14edo: Difference between revisions

Line 1:

<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>2016-12-22 04:04:36 UTC</tt>.

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-26 04:02:43 UTC</tt>.

: The original revision id was <tt>~~602738348~~</tt>.

: The original revision id was <tt>602812062</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.

Line 10:

[[toc|flat]]

=**Intervals**=

|| **~~DEGREE~~** ||||= ~~[[xenharmonic/Ups and Downs Notation|up/down]]~~

||< **Degree** ||= **Cents** ||= **Approximate**

~~[[xenharmonic/Ups and Downs Notation| notation]] ||~~ **~~CENTS~~** ||= **Approximate**

**Ratios 1 *** ||= **Approximate**

**Ratios 1``*``** ||= **Approximate**

**Ratios 2** ****** ||= Nearest

**Ratios 2** **``**``** ||= Nearest

Harmonic ||||||= [[xenharmonic/Ups and Downs Notation|up/down]]

Harmonic || Interval Type ||

[[xenharmonic/Ups and Downs Notation| notation]] ||= Interval Type ||

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

||< 0 ||= 0 ||= 1/1 ||= 1/1 ||= 1 ||= unison ||= 1 ||= D ||= Unison ||

|| 1 ||= ~~C^, Dv~~ ||~~= up-unison,~~

||< 1 ||= 85.714 ||= 20/19, 19/18, 18/17 ||= 22/21, 28/27, 21/20 ||= 67 ||= up-unison,

~~down-2nd~~ || 85.714 ||= 20/19, 19/18, 18/17 ||= 22/21, 28/27, 21/20 ||= 67 || ~~Narrow Minor~~ 2nd ||

down-2nd ||= ^1, v2 ||= D^, Ev ||= Narrow Minor 2nd ||

~~|| 2~~ ||= D ||= 2nd || 171.429 ||= 11/10, 10/9,

||< 2 ||= 171.429 ||= 11/10, 10/9,

19/17 ||= 9/8, 10/9,

11/10, 12/11 ||= 71 || Neutral 2nd, or

11/10, 12/11 ||= 71 ||= 2nd ||= 2 ||= E ||= Neutral 2nd, or

Narrow Major 2nd ||

|| 3· ||= ~~D^, Ev ||= up-2nd,~~

||< 3· ||= 257.143 ||= 22/19, 20/17 ||= 7/6, 8/7 ||= 37 ||= up-2nd,

~~down-3rd ||~~ 257.143 ||= 22/19, 20/17 ||= 7/6, 8/7 ||= 37 || ~~Subminor~~ 3rd ||

down-3rd ||= ^2, v3 ||= E^, Fv ||= Subminor 3rd ||

~~|| 4~~ ||= E ||= 3rd || 342.857 ||= 11/9, 17/14 ||= 11/9, 5/4, 6/5 ||= 39 || ~~Neutral~~ 3rd ||

||< 4 ||= 342.857 ||= 11/9, 17/14 ||= 11/9, 5/4, 6/5 ||= 39 ||= 3rd ||= 3 ||= F ||= Neutral 3rd ||

|| 5· ||= ~~E^, Fv~~ ||~~= up-3rd,~~

||< 5· ||= 428.571 ||= 9/7, 14/11,

~~down-4th~~ || 428.571 ||= 9/7, 14/11,

22/17 ||= 9/7, 14/11 ||= 41 ||= up-3rd,

22/17 ||= 9/7, 14/11 ||= 41 || ~~Supermajor~~ 3rd ||

down-4th ||= ^3, v4 ||= F^, Gv ||= Supermajor 3rd ||

|| 6 ||= F ||= ~~4th~~ || 514.286 ||= 19/14 ||= 4/3, 11/8 ||= 43 || ~~Wide~~ 4th ||

||< 6 ||= 514.286 ||= 19/14 ||= 4/3, 11/8 ||= 43 ||= 4th ||= 4 ||= G ||= Wide 4th ||

|| 7· ||= ~~F^, Gv~~ ||~~= up-4th,~~

||< 7· ||= 600 ||= 7/5, 10/7 ||= 7/5, 10/7 ||= 91 ||= up-4th,

~~down-5th~~ || 600 ||= 7/5, 10/7 ||= 7/5, 10/7 ||= 91 || ~~Tritone ||~~

down-5th ||= ^4, v5 ||= G^, Av ||= Tritone ||

|| 8 ||= G ||= ~~5th~~ || 685.714 ||= 28/19 ||= 3/2, 16/11 ||= 95 || ~~Narrow~~ 5th ||

||< 8 ||= 685.714 ||= 28/19 ||= 3/2, 16/11 ||= 95 ||= 5th ||= 5 ||= A ||= Narrow 5th ||

|| 9· ||= ~~G^, Av~~ ||~~= up-5th,~~

||< 9· ||= 771.429 ||= 14/9, 11/7,

~~down-6th~~ || 771.429 ||= 14/9, 11/7,

17/11 ||= ||= 25 ||= up-5th,

17/11 ||= ||= 25 || ~~Subminor~~ 6th ||

down-6th ||= ^5, v6 ||= A^, Bv ||= Subminor 6th ||

~~|| 10~~ ||= A ||= 6th || 857.143 ||= 18/11 ||= 18/11, 8/5, 5/3 ||= 105 || ~~Neutral~~ 6th ||

||< 10 ||= 857.143 ||= 18/11 ||= 18/11, 8/5, 5/3 ||= 105 ||= 6th ||= 6 ||= B ||= Neutral 6th ||

|| ~~11·~~ ||= ~~A^, Bv~~ ||~~= up-6th,~~

||< 11· ||= 942.857 ||= 19/11, 17/10 ||= 12/7, 7/4 ||= 55 ||= up-6th,

~~down-7th~~ || 942.857 ||= 19/11, 17/10 ||= 12/7, 7/4 ||= 55 || ~~Supermajor~~ 6th ||

down-7th ||= ^6, v7 ||= B^, Cv ||= Supermajor 6th ||

|| 12 ||= B ||= ~~7th~~ || 1028.571 ||= 20/11, 9/5,

||< 12 ||= 1028.571 ||= 20/11, 9/5,

34/19 ||= 16/9, 9/5,

20/11, 11/6 ||= 29 || Neutral 7th, or

20/11, 11/6 ||= 29 ||= 7th ||= 7 ||= C ||= Neutral 7th, or

Wide Minor 7th ||

|| 13 ||= ~~B^, Cv ||= up-7th,~~

||< 13 ||= 1114.286 ||= 19/10, 36/19,

~~down-8ve ||~~ 1114.286 ||= 19/10, 36/19,

17/9 ||= 21/11, 27/14, 40/21 ||= 61 ||= up-7th,

17/9 ||= 21/11, 27/14, 40/21 ||= 61 || ~~Wide Major~~ 7th ||

down-8ve ||= ^7, v8 ||= C^, Dv ||= Wide Major 7th ||

|| ~~14··(or 0)~~ ||= C ||= ~~8ve~~ || 1200 ||= 2/1 ||= 2/1 ||= 2 || Octave ||

||< 14·· ||= 1200 ||= 2/1 ||= 2/1 ||= 2 ||= 8ve ||= 8 ||= D ||= Octave ||

``*``based on treating 14-EDO as a 2.7/5.9/5.11/5.17/5.19/5 [[subgroup]]; other approaches are possible.

* based on treating 14-EDO as a 2.7/5.9/5.11/5.17/5.19/5 [[subgroup]]; other approaches are possible.

