [[Ups and Downs Notation|Up/down]]

||= **Degree** ||= **Cents** ||||= [[Ups and Downs Notation|Up/down]]

[[Ups and Downs Notation|Notation]] || **5L3s**

[[Ups and Downs Notation|Notation]] ||< ||= **5L3s**

**Octotonic**

**Notation** ||= **D.-R. Interval**

**Types** ||= **Approximate**

**Ratios *1** ||= **Approximate****Ratios *2** ~~||=~~ **~~Approximate~~****Ratios *3** ||

**Ratios *1** ||= **Approximate****Ratios *2** ||= **Approximate****Ratios *3** ||

~~|| 0 || 0~~ ||= ~~C ||= unison || C ||= Unison~~ ||~~= 1/1~~ ||= ~~1/1~~ ||= ~~1/1~~ ||

||= 0 ||= 0 ||> 1 ||= _____unison_____ ||< C ||= C ||= Unison ||= 1/1 ||= 1/1 ||= 1/1 ||

|| 1 || ~~57.143, 68.571~~

||= 1 ||= 57.14 ||> ^1

~~17°~~<~~span style="background-color: #ffffff;">8'34"~~ ||= C~~^/Dvv~~ ||= ~~up unison,~~

vv2 ||= up unison,

~~double-down~~

double-down 2nd ||< C^

~~2nd~~ |~~| C#~~ ||= ~~Subminor 2nd~~ ||= 28/~~27, 30/29~~ ||= ~~35/34, 36/35~~ ||= ~~64/63~~ ||

Dvv ||= C# ||= Subminor 2nd ||= 28/27, 30/29 ||= 35/34, 36/35 ||= 64/63 ||

|| ~~2 || 114.286~~, ~~137.143~~

||= 2 ||= 114.29 ||> ^^1

~~34°~~<~~span style~~=~~"background-color:~~ #~~ffffff;">17'9"~~ ||= ~~C^^~~/Dv ||= ~~double-up~~

v2 ||= double-up unison,

~~unison~~,

down 2nd ||< C^^

~~down 2nd~~ || Db ||= ~~Minor 2nd~~ ||= ~~16/15, 15/14, 29/27~~ ||= ~~18/17~~ ||= 16/15, 25/24 ||

Dv ||= Db ||= Minor 2nd ||= 16/15, 15/14, 29/27 ||= 18/17 ||= 16/15, 25/24 ||

|| 3 || 171.~~429, 205.714~~

||= 3 ||= 171.43 ||> 2 ||= perfect 2nd ||< D ||= D ||= Submajor 2nd ||= 10/9, 32/29 ||= 10/9,11/10 ||= 9/8 ||

<~~span style~~=~~"background-color: #ffffff;">51°25'43"~~<~~/span>~~ ||= D ||= ~~perfect~~ 2nd || ~~D ||= Submajor 2nd ||=~~ 10/9, 32/29 ||= 10/9,11/10 ||= 9/8 ||

||= 4 ||= 228.57 ||> ^2

|| 4 || 228.~~571, 274.286~~

vv3 ||= up 2nd,

~~68°~~<~~span style~~=~~"background~~-~~color: #ffffff;">34'17"~~<~~/span> ||=~~ D^/Evv ||= ~~up 2nd,~~

double-down 3rd ||< D^

~~double-down 3rd ||~~ D# ||= Supermajor 2nd ||= 8/7 ||= 8/7 ||= 8/7, 10/9, 11/10 ||

Evv ||= D# ||= Supermajor 2nd ||= 8/7 ||= 8/7 ||= 8/7, 10/9, 11/10 ||

|| 5 || 285.~~714, 342.857~~

||= 5 ||= 285.71 ||> ^^2

~~85°~~<~~span style="background-color: #ffffff;">42'51" ||= D^^/Ev~~ ||= double-up

v3 ||= double-up 2nd,

2nd,

down 3rd ||< D^^

down 3rd || Eb ||= Subminor 3rd ||= 27/23, 32/27 ||= 13/11, 20/17 ||= 6/5, 7/6 ||

Ev ||= Eb ||= Subminor 3rd ||= 27/23, 32/27 ||= 13/11, 20/17 ||= 6/5, 7/6 ||

|| 6 || 342.~~857, 411.429~~

||= 6 ||= 342.86 ||> 3 ||= perfect 3rd ||< E ||= E ||= Neutral 3rd ||= 28/23 ||= 11/9 ||= 16/13 ||

<~~span style~~=~~"background-color: #ffffff;">102°51'26"~~<~~/span> ||=~~ E ||= ~~perfect 3rd ||~~ E ||= Neutral 3rd ||= 28/23 ||= 11/9 ||= 16/13 ||

||= 7 ||= 400 ||> ^3

|| 7 || 400~~, 480~~

vv4 ||= up 3rd,

~~120°~~ ||~~= E~~^~~/Fvv~~ ||= up 3rd,

double-down 4th ||< E^

double-down

Fvv ||= E#/Fb ||= Major 3rd ||= 29/23 ||= 44/35 ||= 5/4, 9/7, 11/9, 14/11 ||

~~4th~~ || E#/Fb ||= Major 3rd ||= 29/23 ||= 44/35 ||= 5/4, 9/7, 11/9, 14/11 ||

||= 8 ||= 457.14 ||> ^^3

|| 8 || 457.~~143, 548.571~~

v4 ||= double-up 3rd,

~~137°~~<~~span style~~=~~"background~~-~~color: #ffffff~~; ~~line-height: 1.5;">8'34" ||= E~~^^/Fv ||= ~~double-up~~

down 4th ||< E^^

~~3rd,~~

Fv ||= F ||= Third-Fourth ||= 30/23 ||= 13/10, 17/13, 22/17 ||= 13/10 ||

~~down 4th || F~~ ||= Third-Fourth ||= 30/23 ||= 13/10, 17/13, 22/17 ||= 13/10 ||

||= 9 ||= 514.29 ||> 4 ||= perfect 4th ||< F ||= F# ||= Acute 4th ||= 161/120, 256/189 ||= 35/26 ||= 4/3, 18/13 ||

|| 9 || 514.~~286, 617.143~~

||= 10 ||= 571.43 ||> ^4

<~~span style~~=~~"background-color: #ffffff;">154°17'9"~~<~~/span> ||=~~ F ||= ~~perfect 4th ||~~ F# ||= Acute 4th ||= 161/120, 256/189 ||= 35/26 ||= 4/3, 18/13 ||

vv5 ||= up 4th,

|| 10 || 571.~~429~~, ~~685.714~~

double-down 5th ||< F^

~~171°~~<~~span style="background-color: #ffffff;">25'43"~~ ||= ~~F^/Gvv~~ ||= ~~up 4th,~~

