24edo: 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:~~hstraub~~|~~hstraub~~]] and made on <tt>2014-10-06 09:32:16 UTC</tt>.

: This revision was by author [[User:k9assassin|k9assassin]] and made on <tt>2014-10-12 09:31:49 UTC</tt>.

: The original revision id was <tt>~~525247640~~</tt>.

: The original revision id was <tt>526116212</tt>.

: The revision comment was: <tt>~~Reverted to Oct 6, 2014 6:28 am: Undo~~</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.

<h4>Original Wikitext content:</h4>

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..

tridecimal subfourth ||

||= 550 ||= major fourth, ~~over~~-~~fourth~~ ||= [[11_8|11/8]] ||= 551.318 ||= undecimal superfourth, harmonic 11th ||

||= 550 ||= major fourth, Under-fifth ||= [[11_8|11/8]] ||= 551.318 ||= undecimal superfourth, harmonic 11th ||

||= 650 ||= minor fifth~~, Under-Fifth~~ ||= [[16_11|16/11]] ||= 648.682 ||= undecimal subfifth, 11th subharmonic ||

||= 650 ||= minor fifth ||= [[16_11|16/11]] ||= 648.682 ||= undecimal subfifth, 11th subharmonic ||

||= 750 ||= major fifth, subminor sixth, arto sixth

||= 750 ||= major fifth, subminor sixth, arto sixth ||= [[20_13|20/13]]

~~Over-fifth,~~ ||= [[20_13|20/13]]

[[54_35|54/35]]

[[17_11|17/11]] ||= 745.786

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..

17-limit subminor sixth ||

||= 850 ||= neutral sixth ||= [[13_8|13/8]]

||= 850 ||= neutral sixth, Over fifth ||= [[13_8|13/8]]

[[44_27|44/27]]

[[18_11|18/11]] ||= 840.528

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As for entirely new chords, 24edo features many possibilities for chords. The most obvious is the neutral triad 0-7-14 however there are other options such as

0-9-14 (~~Tendo~~ Triad) and 0-5-14 (~~Arto~~ Triad), the chord names being based on what kind of third is in the chord.

0-9-14 (Ultra Triad) and 0-5-14 (Infra Triad), the chord names being based on what kind of third is in the chord.

These chords though tend to lack the forcefulness to sound like resolved, tonal sonorities but can be resolved of that issue by using tetrads in place of triads.

For example, the neutral triad can have the neutral 7th added to it to make a full neutral tetrad: 0-7-14-21. However, another option is to replace the neutral third with an 11/8 to produce a sort of 11 limit neutral tetrad. 0-14-21-35 William Lynch considers this chord to be the most consonant tetrad in 24edo involving a neutral tonality. 24 edo also is very good at 15 limit and does 13 quite well allowing barbodos 10:13:15 and barbodos minor triad 26:30:39 to be used as an entirely new harmonic system. ~~See Arto and Tendo Theory~~

For example, the neutral triad can have the neutral 7th added to it to make a full neutral tetrad: 0-7-14-21. However, another option is to replace the neutral third with an 11/8 to produce a sort of 11 limit neutral tetrad. 0-14-21-35 William Lynch considers this chord to be the most consonant tetrad in 24edo involving a neutral tonality. 24 edo also is very good at 15 limit and does 13 quite well allowing barbodos 10:13:15 and barbodos minor triad 26:30:39 to be used as an entirely new harmonic system.

William Lynch considers these as some possible good tetrads:

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|| tendo || 0 9 14 19 || 1 ^3 5 bv7 || ... ||

Due to convenience, the names Arto and tendo have been changed to Ultra and Infra.

=Naming Chords in 24edo=

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|| {{**2 8 3 6 5**}} || Anchihoye: Ethiopia ||

|| {{**5 5 4 5 5**}} || Quasi-equal Pentatonic - [[MOSScales|MOS]] of type [[4L 1s|4L 1s (bug)]] ||

|| {{**5 5 5 5 4**}} || Hába's Pentatonic - [[MOSScales|MOS]] of type [[4L 1s|4L 1s (bug)]] ||

|||| ====Hexatonic:==== ||

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<td style="text-align: center;">550

</td>

<td style="text-align: center;">major fourth, ~~over~~-~~fourth~~

<td style="text-align: center;">major fourth, Under-fifth

</td>

Line 1,059:

<td style="text-align: center;">650

</td>

<td style="text-align: center;">minor fifth~~, Under-Fifth~~

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

</td>

Line 1,072:

</td>

<td style="text-align: center;">major fifth, subminor sixth, arto sixth

~~Over-fifth, ~~

</td>

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Line 1,089:

<td style="text-align: center;">850

</td>

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

<td style="text-align: center;">neutral sixth, Over fifth

</td>

Line 1,208:

Line 1,207:

As for entirely new chords, 24edo features many possibilities for chords. The most obvious is the neutral triad 0-7-14 however there are other options such as

0-9-14 (~~Tendo~~ Triad) and 0-5-14 (~~Arto~~ Triad), the chord names being based on what kind of third is in the chord.