``**``based on treating 14edo as an 11-limit temperament

** based on treating 14edo as an 11-limit temperament

=Chord Names=

Line 113:

=Commas=

14 EDO [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes the val < 14 22 33 39 48 52/1 |.)

14 EDO [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes the val < 14 22 33 39 48 52 |.)

||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||

||= 2187/2048 ||< | -11 7 > ||> 113.69 ||= Apotome ||= ||

Line 175:

<a href="#Intervals">Intervals</a> | <a href="#Chord Names">Chord Names</a> | <a href="#Rank two temperaments">Rank two temperaments</a> | <a href="#Harmony">Harmony</a> | <a href="#Notation">Notation</a> | <a href="#Images">Images</a> | <a href="#Commas">Commas</a> | <a href="#Modes">Modes</a> | <a href="#Books">Books</a> | <a href="#Compositions">Compositions</a>

<a href="#Intervals">Intervals</a> | <a href="#Chord Names">Chord Names</a> | <a href="#Rank two temperaments">Rank two temperaments</a> | <a href="#Harmony">Harmony</a> | <a href="#Notation">Notation</a> | <a href="#Images">Images</a> | <a href="#Commas">Commas</a> | <a href="#Modes">Modes</a> | <a href="#Books">Books</a> | <a href="#Compositions">Compositions</a>

<h1 id="toc0"><a name="Intervals"></a>Intervals</h1>

<h1 id="toc0"><a name="Intervals"></a>Intervals</h1>

<tr>

<td>~~DEGREE~~

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

</td>

<td ~~colspan="2"~~ style="text-align: center;"~~><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation">up/down</a> ~~

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

~~<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation"> notation</a> ~~

~~</td>~~

~~<td~~>~~CENTS~~

</td>

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

Ratios 1~~*~~

Ratios 1 *

</td>

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

Ratios 2 ~~**~~

Ratios 2 **

</td>

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

Harmonic

</td>

<td>Interval Type

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation"> notation</a>

</td>

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

</td>

</tr>

<tr>

~~<td>0 ~~

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

~~</td>~~

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

</td>

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

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

</td>

<td>0

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

</td>

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

</td>

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

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

</td>

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

</td>

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

</td>

<td>Unison

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

</td>

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

</td>

</tr>

<tr>

~~<td>1 ~~

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

~~</td>~~

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

</td>

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

<td style="text-align: center;">85.714

~~down-2nd ~~

~~</td>~~

~~<td~~>85.714

</td>

<td style="text-align: center;">20/19, 19/18, 18/17

Line 234:

Line 231:

<td style="text-align: center;">67

</td>

<td>Narrow Minor 2nd

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

down-2nd

</td>

<td style="text-align: center;">^1, v2

</td>

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

</td>

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

</td>

</tr>

<tr>

<td>2

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

</td>

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

<td style="text-align: center;">171.429

~~</td>~~

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

~~</td>~~

~~<td~~>171.429

</td>

<td style="text-align: center;">11/10, 10/9,

Line 254:

<td style="text-align: center;">71

</td>

<td>Neutral 2nd, or

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

</td>

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

</td>

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

</td>

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

Narrow Major 2nd

</td>

</tr>

<tr>

~~<td>3· ~~

<td style="text-align: left;">3·

~~</td>~~

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

~~</td>~~

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

~~down-3rd~~

</td>

<td>257.143

<td style="text-align: center;">257.143

</td>

<td style="text-align: center;">22/19, 20/17

Line 274:

Line 275:

<td style="text-align: center;">37

</td>

<td>Subminor 3rd

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

down-3rd

</td>

<td style="text-align: center;">^2, v3

</td>

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

</td>

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

</td>

</tr>

<tr>

~~<td>4 ~~

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

~~</td>~~

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

~~</td>~~

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

</td>

<td>342.857

<td style="text-align: center;">342.857

</td>

<td style="text-align: center;">11/9, 17/14

Line 292:

Line 296:

<td style="text-align: center;">39

</td>

<td>Neutral 3rd

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

</td>

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

</td>

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

</td>

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

</td>

</tr>

<tr>

<td>5·

<td style="text-align: left;">5·

</td>

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

<td style="text-align: center;">428.571

~~</td>~~

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

~~down-4th ~~

~~</td>~~

~~<td~~>428.571

</td>

<td style="text-align: center;">9/7, 14/11,

Line 312:

Line 317:

<td style="text-align: center;">41

</td>

<td>Supermajor 3rd

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

down-4th

</td>

<td style="text-align: center;">^3, v4

</td>

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

</td>

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

</td>

</tr>

<tr>

<td>6

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

</td>

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

<td style="text-align: center;">514.286

~~</td>~~

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

~~</td>~~

~~<td~~>514.286

</td>

<td style="text-align: center;">19/14

Line 330:

Line 338:

<td style="text-align: center;">43

</td>

<td>Wide 4th

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

</td>

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

</td>

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

</td>

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

</td>

</tr>

<tr>

<td>7·

<td style="text-align: left;">7·

</td>

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

<td style="text-align: center;">600

~~</td>~~

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

~~down-5th ~~

~~</td>~~

~~<td~~>600

</td>

<td style="text-align: center;">7/5, 10/7

Line 349:

Line 358:

<td style="text-align: center;">91

</td>

<td>Tritone

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

down-5th

</td>

<td style="text-align: center;">^4, v5

</td>

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

</td>

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

</td>

</tr>

<tr>

~~<td>8 ~~

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

~~</td>~~

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

~~</td>~~

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

</td>

<td>685.714

<td style="text-align: center;">685.714

</td>

<td style="text-align: center;">28/19

Line 367:

Line 379:

<td style="text-align: center;">95

</td>

<td>Narrow 5th

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

</td>

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

</td>

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

</td>

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

</td>

</tr>

<tr>

<td>9·

<td style="text-align: left;">9·

</td>

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

<td style="text-align: center;">771.429

~~</td>~~

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

~~down-6th ~~

~~</td>~~

~~<td~~>771.429

</td>

<td style="text-align: center;">14/9, 11/7,

Line 387:

Line 400:

<td style="text-align: center;">25

</td>

<td>Subminor 6th

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

down-6th

</td>

<td style="text-align: center;">^5, v6

</td>

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

</td>

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

</td>

</tr>

<tr>

<td>10

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

</td>

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

<td style="text-align: center;">857.143

~~</td>~~

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

~~</td>~~

~~<td~~>857.143

</td>

<td style="text-align: center;">18/11

Line 405:

Line 421:

<td style="text-align: center;">105

</td>

<td>Neutral 6th

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

</td>

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

</td>

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

</td>

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

</td>

</tr>

<tr>

<td>11·

<td style="text-align: left;">11·

</td>

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

<td style="text-align: center;">942.857

~~</td>~~

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

~~down-7th ~~

~~</td>~~

~~<td~~>942.857

</td>

<td style="text-align: center;">19/11, 17/10

Line 424:

Line 441:

<td style="text-align: center;">55

</td>

<td>Supermajor 6th

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

down-7th

</td>

<td style="text-align: center;">^6, v7

</td>

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

</td>

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

</td>

</tr>

<tr>

<td>12

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

</td>

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

<td style="text-align: center;">1028.571

~~</td>~~

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

~~</td>~~

~~<td~~>1028.571

</td>

<td style="text-align: center;">20/11, 9/5,

Line 444:

Line 464:

<td style="text-align: center;">29

</td>

<td>Neutral 7th, or

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

</td>

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

</td>

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

</td>

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

Wide Minor 7th

</td>

</tr>

<tr>

~~<td>13 ~~

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

~~</td>~~

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

</td>

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

<td style="text-align: center;">1114.286

~~down-8ve ~~

~~</td>~~

~~<td~~>1114.286

</td>

<td style="text-align: center;">19/10, 36/19,

Line 465:

Line 486:

<td style="text-align: center;">61

</td>

<td>Wide Major 7th

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

down-8ve

</td>

<td style="text-align: center;">^7, v8

</td>

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

</td>

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

</td>

</tr>

<tr>

<td>14··~~(or 0)~~

<td style="text-align: left;">14··

</td>

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

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

~~</td>~~

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

~~</td>~~

~~<td~~>1200

</td>

<td style="text-align: center;">2/1

Line 483:

Line 507:

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

</td>

<td>Octave

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

</td>

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

</td>

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

</td>

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

</td>

</tr>

</table>

<~~!-- ws:start:WikiTextRawRule:02:``*`` --~~>*<~~!-- ws:end:WikiTextRawRule:02 --~~>based on treating 14-EDO as a 2.7/5.9/5.11/5.17/5.19/5 <a class="wiki_link" href="/subgroup">subgroup</a>; other approaches are possible.