Gvv ||= Gb ||= Narrow Tritone ||= 32/23 ||= 18/13 ||= 7/5, 11/8 ||

~~double-down~~

||= 11 ||= 628.57 ||> ^^4

~~5th || Gb ||= Narrow~~ Tritone ||= 32/23 ||= 18/13 ||= 7/5, 11/8 ||

v5 ||= double-up 4th,

|| 11 || 628.~~571, 754.286~~

down 5th ||< F^^

~~188°~~<~~span style~~=~~"background~~-~~color: #ffffff;">34'17"~~<~~/span> ||= F~~^^/Gv ||= ~~double-up~~

Gv ||= G ||= Wide Tritone ||= 23/16 ||= 13/9 ||= 10/7, 16/11 ||

~~4th,~~

||= 12 ||= 685.71 ||> 5 ||= perfect 5th ||< G ||= G# ||= Grave 5th ||= 189/128, 240/161 ||= 52/35 ||= 3/2, 13/9 ||

~~down 5th ||~~ G ||= Wide Tritone ||= 23/16 ||= 13/9 ||= 10/7, 16/11 ||

||= 13 ||= 742.86 ||> ^5

|| 12 || 685.~~714, 824.857~~

vv6 ||= up 5th,

~~205°42'51"</span&~~gt; ||= G ||~~= perfect 5th~~ || G# ||= Grave 5th ||= 189/128, 240/161 ||= 52/35 ||= 3/2, 13/9 ||

double-down 6th ||< G^

|| 13 || 742.~~857, 891.428~~

Avv ||= Hb ||= Fifth-Sixth ||= 23/15 ||= 17/11, 20/13, 26/17 ||= 20/13 ||

~~222°~~<~~span style~~=~~"background-color: #ffffff;">51'26"~~<~~/span> ||=~~ G^/Avv ||= ~~up 5th,~~

||= 14 ||= 800 ||> ^^5

~~double-down~~

v6 ||= double-up 5th,

~~6th ||~~ Hb ||= Fifth-Sixth ||= 23/15 ||= 17/11, 20/13, 26/17 ||= 20/13 ||

down 6th ||< G^^

|| 14 || 800~~, 960~~

Av ||= H ||= Minor 6th ||= 46/29 ||= 35/22 ||= 8/5, 11/7, 14/9, 18/11 ||

~~240°~~ ||~~= G~~^^~~/Av~~ ||= double-up

||= 15 ||= 857.14 ||> 6 ||= perfect 6th ||< A ||= H#/Ab ||= Neutral 6th ||= 23/14 ||= 18/11 ||= 13/8 ||

5th, down 6th || H ||= Minor 6th ||= 46/29 ||= 35/22 ||= 8/5, 11/7, 14/9, 18/11 ||

||= 16 ||= 914.29 ||> ^6

|| 15 || 857.~~143, 1028.571~~

vv7 ||= up 6th,

<~~span style~~=~~"background-color: #ffffff;">257°8'34"~~<~~/span> ||=~~ A ||= ~~perfect 6th ||~~ H#/Ab ||= Neutral 6th ||= 23/14 ||= 18/11 ||= 13/8 ||

double-down 7th ||< A^

|| 16 || 914.~~286~~, ~~1097.143~~

Bvv ||= A ||= Supermajor 6th ||= 27/16, 46/27 ||= 17/10, 22/13 ||= 5/3, 12/7 ||

~~274°~~<~~span style="background-color: #ffffff;">17'9"~~ ||= A~~^/Bvv~~ ||= up 6th,

||= 17 ||= 971.43 ||> ^^6

~~double-down~~

v7 ||= double-up 6th,

~~7th || A ||= Supermajor 6th |~~|= 27/16, 46/27 ||= 17/10, 22/13 ||= 5/3, 12/7 ||

down 7th ||< A^^

|| 17 || 971.~~429, 1165.714~~

Bv ||= A# ||= Subminor 7th ||= 7/4 ||= 7/4 ||= 7/4, 9/5, 20/11 ||

~~391°~~<~~span style~~=~~"background~~-~~color: #ffffff;">25'43"~~<~~/span> ||= A~~^^/Bv ||= ~~double-up~~

||= 18 ||= 1028.57 ||> 7 ||= perfect 7th ||< B ||= Bb ||= Supraminor 7th ||= 29/16, 9/5 ||= 9/5, 20/11 ||= 16/9 ||

~~6th,~~

||= 19 ||= 1085.71 ||> ^7

~~down 7th ||~~ A# ||= Subminor 7th ||= 7/4 ||= 7/4 ||= 7/4, 9/5, 20/11 ||

vv8 ||= up 7th,

|| 18 || 1028.~~571, 1234.286~~

double-down 8ve ||< B^

<~~span style~~=~~"background-color: #ffffff;">308°34'17"~~<~~/span> ||=~~ B ||= ~~perfect 7th ||~~ Bb ||= Supraminor 7th ||= 29/16, 9/5 ||= 9/5, 20/11 ||= 16/9 ||

Cvv ||= B ||= Major 7th ||= 15/8 ||= 17/9 ||= 15/8, 48/25 ||

|| 19 || 1085.~~714, 1302.857~~

||= 20 ||= 1142.86 ||> ^^7

~~325°~~<~~span style~~=~~"background~~-~~color: #ffffff;">42'51"~~<~~/span>~~ ||= ~~B^/Cvv ||= up 7th,~~

v8 ||= double-up 7th,

~~double-down~~

down 8ve ||< B^^

~~8ve ||~~ B ||= Major 7th ||= 15/8 ||= 17/9 ||= 15/8, 48/25 ||

Cv ||= B#/Cb ||= Supermajor 7th ||= 27/14, 29/15 ||= 35/18, 68/35 ||= 63/32 ||

|| 20 || 1142.~~857, 1371.429~~

||= 21 ||= 1200 ||> 8 ||= 8ve ||< C ||= C ||= Octave ||= 2/1 ||= 2/1 ||= 2/1 ||

~~342°~~<~~span style~~=~~"background~~-~~color: #ffffff;">8'34"~~<~~/span> ||= B~~^^/Cv ||= ~~double-up~~

~~7th, down 8ve ||~~ B#/Cb ||= Supermajor 7th ||= 27/14, 29/15 ||= 35/~~18, 68/35 ||= 63/32 ||~~

~~|| 21 || 1200, 1440~~

~~360° ||=~~ C ||= ~~8ve ||~~ C ||= Octave ||= 2/1 ||= 2/1 ||= 2/1 ||

*1: based on treating 21-EDO as a 2.7.15.23.27.29 subgroup temperament

Line 205:

