24edo: Difference between revisions
Wikispaces>spt3125 **Imported revision 489603154 - Original comment: ** |
Wikispaces>cookiemeows **Imported revision 491208450 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:cookiemeows|cookiemeows]] and made on <tt>2014-02-22 10:32:15 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>491208450</tt>.<br> | ||
: The revision comment was: <tt></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> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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The tunings supplied by 72 cannot be used for all low-limit just intervals, but they can be used on the 17-limit [[k*N subgroups|3*24 subgroup]] 2.3.125.35.11.325.17 [[just intonation subgroup]], making some of the excellent approximations of 72 available in 24edo. Chords based on this subgroup afford considerable scope for harmony, including in particular intervals and chords using only 2, 3, 11 and 17. Another approach would be to treat 24-EDO as a 2.3.11.17.19 subgroup temperament, on which it is quite accurate. | The tunings supplied by 72 cannot be used for all low-limit just intervals, but they can be used on the 17-limit [[k*N subgroups|3*24 subgroup]] 2.3.125.35.11.325.17 [[just intonation subgroup]], making some of the excellent approximations of 72 available in 24edo. Chords based on this subgroup afford considerable scope for harmony, including in particular intervals and chords using only 2, 3, 11 and 17. Another approach would be to treat 24-EDO as a 2.3.11.17.19 subgroup temperament, on which it is quite accurate. | ||
|| Degree || Cents ||= Approximate Ratios* || | || [[#|Degree]] || Cents ||= Approximate Ratios* || | ||
|| 0 || 0 ||= 1/1 || | || 0 || 0 ||= 1/1 || | ||
|| 1 || 50 ||= 33/32, 34/33 || | || 1 || 50 ||= 33/32, 34/33 || | ||
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Its inversion, 0-3-6-10-14 ("minor") | Its inversion, 0-3-6-10-14 ("minor") | ||
0-7-14 ("neutral") | 0-7-14 ("neutral") | ||
0-5-10 (another kind of "neutral", splitting the fourth in two. The 0-5-10 can be extended into a pentatonic scale, 0-5-10-14-19-24 ([[godzilla]]), that is close to equi-pentatonic and also close to several Indonesian šlêndros. In a similar way 0-7-14 extends to 0-4-7-11-14-18-21-24 ([[mohajira]]), a heptatonic scale close to several Arabic scales.) | 0-5-10 (another kind of "neutral", splitting the fourth in two. The 0-5-10 can be extended into a pentatonic scale, 0-5-10-14-19-24 ([[godzilla]]), that is [[#|close]] to equi-pentatonic and also close to several Indonesian šlêndros. In a similar way 0-7-14 extends to 0-4-7-11-14-18-21-24 ([[mohajira]]), a heptatonic scale close to several Arabic scales.) | ||
===Commas=== | ===Commas=== | ||
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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 (Tendo Triad) and 0-5-14 (Arto 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. | 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. | 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 | ||
William Lynch considers these | William Lynch considers these as some possible good tetrads: | ||
[[image:Three chords.PNG]] | [[image:Three chords.PNG]] | ||
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=Naming Chords in 24edo= | =Naming Chords in 24edo= | ||
Naming chords in 24edo can be achieved by adding a few things to the already existing set of terms that are used to name 12edo chords. | Naming chords in 24edo can be achieved by adding a few things to the already [[#|existing]] set of terms that are used to name 12edo chords. | ||
They are: | They are: | ||
Super + perfect interval such as "perfect fifth" means to raise it by a quarter tone | Super + perfect interval such as "perfect fifth" means to raise it by a quarter tone | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<td>Degree<br /> | <td>[[#|Degree]]<br /> | ||
</td> | </td> | ||
<td>Cents<br /> | <td>Cents<br /> | ||
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Its inversion, 0-3-6-10-14 (&quot;minor&quot;)<br /> | Its inversion, 0-3-6-10-14 (&quot;minor&quot;)<br /> | ||
0-7-14 (&quot;neutral&quot;)<br /> | 0-7-14 (&quot;neutral&quot;)<br /> | ||
0-5-10 (another kind of &quot;neutral&quot;, splitting the fourth in two. The 0-5-10 can be extended into a pentatonic scale, 0-5-10-14-19-24 (<a class="wiki_link" href="/godzilla">godzilla</a>), that is close to equi-pentatonic and also close to several Indonesian šlêndros. In a similar way 0-7-14 extends to 0-4-7-11-14-18-21-24 (<a class="wiki_link" href="/mohajira">mohajira</a>), a heptatonic scale close to several Arabic scales.)<br /> | 0-5-10 (another kind of &quot;neutral&quot;, splitting the fourth in two. The 0-5-10 can be extended into a pentatonic scale, 0-5-10-14-19-24 (<a class="wiki_link" href="/godzilla">godzilla</a>), that is [[#|close]] to equi-pentatonic and also close to several Indonesian šlêndros. In a similar way 0-7-14 extends to 0-4-7-11-14-18-21-24 (<a class="wiki_link" href="/mohajira">mohajira</a>), a heptatonic scale close to several Arabic scales.)<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:7:&lt;h3&gt; --><h3 id="toc2"><a name="x24edo as a temperament--Commas"></a><!-- ws:end:WikiTextHeadingRule:7 -->Commas</h3> | <!-- ws:start:WikiTextHeadingRule:7:&lt;h3&gt; --><h3 id="toc2"><a name="x24edo as a temperament--Commas"></a><!-- ws:end:WikiTextHeadingRule:7 -->Commas</h3> | ||
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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.<br /> | 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.<br /> | ||
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.<br /> | 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.<br /> | ||
For example, the neutral triad can have the neutral 7th added to it to make a full neutral tetrad: 0-7-14-21. | 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<br /> | ||
<br /> | <br /> | ||
William Lynch considers these | William Lynch considers these as some possible good tetrads:<br /> | ||
<br /> | <br /> | ||
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<!-- ws:start:WikiTextHeadingRule:17:&lt;h1&gt; --><h1 id="toc7"><a name="Naming Chords in 24edo"></a><!-- ws:end:WikiTextHeadingRule:17 -->Naming Chords in 24edo</h1> | <!-- ws:start:WikiTextHeadingRule:17:&lt;h1&gt; --><h1 id="toc7"><a name="Naming Chords in 24edo"></a><!-- ws:end:WikiTextHeadingRule:17 -->Naming Chords in 24edo</h1> | ||
<br /> | <br /> | ||
Naming chords in 24edo can be achieved by adding a few things to the already existing set of terms that are used to name 12edo chords.<br /> | Naming chords in 24edo can be achieved by adding a few things to the already [[#|existing]] set of terms that are used to name 12edo chords.<br /> | ||
They are:<br /> | They are:<br /> | ||
Super + perfect interval such as &quot;perfect fifth&quot; means to raise it by a quarter tone<br /> | Super + perfect interval such as &quot;perfect fifth&quot; means to raise it by a quarter tone<br /> | ||