The Biosphere: Difference between revisions
Wikispaces>mbattaglia1 **Imported revision 224001534 - Original comment: ** |
Wikispaces>mbattaglia1 **Imported revision 255422826 - 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>2011-09-18 21:34:20 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>255422826</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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Subgroup: 2.3.7.13/5 | Subgroup: 2.3.7.13/5 | ||
Comma: 91/90 | Comma: 91/90 | ||
Map: | Map: | ||
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<0 0 1 -1| | <0 0 1 -1| | ||
EDOs: 46 | EDOs: 46 | ||
=**Biosphere**= | =**Biosphere**= | ||
| Line 38: | Line 36: | ||
<0 0 0 1 0 -1| | <0 0 0 1 0 -1| | ||
<0 0 0 0 1 0| | <0 0 0 0 1 0| | ||
EDOs: 46 | |||
EDOs: 46 | |||
| Line 47: | Line 44: | ||
Commas: 91/90, 64/63 | Commas: 91/90, 64/63 | ||
[[POTE tuning|POTE generator]]: ~4/3 = 486.090 | [[POTE tuning|POTE generator]]: ~4/3 = 486.090 | ||
Map: [<1 2 2 3|, < 0 -1 2 -4|] | Map: [<1 2 2 3|, < 0 -1 2 -4|] | ||
EDOs: 27,32 | EDOs: 27, 32 | ||
Oceanfront is very similar to the familiar 7-limit superpyth temperament, in which 16/9 is equated with 7/4, 32/27 equated with 7/6, and 81/64 with 9/7. Oceanfront aims to equate 81/64 with 13/10 instead, however, so the fifths are even sharper than those of superpyth - 713.910 cents is the optimal POTE generator. The general structure of this scale is similar to that of meantone[7], except that the "major" triads in this scale are 10:13:15, and the minor triads are 6:7:9. | Oceanfront is very similar to the familiar 7-limit superpyth temperament, in which 16/9 is equated with 7/4, 32/27 equated with 7/6, and 81/64 with 9/7. Oceanfront aims to equate 81/64 with 13/10 instead, however, so the fifths are even sharper than those of superpyth - 713.910 cents is the optimal POTE generator. The general structure of this scale is similar to that of meantone[7], except that the "major" triads in this scale are 10:13:15, and the minor triads are 6:7:9. | ||
The sharp fifths of this scale can be a little more dissonant than meantone ears are used to, as can the flat fifths of something like mavila. This scale is very much like a brighter cousin of mavila in that regard. | The sharp fifths of this scale can be a little more dissonant than meantone ears are used to, as can the flat fifths of something like mavila. This scale is very much like a brighter cousin of mavila in that regard. | ||
==**Oceanfront Children**== | ==**Oceanfront Children**== | ||
| Line 69: | Line 62: | ||
Map: [< 1 2 6 2 7|, <0 -1 -9 2 -8|] | Map: [< 1 2 6 2 7|, <0 -1 -9 2 -8|] | ||
EDOs: 32 | EDOs: 32 | ||
This temperament extends superpyth as you'd expect. | This temperament extends superpyth as you'd expect. | ||
===[[#Rank two temperaments-Decitonic]]Porcupinefish=== | ===[[#Rank two temperaments-Decitonic]]Porcupinefish=== | ||
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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|] | ||
EDOs: 37, 59 | EDOs: 37, 59 | ||
Porcupinefish is the 13-limit extension of porcupine that you get by adding 91/90 to the usual mix of porcupine temperaments. Its name is derived from that it is a combination of the porcupine and oceanfront temperaments. | Porcupinefish is the 13-limit extension of porcupine that you get by adding 91/90 to the usual mix of porcupine temperaments. Its name is derived from that it is a combination of the porcupine and oceanfront temperaments. | ||
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Map: [<1 2 3 2|, <0 -2 -1 -3|] | Map: [<1 2 3 2|, <0 -2 -1 -3|] | ||
EDOs: 19, 24 | EDOs: 19, 24 | ||
