14edo: 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:~~igliashon~~|~~igliashon~~]] and made on <tt>2011-07-~~18 22~~:49:47 UTC</tt>.

: This revision was by author [[User:guest|guest]] and made on <tt>2011-07-21 00:03:10 UTC</tt>.

: The original revision id was <tt>~~241875649~~</tt>.

: The original revision id was <tt>242215355</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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==**14-EDO intervals:**==

|| **DEGREE** || **NOTE** || **CENTS** || **~~Nearest~~**

|| **DEGREE** || **NOTE** || **CENTS** ||= **Approximate**

**Ratio** || **Cents** || **~~Error~~** ||= **~~Approximate~~**

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

**~~Just Interval~~** ||= **Nearest**

**Harmonic** || **Interval Type** ||

**Harmonic** ||

|| 0 || C || 0 ||= 1/1 ||= 1 || Unison ||

|| 0 || **C** || 0 || **1/1~~** || 0 || **None**~~ ||= 1/1 ||~~= 1~~ ||

|| 1 || C* || 85.714 ||= 81/77, 126/121 ||= 67 || Narrow Minor 2nd ||

|| 1 || C* || 85.714 || 21/~~20 || 84.467 || +1.247~~ ||= ||~~= 67~~ ||

|| 2 || D || 171.429 ||= 11/10, 10/9 ||= 71 || Neutral 2nd, or

|| 2 || D || 171.429 ~~|| 32/29 || 170.423 || +1.006~~ ||= 11/10, 10/9 ||= 71 ||

Narrow Major 2nd ||

|| **3·** || **D*** || **257.143~~** || **36/31** || **258.874** || **-1.731**~~ ||= 7/6, 8/7 ||= 37 ||

|| 3· || D* || 257.143 ||= 81/70, 90/77 ||= 37 || Subminor 3rd ||

|| 4 || E || 342.857 ~~|| 39/32 || 342.483 || +0.374~~ ||= 11/9 ||= 39 ||

|| 4 || E || 342.857 ||= 11/9 ||= 39 || Neutral 3rd ||

|| **5·** || **E*** || **428.571~~** || **32/25** || **427.373** || **+1.198**~~ ||= 9/7 ||= 41 ||

|| 5· || E* || 428.571 ||= 9/7, 14/11 ||= 41 || Supermajor 3rd ||

|| 6 || F || 514.286 || 39/~~29 || 512.905 || +1.381~~ ||= ~~4/3~~ ||~~= 43~~ ||

|| 6 || F || 514.286 ||= 110/81, 121/90 ||= 43 || Wide 4th ||

|| **7·** || **F*** || **600~~** || **99/70** || **600.088** || **-0.088**~~ ||= 7/5, 10/7 ||= 91 ||

|| 7· || F* || 600 ||= 7/5, 10/7 ||= 91 || Tritone ||

|| 8 || G || 685.714 || 58/~~39 || 687.095 || -1.381~~ ||= ~~3/2~~ ||~~= 95~~ ||

|| 8 || G || 685.714 ||= 81/55, 180/121 ||= 95 || Narrow 5th ||

|| **9·** || **G*** || **771.429~~** || **25/16** || **772.627** || **-1.198**~~ ||= 14/9 ||= 25 ||

|| 9· || G* || 771.429 ||= 14/9, 11/7 ||= 25 || Subminor 6th ||

|| 10 || A || 857.143 ~~|| 64/39 || 857.517 || -0.374~~ ||= 18/11 ||= 105 ||

|| 10 || A || 857.143 ||= 18/11 ||= 105 || Neutral 6th ||

|| **11·** || **A*** || **942.857~~** || **31/18** || **941.126** || **+1.731**~~ ||= 12/7, 7/4 ||= 55 ||

|| 11· || A* || 942.857 ||= 140/81, 77/45 ||= 55 || Supermajor 6th ||

|| 12 || B || 1028.571 ~~|| 29/16 || 1029.577 || -1.006~~ ||= 20/11, 9/5 ||= 29 ||

|| 12 || B || 1028.571 ||= 20/11, 9/5 ||= 29 || Neutral 7th, or

|| 13 || B* || 1114.286 || 40/~~21 || 1115.533 || -1.247~~ ||= ||~~= 61~~ ||

Wide Minor 7th ||

|| **14··(or 0)** || **C** || **1200** || **2/1** || ~~**1200**~~ || ~~**None**~~ ||= 2/~~1 ||= 2 ||~~

