The Biosphere: Difference between revisions
Wikispaces>mbattaglia1 **Imported revision 255422826 - Original comment: ** |
Wikispaces>mbattaglia1 **Imported revision 267088920 - 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- | : This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2011-10-21 00:13:24 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>267088920</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The biosphere is the name given to the collection of temperaments that are children of or related to **//biome temperament//**, the rank 3 2.3.7.13/5 subgroup temperament eliminating 91/90, and **//biosphere temperament//**, its rank five full 13-limit extension. The term "biome" loosely means "ecosystem" or "climate." | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The biosphere is the name given to the collection of temperaments that are children of or related to **//biome temperament//**, the rank 3 2.3.7.13/5 subgroup temperament eliminating 91/90, and **//biosphere temperament//**, its rank five full 13-limit extension. The term "biome" loosely means "ecosystem" or "climate." | ||
The next low-numbered triad after 4:5:6 with a 3/2 on the outside is 6:7:9, but its inversion, 14:18:21, can sound extremely dissonant. On the other hand, you also have 10:13:15, which is another standout triad of low complexity with a fifth on the outside, but its inversion, 26:30:39, is also relatively complex. Tempering out 91/90 makes both of these problems disappear by connecting the two together, such that the utonal inverse of 6:7:9 becomes 10:13:15 | The next low-numbered triad after 4:5:6 with a 3/2 on the outside is 6:7:9, but its inversion, 14:18:21, can sound extremely dissonant to those not used to 9-limit harmony. On the other hand, you also have 10:13:15, which is another standout triad of low complexity with a fifth on the outside, but its inversion, 26:30:39, is also relatively complex. Tempering out 91/90 makes both of these problems disappear by connecting the two together, such that the utonal inverse of 6:7:9 becomes 10:13:15. | ||
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. | ||
| Line 24: | Line 24: | ||
<0 0 1 -1| | <0 0 1 -1| | ||
EDOs: 46 | EDOs: 14, 17, 22, 27, 32, 46 | ||
=**Biosphere**= | =**Biosphere**= | ||
| Line 55: | Line 55: | ||
==**Oceanfront Children**== | ==**Oceanfront Children**== | ||
===[[#Rank two temperaments-Decitonic]]Ultrapyth=== | ===[[#Rank two temperaments-Decitonic]]Ultrapyth=== | ||
Subgroup: 2.3.5.7.13 | Subgroup: 2.3.5.7.11.13 | ||
Commas: 91/90, 64/63, 245/243 | Commas: 91/90, 64/63, 78/77, 245/243 | ||
[[POTE tuning|POTE generator]]: ~4/3 = | [[POTE tuning|POTE generator]]: ~4/3 = 489.521 | ||
Map: [< 1 2 6 2 | Map: [< 1 2 6 2 10 9|, <0 -1 -9 2 -16 -13|] | ||
EDOs: 32 | EDOs: 27, 32, 37 | ||
This temperament extends superpyth as you'd expect. | This temperament extends superpyth as you'd expect. | ||
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Commas: 91/90, 64/63, 250/243, 121/120 | Commas: 91/90, 64/63, 250/243, 121/120 | ||
[[POTE tuning|POTE generator]]: ~10/9 = 162.474 | [[POTE tuning|POTE generator]]: ~10/9 = 162.474 | ||
Map: [<1 2 3 2 -1 1|, <0 -3 -5 6 33 20|] | Map: [<1 2 3 2 -1 1|, <0 -3 -5 6 33 20|] | ||
| Line 81: | Line 81: | ||
Commas: 91/90, 49/48 | Commas: 91/90, 49/48 | ||
[[POTE tuning|POTE generator]]: ~ | [[POTE tuning|POTE generator]]: ~7/6 = 251.507 | ||
Map: [<1 2 3 2|, <0 -2 -1 -3|] | Map: [<1 2 3 2|, <0 -2 -1 -3|] | ||
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= = </pre></div> | = = </pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>The Biosphere</title></head><body>The biosphere is the name given to the collection of temperaments that are children of or related to <strong><em>biome temperament</em></strong>, the rank 3 2.3.7.13/5 subgroup temperament eliminating 91/90, and <strong><em>biosphere temperament</em></strong>, its rank five full 13-limit extension. The term &quot;biome&quot; loosely means &quot;ecosystem&quot; or &quot;climate.&quot; | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>The Biosphere</title></head><body>The biosphere is the name given to the collection of temperaments that are children of or related to <strong><em>biome temperament</em></strong>, the rank 3 2.3.7.13/5 subgroup temperament eliminating 91/90, and <strong><em>biosphere temperament</em></strong>, its rank five full 13-limit extension. The term &quot;biome&quot; loosely means &quot;ecosystem&quot; or &quot;climate.&quot;<br /> | ||