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<tr>

<td>Degree

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

</td>

<td>Cents ~~coarse/fine, DMS Value~~

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

</td>

<a class="wiki_link" href="/Ups%20and%20Downs%20Notation">Notation</a>

</td>

<td>5L3s

</td>

<td style="text-align: center;">5L3s

Octotonic

Notation

</td>

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Ratios *1

</td>

<td style="text-align: center;">ApproximateRatios *2

<td style="text-align: center;">ApproximateRatios *2

</td>

<td style="text-align: center;">ApproximateRatios *3

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</tr>

<tr>

<td>0

<td style="text-align: center;">0

</td>

<td style="text-align: center;">0

</td>

<td>0

<td style="text-align: right;">1

</td>

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

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

</td>

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

<td style="text-align: left;">C

</td>

<td>C

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

</td>

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

Line 247:

Line 249:

</tr>

<tr>

<td>1

<td style="text-align: center;">1

</td>

<td~~>57.143, 68.571 ~~

<td style="text-align: center;">57.14

~~17°<span~~ style="~~background~~-~~color~~: ~~#ffffff~~;">~~8'34&quot;~~

</td>

<td style="text-align: ~~center~~;">C^/~~Dvv~~

<td style="text-align: right;">^1

vv2

</td>

<td style="text-align: center;">up unison,

double-down~~ ~~

double-down 2nd

2nd

</td>

<td>C#

<td style="text-align: left;">C^

Dvv

</td>

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

</td>

<td style="text-align: center;">Subminor 2nd

Line 270:

Line 274:

</tr>

<tr>

<td>2

<td style="text-align: center;">2

</td>

<td~~>114.286, 137.143 ~~

<td style="text-align: center;">114.29

~~34°<span~~ style="~~background~~-~~color~~: ~~#ffffff~~;">~~17'9&quot;~~

</td>

<td style="text-align: ~~center~~;">C^^/Dv

<td style="text-align: right;">^^1

v2

</td>

<td style="text-align: center;">double-up~~ ~~

<td style="text-align: center;">double-up unison,

unison,

down 2nd

</td>

<td>Db

<td style="text-align: left;">C^^

Dv

</td>

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

</td>

<td style="text-align: center;">Minor 2nd

Line 293:

Line 299:

</tr>

<tr>

<td>3

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

</td>

<td~~>171.429, 205.714 ~~

<td style="text-align: center;">171.43

~~<span~~ style="~~background~~-~~color~~: ~~#ffffff~~;">~~51°25'~~43~~&quot;~~

</td>

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

<td style="text-align: right;">2

</td>

<td style="text-align: center;">perfect 2nd

</td>

<td>D

<td style="text-align: left;">D

</td>

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

</td>

<td style="text-align: center;">Submajor 2nd

Line 314:

Line 321:

</tr>

<tr>

<td>4

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

</td>

<td~~>228.571, 274.286 ~~

<td style="text-align: center;">228.57

~~68°<span~~ style="~~background~~-~~color~~: ~~#ffffff~~;">~~34'17&quot;~~

</td>

<td style="text-align: ~~center~~;">D^/~~Evv~~

<td style="text-align: right;">^2

vv3

</td>

<td style="text-align: center;">up 2nd,

double-down 3rd

</td>

<td>D#

<td style="text-align: left;">D^

Evv

</td>

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

</td>

<td style="text-align: center;">Supermajor 2nd

Line 336:

Line 346:

</tr>

<tr>

<td>5

<td style="text-align: center;">5

</td>

<td~~>285.714, 342.857 ~~

<td style="text-align: center;">285.71

~~85°<span~~ style="~~background~~-~~color~~: ~~#ffffff~~;">~~42'51&quot;~~

</td>

<td style="text-align: ~~center~~;">D^^/Ev

<td style="text-align: right;">^^2

v3

</td>

<td style="text-align: center;">double-up~~ ~~

<td style="text-align: center;">double-up 2nd,

2nd,

down 3rd

</td>

<td>Eb

<td style="text-align: left;">D^^

Ev

</td>

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

</td>

<td style="text-align: center;">Subminor 3rd

Line 359:

Line 371:

</tr>

<tr>

<td>6

<td style="text-align: center;">6

</td>

<td~~>342.857, 411.429 ~~

<td style="text-align: center;">342.86

~~<span~~ style="~~background~~-~~color~~: ~~#ffffff~~;">~~102°51'26&quot;~~

</td>

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

<td style="text-align: right;">3

</td>

<td style="text-align: center;">perfect 3rd

</td>

<td>E

<td style="text-align: left;">E

</td>

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

</td>

<td style="text-align: center;">Neutral 3rd

Line 380:

Line 393:

</tr>

<tr>

<td>7

<td style="text-align: center;">7

</td>

<td>400~~, 480 ~~

<td style="text-align: center;">400

~~120°~~

</td>

<td style="text-align: ~~center~~;">E^/~~Fvv~~

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

vv4

</td>

<td style="text-align: center;">up 3rd,

double-down~~ ~~

double-down 4th

4th

</td>

<td>E#/Fb

<td style="text-align: left;">E^

Fvv

</td>

<td style="text-align: center;">E#/Fb

</td>

<td style="text-align: center;">Major 3rd

Line 403:

Line 418:

</tr>

<tr>

<td>8

<td style="text-align: center;">8

</td>

<td~~>457.143, 548.571 ~~

<td style="text-align: center;">457.14

~~137°<span~~ style="~~background~~-~~color~~: ~~#ffffff; line-height: 1.5~~;">~~8'34&quot;~~

</td>

<td style="text-align: ~~center~~;">E^^/Fv

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

v4

</td>

<td style="text-align: center;">double-up~~ ~~

<td style="text-align: center;">double-up 3rd,

3rd,

down 4th

</td>

<td>F

<td style="text-align: left;">E^^

Fv

</td>

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

</td>

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

Line 426:

Line 443:

</tr>

<tr>

<td>9

<td style="text-align: center;">9

</td>

<td~~>514.286, 617.143 ~~

<td style="text-align: center;">514.29

~~<span~~ style="~~background~~-~~color~~: ~~#ffffff~~;">~~154°17'9&quot;~~

</td>

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

<td style="text-align: right;">4

</td>

<td style="text-align: center;">perfect 4th

</td>

<td>F#

<td style="text-align: left;">F

</td>

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

</td>

<td style="text-align: center;">Acute 4th

Line 447:

Line 465:

</tr>

<tr>

<td>10

<td style="text-align: center;">10

</td>

<td~~>571.429, 685.714 ~~

<td style="text-align: center;">571.43

~~171°<span~~ style="~~background~~-~~color~~: ~~#ffffff~~;">~~25'~~43~~&quot;~~

</td>

<td style="text-align: ~~center~~;">F^/~~Gvv~~

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

vv5

</td>

<td style="text-align: center;">up 4th,

double-down~~ ~~

double-down 5th

5th

</td>

<td>Gb

<td style="text-align: left;">F^

Gvv

</td>

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

</td>

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

Line 470:

Line 490:

</tr>

<tr>

<td>11

<td style="text-align: center;">11

</td>

<td~~>628.571, 754.286 ~~

<td style="text-align: center;">628.57

~~188°<span~~ style="~~background~~-~~color~~: ~~#ffffff~~;">~~34'17&quot;~~

</td>

<td style="text-align: ~~center~~;">F^^/Gv

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

v5

</td>

<td style="text-align: center;">double-up~~ ~~

<td style="text-align: center;">double-up 4th,

4th,

down 5th

</td>

<td>G

<td style="text-align: left;">F^^

Gv

</td>

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

</td>

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

Line 493:

Line 515:

</tr>

<tr>

<td>12

<td style="text-align: center;">12

</td>

<td~~>685.714, 824.857 ~~

<td style="text-align: center;">685.71

~~<span~~ style="~~background~~-~~color~~: ~~#ffffff~~;">~~205°42'51&quot;~~

</td>

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

<td style="text-align: right;">5

</td>

<td style="text-align: center;">perfect 5th

</td>

<td>G#

<td style="text-align: left;">G

</td>

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

</td>

<td style="text-align: center;">Grave 5th

Line 514:

Line 537:

</tr>

<tr>

<td>13

<td style="text-align: center;">13

</td>

<td~~>742.857, 891.428 ~~

<td style="text-align: center;">742.86

~~222°<span~~ style="~~background~~-~~color~~: ~~#ffffff~~;">~~51'26&quot;~~

</td>

<td style="text-align: ~~center~~;">G^/~~Avv~~

<td style="text-align: right;">^5

vv6

</td>

<td style="text-align: center;">up 5th,

double-down~~ ~~

double-down 6th

6th

</td>

<td>Hb

<td style="text-align: left;">G^

Avv

</td>

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

</td>

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

Line 537:

Line 562:

</tr>

<tr>

<td>14

<td style="text-align: center;">14

</td>

<td>800~~, 960 ~~

<td style="text-align: center;">800

~~240°~~

</td>

<td style="text-align: ~~center~~;">G^^/Av

<td style="text-align: right;">^^5

v6

</td>

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

<td style="text-align: center;">double-up 5th,

~~5th,~~ down 6th

down 6th

</td>

<td>H

<td style="text-align: left;">G^^

Av

</td>

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

</td>

<td style="text-align: center;">Minor 6th

Line 559:

Line 587:

</tr>

<tr>

<td>15

<td style="text-align: center;">15

</td>

<td~~>857.143, 1028.571 ~~

<td style="text-align: center;">857.14

~~<span~~ style="~~background~~-~~color~~: ~~#ffffff~~;">~~257°8'34&quot;~~

</td>

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

<td style="text-align: right;">6

</td>

<td style="text-align: center;">perfect 6th

</td>

<td>H#/Ab

<td style="text-align: left;">A

</td>

<td style="text-align: center;">H#/Ab

</td>

<td style="text-align: center;">Neutral 6th

Line 580:

Line 609:

</tr>

<tr>

<td>16

<td style="text-align: center;">16

</td>

<td~~>914.286, 1097.143 ~~

<td style="text-align: center;">914.29

~~274°<span~~ style="~~background~~-~~color~~: ~~#ffffff~~;">~~17'9&quot;~~

</td>

<td style="text-align: ~~center~~;">A^/~~Bvv~~

<td style="text-align: right;">^6

vv7

</td>

<td style="text-align: center;">up 6th,

double-down~~ ~~

double-down 7th

7th

</td>

<td>A

<td style="text-align: left;">A^

Bvv

</td>

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

</td>

<td style="text-align: center;">Supermajor 6th

Line 603:

Line 634:

</tr>

<tr>

<td>17

<td style="text-align: center;">17

</td>

<td~~>971.429, 1165.714 ~~

<td style="text-align: center;">971.43

~~391°<span~~ style="~~background~~-~~color~~: ~~#ffffff~~;">~~25'~~43~~&quot;~~

</td>

<td style="text-align: ~~center~~;">A^^/Bv

<td style="text-align: right;">^^6

v7

</td>

<td style="text-align: center;">double-up~~ ~~

<td style="text-align: center;">double-up 6th,

6th,

down 7th

</td>

<td>A#

<td style="text-align: left;">A^^

Bv

</td>

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

</td>

<td style="text-align: center;">Subminor 7th

Line 626:

Line 659:

</tr>

<tr>

<td>18

<td style="text-align: center;">18

</td>

<td~~>1028.571, 1234.286 ~~

<td style="text-align: center;">1028.57

~~<span~~ style="~~background~~-~~color~~: ~~#ffffff~~;">~~308°34'17&quot;~~

</td>

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

<td style="text-align: right;">7

</td>

<td style="text-align: center;">perfect 7th

</td>

<td>Bb

<td style="text-align: left;">B

</td>

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

</td>

<td style="text-align: center;">Supraminor 7th

Line 647:

Line 681:

</tr>

<tr>

<td>19

<td style="text-align: center;">19

</td>

<td~~>1085.714, 1302.857 ~~

<td style="text-align: center;">1085.71

~~325°<span~~ style="~~background~~-~~color~~: ~~#ffffff~~;">~~42'51&quot;~~

</td>

<td style="text-align: ~~center~~;">B^/~~Cvv~~

<td style="text-align: right;">^7

vv8

</td>

<td style="text-align: center;">up 7th,

double-down

double-down 8ve

~~8ve~~

</td>

<td style="text-align: left;">B^

Cvv

</td>

<td>B

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

</td>

<td style="text-align: center;">Major 7th

Line 670:

Line 706:

</tr>

<tr>

<td>20

<td style="text-align: center;">20

</td>

<td~~>1142.857, 1371.429 ~~

<td style="text-align: center;">1142.86

~~342°<span~~ style="~~background~~-~~color~~: ~~#ffffff~~;">~~8'34&quot;~~

</td>

<td style="text-align: ~~center~~;">B^^/Cv

<td style="text-align: right;">^^7

v8

</td>

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

<td style="text-align: center;">double-up 7th,

~~7th,~~ down 8ve

down 8ve

</td>

<td>B#/Cb

<td style="text-align: left;">B^^

Cv

</td>

<td style="text-align: center;">B#/Cb

</td>

<td style="text-align: center;">Supermajor 7th

Line 692:

Line 731:

</tr>

<tr>

<td>21

<td style="text-align: center;">21

</td>

<td>1200~~, 1440 ~~

<td style="text-align: center;">1200

~~360°~~

</td>

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

<td style="text-align: right;">8

</td>

<td style="text-align: center;">8ve

</td>

<td>C

<td style="text-align: left;">C

</td>

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

</td>

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

Line 1,233:

Line 1,273:

<h1 id="toc7"><a name="Books / Literature:"></a>Books / Literature:</h1>

Sword, Ron. &quot;Icosihenaphonic Scales for Guitar&quot;. IAAA Press. 1st ed: July 2009.