|| 13 || B* || 1114.286 ||= 154/81, 121/63 ||= 61 || Wide Major 7th ||

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

*based on treating 14-EDO as a 2.11/5.11/7.11/9 subgroup; other approaches are possible.

==Harmony==

The character of 14-EDO does not well serve those seeking low-limit JI approaches, with the exception of 5:7:9:11 (which is quite well approximated, relative to other JI approximations of the low-numbered EDOs~~, and in 28-EDO we can bump that up to 4:5:7:9:11, perhaps even 4:5:6:7:9:11 if we are feeling charitable~~)~~. 6:7:9 appears to be better-approximated than it actually sounds, though it is still reasonably consonant~~.

The character of 14-EDO does not well serve those seeking low-limit JI approaches, with the exception of 5:7:9:11 (which is quite well approximated, relative to other JI approximations of the low-numbered EDOs).

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.

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</td>

<td>CENTS

~~</td>~~

~~<td>Nearest ~~

~~Ratio ~~

~~</td>~~

~~<td>Cents ~~

~~</td>~~

~~<td>Error ~~

</td>

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

~~Just Interval~~

Ratios*

</td>

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

Harmonic

</td>

<td>Interval Type

</td>

</tr>

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<td>0

</td>

<td~~><strong~~>C~~~~

<td>C

</td>

<td>0

~~</td>~~

~~<td>1/1 ~~

~~</td>~~

~~<td>0 ~~

~~</td>~~

~~<td>None ~~

</td>

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

</td>

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

</td>

<td>Unison

</td>

</tr>

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<td>85.714

</td>

<td>21/20

<td style="text-align: center;">81/77, 126/121

</td>

~~<td>84.467 ~~

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

~~</td>~~

~~<td>+1.247 ~~

~~</td>~~

</td>

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

<td>Narrow Minor 2nd

</td>

</tr>

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</td>

<td>171.429

~~</td>~~

~~<td>32/29 ~~

~~</td>~~

~~<td>170.423 ~~

~~</td>~~

~~<td>+1.006 ~~

</td>

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

</td>

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

</td>

<td>Neutral 2nd, or

Narrow Major 2nd

</td>

</tr>

<tr>

<td~~><strong~~>3·~~~~

<td>3·

</td>

<td~~><strong~~>D~~~~*

<td>D*

</td>

<td~~><strong~~>257.143~~~~

<td>257.143

</td>

<td~~&gt~~;~~<strong~~>36/~~31<~~/~~strong>~~

<td style="text-align: center;">81/70, 90/77

</td>

<td~~>258.874&lt~~;~~/strong~~>

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

</td>

<td>~~-1.731 ~~

<td>Subminor 3rd

~~</td>~~

~~<td style="text-align: center;">7/6, 8/7 ~~

~~</td>~~

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

</td>

</tr>

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</td>

<td>342.857

~~</td>~~

~~<td>39/32 ~~

~~</td>~~

~~<td>342.483 ~~

~~</td>~~

~~<td>+0.374 ~~

</td>

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

</td>

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

</td>

<td>Neutral 3rd

</td>

</tr>

<tr>

<td~~><strong~~>5·~~~~

<td>5·

</td>

<td~~><strong~~>E~~~~*

<td>E*

</td>

<td~~><strong~~>428.571~~~~

<td>428.571

</td>

<td~~&gt~~;~~<strong~~>32/~~25<~~/~~strong>~~

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

</td>

~~<td>427.373 ~~

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

~~</td>~~

~~<td>+1.198 ~~

~~</td>~~

<td style="text-align: center;">~~9/7~~

</td>

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

