24edo: Difference between revisions
Wikispaces>hstraub **Imported revision 525246948 - Original comment: ** |
Wikispaces>hstraub **Imported revision 525247380 - 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:hstraub|hstraub]] and made on <tt>2014-10-06 09: | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2014-10-06 09:30:55 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>525247380</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 || | ||~ [[#|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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|| 12 || 1\24 || [[Catler]] || | || 12 || 1\24 || [[Catler]] || | ||
=Scales / Modes= | =Scales / Modes= | ||
||||~ ====Pentatonic:==== || | |||
|||| ====Pentatonic:==== || | |||
|| {{**2 8 3 6 5**}} || Anchihoye: Ethiopia || | || {{**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 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:==== || | ||||~ ====Hexatonic:==== || | ||
|| {{**1 1 8 4 2 8**}} || Spondeiakos || | || {{**1 1 8 4 2 8**}} || Spondeiakos || | ||
|||| ====Heptatonic:==== || | ||||~ ====Heptatonic:==== || | ||
|| {{**1 1 8 1 1 8 4**}} || Enharmonic Mixolydian || | || {{**1 1 8 1 1 8 4**}} || Enharmonic Mixolydian || | ||
|| {{**1 8 1 1 8 4 1**}} || Enharmonic Lydian || | || {{**1 8 1 1 8 4 1**}} || Enharmonic Lydian || | ||
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|| {{**4 4 2 3 1 4 6**}} || Daniel-mode of Spanish-Arab Jews || | || {{**4 4 2 3 1 4 6**}} || Daniel-mode of Spanish-Arab Jews || | ||
|||| ====Octatonic:==== || | ||||~ ====Octatonic:==== || | ||
|| {{**3 3 3 3 3 3 3 3**}} || 8-equal, Wyschnegradsky's octatonic || | || {{**3 3 3 3 3 3 3 3**}} || 8-equal, Wyschnegradsky's octatonic || | ||
|| {{**3 3 4 4 2 1 3 4**}} || Maqam Bayati || | || {{**3 3 4 4 2 1 3 4**}} || Maqam Bayati || | ||
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|| {{**1 4 4 2 4 4 4 1**}} || Giancarlo Dalmonte's new quarter-tone scale (see [[http://www.ottavanota.info/|http://www.ottavanota.info]]) || | || {{**1 4 4 2 4 4 4 1**}} || Giancarlo Dalmonte's new quarter-tone scale (see [[http://www.ottavanota.info/|http://www.ottavanota.info]]) || | ||
|||| ====Enneatonic:==== || | ||||~ ====Enneatonic:==== || | ||
|| {{**1 2 3 4 4 1 2 3 4**}} || Progressive Enneatonic || | || {{**1 2 3 4 4 1 2 3 4**}} || Progressive Enneatonic || | ||
|| {{**4 1 4 1 4 1 4 1 4**}} || de Vries 9-tone - [[MOSScales|MOS]] of type [[5L 4s|5L 4s (unfair bug)]] || | || {{**4 1 4 1 4 1 4 1 4**}} || de Vries 9-tone - [[MOSScales|MOS]] of type [[5L 4s|5L 4s (unfair bug)]] || | ||
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|| {{**4 4 2 1 3 2 2 4 2**}} || Maqam Shawq Afza || | || {{**4 4 2 1 3 2 2 4 2**}} || Maqam Shawq Afza || | ||
|||| ====Decatonic:==== || | ||||~ ====Decatonic:==== || | ||
|| {{**2 3 2 3 2 2 3 2 3 2**}} || Young Decatonic - [[MOSScales|MOS]] of type [[4L 5s|4L 5s (fair bug)]] || | || {{**2 3 2 3 2 2 3 2 3 2**}} || Young Decatonic - [[MOSScales|MOS]] of type [[4L 5s|4L 5s (fair bug)]] || | ||
|| {{**2 2 1 2 2 2 1 2 2 1 2 2 2 1**}} || Young Half-Octave Diatonic - [[MOSScales|MOS]] of type [[10L 4s]] || | || {{**2 2 1 2 2 2 1 2 2 1 2 2 2 1**}} || Young Half-Octave Diatonic - [[MOSScales|MOS]] of type [[10L 4s]] || | ||
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|| {{**4 3 1 2 1 3 4 2 1 3**}} || Maqam Yakah || | || {{**4 3 1 2 1 3 4 2 1 3**}} || Maqam Yakah || | ||
|||| ====Hendecatonic:==== || | ||||~ ====Hendecatonic:==== || | ||
|| {{**4 2 1 3 2 2 2 2 3 1 2**}} || Maqam Hayyan || | || {{**4 2 1 3 2 2 2 2 3 1 2**}} || Maqam Hayyan || | ||