<ul><li>based on treating 14-EDO as a 2.7/5.9/5.11/5.17/5.19/5 <a class="wiki_link" href="/subgroup">subgroup</a>; other approaches are possible.</li></ul>** based on treating 14edo as an 11-limit temperament

~~**~~based on treating 14edo as an 11-limit temperament

<h1 id="toc1"><a name="Chord Names"></a>Chord Names</h1>

<h1 id="toc1"><a name="Chord Names"></a>Chord Names</h1>

Ups and downs can be used to name 14edo chords. Because every interval is perfect, the quality can be omitted, and the words major, minor, augmented and diminished are never used.

Line 508:

Line 537:

<object id="example" type="image/svg+xml" data="http://xenharmonic.wikispaces.com/file/view/14ed2-001.svg">alt : Your browser has no SVG support.</object>

<object id="example" type="image/svg+xml" data="http://xenharmonic.wikispaces.com/file/view/14ed2-001.svg">alt : Your browser has no SVG support.</object>

<div class="objectEmbed"><a href="/file/view/14ed2-001.svg/480713166/14ed2-001.svg" onclick="ws.common.trackFileLink('/file/view/14ed2-001.svg/480713166/14ed2-001.svg');"><img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="14ed2-001.svg" /></a><div><a href="/file/view/14ed2-001.svg/480713166/14ed2-001.svg" onclick="ws.common.trackFileLink('/file/view/14ed2-001.svg/480713166/14ed2-001.svg');" class="filename" title="14ed2-001.svg">14ed2-001.svg</a> <ul><li><a href="/file/detail/14ed2-001.svg">Details</a></li><li><a href="/file/view/14ed2-001.svg/480713166/14ed2-001.svg">Download</a></li><li style="color: #666">15 KB</li></ul></div></div>

<div class="objectEmbed"><a href="/file/view/14ed2-001.svg/480713166/14ed2-001.svg" onclick="ws.common.trackFileLink('/file/view/14ed2-001.svg/480713166/14ed2-001.svg');"><img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="14ed2-001.svg" /></a><div><a href="/file/view/14ed2-001.svg/480713166/14ed2-001.svg" onclick="ws.common.trackFileLink('/file/view/14ed2-001.svg/480713166/14ed2-001.svg');" class="filename" title="14ed2-001.svg">14ed2-001.svg</a> <ul><li><a href="/file/detail/14ed2-001.svg">Details</a></li><li><a href="/file/view/14ed2-001.svg/480713166/14ed2-001.svg">Download</a></li><li style="color: #666">15 KB</li></ul></div></div>

<h1 id="toc2"><a name="Rank two temperaments"></a>Rank two temperaments</h1>

<h1 id="toc2"><a name="Rank two temperaments"></a>Rank two temperaments</h1>

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/List%20of%2014edo%20rank%20two%20temperaments%20by%20badness">List of 14edo rank two temperaments by badness</a>

<h1 id="toc3"><a name="Harmony"></a>Harmony</h1>

<h1 id="toc3"><a name="Harmony"></a>Harmony</h1>

The character of 14-EDO does not well serve those seeking low-limit JI approaches, with the exception of 5:7:9:11:17:19 (which is quite well approximated, relative to other JI approximations of the low-numbered EDOs). However, the ratios 7/5, 7/6, 9/7, 10/7, 10/9, 11/7, 11/9, and 11/10 are all recognizably approximated, and if you accept that 14edo offers approximations of these intervals, you end up with a low-complexity, high-damage 11-limit temperament where the commas listed at the bottom of this page are tempered out. This leads to some of the bizarre equivalences described in the second &quot;Approximate Ratios&quot; column in the table above.

14-EDO has quite a bit of xenharmonic appeal, in a similar way to 17-EDO, on account of having three types of 3rd and three types of 6th, rather than the usual two of 12-TET. Since 14-EDO also has a recognizable 4th and 5th, this makes it good for those wishing to explore alternative triadic harmonies without adding significantly more notes. It possesses a triad-rich 9-note MOS scale of 5L4s, wherein 7 of 9 notes are tonic to a subminor, supermajor, and/or neutral triad.

<h3 id="toc4"><a name="Harmony--Titanium[9]"></a>Titanium[9]</h3>

<h3 id="toc4"><a name="Harmony--Titanium[9]"></a>Titanium[9]</h3>

14edo is also the largest edo whose patent val supports <a class="wiki_link" href="/titanium">titanium</a> temperament, tempering out the chromatic semitone (21:20), and falling toward the &quot;brittle&quot; (fifths wider than in 9edo) end of that spectrum. Titanium is one of the simplest 7-limit temperaments, although rather inaccurate (the 7:5 is mapped onto 6\14, over 70 cents flat). Its otonal/major and utonal/minor tetrads are inversions of one another, which allows a greater variety of chord progressions (since different inversions of the same chord may have very different expressive qualities). Despite being so heavily tempered, the tetrads are still recognizable and aren't unpleasant-sounding as long as one uses the right timbres (&quot;bell-like&quot; or opaque-sounding ones probably work best). Titanium forms enneatonic modes which are melodically strong and are very similar to diatonic modes, only with two mediants and submediants instead of one. Titanium[9] has similarities to mavila, slendro, and pelog scales as well.

Line 541:

Line 570:

14\14: The 10th9 or &quot;enneatonic decave&quot;, (i. e., the octave, 2:1).

<h1 id="toc5"><a name="Notation"></a>Notation</h1>

<h1 id="toc5"><a name="Notation"></a>Notation</h1>

<a class="wiki_link" href="/Ivor%20Darreg">Ivor Darreg</a> wrote in <a class="wiki_link_ext" href="http://sonic-arts.org/darreg/dar15.htm" rel="nofollow">this article</a>:

Line 548:

Line 577:

The following chart (made by <a class="wiki_link" href="/T%C3%BAtim%20Dennsuul%20Wafiil">TDW</a>) shows this recommendation as &quot;standard notation&quot; as well as a proposed alternative.

<table class="captionBox"><tr><td class="captionedImage"><img src="/file/view/Ciclo_Tetradecafon%C3%ADa.png/233692646/456x468/Ciclo_Tetradecafon%C3%ADa.png" alt="Ciclo_Tetradecafonía.png" title="Ciclo_Tetradecafonía.png" style="height: 468px; width: 456px;" /></td></tr><tr><td class="imageCaption">Intervallic Cycle of 14 steps Equal per Octave</td></tr></table>

<table class="captionBox"><tr><td class="captionedImage"><img src="/file/view/Ciclo_Tetradecafon%C3%ADa.png/233692646/456x468/Ciclo_Tetradecafon%C3%ADa.png" alt="Ciclo_Tetradecafonía.png" title="Ciclo_Tetradecafonía.png" style="height: 468px; width: 456px;" /></td></tr><tr><td class="imageCaption">Intervallic Cycle of 14 steps Equal per Octave</td></tr></table>

<h1 id="toc6"><a name="Images"></a>Images</h1>

<h1 id="toc6"><a name="Images"></a>Images</h1>

<img src="/file/view/14edo%20wheel.png/516971016/343x343/14edo%20wheel.png" alt="14edo wheel.png" title="14edo wheel.png" style="height: 343px; width: 343px;" />

<img src="/file/view/14edo%20wheel.png/516971016/343x343/14edo%20wheel.png" alt="14edo wheel.png" title="14edo wheel.png" style="height: 343px; width: 343px;" />

<h1 id="toc7"><a name="Commas"></a>Commas</h1>

<h1 id="toc7"><a name="Commas"></a>Commas</h1>

14 EDO <a class="wiki_link" href="/tempering%20out">tempers out</a> the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes the val &lt; 14 22 33 39 48 52/1 |.)