<td>Supermajor 3rd

</td>

</tr>

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<td>514.286

</td>

<td>39/29

<td style="text-align: center;">110/81, 121/90

</td>

~~<td>512.905 ~~

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

~~</td>~~

~~<td>+1.381 ~~

~~</td>~~

<td style="text-align: center;">~~4/3~~

</td>

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

<td>Wide 4th

</td>

</tr>

<tr>

<td~~><strong~~>7·~~~~

<td>7·

</td>

<td~~><strong~~>F~~~~*

<td>F*

</td>

<td~~><strong~~>600~~ ~~

<td>600

~~</td>~~

~~<td>99/70 ~~

~~</td>~~

~~<td>600.088 ~~

~~</td>~~

~~<td>-0.088~~

</td>

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

</td>

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

</td>

<td>Tritone

</td>

</tr>

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<td>685.714

</td>

<td>58/39

<td style="text-align: center;">81/55, 180/121

</td>

<td>~~687.095~~

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

</td>

<td>~~-1.381 ~~

<td>Narrow 5th

~~</td>~~

~~<td style="text-align: center;">3/2 ~~

~~</td>~~

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

</td>

</tr>

<tr>

<td~~><strong~~>9·~~~~

<td>9·

</td>

<td~~><strong~~>G~~~~*

<td>G*

</td>

<td~~><strong~~>771.429~~~~

<td>771.429

</td>

<td~~&gt~~;~~<strong~~>25/~~16<~~/~~strong>~~

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

</td>

<td~~>772.627&lt~~;~~/strong~~>

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

</td>

<td>~~-1.198 ~~

<td>Subminor 6th

~~</td>~~

~~<td style="text-align: center;">14/9 ~~

~~</td>~~

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

</td>

</tr>

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</td>

<td>857.143

~~</td>~~

~~<td>64/39 ~~

~~</td>~~

~~<td>857.517 ~~

~~</td>~~

~~<td>-0.374 ~~

</td>

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

</td>

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

</td>

<td>Neutral 6th

</td>

</tr>

<tr>

<td~~><strong~~>11·~~~~

<td>11·

</td>

<td~~><strong~~>A~~~~*

<td>A*

</td>

<td~~><strong~~>942.857~~~~

<td>942.857

</td>

<td~~&gt~~;~~<strong~~>31/~~18<~~/~~strong>~~

<td style="text-align: center;">140/81, 77/45

</td>

<td~~>941.126&lt~~;~~/strong~~>

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

</td>

<td>~~+1.731 ~~

<td>Supermajor 6th

~~</td>~~

~~<td style="text-align: center;">12/7, 7/4 ~~

~~</td>~~

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

</td>

</tr>

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</td>

<td>1028.571

~~</td>~~

~~<td>29/16 ~~

~~</td>~~

~~<td>1029.577 ~~

~~</td>~~

~~<td>-1.006 ~~

</td>

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

</td>

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

</td>

<td>Neutral 7th, or

Wide Minor 7th

</td>

</tr>

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<td>1114.286

</td>

<td>40/21

<td style="text-align: center;">154/81, 121/63

</td>

~~<td>1115.533 ~~

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

~~</td>~~

~~<td>-1.247 ~~

~~</td>~~

</td>

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

<td>Wide Major 7th

</td>

</tr>

<tr>

<td~~><strong~~>14··(or 0)~~ ~~

<td>14··(or 0)

~~</td>~~

~~<td>C ~~

~~</td>~~

~~<td>1200 ~~

~~</td>~~

~~<td>2/1~~

</td>

<td>~~1200~~

<td>C

</td>

<td>~~None~~

<td>1200

</td>

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

</td>

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

</td>

<td>Octave

</td>

</tr>

</table>

*based on treating 14-EDO as a 2.11/5.11/7.11/9 subgroup; other approaches are possible.

