Titanium: Difference between revisions

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<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:MasonGreen1|MasonGreen1]] and made on <tt>2016-07-13 00:13:34 UTC</tt>.<br>

: This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2016-07-13 00:22:23 UTC</tt>.<br>

: The original revision id was <tt>~~586854051~~</tt>.<br>

: The original revision id was <tt>586854279</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>

<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">**Titanium** is Mason Green's proposed name for a remarkable low-complexity, though high-badness 7-limit temperament. Titanium tempers out the septimal chromatic semitone (21:20), making it a [[Septisemi temperaments|septisemi]] temperament, and the slendro diesis (49:48), making it part of the [[slendro clan]]. As such, 6:5, 7:6, and 8:7 are all represented by the same interval (which, in fact, is the generator). Two of these generators make a very sharp fourth (which is also a very flat 7:5). ~~Finally, since~~ three fifths make a minor (not major) sixth, and four make a minor (not major) third, it is also a [[pelogic]] temperament. Finally it can be also considered a sort of messed-up variant of [[orwell]] temperament as well, since the generator falls into the same range of sizes.

<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">**Titanium** is Mason Green's proposed name for a remarkable low-complexity, though high-badness 7-limit temperament. Titanium tempers out the septimal chromatic semitone (21:20), making it a [[Septisemi temperaments|septisemi]] temperament, and the slendro diesis (49:48), making it part of the [[slendro clan]]. As such, 6:5, 7:6, and 8:7 are all represented by the same interval (which, in fact, is the generator). Two of these generators make a very sharp fourth (which is also a very flat 7:5). Since three fifths make a minor (not major) sixth, and four make a minor (not major) third, it is also a [[pelogic]] temperament. Finally it can be also considered a sort of messed-up variant of [[orwell]] temperament as well, since the generator falls into the same range of sizes.

The edos whose patent vals support titanium are [[4edo]], [[5edo]], [[9edo]], and [[14edo]]. Many other edos can be used as non-patent vals, such as 13.

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Titanium does not extend well to the 9-odd-limit since the 3:2 is already extremely flat. However, beyond the 9th harmonic it performs better, with the 11th and 13th harmonics having passable mappings (tempering out 33:32 and 65:64, respectively). While pure octaves are possible, titanium (especially the ductile version) also benefits greatly from octave stretching, since the 3rd, 7th, 11th, and 13th harmonics are all flat, while the 5th is near-just in the above example. An octave of around 1205-1207 cents is worth trying.</pre></div>

<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>Titanium</title></head><body><strong>Titanium</strong> is Mason Green's proposed name for a remarkable low-complexity, though high-badness 7-limit temperament. Titanium tempers out the septimal chromatic semitone (21:20), making it a <a class="wiki_link" href="/Septisemi%20temperaments">septisemi</a> temperament, and the slendro diesis (49:48), making it part of the <a class="wiki_link" href="/slendro%20clan">slendro clan</a>. As such, 6:5, 7:6, and 8:7 are all represented by the same interval (which, in fact, is the generator). Two of these generators make a very sharp fourth (which is also a very flat 7:5). ~~Finally, since~~ three fifths make a minor (not major) sixth, and four make a minor (not major) third, it is also a <a class="wiki_link" href="/pelogic">pelogic</a> temperament. Finally it can be also considered a sort of messed-up variant of <a class="wiki_link" href="/orwell">orwell</a> temperament as well, since the generator falls into the same range of sizes.<br />

<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>Titanium</title></head><body><strong>Titanium</strong> is Mason Green's proposed name for a remarkable low-complexity, though high-badness 7-limit temperament. Titanium tempers out the septimal chromatic semitone (21:20), making it a <a class="wiki_link" href="/Septisemi%20temperaments">septisemi</a> temperament, and the slendro diesis (49:48), making it part of the <a class="wiki_link" href="/slendro%20clan">slendro clan</a>. As such, 6:5, 7:6, and 8:7 are all represented by the same interval (which, in fact, is the generator). Two of these generators make a very sharp fourth (which is also a very flat 7:5). Since three fifths make a minor (not major) sixth, and four make a minor (not major) third, it is also a <a class="wiki_link" href="/pelogic">pelogic</a> temperament. Finally it can be also considered a sort of messed-up variant of <a class="wiki_link" href="/orwell">orwell</a> temperament as well, since the generator falls into the same range of sizes.<br />

<br />

The edos whose patent vals support titanium are <a class="wiki_link" href="/4edo">4edo</a>, <a class="wiki_link" href="/5edo">5edo</a>, <a class="wiki_link" href="/9edo">9edo</a>, and <a class="wiki_link" href="/14edo">14edo</a>. Many other edos can be used as non-patent vals, such as 13.<br />