0-9-14 (Ultra Triad) and 0-5-14 (Infra Triad), the chord names being based on what kind of third is in the chord.

These chords though tend to lack the forcefulness to sound like resolved, tonal sonorities but can be resolved of that issue by using tetrads in place of triads.

For example, the neutral triad can have the neutral 7th added to it to make a full neutral tetrad: 0-7-14-21. However, another option is to replace the neutral third with an 11/8 to produce a sort of 11 limit neutral tetrad. 0-14-21-35 William Lynch considers this chord to be the most consonant tetrad in 24edo involving a neutral tonality. 24 edo also is very good at 15 limit and does 13 quite well allowing barbodos 10:13:15 and barbodos minor triad 26:30:39 to be used as an entirely new harmonic system. ~~See Arto and Tendo Theory~~

For example, the neutral triad can have the neutral 7th added to it to make a full neutral tetrad: 0-7-14-21. However, another option is to replace the neutral third with an 11/8 to produce a sort of 11 limit neutral tetrad. 0-14-21-35 William Lynch considers this chord to be the most consonant tetrad in 24edo involving a neutral tonality. 24 edo also is very good at 15 limit and does 13 quite well allowing barbodos 10:13:15 and barbodos minor triad 26:30:39 to be used as an entirely new harmonic system.

William Lynch considers these as some possible good tetrads:

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Due to convenience, the names Arto and tendo have been changed to Ultra and Infra.