<h2 id="toc2"><a name="x14 tone equal temperament-Harmony"></a>Harmony</h2>

The character of 14-EDO does not well serve those seeking low-limit JI approaches, with the exception of 5:7:9:11 (which is quite well approximated, relative to other JI approximations of the low-numbered EDOs~~, and in 28-EDO we can bump that up to 4:5:7:9:11, perhaps even 4:5:6:7:9:11 if we are feeling charitable~~)~~. 6:7:9 appears to be better-approximated than it actually sounds, though it is still reasonably consonant~~.

The character of 14-EDO does not well serve those seeking low-limit JI approaches, with the exception of 5:7:9:11 (which is quite well approximated, relative to other JI approximations of the low-numbered EDOs).

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.

<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>

<h2 id="toc3"><a name="x14 tone equal temperament-Commas:"></a>Commas:</h2>

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<h2 id="toc5"><a name="x14 tone equal temperament-Instruments:"></a>Instruments:</h2>

<img src="http://4.bp.blogspot.com/_7rDA1Q80rL8/S9M8H2YTpaI/AAAAAAAAAHM/Qkxp5gioOF0/s1600/14edo+guitar+%282%29.jpg" alt="external image 14edo+guitar+%282%29.jpg" title="external image 14edo+guitar+%282%29.jpg" style="height: 256px; width: 750px;" />

<img src="http://4.bp.blogspot.com/_7rDA1Q80rL8/S9M8H2YTpaI/AAAAAAAAAHM/Qkxp5gioOF0/s1600/14edo+guitar+%282%29.jpg" alt="external image 14edo+guitar+%282%29.jpg" title="external image 14edo+guitar+%282%29.jpg" style="height: 256px; width: 750px;" />

A Tetradecaphonic Guitar. 14-EDO Guitar by Ron Sword.

<h2 id="toc6"><a name="x14 tone equal temperament-Books:"></a>Books:</h2>

<img src="/file/view/Libro_Tetradecaf%C3%B3nico.PNG/163539671/360x431/Libro_Tetradecaf%C3%B3nico.PNG" alt="Libro_Tetradecafónico.PNG" title="Libro_Tetradecafónico.PNG" style="height: 431px; width: 360px;" />

<img src="/file/view/Libro_Tetradecaf%C3%B3nico.PNG/163539671/360x431/Libro_Tetradecaf%C3%B3nico.PNG" alt="Libro_Tetradecafónico.PNG" title="Libro_Tetradecafónico.PNG" style="height: 431px; width: 360px;" />