<br /> | <br /> | ||
The next low-numbered triad after 4:5:6 with a 3/2 on the outside is 6:7:9, but its inversion, 14:18:21, can sound extremely dissonant. On the other hand, you also have 10:13:15, which is another standout triad of low complexity with a fifth on the outside, but its inversion, 26:30:39, is also relatively complex. Tempering out 91/90 makes both of these problems disappear by connecting the two together, such that the utonal inverse of 6:7:9 becomes 10:13:15 | The next low-numbered triad after 4:5:6 with a 3/2 on the outside is 6:7:9, but its inversion, 14:18:21, can sound extremely dissonant to those not used to 9-limit harmony. On the other hand, you also have 10:13:15, which is another standout triad of low complexity with a fifth on the outside, but its inversion, 26:30:39, is also relatively complex. Tempering out 91/90 makes both of these problems disappear by connecting the two together, such that the utonal inverse of 6:7:9 becomes 10:13:15.<br /> | ||
<br /> | <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 /> | 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 /> | ||
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&lt;0 0 1 -1|<br /> | &lt;0 0 1 -1|<br /> | ||
<br /> | <br /> | ||
EDOs: 46<br /> | EDOs: 14, 17, 22, 27, 32, 46<br /> | ||
<br /> | <br /> | ||
<!-- 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:4:&lt;h1&gt; --><h1 id="toc2"><a name="Biosphere"></a><!-- ws:end:WikiTextHeadingRule:4 --><strong>Biosphere</strong></h1> | ||
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<!-- 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: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:12:&lt;h3&gt; --><h3 id="toc6"><a name="Oceanfront-Oceanfront Children-Ultrapyth"></a><!-- ws:end:WikiTextHeadingRule:12 --><!-- ws:start:WikiTextAnchorRule:24:&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:24 -->Ultrapyth</h3> | <!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name="Oceanfront-Oceanfront Children-Ultrapyth"></a><!-- ws:end:WikiTextHeadingRule:12 --><!-- ws:start:WikiTextAnchorRule:24:&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:24 -->Ultrapyth</h3> | ||
Subgroup: 2.3.5.7.13<br /> | Subgroup: 2.3.5.7.11.13<br /> | ||
Commas: 91/90, 64/63, 245/243<br /> | Commas: 91/90, 64/63, 78/77, 245/243<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~4/3 = | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~4/3 = 489.521<br /> | ||
<br /> | <br /> | ||
Map: [&lt; 1 2 6 2 | Map: [&lt; 1 2 6 2 10 9|, &lt;0 -1 -9 2 -16 -13|]<br /> | ||
EDOs: 32<br /> | EDOs: 27, 32, 37<br /> | ||
<br /> | <br /> | ||
This temperament extends superpyth as you'd expect.<br /> | This temperament extends superpyth as you'd expect.<br /> | ||
| Line 164: | Line 164: | ||
Commas: 91/90, 64/63, 250/243, 121/120<br /> | Commas: 91/90, 64/63, 250/243, 121/120<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~10/9 = 162.474 | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~10/9 = 162.474<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 2 3 2 -1 1|, &lt;0 -3 -5 6 33 20|]<br /> | Map: [&lt;1 2 3 2 -1 1|, &lt;0 -3 -5 6 33 20|]<br /> | ||
| Line 176: | Line 176: | ||
Commas: 91/90, 49/48<br /> | Commas: 91/90, 49/48<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~ | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~7/6 = 251.507<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 2 3 2|, &lt;0 -2 -1 -3|]<br /> | Map: [&lt;1 2 3 2|, &lt;0 -2 -1 -3|]<br /> | ||