<img src="http://www.ronsword.com/images/ron1.jpg" alt="external image ron1.jpg" title="external image ron1.jpg" style="height: 188px; width: 254px;" /><img src="http://www.swordguitars.com/21tetsm.JPG" alt="external image 21tetsm.JPG" title="external image 21tetsm.JPG" style="height: 191px; width: 363px;" />

<img src="http://www.ronsword.com/images/ron1.jpg" alt="external image ron1.jpg" title="external image ron1.jpg" style="height: 188px; width: 254px;" /><img src="http://www.swordguitars.com/21tetsm.JPG" alt="external image 21tetsm.JPG" title="external image 21tetsm.JPG" style="height: 191px; width: 363px;" />

21-edo Icosihenaphonic Acoustic Guitar (Ron Sword)

@@ 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>2016-12-07 21:23:55 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-22 04:46:43 UTC</tt>.<br>
-: The original revision id was <tt>601671926</tt>.<br>
+: The original revision id was <tt>602739102</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 19: / Line 19: @@
 The patent val for 21edo tempers out 128/125 and 2187/2000 in the 5-limit, and supplies the optimal patent val for the 5-limit [[Laconic Family|laconic]] temperament tempering out 2187/2000, and also the optimal patent val for 7-limit, 11-limit and 13-limit laconic, spartan and gorgo temperaments. These temperaments lead to some "interesting" mappings, where 10/9 is larger than 9/8, 11/9 is larger than 16/13, and 8/7 maps to the same interval as 10/9, for instance.
-|| **Degree** || **Cents coarse/fine, DMS Value** ||||= [[Ups and Downs Notation|Up/down]]
+||= **Degree** ||= **Cents** ||||= [[Ups and Downs Notation|Up/down]]
-[[Ups and Downs Notation|Notation]] || **5L3s**
+[[Ups and Downs Notation|Notation]] ||&lt;   ||= **5L3s**
+**Octotonic**
 **Notation** ||= **D.-R. Interval**
 **Types** ||= **Approximate**
-**Ratios *1** ||= &lt;span style="display: block; text-align: center;"&gt;**Approximate****Ratios *2**&lt;/span&gt; ||= &lt;span style="display: block; text-align: center;"&gt;**Approximate**&lt;/span&gt;**Ratios *3** ||
+**Ratios *1** ||= &lt;span style="display: block; text-align: center;"&gt;**Approximate**&lt;/span&gt;&lt;span style="display: block; text-align: center;"&gt;**Ratios *2**&lt;/span&gt; ||= &lt;span style="display: block; text-align: center;"&gt;**Approximate**&lt;/span&gt;**Ratios *3** ||
-|| 0 || 0 ||= C ||= unison || C ||= Unison ||= 1/1 ||= 1/1 ||= 1/1 ||
+||= 0 ||= 0 ||&gt; 1 ||= _____unison_____ ||&lt; C ||= C ||= Unison ||= 1/1 ||= 1/1 ||= 1/1 ||
-|| 1 || 57.143, 68.571
+||= 1 ||= 57.14 ||&gt; ^1
-°&lt;span style="background-color: #ffffff;"&gt;8'34"&lt;/span&gt; ||= C^/Dvv ||= up unison,
+vv2 ||= up unison,
-double-down
+double-down 2nd ||&lt; C^
-nd || C# ||= Subminor 2nd ||= 28/27, 30/29 ||= 35/34, 36/35 ||= 64/63 ||
+Dvv ||= C# ||= Subminor 2nd ||= 28/27, 30/29 ||= 35/34, 36/35 ||= 64/63 ||
-|| 2 || 114.286, 137.143
+||= 2 ||= 114.29 ||&gt; ^^1
-°&lt;span style="background-color: #ffffff;"&gt;17'9"&lt;/span&gt; ||= C^^/Dv ||= double-up
+v2 ||= double-up unison,
-unison,
+down 2nd ||&lt; C^^
-down 2nd || Db ||= Minor 2nd ||= 16/15, 15/14, 29/27 ||= 18/17 ||= 16/15, 25/24 ||
+Dv ||= Db ||= Minor 2nd ||= 16/15, 15/14, 29/27 ||= 18/17 ||= 16/15, 25/24 ||
-|| 3 || 171.429, 205.714
+||= 3 ||= 171.43 ||&gt; 2 ||= perfect 2nd ||&lt; D ||= D ||= Submajor 2nd ||= 10/9, 32/29 ||= 10/9,11/10 ||= 9/8 ||
-&lt;span style="background-color: #ffffff;"&gt;51°25'43"&lt;/span&gt; ||= D ||= perfect 2nd || D ||= Submajor 2nd ||= 10/9, 32/29 ||= 10/9,11/10 ||= 9/8 ||
+||= 4 ||= 228.57 ||&gt; ^2
-|| 4 || 228.571, 274.286
+vv3 ||= up 2nd,
-°&lt;span style="background-color: #ffffff;"&gt;34'17"&lt;/span&gt; ||= D^/Evv ||= up 2nd,
+double-down 3rd ||&lt; D^
-double-down 3rd || D# ||= Supermajor 2nd ||= 8/7 ||= 8/7 ||= 8/7, 10/9, 11/10 ||
+Evv ||= D# ||= Supermajor 2nd ||= 8/7 ||= 8/7 ||= 8/7, 10/9, 11/10 ||
-|| 5 || 285.714, 342.857
+||= 5 ||= 285.71 ||&gt; ^^2
-°&lt;span style="background-color: #ffffff;"&gt;42'51"&lt;/span&gt; ||= D^^/Ev ||= double-up
+v3 ||= double-up 2nd,
-nd,
+down 3rd ||&lt; D^^
-down 3rd || Eb ||= Subminor 3rd ||= 27/23, 32/27 ||= 13/11, 20/17 ||= 6/5, 7/6 ||
+Ev ||= Eb ||= Subminor 3rd ||= 27/23, 32/27 ||= 13/11, 20/17 ||= 6/5, 7/6 ||
-|| 6 || 342.857, 411.429
+||= 6 ||= 342.86 ||&gt; 3 ||= perfect 3rd ||&lt; E ||= E ||= Neutral 3rd ||= 28/23 ||= 11/9 ||= 16/13 ||
-&lt;span style="background-color: #ffffff;"&gt;102°51'26"&lt;/span&gt; ||= E ||= perfect 3rd || E ||= Neutral 3rd ||= 28/23 ||= 11/9 ||= 16/13 ||
+||= 7 ||= 400 ||&gt; ^3
-|| 7 || 400, 480
+vv4 ||= up 3rd,
-° ||= E^/Fvv ||= up 3rd,
+double-down 4th ||&lt; E^
-double-down
+Fvv ||= E#/Fb ||= Major 3rd ||= 29/23 ||= 44/35 ||= 5/4, 9/7, 11/9, 14/11 ||
-th || E#/Fb ||= Major 3rd ||= 29/23 ||= 44/35 ||= 5/4, 9/7, 11/9, 14/11 ||
+||= 8 ||= 457.14 ||&gt; ^^3
-|| 8 || 457.143, 548.571
+v4 ||= double-up 3rd,
-°&lt;span style="background-color: #ffffff; line-height: 1.5;"&gt;8'34"&lt;/span&gt; ||= E^^/Fv ||= double-up
+down 4th ||&lt; E^^
-rd,
+Fv ||= F ||= Third-Fourth ||= 30/23 ||= 13/10, 17/13, 22/17 ||= 13/10 ||
-down 4th || F ||= Third-Fourth ||= 30/23 ||= 13/10, 17/13, 22/17 ||= 13/10 ||
+||= 9 ||= 514.29 ||&gt; 4 ||= perfect 4th ||&lt; F ||= F# ||= Acute 4th ||= 161/120, 256/189 ||= 35/26 ||= 4/3, 18/13 ||
-|| 9 || 514.286, 617.143
+||= 10 ||= 571.43 ||&gt; ^4
-&lt;span style="background-color: #ffffff;"&gt;154°17'9"&lt;/span&gt; ||= F ||= perfect 4th || F# ||= Acute 4th ||= 161/120, 256/189 ||= 35/26 ||= 4/3, 18/13 ||
+vv5 ||= up 4th,
-|| 10 || 571.429, 685.714
+double-down 5th ||&lt; F^
-°&lt;span style="background-color: #ffffff;"&gt;25'43"&lt;/span&gt; ||= F^/Gvv ||= up 4th,
+Gvv ||= Gb ||= Narrow Tritone ||= 32/23 ||= 18/13 ||= 7/5, 11/8 ||
-double-down
+||= 11 ||= 628.57 ||&gt; ^^4
-th || Gb ||= Narrow Tritone ||= 32/23 ||= 18/13 ||= 7/5, 11/8 ||
+v5 ||= double-up 4th,
-|| 11 || 628.571, 754.286
+down 5th ||&lt; F^^
-°&lt;span style="background-color: #ffffff;"&gt;34'17"&lt;/span&gt; ||= F^^/Gv ||= double-up
+Gv ||= G ||= Wide Tritone ||= 23/16 ||= 13/9 ||= 10/7, 16/11 ||
-th,
+||= 12 ||= 685.71 ||&gt; 5 ||= perfect 5th ||&lt; G ||= G# ||= Grave 5th ||= 189/128, 240/161 ||= 52/35 ||= 3/2, 13/9 ||
-down 5th || G ||= Wide Tritone ||= 23/16 ||= 13/9 ||= 10/7, 16/11 ||
+||= 13 ||= 742.86 ||&gt; ^5
-|| 12 || 685.714, 824.857
+vv6 ||= up 5th,
-&lt;span style="background-color: #ffffff;"&gt;205°42'51"&lt;/span&gt; ||= G ||= perfect 5th || G# ||= Grave 5th ||= 189/128, 240/161 ||= 52/35 ||= 3/2, 13/9 ||
+double-down 6th ||&lt; G^
-|| 13 || 742.857, 891.428
+Avv ||= Hb ||= Fifth-Sixth ||= 23/15 ||= 17/11, 20/13, 26/17 ||= 20/13 ||
-°&lt;span style="background-color: #ffffff;"&gt;51'26"&lt;/span&gt; ||= G^/Avv ||= up 5th,
+||= 14 ||= 800 ||&gt; ^^5
-double-down
+v6 ||= double-up 5th,
-th || Hb ||= Fifth-Sixth ||= 23/15 ||= 17/11, 20/13, 26/17 ||= 20/13 ||
+down 6th ||&lt; G^^
-|| 14 || 800, 960
+Av ||= H ||= Minor 6th ||= 46/29 ||= 35/22 ||= 8/5, 11/7, 14/9, 18/11 ||
-° ||= G^^/Av ||= double-up
+||= 15 ||= 857.14 ||&gt; 6 ||= perfect 6th ||&lt; A ||= H#/Ab ||= Neutral 6th ||= 23/14 ||= 18/11 ||= 13/8 ||
-th, down 6th || H ||= Minor 6th ||= 46/29 ||= 35/22 ||= 8/5, 11/7, 14/9, 18/11 ||
+||= 16 ||= 914.29 ||&gt; ^6
-|| 15 || 857.143, 1028.571
+vv7 ||= up 6th,
-&lt;span style="background-color: #ffffff;"&gt;257°8'34"&lt;/span&gt; ||= A ||= perfect 6th || H#/Ab ||= Neutral 6th ||= 23/14 ||= 18/11 ||= 13/8 ||
+double-down 7th ||&lt; A^
-|| 16 || 914.286, 1097.143
+Bvv ||= A ||= Supermajor 6th ||= 27/16, 46/27 ||= 17/10, 22/13 ||= 5/3, 12/7 ||
-°&lt;span style="background-color: #ffffff;"&gt;17'9"&lt;/span&gt; ||= A^/Bvv ||= up 6th,