Tropic is the merger of the biosphere and the archipelago. It is also a subgroup relative of semaphore temperament, since 49/48 vanishes. Of note is that 676/675 vanishes, so that two 7/6's (or 15/13)'s is equated with 4/3. While this temperament doesn't take advantage of the nearly pure harmonies that biome tempering can offer, particularly where 7/4 is involved, it still has some use, particularly for those who don't mind a bit more error in their tunings. | Tropic is the merger of the biosphere and the archipelago. It is also a subgroup relative of semaphore temperament, since 49/48 vanishes. Of note is that 676/675 vanishes, so that two 7/6's (or 15/13)'s is equated with 4/3. While this temperament doesn't take advantage of the nearly pure harmonies that biome tempering can offer, particularly where 7/4 is involved, it still has some use, particularly for those who don't mind a bit more error in their tunings. | ||
=[[#Rank two temperaments-Decitonic]]Avian= | |||
Subgroup: 2.3.5.7.13 | |||
Commas: 91/90, 245/243 | |||
=[[#Rank two temperaments-Decitonic]] | |||
Subgroup: 2.3.7.13 | |||
Commas: 91/90, | |||
[[POTE tuning|POTE generator]]: | [[POTE tuning|POTE generator]]: 443.322 | ||
Map: | Map: [<1 -1 -1 -2 0|, <0 7 9 13 10|] | ||
EDOs: | EDOs: 19, 27, 46 | ||
= = </pre></div> | = = </pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
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Subgroup: 2.3.7.13/5<br /> | Subgroup: 2.3.7.13/5<br /> | ||
Comma: 91/90<br /> | Comma: 91/90<br /> | ||
<br /> | <br /> | ||
Map:<br /> | Map:<br /> | ||
| Line 150: | Line 119: | ||
&lt;0 0 1 -1|<br /> | &lt;0 0 1 -1|<br /> | ||
<br /> | <br /> | ||
EDOs: 46 | EDOs: 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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&lt;0 0 0 1 0 -1|<br /> | &lt;0 0 0 1 0 -1|<br /> | ||
&lt;0 0 0 0 1 0|<br /> | &lt;0 0 0 0 1 0|<br /> | ||
EDOs: 46<br /> | |||
<br /> | <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:22:&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:22 -->Rank two temperaments</h1> | |||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Rank two temperaments"></a><!-- ws:end:WikiTextHeadingRule:6 --><!-- ws:start:WikiTextAnchorRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Oceanfront"></a><!-- ws:end:WikiTextHeadingRule:8 --><!-- ws:start:WikiTextAnchorRule:23:&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:23 --><span style="color: #000000;">Oceanfront</span></h1> | ||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Oceanfront"></a><!-- ws:end:WikiTextHeadingRule:8 --><!-- ws:start:WikiTextAnchorRule: | |||
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 /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~4/3 = 486.090 | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~4/3 = 486.090<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 2 2 3|, &lt; 0 -1 2 -4|]<br /> | Map: [&lt;1 2 2 3|, &lt; 0 -1 2 -4|]<br /> | ||
EDOs: 27,32 | EDOs: 27, 32<br /> | ||
<br /> | <br /> | ||
Oceanfront is very similar to the familiar 7-limit superpyth temperament, in which 16/9 is equated with 7/4, 32/27 equated with 7/6, and 81/64 with 9/7. Oceanfront aims to equate 81/64 with 13/10 instead, however, so the fifths are even sharper than those of superpyth - 713.910 cents is the optimal POTE generator. The general structure of this scale is similar to that of meantone[7], except that the &quot;major&quot; triads in this scale are 10:13:15, and the minor triads are 6:7:9.<br /> | Oceanfront is very similar to the familiar 7-limit superpyth temperament, in which 16/9 is equated with 7/4, 32/27 equated with 7/6, and 81/64 with 9/7. Oceanfront aims to equate 81/64 with 13/10 instead, however, so the fifths are even sharper than those of superpyth - 713.910 cents is the optimal POTE generator. The general structure of this scale is similar to that of meantone[7], except that the &quot;major&quot; triads in this scale are 10:13:15, and the minor triads are 6:7:9.<br /> | ||
<br /> | <br /> | ||
The sharp fifths of this scale can be a little more dissonant than meantone ears are used to, as can the flat fifths of something like mavila. This scale is very much like a brighter cousin of mavila in that regard.<br /> | The sharp fifths of this scale can be a little more dissonant than meantone ears are used to, as can the flat fifths of something like mavila. This scale is very much like a brighter cousin of mavila in that regard.<br /> | ||
<br /> | <br /> | ||