|||| ====Tridecatonic:==== || | ||||~ ====Tridecatonic:==== || | ||
|| {{**1 2 2 2 2 2 2 1 2 2 2 2 2**}} || de Vries 13-tone - [[MOSScales|MOS]] of type [[11L 2s]] || | || {{**1 2 2 2 2 2 2 1 2 2 2 2 2**}} || de Vries 13-tone - [[MOSScales|MOS]] of type [[11L 2s]] || | ||
|| {{**2 2 2 2 2 1 2 2 2 2 2 2 1**}} || Agmon Diatonic DS5, Ivan Wyschnegradsky's diatonicized chromatic scale - [[MOSScales|MOS]] of type [[11L 2s]] || | || {{**2 2 2 2 2 1 2 2 2 2 2 2 1**}} || Agmon Diatonic DS5, Ivan Wyschnegradsky's diatonicized chromatic scale - [[MOSScales|MOS]] of type [[11L 2s]] || | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
< | <th>[[#|Degree]]<br /> | ||
</ | </th> | ||
< | <th>Cents<br /> | ||
</ | </th> | ||
< | <th>Approximate Ratios*<br /> | ||
</ | </th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
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<!-- ws:start:WikiTextHeadingRule:23:&lt;h1&gt; --><h1 id="toc10"><a name="Scales / Modes"></a><!-- ws:end:WikiTextHeadingRule:23 -->Scales / Modes</h1> | <!-- ws:start:WikiTextHeadingRule:23:&lt;h1&gt; --><h1 id="toc10"><a name="Scales / Modes"></a><!-- ws:end:WikiTextHeadingRule:23 -->Scales / Modes</h1> | ||
<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
< | <th colspan="2"><!-- ws:start:WikiTextHeadingRule:25:&lt;h4&gt; --><h4 id="toc11"><a name="Scales / Modes---Pentatonic:"></a><!-- ws:end:WikiTextHeadingRule:25 -->Pentatonic:</h4> | ||
</ | </th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
< | <th colspan="2"><!-- ws:start:WikiTextHeadingRule:27:&lt;h4&gt; --><h4 id="toc12"><a name="Scales / Modes---Hexatonic:"></a><!-- ws:end:WikiTextHeadingRule:27 -->Hexatonic:</h4> | ||
</ | </th> | ||
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<tr> | <tr> | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
< | <th colspan="2"><!-- ws:start:WikiTextHeadingRule:29:&lt;h4&gt; --><h4 id="toc13"><a name="Scales / Modes---Heptatonic:"></a><!-- ws:end:WikiTextHeadingRule:29 -->Heptatonic:</h4> | ||
</ | </th> | ||
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<tr> | <tr> | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
< | <th colspan="2"><!-- ws:start:WikiTextHeadingRule:31:&lt;h4&gt; --><h4 id="toc14"><a name="Scales / Modes---Octatonic:"></a><!-- ws:end:WikiTextHeadingRule:31 -->Octatonic:</h4> | ||
</ | </th> | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
< | <th colspan="2"><!-- ws:start:WikiTextHeadingRule:33:&lt;h4&gt; --><h4 id="toc15"><a name="Scales / Modes---Enneatonic:"></a><!-- ws:end:WikiTextHeadingRule:33 -->Enneatonic:</h4> | ||
</ | </th> | ||
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<tr> | <tr> | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
< | <th colspan="2"><!-- ws:start:WikiTextHeadingRule:35:&lt;h4&gt; --><h4 id="toc16"><a name="Scales / Modes---Decatonic:"></a><!-- ws:end:WikiTextHeadingRule:35 -->Decatonic:</h4> | ||
</ | </th> | ||
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<tr> | <tr> | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
< | <th colspan="2"><!-- ws:start:WikiTextHeadingRule:37:&lt;h4&gt; --><h4 id="toc17"><a name="Scales / Modes---Hendecatonic:"></a><!-- ws:end:WikiTextHeadingRule:37 -->Hendecatonic:</h4> | ||
</ | </th> | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
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< | <th colspan="2"><!-- ws:start:WikiTextHeadingRule:39:&lt;h4&gt; --><h4 id="toc18"><a name="Scales / Modes---Tridecatonic:"></a><!-- ws:end:WikiTextHeadingRule:39 -->Tridecatonic:</h4> | ||
</ | </th> | ||
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