The Biosphere: Difference between revisions

Line 1:

<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2011-04-25 03:45:24 UTC</tt>.

: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2011-04-25 03:45:59 UTC</tt>.

: The original revision id was <tt>~~222627552~~</tt>.

: The original revision id was <tt>222627582</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Line 8:

<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." This temperament is so named because temperaments that arise from eliminating 91/90 can evoke synesthetic associations of different "natural" settings, some very familiar and others fresh and exotic.

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. Hence, you end up with a tonal system that relates and connects two of the most xenharmonic triads in existence (at least those with 3/2 on the outside). 91/90 tempering thus enriches septimal harmony by increasing the concordance of ~~"utonal" 7-limit harmony~~.

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. Hence, you end up with a tonal system that relates and connects two of the most xenharmonic triads in existence (at least those with 3/2 on the outside). 91/90 tempering thus enriches septimal harmony by increasing the concordance of its utonalities.

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 123:

<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 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 &quot;biome&quot; loosely means &quot;ecosystem&quot; or &quot;climate.&quot; This temperament is so named because temperaments that arise from eliminating 91/90 can evoke synesthetic associations of different &quot;natural&quot; settings, some very familiar and others fresh and exotic.

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. Hence, you end up with a tonal system that relates and connects two of the most xenharmonic triads in existence (at least those with 3/2 on the outside). 91/90 tempering thus enriches septimal harmony by increasing the concordance of ~~&quot;utonal&quot; 7-limit harmony~~.

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. Hence, you end up with a tonal system that relates and connects two of the most xenharmonic triads in existence (at least those with 3/2 on the outside). 91/90 tempering thus enriches septimal harmony by increasing the concordance of its utonalities.

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 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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 03:45:24 UTC</tt>.<br>
+: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2011-04-25 03:45:59 UTC</tt>.<br>
-: The original revision id was <tt>222627552</tt>.<br>
+: The original revision id was <tt>222627582</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>
@@ Line 8: / Line 8: @@
 <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." This temperament is so named because temperaments that arise from eliminating 91/90 can evoke synesthetic associations of different "natural" settings, some very familiar and others fresh and exotic.
-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. Hence, you end up with a tonal system that relates and connects two of the most xenharmonic triads in existence (at least those with 3/2 on the outside). 91/90 tempering thus enriches septimal harmony by increasing the concordance of "utonal" 7-limit harmony.
+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. Hence, you end up with a tonal system that relates and connects two of the most xenharmonic triads in existence (at least those with 3/2 on the outside). 91/90 tempering thus enriches septimal harmony by increasing the concordance of its utonalities.
 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 123: / Line 123: @@
 <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">&lt;html&gt;&lt;head&gt;&lt;title&gt;The Biosphere&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The biosphere is the name given to the collection of temperaments that are children of or related to &lt;strong&gt;&lt;em&gt;biome temperament&lt;/em&gt;&lt;/strong&gt;, the rank 3 2.3.7.13/5 subgroup temperament eliminating 91/90, and &lt;strong&gt;&lt;em&gt;biosphere temperament&lt;/em&gt;&lt;/strong&gt;, its rank five full 13-limit extension. The term &amp;quot;biome&amp;quot; loosely means &amp;quot;ecosystem&amp;quot; or &amp;quot;climate.&amp;quot; This temperament is so named because temperaments that arise from eliminating 91/90 can evoke synesthetic associations of different &amp;quot;natural&amp;quot; settings, some very familiar and others fresh and exotic.&lt;br /&gt;
 &lt;br /&gt;
-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. Hence, you end up with a tonal system that relates and connects two of the most xenharmonic triads in existence (at least those with 3/2 on the outside). 91/90 tempering thus enriches septimal harmony by increasing the concordance of &amp;quot;utonal&amp;quot; 7-limit harmony.&lt;br /&gt;
+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. Hence, you end up with a tonal system that relates and connects two of the most xenharmonic triads in existence (at least those with 3/2 on the outside). 91/90 tempering thus enriches septimal harmony by increasing the concordance of its utonalities.&lt;br /&gt;
 &lt;br /&gt;
 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.&lt;br /&gt;