<!-- 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: | <!-- 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: 2.3.5.7.13<br /> | ||
Commas: 91/90, 64/63, 245/243<br /> | Commas: 91/90, 64/63, 245/243<br /> | ||
| Line 193: | Line 157: | ||
Map: [&lt; 1 2 6 2 7|, &lt;0 -1 -9 2 -8|]<br /> | Map: [&lt; 1 2 6 2 7|, &lt;0 -1 -9 2 -8|]<br /> | ||
EDOs: 32<br /> | EDOs: 32<br /> | ||
<br /> | <br /> | ||
This temperament extends superpyth as you'd expect.<br /> | This temperament extends superpyth as you'd expect.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:14:&lt;h3&gt; --><h3 id="toc7"><a name="Oceanfront-Oceanfront Children-Porcupinefish"></a><!-- ws:end:WikiTextHeadingRule:14 --><!-- ws:start:WikiTextAnchorRule:25:&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:25 -->Porcupinefish</h3> | |||
<!-- ws:start:WikiTextHeadingRule:14:&lt;h3&gt; --><h3 id="toc7"><a name="Oceanfront-Oceanfront Children-Porcupinefish"></a><!-- ws:end:WikiTextHeadingRule:14 --><!-- ws:start:WikiTextAnchorRule: | |||
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 /> | ||
| Line 207: | Line 168: | ||
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 /> | ||
EDOs: 37, 59<br /> | EDOs: 37, 59<br /> | ||
<br /> | <br /> | ||
Porcupinefish is the 13-limit extension of porcupine that you get by adding 91/90 to the usual mix of porcupine temperaments. Its name is derived from that it is a combination of the porcupine and oceanfront temperaments.<br /> | Porcupinefish is the 13-limit extension of porcupine that you get by adding 91/90 to the usual mix of porcupine temperaments. Its name is derived from that it is a combination of the porcupine and oceanfront temperaments.<br /> | ||
<br /> | <br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Tropic"></a><!-- ws:end:WikiTextHeadingRule:16 --><!-- ws:start:WikiTextAnchorRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Tropic"></a><!-- ws:end:WikiTextHeadingRule:16 --><!-- 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-Decitonic&quot; title=&quot;Anchor: Rank two temperaments-Decitonic&quot;/&gt; --><a name="Rank two temperaments-Decitonic"></a><!-- ws:end:WikiTextAnchorRule:26 -->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 /> | ||
| Line 220: | Line 180: | ||
Map: [&lt;1 2 3 2|, &lt;0 -2 -1 -3|]<br /> | Map: [&lt;1 2 3 2|, &lt;0 -2 -1 -3|]<br /> | ||
EDOs: 19, 24<br /> | EDOs: 19, 24<br /> | ||
<br /> | <br /> | ||
Tropic is the merger of the biosphere and the archipelago. It is also a subgroup relative of semaphore temperament, since 49/48 vanishes. Of note is that 676/675 vanishes, so that two 7/6's (or 15/13)'s is equated with 4/3. While this temperament doesn't take advantage of the nearly pure harmonies that biome tempering can offer, particularly where 7/4 is involved, it still has some use, particularly for those who don't mind a bit more error in their tunings.<br /> | Tropic is the merger of the biosphere and the archipelago. It is also a subgroup relative of semaphore temperament, since 49/48 vanishes. Of note is that 676/675 vanishes, so that two 7/6's (or 15/13)'s is equated with 4/3. While this temperament doesn't take advantage of the nearly pure harmonies that biome tempering can offer, particularly where 7/4 is involved, it still has some use, particularly for those who don't mind a bit more error in their tunings.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="Avian"></a><!-- ws:end:WikiTextHeadingRule:18 --><!-- 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 -->Avian</h1> | |||
Subgroup: 2.3.5.7.13<br /> | |||
Commas: 91/90, 245/243<br /> | |||
<!-- ws:start:WikiTextHeadingRule:18:&lt; | |||
Subgroup: 2.3.7.13 | |||
Commas: 91/90, | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 443.322<br /> | ||
<br /> | <br /> | ||
Map: | Map: [&lt;1 -1 -1 -2 0|, &lt;0 7 9 13 10|]<br /> | ||
EDOs: 19, 27, 46<br /> | |||
<br /> | <br /> | ||
<br /> | <br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><!-- ws:end:WikiTextHeadingRule:20 --> </h1> | ||
</body></html></pre></div> | </body></html></pre></div> | ||