<h1 id="toc8"><a name="Naming Chords in 24edo"></a>Naming Chords in 24edo</h1>

@@ 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:hstraub|hstraub]] and made on <tt>2014-10-06 09:32:16 UTC</tt>.<br>
+: This revision was by author [[User:k9assassin|k9assassin]] and made on <tt>2014-10-12 09:31:49 UTC</tt>.<br>
-: The original revision id was <tt>525247640</tt>.<br>
+: The original revision id was <tt>526116212</tt>.<br>
-: The revision comment was: <tt>Reverted to Oct 6, 2014 6:28 am: Undo</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>
 <h4>Original Wikitext content:</h4>
@@ Line 116: / Line 116: @@
 ..
 tridecimal subfourth ||
-||= 550 ||= major fourth, over-fourth ||= [[11_8|11/8]] ||= 551.318 ||= undecimal superfourth, harmonic 11th ||
+||= 550 ||= major fourth, Under-fifth ||= [[11_8|11/8]] ||= 551.318 ||= undecimal superfourth, harmonic 11th ||
-||= 650 ||= minor fifth, Under-Fifth ||= [[16_11|16/11]] ||= 648.682 ||= undecimal subfifth, 11th subharmonic ||
+||= 650 ||= minor fifth ||= [[16_11|16/11]] ||= 648.682 ||= undecimal subfifth, 11th subharmonic ||
-||= 750 ||= major fifth, subminor sixth, arto sixth
+||= 750 ||= major fifth, subminor sixth, arto sixth ||= [[20_13|20/13]]
-Over-fifth, ||= [[20_13|20/13]]
 [[54_35|54/35]]
 [[17_11|17/11]] ||= 745.786
@@ Line 126: / Line 125: @@
 ..
 -limit subminor sixth ||
-||= 850 ||= neutral sixth ||= [[13_8|13/8]]
+||= 850 ||= neutral sixth, Over fifth ||= [[13_8|13/8]]
 [[44_27|44/27]]
 [[18_11|18/11]] ||= 840.528
@@ Line 201: / Line 200: @@
 As for entirely new chords, 24edo features many possibilities for chords. The most obvious is the neutral triad 0-7-14 however there are other options such as
--9-14 (Tendo Triad) and 0-5-14 (Arto Triad), the chord names being based on what kind of third is in the chord.
+-9-14 (Ultra Triad) and 0-5-14 (Infra Triad), the chord names being based on what kind of third is in the chord.
 These chords though tend to lack the forcefulness to sound like resolved, tonal sonorities but can be resolved of that issue by using tetrads in place of triads.
-For example, the neutral triad can have the neutral 7th added to it to make a full neutral tetrad: 0-7-14-21. However, another option is to replace the neutral third with an 11/8 to produce a sort of 11 limit neutral tetrad. 0-14-21-35 William Lynch considers this chord to be the most consonant tetrad in 24edo involving a neutral tonality. 24 edo also is very good at 15 limit and does 13 quite well allowing barbodos 10:13:15 and barbodos minor triad 26:30:39 to be used as an entirely new harmonic system. See Arto and Tendo Theory
+For example, the neutral triad can have the neutral 7th added to it to make a full neutral tetrad: 0-7-14-21. However, another option is to replace the neutral third with an 11/8 to produce a sort of 11 limit neutral tetrad. 0-14-21-35 William Lynch considers this chord to be the most consonant tetrad in 24edo involving a neutral tonality. 24 edo also is very good at 15 limit and does 13 quite well allowing barbodos 10:13:15 and barbodos minor triad 26:30:39 to be used as an entirely new harmonic system.
 William Lynch considers these as some possible good tetrads:
@@ Line 214: / Line 213: @@
 || tendo || 0 9 14 19 || 1 ^3 5 bv7 || ... ||
+Due to convenience, the names Arto and tendo have been changed to Ultra and Infra.
 =Naming Chords in 24edo=
@@ Line 253: / Line 253: @@
 || {{**2 8 3 6 5**}} || Anchihoye: Ethiopia ||
 || {{**5 5 4 5 5**}} || Quasi-equal Pentatonic - [[MOSScales|MOS]] of type [[4L 1s|4L 1s (bug)]] ||
-|| {{**5 5 5 5 4**}} || Hába's Pentatonic - [[MOSScales|MOS]] of type [[4L 1s|4L 1s (bug)]]  ||
+|| {{**5 5 5 5 4**}} || Hába's Pentatonic - [[MOSScales|MOS]] of type [[4L 1s|4L 1s (bug)]] ||
 |||| ====Hexatonic:==== ||
@@ Line 1,047: / Line 1,047: @@
          &lt;td style="text-align: center;"&gt;550&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;major fourth, over-fourth&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;major fourth, Under-fifth&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/11_8"&gt;11/8&lt;/a&gt;&lt;br /&gt;
@@ Line 1,059: / Line 1,059: @@
          &lt;td style="text-align: center;"&gt;650&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;minor fifth, Under-Fifth&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;minor fifth&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/16_11"&gt;16/11&lt;/a&gt;&lt;br /&gt;
@@ Line 1,072: / Line 1,072: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;major fifth, subminor sixth, arto sixth&lt;br /&gt;
-Over-fifth,&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/20_13"&gt;20/13&lt;/a&gt;&lt;br /&gt;
@@ Line 1,090: / Line 1,089: @@
          &lt;td style="text-align: center;"&gt;850&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;neutral sixth&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;neutral sixth, Over fifth&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/13_8"&gt;13/8&lt;/a&gt;&lt;br /&gt;
@@ Line 1,208: / Line 1,207: @@
 &lt;br /&gt;
 As for entirely new chords, 24edo features many possibilities for chords. The most obvious is the neutral triad 0-7-14 however there are other options such as&lt;br /&gt;
--9-14 (Tendo Triad) and 0-5-14 (Arto Triad), the chord names being based on what kind of third is in the chord.&lt;br /&gt;
+-9-14 (Ultra Triad) and 0-5-14 (Infra Triad), the chord names being based on what kind of third is in the chord.&lt;br /&gt;
 These chords though tend to lack the forcefulness to sound like resolved, tonal sonorities but can be resolved of that issue by using tetrads in place of triads.&lt;br /&gt;
-For example, the neutral triad can have the neutral 7th added to it to make a full neutral tetrad: 0-7-14-21. However, another option is to replace the neutral third with an 11/8 to produce a sort of 11 limit neutral tetrad. 0-14-21-35 William Lynch considers this chord to be the most consonant tetrad in 24edo involving a neutral tonality. 24 edo also is very good at 15 limit and does 13 quite well allowing barbodos 10:13:15 and barbodos minor triad 26:30:39 to be used as an entirely new harmonic system. See Arto and Tendo Theory&lt;br /&gt;
+For example, the neutral triad can have the neutral 7th added to it to make a full neutral tetrad: 0-7-14-21. However, another option is to replace the neutral third with an 11/8 to produce a sort of 11 limit neutral tetrad. 0-14-21-35 William Lynch considers this chord to be the most consonant tetrad in 24edo involving a neutral tonality. 24 edo also is very good at 15 limit and does 13 quite well allowing barbodos 10:13:15 and barbodos minor triad 26:30:39 to be used as an entirely new harmonic system. &lt;br /&gt;
 &lt;br /&gt;
 William Lynch considers these as some possible good tetrads:&lt;br /&gt;
@@ Line 1,262: / Line 1,261: @@
 &lt;br /&gt;
+Due to convenience, the names Arto and tendo have been changed to Ultra and Infra. &lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:19:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Naming Chords in 24edo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:19 --&gt;Naming Chords in 24edo&lt;/h1&gt;