14 EDO <a class="wiki_link" href="/tempering%20out">tempers out</a> the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes the val &lt; 14 22 33 39 48 52 |.)

Line 718:

Line 747:

<h1 id="toc8"><a name="Modes"></a><a class="wiki_link" href="/modes">Modes</a></h1>

<h1 id="toc8"><a name="Modes"></a><a class="wiki_link" href="/modes">Modes</a></h1>

5 5 4 - <a class="wiki_link" href="/MOSScales">MOS</a> of <a class="wiki_link" href="/2L1s">2L1s</a>

5 4 5 - <a class="wiki_link" href="/MOSScales">MOS</a> of <a class="wiki_link" href="/2L1s">2L1s</a>

Line 743:

Line 772:

<h1 id="toc9"><a name="Books"></a>Books</h1>

<h1 id="toc9"><a name="Books"></a>Books</h1>

<img src="/file/view/Libro_Tetradecaf%C3%B3nico.PNG/163539671/Libro_Tetradecaf%C3%B3nico.PNG" alt="Libro_Tetradecafónico.PNG" title="Libro_Tetradecafónico.PNG" />

<img src="/file/view/Libro_Tetradecaf%C3%B3nico.PNG/163539671/Libro_Tetradecaf%C3%B3nico.PNG" alt="Libro_Tetradecafónico.PNG" title="Libro_Tetradecafónico.PNG" />

Sword, Ron. &quot;Tetradecaphonic Scales for Guitar&quot; IAAA Press. First Ed: June 2009.

<h1 id="toc10"><a name="Compositions"></a>Compositions</h1>

<h1 id="toc10"><a name="Compositions"></a>Compositions</h1>

<a class="wiki_link_ext" href="http://split-notes.com/004/" rel="nofollow">NANA WODORI</a> by knowsur

<a class="wiki_link_ext" href="http://micro.soonlabel.com/0-praxis/audio/August/august_03_thereminnards.mp3" rel="nofollow">Thereminnards</a> by Ralph Lewis