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

@@ 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:igliashon|igliashon]] and made on <tt>2011-07-18 22:49:47 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2011-07-21 00:03:10 UTC</tt>.<br>
-: The original revision id was <tt>241875649</tt>.<br>
+: The original revision id was <tt>242215355</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 9: / Line 9: @@
 ==**14-EDO intervals:**==
-|| **DEGREE** || **NOTE** || **CENTS** || **Nearest**
+|| **DEGREE** || **NOTE** || **CENTS** ||= **Approximate**
-**Ratio** || **Cents** || **Error** ||= **Approximate**
+**Ratios*** ||= **Nearest**
-**Just Interval** ||= **Nearest**
+**Harmonic** || **Interval Type** ||
-**Harmonic** ||
+|| 0 || C || 0 ||= 1/1 ||= 1 || Unison ||
-|| 0 || **C** || 0 || **1/1** || 0 || **None** ||= 1/1 ||= 1 ||
+|| 1 || C* || 85.714 ||= 81/77, 126/121 ||= 67 || Narrow Minor 2nd ||
-|| 1 || C* || 85.714 || 21/20 || 84.467 || +1.247 ||=   ||= 67 ||
+|| 2 || D || 171.429 ||= 11/10, 10/9 ||= 71 || Neutral 2nd, or
-|| 2 || D || 171.429 || 32/29 || 170.423 || +1.006 ||= 11/10, 10/9 ||= 71 ||
+Narrow Major 2nd ||
-|| **3·** || **D*** || **257.143** || **36/31** || **258.874** || **-1.731** ||= 7/6, 8/7 ||= 37 ||
+|| 3· || D* || 257.143 ||= 81/70, 90/77 ||= 37 || Subminor 3rd ||
-|| 4 || E || 342.857 || 39/32 || 342.483 || +0.374 ||= 11/9 ||= 39 ||
+|| 4 || E || 342.857 ||= 11/9 ||= 39 || Neutral 3rd ||
-|| **5·** || **E*** || **428.571** || **32/25** || **427.373** || **+1.198** ||= 9/7 ||= 41 ||
+|| 5· || E* || 428.571 ||= 9/7, 14/11 ||= 41 || Supermajor 3rd ||
-|| 6 || F || 514.286 || 39/29 || 512.905 || +1.381 ||= 4/3 ||= 43 ||
+|| 6 || F || 514.286 ||= 110/81, 121/90 ||= 43 || Wide 4th ||
-|| **7·** || **F*** || **600** || **99/70** || **600.088** || **-0.088** ||= 7/5, 10/7 ||= 91 ||
+|| 7· || F* || 600 ||= 7/5, 10/7 ||= 91 || Tritone ||
-|| 8 || G || 685.714 || 58/39 || 687.095 || -1.381 ||= 3/2 ||= 95 ||
+|| 8 || G || 685.714 ||= 81/55, 180/121 ||= 95 || Narrow 5th ||
-|| **9·** || **G*** || **771.429** || **25/16** || **772.627** || **-1.198** ||= 14/9 ||= 25 ||
+|| 9· || G* || 771.429 ||= 14/9, 11/7 ||= 25 || Subminor 6th ||
-|| 10 || A || 857.143 || 64/39 || 857.517 || -0.374 ||= 18/11 ||= 105 ||
+|| 10 || A || 857.143 ||= 18/11 ||= 105 || Neutral 6th ||
-|| **11·** || **A*** || **942.857** || **31/18** || **941.126** || **+1.731** ||= 12/7, 7/4 ||= 55 ||
+|| 11· || A* || 942.857 ||= 140/81, 77/45 ||= 55 || Supermajor 6th ||
-|| 12 || B || 1028.571 || 29/16 || 1029.577 || -1.006 ||= 20/11, 9/5 ||= 29 ||
+|| 12 || B || 1028.571 ||= 20/11, 9/5 ||= 29 || Neutral 7th, or
-|| 13 || B* || 1114.286 || 40/21 || 1115.533 || -1.247 ||=   ||= 61 ||
+Wide Minor 7th ||
-|| **14··(or 0)** || **C** || **1200** || **2/1** || **1200** || **None** ||= 2/1 ||= 2 ||
+|| 13 || B* || 1114.286 ||= 154/81, 121/63 ||= 61 || Wide Major 7th ||
+|| 14··(or 0) || C || 1200 ||= 2/1 ||= 2 || Octave ||
+*based on treating 14-EDO as a 2.11/5.11/7.11/9 subgroup; other approaches are possible.
 ==Harmony==
-The character of 14-EDO does not well serve those seeking low-limit JI approaches, with the exception of 5:7:9:11 (which is quite well approximated, relative to other JI approximations of the low-numbered EDOs, and in 28-EDO we can bump that up to 4:5:7:9:11, perhaps even 4:5:6:7:9:11 if we are feeling charitable). 6:7:9 appears to be better-approximated than it actually sounds, though it is still reasonably consonant.
+The character of 14-EDO does not well serve those seeking low-limit JI approaches, with the exception of 5:7:9:11 (which is quite well approximated, relative to other JI approximations of the low-numbered EDOs).
 -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.
@@ Line 112: / Line 114: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;strong&gt;CENTS&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;Nearest&lt;/strong&gt;&lt;br /&gt;
-&lt;strong&gt;Ratio&lt;/strong&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&gt;&lt;strong&gt;Error&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;Just Interval&lt;/strong&gt;&lt;br /&gt;
+&lt;strong&gt;Ratios&lt;/strong&gt;*&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;strong&gt;Nearest&lt;/strong&gt;&lt;br /&gt;
 &lt;strong&gt;Harmonic&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;Interval Type&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 130: / Line 127: @@
          &lt;td&gt;0&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;C&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;C&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;0&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;1/1&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;0&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;None&lt;/strong&gt;&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&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Unison&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 152: / Line 145: @@
          &lt;td&gt;85.714&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;21/20&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;81/77, 126/121&lt;br /&gt;
 &lt;/td&gt;
-        &lt;td&gt;84.467&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;67&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;+1.247&lt;br /&gt;
-&lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;67&lt;br /&gt;
+         &lt;td&gt;Narrow Minor 2nd&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 169: / Line 158: @@
 &lt;/td&gt;
