The Biosphere: Difference between revisions
Wikispaces>mbattaglia1 **Imported revision 222624792 - Original comment: ** |
Wikispaces>mbattaglia1 **Imported revision 222625016 - 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:mbattaglia1|mbattaglia1]] and made on <tt>2011-04-25 03: | : This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2011-04-25 03:11:51 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>222625016</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 rank-3 biome temperament is of particular theoretical interest because it generates a rank-3 lattice that is analogous to the 5-limit JI lattice. As 5-limit JI is the basis for which all 5-limit linear temperaments are derived, the rank-3 biome temperament can serve as a basis to derive useful 2.3.7.13/5 linear temperaments. Instead of our base triads being 4:5:6 and its utonal inversion 10:12:15, we instead treat 6:7:9 and its utonal inversion 10:13:15 as fundamental to the system. The three dimensions of the system can be thought of as 2/1, 3/2, and 7/6 (or 9/7, or 13/10). 46-EDO is a great tuning for biome, giving nearly-pure harmonies all around, somewhat analogous to the accuracy of 34-EDO or 53-EDO in approximating 5-limit JI. | The rank-3 biome temperament is of particular theoretical interest because it generates a rank-3 lattice that is analogous to the 5-limit JI lattice. As 5-limit JI is the basis for which all 5-limit linear temperaments are derived, the rank-3 biome temperament can serve as a basis to derive useful 2.3.7.13/5 linear temperaments. Instead of our base triads being 4:5:6 and its utonal inversion 10:12:15, we instead treat 6:7:9 and its utonal inversion 10:13:15 as fundamental to the system. The three dimensions of the system can be thought of as 2/1, 3/2, and 7/6 (or 9/7, or 13/10). 46-EDO is a great tuning for biome, giving nearly-pure harmonies all around, somewhat analogous to the accuracy of 34-EDO or 53-EDO in approximating 5-limit JI. | ||
This lattice can also be extended to deal with "higher primes," as can 5-limit JI, | This lattice can also be extended to deal with "higher primes," as can 5-limit JI. However, we instead expand the subgroup outward from the center, so that the "higher primes" we look at are things like like 5, 11, and 13. However, it may prove more useful at first to think purely within the 2.3.7.13/5 subgroup, so as to first come to understand the xenharmonic possibilities of the system. | ||
=Parent Temperaments= | |||
=**Biome | =**Biome**= | ||
Subgroup: 2.3.7.13/5 | |||
Comma: 91/90 | Comma: 91/90 | ||
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EDOs: 46 and some other stuff | EDOs: 46 and some other stuff | ||
=**Biosphere**= | |||
Subgroup: Full 13-limit | |||
Comma: 91/90 | |||
Map: [<I have no idea|, <I have no idea|, <I have no idea|, <I have no idea|, <I have no idea|, <I have no idea|] | |||
EDOs: 46 and some other stuff | |||
=[[#Rank two temperaments]]Rank two temperaments= | =[[#Rank two temperaments]]Rank two temperaments= | ||
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The rank-3 biome temperament is of particular theoretical interest because it generates a rank-3 lattice that is analogous to the 5-limit JI lattice. As 5-limit JI is the basis for which all 5-limit linear temperaments are derived, the rank-3 biome temperament can serve as a basis to derive useful 2.3.7.13/5 linear temperaments. Instead of our base triads being 4:5:6 and its utonal inversion 10:12:15, we instead treat 6:7:9 and its utonal inversion 10:13:15 as fundamental to the system. The three dimensions of the system can be thought of as 2/1, 3/2, and 7/6 (or 9/7, or 13/10). 46-EDO is a great tuning for biome, giving nearly-pure harmonies all around, somewhat analogous to the accuracy of 34-EDO or 53-EDO in approximating 5-limit JI.<br /> | The rank-3 biome temperament is of particular theoretical interest because it generates a rank-3 lattice that is analogous to the 5-limit JI lattice. As 5-limit JI is the basis for which all 5-limit linear temperaments are derived, the rank-3 biome temperament can serve as a basis to derive useful 2.3.7.13/5 linear temperaments. Instead of our base triads being 4:5:6 and its utonal inversion 10:12:15, we instead treat 6:7:9 and its utonal inversion 10:13:15 as fundamental to the system. The three dimensions of the system can be thought of as 2/1, 3/2, and 7/6 (or 9/7, or 13/10). 46-EDO is a great tuning for biome, giving nearly-pure harmonies all around, somewhat analogous to the accuracy of 34-EDO or 53-EDO in approximating 5-limit JI.<br /> | ||
<br /> | <br /> | ||
This lattice can also be extended to deal with &quot;higher primes,&quot; as can 5-limit JI, | This lattice can also be extended to deal with &quot;higher primes,&quot; as can 5-limit JI. However, we instead expand the subgroup outward from the center, so that the &quot;higher primes&quot; we look at are things like like 5, 11, and 13. However, it may prove more useful at first to think purely within the 2.3.7.13/5 subgroup, so as to first come to understand the xenharmonic possibilities of the system.<br /> | ||
<br /> | <br /> | ||
< | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Parent Temperaments"></a><!-- ws:end:WikiTextHeadingRule:0 -->Parent Temperaments</h1> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Biome"></a><!-- ws:end:WikiTextHeadingRule:2 --><strong>Biome</strong></h1> | ||
Comma: 91/90<br /> | Subgroup: 2.3.7.13/5<br /> | ||
Comma: 91/90<br /> | |||
<br /> | <br /> | ||
Map<br /> | Map<br /> | ||
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EDOs: 46 and some other stuff<br /> | EDOs: 46 and some other stuff<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Biosphere"></a><!-- ws:end:WikiTextHeadingRule:4 --><strong>Biosphere</strong></h1> | ||
<!-- ws:start:WikiTextHeadingRule: | Subgroup: Full 13-limit<br /> | ||
Comma: 91/90<br /> | |||
<br /> | |||
Map: [&lt;I have no idea|, &lt;I have no idea|, &lt;I have no idea|, &lt;I have no idea|, &lt;I have no idea|, &lt;I have no idea|]<br /> | |||
<br /> | |||
EDOs: 46 and some other stuff<br /> | |||
<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Rank two temperaments"></a><!-- ws:end:WikiTextHeadingRule:6 --><!-- ws:start:WikiTextAnchorRule:26:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Rank two temperaments&quot; title=&quot;Anchor: Rank two temperaments&quot;/&gt; --><a name="Rank two temperaments"></a><!-- ws:end:WikiTextAnchorRule:26 -->Rank two temperaments</h1> | |||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Oceanfront"></a><!-- ws:end:WikiTextHeadingRule:8 --><!-- ws:start:WikiTextAnchorRule:27:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Rank two temperaments-Decitonic&quot; title=&quot;Anchor: Rank two temperaments-Decitonic&quot;/&gt; --><a name="Rank two temperaments-Decitonic"></a><!-- ws:end:WikiTextAnchorRule:27 --><span style="color: #000000;">Oceanfront</span></h1> | |||
Subgroup: 2.3.7.13/5<br /> | Subgroup: 2.3.7.13/5<br /> | ||
Commas: 91/90, 64/63<br /> | Commas: 91/90, 64/63<br /> | ||
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13-limit: TBD<br /> | 13-limit: TBD<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Oceanfront-Oceanfront Children"></a><!-- ws:end:WikiTextHeadingRule:10 --><strong>Oceanfront Children</strong></h2> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name="Oceanfront-Oceanfront Children-Ultrapyth"></a><!-- ws:end:WikiTextHeadingRule:12 --><!-- ws:start:WikiTextAnchorRule:28:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Rank two temperaments-Decitonic&quot; title=&quot;Anchor: Rank two temperaments-Decitonic&quot;/&gt; --><a name="Rank two temperaments-Decitonic"></a><!-- ws:end:WikiTextAnchorRule:28 -->Ultrapyth</h3> | ||
Subgroup: 2.3.5.7.13<br /> | Subgroup: 2.3.5.7.13<br /> | ||
Commas: 91/90, 64/63, 245/243<br /> | Commas: 91/90, 64/63, 245/243<br /> | ||
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Full 13-limit: TBD<br /> | Full 13-limit: TBD<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h3&gt; --><h3 id="toc7"><a name="Oceanfront-Oceanfront Children-Porcupinefish"></a><!-- ws:end:WikiTextHeadingRule:14 --><!-- ws:start:WikiTextAnchorRule:29:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Rank two temperaments-Decitonic&quot; title=&quot;Anchor: Rank two temperaments-Decitonic&quot;/&gt; --><a name="Rank two temperaments-Decitonic"></a><!-- ws:end:WikiTextAnchorRule:29 -->Porcupinefish</h3> | ||
Subgroup: 13-limit<br /> | Subgroup: 13-limit<br /> | ||
Commas: 91/90, 64/63, 250/243, 121/120<br /> | Commas: 91/90, 64/63, 250/243, 121/120<br /> | ||
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<br /> | <br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Tropic"></a><!-- ws:end:WikiTextHeadingRule:16 --><!-- ws:start:WikiTextAnchorRule:30:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Rank two temperaments-Decitonic&quot; title=&quot;Anchor: Rank two temperaments-Decitonic&quot;/&gt; --><a name="Rank two temperaments-Decitonic"></a><!-- ws:end:WikiTextAnchorRule:30 -->Tropic</h1> | ||
Subgroup: 2.3.7.13/5<br /> | Subgroup: 2.3.7.13/5<br /> | ||
Commas: 91/90, 49/48<br /> | Commas: 91/90, 49/48<br /> | ||
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13-limit: TBD<br /> | 13-limit: TBD<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Tropic-Tropic Children"></a><!-- ws:end:WikiTextHeadingRule:18 -->Tropic Children</h2> | ||
TBD<br /> | TBD<br /> | ||
<br /> | <br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="Pandora"></a><!-- ws:end:WikiTextHeadingRule:20 --><!-- ws:start:WikiTextAnchorRule:31:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Rank two temperaments-Decitonic&quot; title=&quot;Anchor: Rank two temperaments-Decitonic&quot;/&gt; --><a name="Rank two temperaments-Decitonic"></a><!-- ws:end:WikiTextAnchorRule:31 -->Pandora</h1> | ||
Subgroup: 2.3.7.13/5<br /> | Subgroup: 2.3.7.13/5<br /> | ||
Commas: 91/90, ???<br /> | Commas: 91/90, ???<br /> | ||
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13-limit: TBD<br /> | 13-limit: TBD<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="Pandora-Pandora Children"></a><!-- ws:end:WikiTextHeadingRule:22 -->Pandora Children</h2> | ||
TBD<br /> | TBD<br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc12"><!-- ws:end:WikiTextHeadingRule:24 --> </h1> | ||
</body></html></pre></div> | </body></html></pre></div> | ||