@@ 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>2016-12-22 04:04:36 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-26 04:02:43 UTC</tt>.<br>
-: The original revision id was <tt>602738348</tt>.<br>
+: The original revision id was <tt>602812062</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
@@ Line 10: / Line 10: @@
 [[toc|flat]]
 =**Intervals**=
-|| **DEGREE** ||||= [[xenharmonic/Ups and Downs Notation|up/down]]
+||&lt; **Degree** ||= **Cents** ||= **Approximate**
-[[xenharmonic/Ups and Downs Notation| notation]] || **CENTS** ||= **Approximate**
+**Ratios 1 *** ||= **Approximate**
-**Ratios 1``*``** ||= **Approximate**
+**Ratios 2** ****** ||= Nearest
-**Ratios 2** **``**``** ||= Nearest
+Harmonic ||||||= [[xenharmonic/Ups and Downs Notation|up/down]]
-Harmonic || Interval Type ||
+[[xenharmonic/Ups and Downs Notation| notation]] ||= Interval Type ||
-|| 0 ||= C ||= unison || 0 ||= 1/1 ||= 1/1 ||= 1 || Unison ||
+||&lt; 0 ||= 0 ||= 1/1 ||= 1/1 ||= 1 ||= unison ||= 1 ||= D ||= Unison ||
-|| 1 ||= C^, Dv ||= up-unison,
+||&lt; 1 ||= 85.714 ||= 20/19, 19/18, 18/17 ||= 22/21, 28/27, 21/20 ||= 67 ||= up-unison,
-down-2nd || 85.714 ||= 20/19, 19/18, 18/17 ||= 22/21, 28/27, 21/20 ||= 67 || Narrow Minor 2nd ||
+down-2nd ||= ^1, v2 ||= D^, Ev ||= Narrow Minor 2nd ||
-|| 2 ||= D ||= 2nd || 171.429 ||= 11/10, 10/9,
+||&lt; 2 ||= 171.429 ||= 11/10, 10/9,
 /17 ||= 9/8, 10/9,
-/10, 12/11 ||= 71 || Neutral 2nd, or
+/10, 12/11 ||= 71 ||= 2nd ||= 2 ||= E ||= Neutral 2nd, or
 Narrow Major 2nd ||
-|| 3· ||= D^, Ev ||= up-2nd,
+||&lt; 3· ||= 257.143 ||= 22/19, 20/17 ||= 7/6, 8/7 ||= 37 ||= up-2nd,
-down-3rd || 257.143 ||= 22/19, 20/17 ||= 7/6, 8/7 ||= 37 || Subminor 3rd ||
+down-3rd ||= ^2, v3 ||= E^, Fv ||= Subminor 3rd ||
-|| 4 ||= E ||= 3rd || 342.857 ||= 11/9, 17/14 ||= 11/9, 5/4, 6/5 ||= 39 || Neutral 3rd ||
+||&lt; 4 ||= 342.857 ||= 11/9, 17/14 ||= 11/9, 5/4, 6/5 ||= 39 ||= 3rd ||= 3 ||= F ||= Neutral 3rd ||
-|| 5· ||= E^, Fv ||= up-3rd,
+||&lt; 5· ||= 428.571 ||= 9/7, 14/11,
-down-4th || 428.571 ||= 9/7, 14/11,
+/17 ||= 9/7, 14/11 ||= 41 ||= up-3rd,
-/17 ||= 9/7, 14/11 ||= 41 || Supermajor 3rd ||
+down-4th ||= ^3, v4 ||= F^, Gv ||= Supermajor 3rd ||
-|| 6 ||= F ||= 4th || 51&lt;span style="line-height: 1.5;"&gt;4.286&lt;/span&gt; ||= 19/14 ||= 4/3, 11/8 ||= 43 || Wide 4th ||
+||&lt; 6 ||= 51&lt;span style="line-height: 1.5;"&gt;4.286&lt;/span&gt; ||= 19/14 ||= 4/3, 11/8 ||= 43 ||= 4th ||= 4 ||= G ||= Wide 4th ||
-|| 7· ||= F^, Gv ||= up-4th,
+||&lt; 7· ||= 600 ||= 7/5, 10/7 ||= 7/5, 10/7 ||= 91 ||= up-4th,
-down-5th || 600 ||= 7/5, 10/7 ||= 7/5, 10/7 ||= 91 || Tritone ||
+down-5th ||= ^4, v5 ||= G^, Av ||= Tritone ||
-|| 8 ||= G ||= 5th || 685.714 ||= 28/19 ||= 3/2, 16/11 ||= 95 || Narrow 5th ||
+||&lt; 8 ||= 685.714 ||= 28/19 ||= 3/2, 16/11 ||= 95 ||= 5th ||= 5 ||= A ||= Narrow 5th ||
-|| 9· ||= G^, Av ||= up-5th,
+||&lt; 9· ||= 771.429 ||= 14/9, 11/7,
-down-6th || 771.429 ||= 14/9, 11/7,
+/11 ||=   ||= 25 ||= up-5th,
-/11 ||=   ||= 25 || Subminor 6th ||
+down-6th ||= ^5, v6 ||= A^, Bv ||= Subminor 6th ||
-|| 10 ||= A ||= 6th || 857.143 ||= 18/11 ||= 18/11, 8/5, 5/3 ||= 105 || Neutral 6th ||
+||&lt; 10 ||= 857.143 ||= 18/11 ||= 18/11, 8/5, 5/3 ||= 105 ||= 6th ||= 6 ||= B ||= Neutral 6th ||
-|| 11· ||= A^, Bv ||= up-6th,
+||&lt; 11· ||= 942.857 ||= 19/11, 17/10 ||= 12/7, 7/4 ||= 55 ||= up-6th,
-down-7th || 942.857 ||= 19/11, 17/10 ||= 12/7, 7/4 ||= 55 || Supermajor 6th ||
+down-7th ||= ^6, v7 ||= B^, Cv ||= Supermajor 6th ||
-|| 12 ||= B ||= 7th || 1028.571 ||= 20/11, 9/5,
+||&lt; 12 ||= 1028.571 ||= 20/11, 9/5,
 /19 ||= 16/9, 9/5,
-/11, 11/6 ||= 29 || Neutral 7th, or
+/11, 11/6 ||= 29 ||= 7th ||= 7 ||= C ||= Neutral 7th, or
 Wide Minor 7th ||
-|| 13 ||= B^, Cv ||= up-7th,
+||&lt; 13 ||= 1114.286 ||= 19/10, 36/19,
-down-8ve || 1114.286 ||= 19/10, 36/19,
+/9 ||= 21/11, 27/14, 40/21 ||= 61 ||= up-7th,
-/9 ||= 21/11, 27/14, 40/21 ||= 61 || Wide Major 7th ||
+down-8ve ||= ^7, v8 ||= C^, Dv ||= Wide Major 7th ||
-|| 14··(or 0) ||= C ||= 8ve || 1200 ||= 2/1 ||= 2/1 ||= 2 || Octave ||
+||&lt; 14·· ||= 1200 ||= 2/1 ||= 2/1 ||= 2 ||= 8ve ||= 8 ||= D ||= Octave ||
-``*``based on treating 14-EDO as a 2.7/5.9/5.11/5.17/5.19/5 [[subgroup]]; other approaches are possible.
+* based on treating 14-EDO as a 2.7/5.9/5.11/5.17/5.19/5 [[subgroup]]; other approaches are possible.
-&lt;span style="display: block; text-align: center;"&gt;``**``based on treating 14edo as an 11-limit temperament&lt;/span&gt;
+&lt;span style="display: block; text-align: left;"&gt;** based on treating 14edo as an 11-limit temperament&lt;/span&gt;
 =Chord Names=
@@ Line 113: / Line 113: @@
 =Commas=
-EDO [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes the val &lt; 14 22 33 39 48 52/1 |.)
+EDO [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes the val &lt; 14 22 33 39 48 52 |.)
 ||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||
 ||= 2187/2048 ||&lt; | -11 7 &gt; ||&gt; 113.69 ||= Apotome ||=   ||
@@ Line 175: / Line 175: @@
 <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;14edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="display: block; text-align: right;"&gt;&lt;a class="wiki_link" href="/14%E5%B9%B3%E5%9D%87%E5%BE%8B"&gt;日本語&lt;/a&gt;&lt;br /&gt;
 &lt;/span&gt;&lt;br /&gt;
-&lt;!-- ws:start:WikiTextTocRule:27:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt;&lt;a href="#Intervals"&gt;Intervals&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;!-- ws:start:WikiTextTocRule:29: --&gt; | &lt;a href="#Chord Names"&gt;Chord Names&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:29 --&gt;&lt;!-- ws:start:WikiTextTocRule:30: --&gt; | &lt;a href="#Rank two temperaments"&gt;Rank two temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt; | &lt;a href="#Harmony"&gt;Harmony&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;!-- ws:start:WikiTextTocRule:32: --&gt;&lt;!-- ws:end:WikiTextTocRule:32 --&gt;&lt;!-- ws:start:WikiTextTocRule:33: --&gt; | &lt;a href="#Notation"&gt;Notation&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:33 --&gt;&lt;!-- ws:start:WikiTextTocRule:34: --&gt; | &lt;a href="#Images"&gt;Images&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:34 --&gt;&lt;!-- ws:start:WikiTextTocRule:35: --&gt; | &lt;a href="#Commas"&gt;Commas&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:35 --&gt;&lt;!-- ws:start:WikiTextTocRule:36: --&gt; | &lt;a href="#Modes"&gt;Modes&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:36 --&gt;&lt;!-- ws:start:WikiTextTocRule:37: --&gt; | &lt;a href="#Books"&gt;Books&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:37 --&gt;&lt;!-- ws:start:WikiTextTocRule:38: --&gt; | &lt;a href="#Compositions"&gt;Compositions&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:38 --&gt;&lt;!-- ws:start:WikiTextTocRule:39: --&gt;
+&lt;!-- ws:start:WikiTextTocRule:23:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;!-- ws:start:WikiTextTocRule:24: --&gt;&lt;a href="#Intervals"&gt;Intervals&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt; | &lt;a href="#Chord Names"&gt;Chord Names&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;!-- ws:start:WikiTextTocRule:26: --&gt; | &lt;a href="#Rank two temperaments"&gt;Rank two temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt; | &lt;a href="#Harmony"&gt;Harmony&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt;&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;!-- ws:start:WikiTextTocRule:29: --&gt; | &lt;a href="#Notation"&gt;Notation&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:29 --&gt;&lt;!-- ws:start:WikiTextTocRule:30: --&gt; | &lt;a href="#Images"&gt;Images&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt; | &lt;a href="#Commas"&gt;Commas&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;!-- ws:start:WikiTextTocRule:32: --&gt; | &lt;a href="#Modes"&gt;Modes&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:32 --&gt;&lt;!-- ws:start:WikiTextTocRule:33: --&gt; | &lt;a href="#Books"&gt;Books&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:33 --&gt;&lt;!-- ws:start:WikiTextTocRule:34: --&gt; | &lt;a href="#Compositions"&gt;Compositions&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:34 --&gt;&lt;!-- ws:start:WikiTextTocRule:35: --&gt;
-&lt;!-- ws:end:WikiTextTocRule:39 --&gt;&lt;!-- ws:start:WikiTextHeadingRule:5:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:5 --&gt;&lt;strong&gt;Intervals&lt;/strong&gt;&lt;/h1&gt;
+&lt;!-- ws:end:WikiTextTocRule:35 --&gt;&lt;!-- ws:start:WikiTextHeadingRule:1:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:1 --&gt;&lt;strong&gt;Intervals&lt;/strong&gt;&lt;/h1&gt;
 &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: left;"&gt;&lt;strong&gt;Degree&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="2" style="text-align: center;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation"&gt;up/down&lt;/a&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;strong&gt;Cents&lt;/strong&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation"&gt; notation&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;CENTS&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;strong&gt;Approximate&lt;/strong&gt;&lt;br /&gt;
-&lt;strong&gt;Ratios 1&lt;!-- ws:start:WikiTextRawRule:00:``*`` --&gt;*&lt;!-- ws:end:WikiTextRawRule:00 --&gt;&lt;/strong&gt;&lt;br /&gt;
+&lt;strong&gt;Ratios 1 &lt;/strong&gt;*&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;strong&gt;Approximate&lt;/strong&gt;&lt;br /&gt;
-&lt;strong&gt;Ratios 2&lt;/strong&gt; &lt;strong&gt;&lt;!-- ws:start:WikiTextRawRule:01:``**`` --&gt;**&lt;!-- ws:end:WikiTextRawRule:01 --&gt;&lt;/strong&gt;&lt;br /&gt;
+&lt;strong&gt;Ratios 2&lt;/strong&gt; **&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Nearest&lt;br /&gt;