@@ 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:MasonGreen1|MasonGreen1]] and made on <tt>2016-07-13 00:13:34 UTC</tt>.<br>
+: This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2016-07-13 00:22:23 UTC</tt>.<br>
-: The original revision id was <tt>586854051</tt>.<br>
+: The original revision id was <tt>586854279</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>
 <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">**Titanium** is Mason Green's proposed name for a remarkable low-complexity, though high-badness 7-limit temperament. Titanium tempers out the septimal chromatic semitone (21:20), making it a [[Septisemi temperaments|septisemi]] temperament, and the slendro diesis (49:48), making it part of the [[slendro clan]]. As such, 6:5, 7:6, and 8:7 are all represented by the same interval (which, in fact, is the generator). Two of these generators make a very sharp fourth (which is also a very flat 7:5). Finally, since three fifths make a minor (not major) sixth, and four make a minor (not major) third, it is also a [[pelogic]] temperament. Finally it can be also considered a sort of messed-up variant of [[orwell]] temperament as well, since the generator falls into the same range of sizes.
+<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">**Titanium** is Mason Green's proposed name for a remarkable low-complexity, though high-badness 7-limit temperament. Titanium tempers out the septimal chromatic semitone (21:20), making it a [[Septisemi temperaments|septisemi]] temperament, and the slendro diesis (49:48), making it part of the [[slendro clan]]. As such, 6:5, 7:6, and 8:7 are all represented by the same interval (which, in fact, is the generator). Two of these generators make a very sharp fourth (which is also a very flat 7:5). Since three fifths make a minor (not major) sixth, and four make a minor (not major) third, it is also a [[pelogic]] temperament. Finally it can be also considered a sort of messed-up variant of [[orwell]] temperament as well, since the generator falls into the same range of sizes.
 The edos whose patent vals support titanium are [[4edo]], [[5edo]], [[9edo]], and [[14edo]]. Many other edos can be used as non-patent vals, such as 13.
@@ Line 32: / Line 32: @@
 Titanium does not extend well to the 9-odd-limit since the 3:2 is already extremely flat. However, beyond the 9th harmonic it performs better, with the 11th and 13th harmonics having passable mappings (tempering out 33:32 and 65:64, respectively). While pure octaves are possible, titanium (especially the ductile version) also benefits greatly from octave stretching, since the 3rd, 7th, 11th, and 13th harmonics are all flat, while the 5th is near-just in the above example. An octave of around 1205-1207 cents is worth trying.</pre></div>
 <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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Titanium&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;Titanium&lt;/strong&gt; is Mason Green's proposed name for a remarkable low-complexity, though high-badness 7-limit temperament. Titanium tempers out the septimal chromatic semitone (21:20), making it a &lt;a class="wiki_link" href="/Septisemi%20temperaments"&gt;septisemi&lt;/a&gt; temperament, and the slendro diesis (49:48), making it part of the &lt;a class="wiki_link" href="/slendro%20clan"&gt;slendro clan&lt;/a&gt;. As such, 6:5, 7:6, and 8:7 are all represented by the same interval (which, in fact, is the generator). Two of these generators make a very sharp fourth (which is also a very flat 7:5). Finally, since three fifths make a minor (not major) sixth, and four make a minor (not major) third, it is also a &lt;a class="wiki_link" href="/pelogic"&gt;pelogic&lt;/a&gt; temperament. Finally it can be also considered a sort of messed-up variant of &lt;a class="wiki_link" href="/orwell"&gt;orwell&lt;/a&gt; temperament as well, since the generator falls into the same range of sizes.&lt;br /&gt;
+<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;Titanium&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;Titanium&lt;/strong&gt; is Mason Green's proposed name for a remarkable low-complexity, though high-badness 7-limit temperament. Titanium tempers out the septimal chromatic semitone (21:20), making it a &lt;a class="wiki_link" href="/Septisemi%20temperaments"&gt;septisemi&lt;/a&gt; temperament, and the slendro diesis (49:48), making it part of the &lt;a class="wiki_link" href="/slendro%20clan"&gt;slendro clan&lt;/a&gt;. As such, 6:5, 7:6, and 8:7 are all represented by the same interval (which, in fact, is the generator). Two of these generators make a very sharp fourth (which is also a very flat 7:5). Since three fifths make a minor (not major) sixth, and four make a minor (not major) third, it is also a &lt;a class="wiki_link" href="/pelogic"&gt;pelogic&lt;/a&gt; temperament. Finally it can be also considered a sort of messed-up variant of &lt;a class="wiki_link" href="/orwell"&gt;orwell&lt;/a&gt; temperament as well, since the generator falls into the same range of sizes.&lt;br /&gt;
 &lt;br /&gt;
 The edos whose patent vals support titanium are &lt;a class="wiki_link" href="/4edo"&gt;4edo&lt;/a&gt;, &lt;a class="wiki_link" href="/5edo"&gt;5edo&lt;/a&gt;, &lt;a class="wiki_link" href="/9edo"&gt;9edo&lt;/a&gt;, and &lt;a class="wiki_link" href="/14edo"&gt;14edo&lt;/a&gt;. Many other edos can be used as non-patent vals, such as 13.&lt;br /&gt;