+||= 17 ||= 971.43 ||&gt; ^^6
-double-down
+v7 ||= double-up 6th,
-th || A ||= Supermajor 6th ||= 27/16, 46/27 ||= 17/10, 22/13 ||= 5/3, 12/7 ||
+down 7th ||&lt; A^^
-|| 17 || 971.429, 1165.714
+Bv ||= A# ||= Subminor 7th ||= 7/4 ||= 7/4 ||= 7/4, 9/5, 20/11 ||
-°&lt;span style="background-color: #ffffff;"&gt;25'43"&lt;/span&gt; ||= A^^/Bv ||= double-up
+||= 18 ||= 1028.57 ||&gt; 7 ||= perfect 7th ||&lt; B ||= Bb ||= Supraminor 7th ||= 29/16, 9/5 ||= 9/5, 20/11 ||= 16/9 ||
-th,
+||= 19 ||= 1085.71 ||&gt; ^7
-down 7th || A# ||= Subminor 7th ||= 7/4 ||= 7/4 ||= 7/4, 9/5, 20/11 ||
+vv8 ||= up 7th,
-|| 18 || 1028.571, 1234.286
+double-down 8ve ||&lt; B^
-&lt;span style="background-color: #ffffff;"&gt;308°34'17"&lt;/span&gt; ||= B ||= perfect 7th || Bb ||= Supraminor 7th ||= 29/16, 9/5 ||= 9/5, 20/11 ||= 16/9 ||
+Cvv ||= B ||= Major 7th ||= 15/8 ||= 17/9 ||= 15/8, 48/25 ||
-|| 19 || 1085.714, 1302.857
+||= 20 ||= 1142.86 ||&gt; ^^7
-°&lt;span style="background-color: #ffffff;"&gt;42'51"&lt;/span&gt; ||= B^/Cvv ||= up 7th,
+v8 ||= double-up 7th,
-double-down
+down 8ve ||&lt; B^^
-ve || B ||= Major 7th ||= 15/8 ||= 17/9 ||= 15/8, 48/25 ||
+Cv ||= B#/Cb ||= Supermajor 7th ||= 27/14, 29/15 ||= 35/18, 68/35 ||= 63/32 ||
-|| 20 || 1142.857, 1371.429
+||= 21 ||= 1200 ||&gt; 8 ||= 8ve ||&lt; C ||= C ||= Octave ||= 2/1 ||= 2/1 ||= 2/1 ||
-°&lt;span style="background-color: #ffffff;"&gt;8'34"&lt;/span&gt; ||= B^^/Cv ||= double-up
-th, down 8ve || B#/Cb ||= Supermajor 7th ||= 27/14, 29/15 ||= 35/18, 68/35 ||= 63/32 ||
-|| 21 || 1200, 1440
-° ||= C ||= 8ve || C ||= Octave ||= 2/1 ||= 2/1 ||= 2/1 ||
 *1: based on treating 21-EDO as a 2.7.15.23.27.29 subgroup temperament
@@ Line 205: / Line 202: @@
 &lt;table class="wiki_table"&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;strong&gt;Degree&lt;/strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;strong&gt;Degree&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;Cents coarse/fine, DMS Value&lt;/strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;strong&gt;Cents&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td colspan="2" style="text-align: center;"&gt;&lt;a class="wiki_link" href="/Ups%20and%20Downs%20Notation"&gt;Up/down&lt;/a&gt;&lt;br /&gt;
 &lt;a class="wiki_link" href="/Ups%20and%20Downs%20Notation"&gt;Notation&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;5L3s&lt;/strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;strong&gt;5L3s&lt;/strong&gt;&lt;br /&gt;
+&lt;strong&gt;Octotonic&lt;/strong&gt;&lt;br /&gt;
 &lt;strong&gt;Notation&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
@@ Line 221: / Line 221: @@
 &lt;strong&gt;Ratios *1&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;strong&gt;Approximate&lt;/strong&gt;&lt;strong&gt;Ratios *2&lt;/strong&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;strong&gt;Approximate&lt;/strong&gt;&lt;/span&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;strong&gt;Ratios *2&lt;/strong&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;strong&gt;Approximate&lt;/strong&gt;&lt;/span&gt;&lt;strong&gt;Ratios *3&lt;/strong&gt;&lt;br /&gt;
@@ Line 227: / Line 227: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;0&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;0&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;0&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;0&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;C&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;_unison_&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;unison&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;C&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;C&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;C&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Unison&lt;br /&gt;
@@ Line 247: / Line 249: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;57.143, 68.571&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;57.14&lt;br /&gt;
-°&lt;span style="background-color: #ffffff;"&gt;8'34&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;C^/Dvv&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;^1&lt;br /&gt;
+vv2&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;up unison,&lt;br /&gt;
-double-down&lt;br /&gt;
+double-down 2nd&lt;br /&gt;
-nd&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;C#&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;C^&lt;br /&gt;
+Dvv&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;C#&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Subminor 2nd&lt;br /&gt;
@@ Line 270: / Line 274: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;114.286, 137.143&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;114.29&lt;br /&gt;
-°&lt;span style="background-color: #ffffff;"&gt;17'9&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;C^^/Dv&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;^^1&lt;br /&gt;
+v2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;double-up&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;double-up unison,&lt;br /&gt;
-unison,&lt;br /&gt;
 down 2nd&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Db&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;C^^&lt;br /&gt;
+Dv&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Db&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Minor 2nd&lt;br /&gt;
@@ Line 293: / Line 299: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;3&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;171.429, 205.714&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;171.43&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;51°25'43&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;D&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;2&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;perfect 2nd&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;D&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;D&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;D&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Submajor 2nd&lt;br /&gt;
@@ Line 314: / Line 321: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;4&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;4&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;228.571, 274.286&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;228.57&lt;br /&gt;
-°&lt;span style="background-color: #ffffff;"&gt;34'17&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;D^/Evv&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;^2&lt;br /&gt;
+vv3&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;up 2nd,&lt;br /&gt;
 double-down 3rd&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;D#&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;D^&lt;br /&gt;
+Evv&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;D#&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Supermajor 2nd&lt;br /&gt;
@@ Line 336: / Line 346: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;5&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;285.714, 342.857&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;285.71&lt;br /&gt;
-°&lt;span style="background-color: #ffffff;"&gt;42'51&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;D^^/Ev&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;^^2&lt;br /&gt;
+v3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;double-up&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;double-up 2nd,&lt;br /&gt;
-nd, &lt;br /&gt;
 down 3rd&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Eb&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;D^^&lt;br /&gt;