 Harmonic&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Interval Type&lt;br /&gt;
+         &lt;td colspan="3" style="text-align: center;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation"&gt;up/down&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation"&gt; notation&lt;/a&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Interval Type&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-        &lt;td&gt;0&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;0&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;unison&lt;br /&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: center;"&gt;1/1&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;1/1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;1/1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;unison&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Unison&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;D&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Unison&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-        &lt;td&gt;1&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;1&lt;br /&gt;
-&lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;C^, Dv&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;up-unison,&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;85.714&lt;br /&gt;
-down-2nd&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;85.714&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;20/19, 19/18, 18/17&lt;br /&gt;
@@ Line 234: / Line 231: @@
          &lt;td style="text-align: center;"&gt;67&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Narrow Minor 2nd&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;up-unison,&lt;br /&gt;
+down-2nd&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;^1, v2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;D^, Ev&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Narrow Minor 2nd&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;2&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;D&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;171.429&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;2nd&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;171.429&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;11/10, 10/9,&lt;br /&gt;
@@ Line 254: / Line 254: @@
          &lt;td style="text-align: center;"&gt;71&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Neutral 2nd, or&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;2nd&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;2&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 2nd, or&lt;br /&gt;
 Narrow Major 2nd&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-        &lt;td&gt;3·&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;3·&lt;br /&gt;
-&lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;D^, Ev&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;up-2nd,&lt;br /&gt;
-down-3rd&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;257.143&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;257.143&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;22/19, 20/17&lt;br /&gt;
@@ Line 274: / Line 275: @@
          &lt;td style="text-align: center;"&gt;37&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Subminor 3rd&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;up-2nd,&lt;br /&gt;
+down-3rd&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;^2, v3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;E^, Fv&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Subminor 3rd&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-        &lt;td&gt;4&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;4&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;3rd&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;342.857&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;342.857&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;11/9, 17/14&lt;br /&gt;
@@ Line 292: / Line 296: @@
          &lt;td style="text-align: center;"&gt;39&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Neutral 3rd&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;3rd&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;F&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Neutral 3rd&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;5·&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;5·&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;E^, Fv&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;428.571&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;up-3rd,&lt;br /&gt;
-down-4th&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;428.571&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;9/7, 14/11,&lt;br /&gt;
@@ Line 312: / Line 317: @@
          &lt;td style="text-align: center;"&gt;41&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Supermajor 3rd&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;up-3rd,&lt;br /&gt;
+down-4th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;^3, v4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;F^, Gv&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Supermajor 3rd&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;6&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;F&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;51&lt;span style="line-height: 1.5;"&gt;4.286&lt;/span&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;4th&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;51&lt;span style="line-height: 1.5;"&gt;4.286&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;19/14&lt;br /&gt;
@@ Line 330: / Line 338: @@
          &lt;td style="text-align: center;"&gt;43&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Wide 4th&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;4th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;4&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 4th&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;7·&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;7·&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;F^, Gv&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;600&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;up-4th,&lt;br /&gt;
-down-5th&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;600&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;7/5, 10/7&lt;br /&gt;
@@ Line 349: / Line 358: @@
          &lt;td style="text-align: center;"&gt;91&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Tritone&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;up-4th,&lt;br /&gt;
+down-5th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;^4, v5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;G^, Av&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Tritone&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-        &lt;td&gt;8&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;8&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;5th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;685.714&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;685.714&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;28/19&lt;br /&gt;
@@ Line 367: / Line 379: @@
          &lt;td style="text-align: center;"&gt;95&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Narrow 5th&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;5th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;5&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;Narrow 5th&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;9·&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;9·&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;G^, Av&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;771.429&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;up-5th,&lt;br /&gt;
-down-6th&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;771.429&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;14/9, 11/7,&lt;br /&gt;
@@ Line 387: / Line 400: @@
          &lt;td style="text-align: center;"&gt;25&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Subminor 6th&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;up-5th,&lt;br /&gt;
+down-6th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;^5, v6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;A^, Bv&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Subminor 6th&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;10&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;10&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;A&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;857.143&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;6th&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;857.143&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;18/11&lt;br /&gt;
@@ Line 405: / Line 421: @@
          &lt;td style="text-align: center;"&gt;105&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Neutral 6th&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;6th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;B&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Neutral 6th&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;11·&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;11·&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;A^, Bv&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;942.857&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;up-6th,&lt;br /&gt;
-down-7th&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;942.857&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;19/11, 17/10&lt;br /&gt;
@@ Line 424: / Line 441: @@
          &lt;td style="text-align: center;"&gt;55&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Supermajor 6th&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;up-6th,&lt;br /&gt;