          &lt;td&gt;171.429&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;32/29&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;170.423&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;+1.006&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;11/10, 10/9&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;71&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&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;&lt;strong&gt;3·&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;3·&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;D&lt;/strong&gt;*&lt;br /&gt;
+         &lt;td&gt;D*&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;257.143&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;257.143&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;36/31&lt;/strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;81/70, 90/77&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;258.874&lt;/strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;37&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;-1.731&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;Subminor 3rd&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;7/6, 8/7&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;37&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 205: / Line 187: @@
 &lt;/td&gt;
          &lt;td&gt;342.857&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;39/32&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;342.483&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;+0.374&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;11/9&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;39&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Neutral 3rd&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;strong&gt;5·&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;5·&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;E&lt;/strong&gt;*&lt;br /&gt;
+         &lt;td&gt;E*&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;428.571&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;428.571&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;32/25&lt;/strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;9/7, 14/11&lt;br /&gt;
 &lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;427.373&lt;/strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;41&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;+1.198&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;9/7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;41&lt;br /&gt;
+         &lt;td&gt;Supermajor 3rd&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 242: / Line 216: @@
          &lt;td&gt;514.286&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;39/29&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;110/81, 121/90&lt;br /&gt;
 &lt;/td&gt;
-        &lt;td&gt;512.905&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;43&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;+1.381&lt;br /&gt;
-&lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;4/3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;43&lt;br /&gt;
+         &lt;td&gt;Wide 4th&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;strong&gt;7·&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;7·&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;F&lt;/strong&gt;*&lt;br /&gt;
+         &lt;td&gt;F*&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;600&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;600&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;99/70&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;600.088&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;-0.088&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;7/5, 10/7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;91&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Tritone&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 278: / Line 244: @@
          &lt;td&gt;685.714&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;58/39&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;81/55, 180/121&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;687.095&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;95&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;-1.381&lt;br /&gt;
+         &lt;td&gt;Narrow 5th&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;3/2&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;95&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;strong&gt;9·&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;9·&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;G&lt;/strong&gt;*&lt;br /&gt;
+         &lt;td&gt;G*&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;771.429&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;771.429&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;25/16&lt;/strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;14/9, 11/7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;772.627&lt;/strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;25&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;-1.198&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;Subminor 6th&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;14/9&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;25&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 313: / Line 271: @@
 &lt;/td&gt;
          &lt;td&gt;857.143&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;64/39&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;857.517&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;-0.374&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;18/11&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;105&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Neutral 6th&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;strong&gt;11·&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;11·&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;*&lt;br /&gt;