+Ev&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Eb&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Subminor 3rd&lt;br /&gt;
@@ Line 359: / Line 371: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;6&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;342.857, 411.429&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;342.86&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;102°51'26&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;E&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;3&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;perfect 3rd&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;E&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;E&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;E&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Neutral 3rd&lt;br /&gt;
@@ Line 380: / Line 393: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;7&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;400, 480&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;400&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;E^/Fvv&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;^3&lt;br /&gt;
+vv4&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;up 3rd,&lt;br /&gt;
-double-down&lt;br /&gt;
+double-down 4th&lt;br /&gt;
-th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;E#/Fb&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;E^&lt;br /&gt;
+Fvv&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;E#/Fb&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Major 3rd&lt;br /&gt;
@@ Line 403: / Line 418: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;8&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;8&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;457.143, 548.571&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;457.14&lt;br /&gt;
-°&lt;span style="background-color: #ffffff; line-height: 1.5;"&gt;8'34&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;E^^/Fv&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;^^3&lt;br /&gt;
+v4&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;double-up&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;double-up 3rd,&lt;br /&gt;
-rd,&lt;br /&gt;
 down 4th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;F&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;E^^&lt;br /&gt;
+Fv&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;F&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Third-Fourth&lt;br /&gt;
@@ Line 426: / Line 443: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;9&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;9&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;514.286, 617.143&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;514.29&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;154°17'9&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;F&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;4&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;perfect 4th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;F#&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;F&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;F#&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Acute 4th&lt;br /&gt;
@@ Line 447: / Line 465: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;10&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;10&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;571.429, 685.714&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;571.43&lt;br /&gt;
-°&lt;span style="background-color: #ffffff;"&gt;25'43&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;F^/Gvv&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;^4&lt;br /&gt;
+vv5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;up 4th,&lt;br /&gt;
-double-down&lt;br /&gt;
+double-down 5th&lt;br /&gt;
-th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Gb&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;F^&lt;br /&gt;
+Gvv&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Gb&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Narrow Tritone&lt;br /&gt;
@@ Line 470: / Line 490: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;11&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;11&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;628.571, 754.286&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;628.57&lt;br /&gt;
-°&lt;span style="background-color: #ffffff;"&gt;34'17&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;F^^/Gv&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;^^4&lt;br /&gt;
+v5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;double-up&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;double-up 4th,&lt;br /&gt;
-th,&lt;br /&gt;
 down 5th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;G&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;F^^&lt;br /&gt;
+Gv&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;G&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Wide Tritone&lt;br /&gt;
@@ Line 493: / Line 515: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;12&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;12&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;685.714, 824.857&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;685.71&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;205°42'51&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;G&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;perfect 5th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;G#&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;G&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;G#&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Grave 5th&lt;br /&gt;
@@ Line 514: / Line 537: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;13&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;13&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;742.857, 891.428&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;742.86&lt;br /&gt;
-°&lt;span style="background-color: #ffffff;"&gt;51'26&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;G^/Avv&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;^5&lt;br /&gt;
+vv6&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;up 5th,&lt;br /&gt;
-double-down&lt;br /&gt;
+double-down 6th&lt;br /&gt;
-th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Hb&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;G^&lt;br /&gt;
+Avv&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Hb&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Fifth-Sixth&lt;br /&gt;
@@ Line 537: / Line 562: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;14&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;14&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;800, 960&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;800&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;G^^/Av&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;^^5&lt;br /&gt;
+v6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;double-up&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;double-up 5th,&lt;br /&gt;
-th, down 6th&lt;br /&gt;
+down 6th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;H&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;G^^&lt;br /&gt;
+Av&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;H&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Minor 6th&lt;br /&gt;