+down-7th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;^6, v7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;B^, Cv&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Supermajor 6th&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;12&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;12&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;B&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1028.571&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;7th&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1028.571&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;20/11, 9/5,&lt;br /&gt;
@@ Line 444: / Line 464: @@
          &lt;td style="text-align: center;"&gt;29&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Neutral 7th, or&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;7th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;7&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;Neutral 7th, or&lt;br /&gt;
 Wide Minor 7th&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-        &lt;td&gt;13&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;13&lt;br /&gt;
-&lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;B^, Cv&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;up-7th,&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1114.286&lt;br /&gt;
-down-8ve&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1114.286&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;19/10, 36/19,&lt;br /&gt;
@@ Line 465: / Line 486: @@
          &lt;td style="text-align: center;"&gt;61&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Wide Major 7th&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;up-7th,&lt;br /&gt;
+down-8ve&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;^7, v8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;C^, Dv&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Wide Major 7th&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;14··(or 0)&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;14··&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;C&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1200&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;8ve&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1200&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;2/1&lt;br /&gt;
@@ Line 483: / Line 507: @@
          &lt;td style="text-align: center;"&gt;2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Octave&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;8ve&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;8&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;Octave&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
 &lt;/table&gt;
-&lt;!-- ws:start:WikiTextRawRule:02:``*`` --&gt;*&lt;!-- ws:end:WikiTextRawRule:02 --&gt;based on treating 14-EDO as a 2.7/5.9/5.11/5.17/5.19/5 &lt;a class="wiki_link" href="/subgroup"&gt;subgroup&lt;/a&gt;; other approaches are possible.&lt;br /&gt;
+&lt;ul&gt;&lt;li&gt;based on treating 14-EDO as a 2.7/5.9/5.11/5.17/5.19/5 &lt;a class="wiki_link" href="/subgroup"&gt;subgroup&lt;/a&gt;; other approaches are possible.&lt;/li&gt;&lt;/ul&gt;&lt;span style="display: block; text-align: left;"&gt;** based on treating 14edo as an 11-limit temperament&lt;/span&gt;&lt;br /&gt;
-&lt;span style="display: block; text-align: center;"&gt;&lt;!-- ws:start:WikiTextRawRule:03:``**`` --&gt;**&lt;!-- ws:end:WikiTextRawRule:03 --&gt;based on treating 14edo as an 11-limit temperament&lt;/span&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:3:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Chord Names"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:3 --&gt;Chord Names&lt;/h1&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:7:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Chord Names"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:7 --&gt;Chord Names&lt;/h1&gt;
   &lt;br /&gt;
 Ups and downs can be used to name 14edo chords. Because every interval is perfect, the quality can be omitted, and the words major, minor, augmented and diminished are never used.&lt;br /&gt;
@@ Line 508: / Line 537: @@
 &lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextMediaRule:4:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/custom/24802838?h=0&amp;amp;w=0&amp;quot; class=&amp;quot;WikiMedia WikiMediaCustom&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;custom&amp;amp;quot; key=&amp;amp;quot;24802838&amp;amp;quot;&amp;quot; title=&amp;quot;Custom Media&amp;quot;/&amp;gt; --&gt;&lt;object id="example" type="image/svg+xml" data="http://xenharmonic.wikispaces.com/file/view/14ed2-001.svg"&gt;alt : Your browser has no SVG support.&lt;/object&gt;&lt;!-- ws:end:WikiTextMediaRule:4 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/custom/24802838?h=0&amp;amp;w=0&amp;quot; class=&amp;quot;WikiMedia WikiMediaCustom&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;custom&amp;amp;quot; key=&amp;amp;quot;24802838&amp;amp;quot;&amp;quot; title=&amp;quot;Custom Media&amp;quot;/&amp;gt; --&gt;&lt;object id="example" type="image/svg+xml" data="http://xenharmonic.wikispaces.com/file/view/14ed2-001.svg"&gt;alt : Your browser has no SVG support.&lt;/object&gt;&lt;!-- ws:end:WikiTextMediaRule:0 --&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextFileRule:489:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file/14ed2-001.svg?h=52&amp;amp;w=320&amp;quot; class=&amp;quot;WikiFile&amp;quot; id=&amp;quot;wikitext@@file@@14ed2-001.svg&amp;quot; title=&amp;quot;File: 14ed2-001.svg&amp;quot; width=&amp;quot;320&amp;quot; height=&amp;quot;52&amp;quot; /&amp;gt; --&gt;&lt;div class="objectEmbed"&gt;&lt;a href="/file/view/14ed2-001.svg/480713166/14ed2-001.svg" onclick="ws.common.trackFileLink('/file/view/14ed2-001.svg/480713166/14ed2-001.svg');"&gt;&lt;img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="14ed2-001.svg" /&gt;&lt;/a&gt;&lt;div&gt;&lt;a href="/file/view/14ed2-001.svg/480713166/14ed2-001.svg" onclick="ws.common.trackFileLink('/file/view/14ed2-001.svg/480713166/14ed2-001.svg');" class="filename" title="14ed2-001.svg"&gt;14ed2-001.svg&lt;/a&gt;&lt;br /&gt;&lt;ul&gt;&lt;li&gt;&lt;a href="/file/detail/14ed2-001.svg"&gt;Details&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a href="/file/view/14ed2-001.svg/480713166/14ed2-001.svg"&gt;Download&lt;/a&gt;&lt;/li&gt;&lt;li style="color: #666"&gt;15 KB&lt;/li&gt;&lt;/ul&gt;&lt;/div&gt;&lt;/div&gt;&lt;!-- ws:end:WikiTextFileRule:489 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextFileRule:519:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file/14ed2-001.svg?h=52&amp;amp;w=320&amp;quot; class=&amp;quot;WikiFile&amp;quot; id=&amp;quot;wikitext@@file@@14ed2-001.svg&amp;quot; title=&amp;quot;File: 14ed2-001.svg&amp;quot; width=&amp;quot;320&amp;quot; height=&amp;quot;52&amp;quot; /&amp;gt; --&gt;&lt;div class="objectEmbed"&gt;&lt;a href="/file/view/14ed2-001.svg/480713166/14ed2-001.svg" onclick="ws.common.trackFileLink('/file/view/14ed2-001.svg/480713166/14ed2-001.svg');"&gt;&lt;img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="14ed2-001.svg" /&gt;&lt;/a&gt;&lt;div&gt;&lt;a href="/file/view/14ed2-001.svg/480713166/14ed2-001.svg" onclick="ws.common.trackFileLink('/file/view/14ed2-001.svg/480713166/14ed2-001.svg');" class="filename" title="14ed2-001.svg"&gt;14ed2-001.svg&lt;/a&gt;&lt;br /&gt;&lt;ul&gt;&lt;li&gt;&lt;a href="/file/detail/14ed2-001.svg"&gt;Details&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a href="/file/view/14ed2-001.svg/480713166/14ed2-001.svg"&gt;Download&lt;/a&gt;&lt;/li&gt;&lt;li style="color: #666"&gt;15 KB&lt;/li&gt;&lt;/ul&gt;&lt;/div&gt;&lt;/div&gt;&lt;!-- ws:end:WikiTextFileRule:519 --&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:9:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Rank two temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:9 --&gt;Rank two temperaments&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:5:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Rank two temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:5 --&gt;Rank two temperaments&lt;/h1&gt;
   &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/List%20of%2014edo%20rank%20two%20temperaments%20by%20badness"&gt;List of 14edo rank two temperaments by badness&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:11:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Harmony"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:11 --&gt;Harmony&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:7:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Harmony"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:7 --&gt;Harmony&lt;/h1&gt;
   The character of 14-EDO does not well serve those seeking low-limit JI approaches, with the exception of 5:7:9:11:17:19 (which is quite well approximated, relative to other JI approximations of the low-numbered EDOs). However, the ratios 7/5, 7/6, 9/7, 10/7, 10/9, 11/7, 11/9, and 11/10 are all recognizably approximated, and if you accept that 14edo offers approximations of these intervals, you end up with a low-complexity, high-damage 11-limit temperament where the commas listed at the bottom of this page are tempered out. This leads to some of the bizarre equivalences described in the second &amp;quot;Approximate Ratios&amp;quot; column in the table above.&lt;br /&gt;
 &lt;br /&gt;