+         &lt;td&gt;A*&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;942.857&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;942.857&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;31/18&lt;/strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;140/81, 77/45&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;941.126&lt;/strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;55&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;+1.731&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;Supermajor 6th&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;12/7, 7/4&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;55&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 349: / Line 299: @@
 &lt;/td&gt;
          &lt;td&gt;1028.571&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;29/16&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1029.577&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;-1.006&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;20/11, 9/5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;29&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Neutral 7th, or&lt;br /&gt;
+Wide Minor 7th&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 368: / Line 315: @@
          &lt;td&gt;1114.286&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;40/21&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;154/81, 121/63&lt;br /&gt;
 &lt;/td&gt;
-        &lt;td&gt;1115.533&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;61&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;-1.247&lt;br /&gt;
-&lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;61&lt;br /&gt;
+         &lt;td&gt;Wide Major 7th&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;strong&gt;14··(or 0)&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;14··(or 0)&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;C&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;1200&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;2/1&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;1200&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;C&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;None&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;1200&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;2/1&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Octave&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
 &lt;/table&gt;
+*based on treating 14-EDO as a 2.11/5.11/7.11/9 subgroup; other approaches are possible.&lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x14 tone equal temperament-Harmony"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Harmony&lt;/h2&gt;
   &lt;br /&gt;
-The character of 14-EDO does not well serve those seeking low-limit JI approaches, with the exception of 5:7:9:11 (which is quite well approximated, relative to other JI approximations of the low-numbered EDOs, and in 28-EDO we can bump that up to 4:5:7:9:11, perhaps even 4:5:6:7:9:11 if we are feeling charitable). 6:7:9 appears to be better-approximated than it actually sounds, though it is still reasonably consonant.&lt;br /&gt;
+The character of 14-EDO does not well serve those seeking low-limit JI approaches, with the exception of 5:7:9:11 (which is quite well approximated, relative to other JI approximations of the low-numbered EDOs).&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;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:466:&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:466 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:402:&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:402 --&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x14 tone equal temperament-Commas:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;&lt;span style="font-size: 1.3em;"&gt;Commas:&lt;/span&gt;&lt;/h2&gt;
@@ Line 600: / Line 540: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="x14 tone equal temperament-Instruments:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Instruments:&lt;/h2&gt;
-  &lt;!-- ws:start:WikiTextRemoteImageRule:468:&amp;lt;img src=&amp;quot;http://4.bp.blogspot.com/_7rDA1Q80rL8/S9M8H2YTpaI/AAAAAAAAAHM/Qkxp5gioOF0/s1600/14edo+guitar+%282%29.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 256px; width: 750px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://4.bp.blogspot.com/_7rDA1Q80rL8/S9M8H2YTpaI/AAAAAAAAAHM/Qkxp5gioOF0/s1600/14edo+guitar+%282%29.jpg" alt="external image 14edo+guitar+%282%29.jpg" title="external image 14edo+guitar+%282%29.jpg" style="height: 256px; width: 750px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:468 --&gt;&lt;br /&gt;
+  &lt;!-- ws:start:WikiTextRemoteImageRule:404:&amp;lt;img src=&amp;quot;http://4.bp.blogspot.com/_7rDA1Q80rL8/S9M8H2YTpaI/AAAAAAAAAHM/Qkxp5gioOF0/s1600/14edo+guitar+%282%29.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 256px; width: 750px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://4.bp.blogspot.com/_7rDA1Q80rL8/S9M8H2YTpaI/AAAAAAAAAHM/Qkxp5gioOF0/s1600/14edo+guitar+%282%29.jpg" alt="external image 14edo+guitar+%282%29.jpg" title="external image 14edo+guitar+%282%29.jpg" style="height: 256px; width: 750px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:404 --&gt;&lt;br /&gt;
 &lt;em&gt;A Tetradecaphonic Guitar. 14-EDO Guitar by Ron Sword.&lt;/em&gt;&lt;br /&gt;
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 &lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="x14 tone equal temperament-Books:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;&lt;strong&gt;Books:&lt;/strong&gt;&lt;/h2&gt;
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 &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;
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