@@ Line 559: / Line 587: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;15&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;15&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;857.143, 1028.571&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;857.14&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;257°8'34&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;A&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;6&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;perfect 6th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;H#/Ab&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;A&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;H#/Ab&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Neutral 6th&lt;br /&gt;
@@ Line 580: / Line 609: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;16&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;16&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;914.286, 1097.143&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;914.29&lt;br /&gt;
-°&lt;span style="background-color: #ffffff;"&gt;17'9&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;A^/Bvv&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;^6&lt;br /&gt;
+vv7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;up 6th,&lt;br /&gt;
-double-down&lt;br /&gt;
+double-down 7th&lt;br /&gt;
-th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;A&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;A^&lt;br /&gt;
+Bvv&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;A&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Supermajor 6th&lt;br /&gt;
@@ Line 603: / Line 634: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;17&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;17&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;971.429, 1165.714&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;971.43&lt;br /&gt;
-°&lt;span style="background-color: #ffffff;"&gt;25'43&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;A^^/Bv&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;^^6&lt;br /&gt;
+v7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;double-up&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;double-up 6th,&lt;br /&gt;
-th,&lt;br /&gt;
 down 7th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;A#&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;A^^&lt;br /&gt;
+Bv&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;A#&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Subminor 7th&lt;br /&gt;
@@ Line 626: / Line 659: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;18&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;18&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1028.571, 1234.286&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1028.57&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;308°34'17&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;B&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;perfect 7th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Bb&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;B&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Bb&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Supraminor 7th&lt;br /&gt;
@@ Line 647: / Line 681: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;19&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;19&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1085.714, 1302.857&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1085.71&lt;br /&gt;
-°&lt;span style="background-color: #ffffff;"&gt;42'51&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;B^/Cvv&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;^7&lt;br /&gt;
+vv8&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;up 7th,&lt;br /&gt;
-double-down&lt;br /&gt;
+double-down 8ve&lt;br /&gt;
-ve&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: left;"&gt;B^&lt;br /&gt;
+Cvv&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;B&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;B&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Major 7th&lt;br /&gt;
@@ Line 670: / Line 706: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;20&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;20&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1142.857, 1371.429&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1142.86&lt;br /&gt;
-°&lt;span style="background-color: #ffffff;"&gt;8'34&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;B^^/Cv&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;^^7&lt;br /&gt;
+v8&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;double-up&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;double-up 7th,&lt;br /&gt;
-th, down 8ve&lt;br /&gt;
+down 8ve&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;B#/Cb&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;B^^&lt;br /&gt;
+Cv&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;B#/Cb&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Supermajor 7th&lt;br /&gt;
@@ Line 692: / Line 731: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;21&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;21&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1200, 1440&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1200&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;C&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;8&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;8ve&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;C&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;C&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;C&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Octave&lt;br /&gt;
@@ Line 1,233: / Line 1,273: @@
 &lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Books / Literature:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;&lt;strong&gt;Books / Literature:&lt;/strong&gt;&lt;/h1&gt;
   Sword, Ron. &amp;quot;Icosihenaphonic Scales for Guitar&amp;quot;. IAAA Press. 1st ed: July 2009.&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:944:&amp;lt;img src=&amp;quot;http://www.ronsword.com/images/ron1.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 188px; width: 254px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.ronsword.com/images/ron1.jpg" alt="external image ron1.jpg" title="external image ron1.jpg" style="height: 188px; width: 254px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:944 --&gt;&lt;!-- ws:start:WikiTextRemoteImageRule:945:&amp;lt;img src=&amp;quot;http://www.swordguitars.com/21tetsm.JPG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 191px; width: 363px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.swordguitars.com/21tetsm.JPG" alt="external image 21tetsm.JPG" title="external image 21tetsm.JPG" style="height: 191px; width: 363px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:945 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:990:&amp;lt;img src=&amp;quot;http://www.ronsword.com/images/ron1.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 188px; width: 254px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.ronsword.com/images/ron1.jpg" alt="external image ron1.jpg" title="external image ron1.jpg" style="height: 188px; width: 254px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:990 --&gt;&lt;!-- ws:start:WikiTextRemoteImageRule:991:&amp;lt;img src=&amp;quot;http://www.swordguitars.com/21tetsm.JPG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 191px; width: 363px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.swordguitars.com/21tetsm.JPG" alt="external image 21tetsm.JPG" title="external image 21tetsm.JPG" style="height: 191px; width: 363px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:991 --&gt;&lt;br /&gt;
 &lt;strong&gt;&lt;em&gt;21-edo Icosihenaphonic Acoustic Guitar (Ron Sword)&lt;/em&gt;&lt;/strong&gt;&lt;br /&gt;
 &lt;br /&gt;