 -EDO has quite a bit of xenharmonic appeal, in a similar way to 17-EDO, on account of having three types of 3rd and three types of 6th, rather than the usual two of 12-TET. Since 14-EDO also has a recognizable 4th and 5th, this makes it good for those wishing to explore alternative triadic harmonies without adding significantly more notes. It possesses a triad-rich 9-note MOS scale of 5L4s, wherein 7 of 9 notes are tonic to a subminor, supermajor, and/or neutral triad.&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:13:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="Harmony--Titanium[9]"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:13 --&gt;Titanium[9]&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:9:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="Harmony--Titanium[9]"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:9 --&gt;Titanium[9]&lt;/h3&gt;
   &lt;br /&gt;
 edo is also the largest edo whose patent val supports &lt;a class="wiki_link" href="/titanium"&gt;titanium&lt;/a&gt; temperament, tempering out the chromatic semitone (21:20), and falling toward the &amp;quot;brittle&amp;quot; (fifths wider than in 9edo) end of that spectrum. Titanium is one of the simplest 7-limit temperaments, although rather inaccurate (the 7:5 is mapped onto 6\14, over 70 cents flat). Its otonal/major and utonal/minor tetrads are inversions of one another, which allows a greater variety of chord progressions (since different inversions of the same chord may have very different expressive qualities). Despite being so heavily tempered, the tetrads are still recognizable and aren't unpleasant-sounding as long as one uses the right timbres (&amp;quot;bell-like&amp;quot; or opaque-sounding ones probably work best). Titanium forms enneatonic modes which are melodically strong and are very similar to diatonic modes, only with two mediants and submediants instead of one. Titanium[9] has similarities to mavila, slendro, and pelog scales as well.&lt;br /&gt;
@@ Line 541: / Line 570: @@
 \14: The 10th&lt;span style="vertical-align: sub;"&gt;9 &lt;/span&gt;or &amp;quot;enneatonic decave&amp;quot;, (i. e., the octave, 2:1).&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:15:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Notation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:15 --&gt;Notation&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:11:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Notation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:11 --&gt;Notation&lt;/h1&gt;
   &lt;a class="wiki_link" href="/Ivor%20Darreg"&gt;Ivor Darreg&lt;/a&gt; wrote in &lt;a class="wiki_link_ext" href="http://sonic-arts.org/darreg/dar15.htm" rel="nofollow"&gt;this article&lt;/a&gt;:&lt;br /&gt;
 &lt;br /&gt;
@@ Line 548: / Line 577: @@
 The following chart (made by &lt;a class="wiki_link" href="/T%C3%BAtim%20Dennsuul%20Wafiil"&gt;TDW&lt;/a&gt;) shows this recommendation as &amp;quot;standard notation&amp;quot; as well as a proposed alternative.&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:486:&amp;lt;img src=&amp;quot;/file/view/Ciclo_Tetradecafon%C3%ADa.png/233692646/456x468/Ciclo_Tetradecafon%C3%ADa.png&amp;quot; alt=&amp;quot;Intervallic Cycle of 14 steps Equal per Octave&amp;quot; title=&amp;quot;Intervallic Cycle of 14 steps Equal per Octave&amp;quot; style=&amp;quot;height: 468px; width: 456px;&amp;quot; /&amp;gt; --&gt;&lt;table class="captionBox"&gt;&lt;tr&gt;&lt;td class="captionedImage"&gt;&lt;img src="/file/view/Ciclo_Tetradecafon%C3%ADa.png/233692646/456x468/Ciclo_Tetradecafon%C3%ADa.png" alt="Ciclo_Tetradecafonía.png" title="Ciclo_Tetradecafonía.png" style="height: 468px; width: 456px;" /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="imageCaption"&gt;Intervallic Cycle of 14 steps Equal per Octave&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;!-- ws:end:WikiTextLocalImageRule:486 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:516:&amp;lt;img src=&amp;quot;/file/view/Ciclo_Tetradecafon%C3%ADa.png/233692646/456x468/Ciclo_Tetradecafon%C3%ADa.png&amp;quot; alt=&amp;quot;Intervallic Cycle of 14 steps Equal per Octave&amp;quot; title=&amp;quot;Intervallic Cycle of 14 steps Equal per Octave&amp;quot; style=&amp;quot;height: 468px; width: 456px;&amp;quot; /&amp;gt; --&gt;&lt;table class="captionBox"&gt;&lt;tr&gt;&lt;td class="captionedImage"&gt;&lt;img src="/file/view/Ciclo_Tetradecafon%C3%ADa.png/233692646/456x468/Ciclo_Tetradecafon%C3%ADa.png" alt="Ciclo_Tetradecafonía.png" title="Ciclo_Tetradecafonía.png" style="height: 468px; width: 456px;" /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="imageCaption"&gt;Intervallic Cycle of 14 steps Equal per Octave&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;!-- ws:end:WikiTextLocalImageRule:516 --&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:17:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Images"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:17 --&gt;Images&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:13:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Images"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:13 --&gt;Images&lt;/h1&gt;
   &lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:487:&amp;lt;img src=&amp;quot;/file/view/14edo%20wheel.png/516971016/343x343/14edo%20wheel.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 343px; width: 343px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/14edo%20wheel.png/516971016/343x343/14edo%20wheel.png" alt="14edo wheel.png" title="14edo wheel.png" style="height: 343px; width: 343px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:487 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:517:&amp;lt;img src=&amp;quot;/file/view/14edo%20wheel.png/516971016/343x343/14edo%20wheel.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 343px; width: 343px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/14edo%20wheel.png/516971016/343x343/14edo%20wheel.png" alt="14edo wheel.png" title="14edo wheel.png" style="height: 343px; width: 343px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:517 --&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:19:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:19 --&gt;Commas&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:15:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:15 --&gt;Commas&lt;/h1&gt;
-EDO &lt;a class="wiki_link" href="/tempering%20out"&gt;tempers out&lt;/a&gt; the following &lt;a class="wiki_link" href="/comma"&gt;comma&lt;/a&gt;s. (Note: This assumes the val &amp;lt; 14 22 33 39 48 52/1 |.)&lt;br /&gt;
+EDO &lt;a class="wiki_link" href="/tempering%20out"&gt;tempers out&lt;/a&gt; the following &lt;a class="wiki_link" href="/comma"&gt;comma&lt;/a&gt;s. (Note: This assumes the val &amp;lt; 14 22 33 39 48 52 |.)&lt;br /&gt;
@@ Line 718: / Line 747: @@
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:21:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Modes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:21 --&gt;&lt;strong&gt;&lt;a class="wiki_link" href="/modes"&gt;Modes&lt;/a&gt;&lt;/strong&gt;&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:17:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Modes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:17 --&gt;&lt;strong&gt;&lt;a class="wiki_link" href="/modes"&gt;Modes&lt;/a&gt;&lt;/strong&gt;&lt;/h1&gt;
 5 4 - &lt;span style="cursor: pointer;"&gt;&lt;a class="wiki_link" href="/MOSScales"&gt;MOS&lt;/a&gt;&lt;/span&gt; of &lt;span style="cursor: pointer;"&gt;&lt;a class="wiki_link" href="/2L1s"&gt;2L1s&lt;/a&gt;&lt;/span&gt;&lt;br /&gt;
 4 5 - &lt;span style="cursor: pointer;"&gt;&lt;a class="wiki_link" href="/MOSScales"&gt;MOS&lt;/a&gt;&lt;/span&gt; of &lt;span style="cursor: pointer;"&gt;&lt;a class="wiki_link" href="/2L1s"&gt;2L1s&lt;/a&gt;&lt;/span&gt;&lt;br /&gt;
@@ Line 743: / Line 772: @@
 &lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:23:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Books"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:23 --&gt;Books&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:19:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Books"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:19 --&gt;Books&lt;/h1&gt;
-  &lt;!-- ws:start:WikiTextLocalImageRule:488:&amp;lt;img src=&amp;quot;/file/view/Libro_Tetradecaf%C3%B3nico.PNG/163539671/Libro_Tetradecaf%C3%B3nico.PNG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/Libro_Tetradecaf%C3%B3nico.PNG/163539671/Libro_Tetradecaf%C3%B3nico.PNG" alt="Libro_Tetradecafónico.PNG" title="Libro_Tetradecafónico.PNG" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:488 --&gt;&lt;br /&gt;
+  &lt;!-- ws:start:WikiTextLocalImageRule:518:&amp;lt;img src=&amp;quot;/file/view/Libro_Tetradecaf%C3%B3nico.PNG/163539671/Libro_Tetradecaf%C3%B3nico.PNG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/Libro_Tetradecaf%C3%B3nico.PNG/163539671/Libro_Tetradecaf%C3%B3nico.PNG" alt="Libro_Tetradecafónico.PNG" title="Libro_Tetradecafónico.PNG" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:518 --&gt;&lt;br /&gt;
 &lt;em&gt;Sword, Ron. &amp;quot;Tetradecaphonic Scales for Guitar&amp;quot; IAAA Press. First Ed: June 2009.&lt;/em&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:25:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc10"&gt;&lt;a name="Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:25 --&gt;&lt;strong&gt;Compositions&lt;/strong&gt;&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:21:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc10"&gt;&lt;a name="Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:21 --&gt;&lt;strong&gt;Compositions&lt;/strong&gt;&lt;/h1&gt;
   &lt;a class="wiki_link_ext" href="http://split-notes.com/004/" rel="nofollow"&gt;NANA WODORI&lt;/a&gt; by knowsur&lt;br /&gt;
 &lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/0-praxis/audio/August/august_03_thereminnards.mp3" rel="nofollow"&gt;Thereminnards&lt;/a&gt; by Ralph Lewis&lt;br /&gt;