Titanium: Difference between revisions
Wikispaces>MasonGreen1 **Imported revision 586918925 - Original comment: ** |
Wikispaces>MasonGreen1 **Imported revision 586921111 - 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:MasonGreen1|MasonGreen1]] and made on <tt>2016-07-14 11: | : This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2016-07-14 11:59:32 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>586921111</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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Ductile 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. | Ductile 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. | ||
A good example of brittle titanium comes from using the [[23edo|23cd]] val, where the generator is about 261 cents and the fifths about 678 cents. The "5:4" is significantly sharp in this case and is actually very close to a just 14:11, making this situation akin to [[fudging]]. The 7:4 and 3:2 are both more accurate, but the 7:5 less so. The 11th harmonic is flatter than in ductile titanium, and the 13th harmonic is not matched well at all. [[14edo]]'s patent val gives a more expressive version of brittle titanium.</pre></div> | A good example of brittle titanium comes from using the [[23edo|23cd]] val, where the generator is about 261 cents and the fifths about 678 cents. The "5:4" is significantly sharp in this case and is actually very close to a just 14:11, making this situation akin to [[fudging]]. The 7:4 and 3:2 are both more accurate, but the 7:5 less so. The 11th harmonic is flatter than in ductile titanium, and the 13th harmonic is not matched well at all. [[14edo]]'s patent val gives a more expressive version of brittle titanium. | ||
===Suggested timbre=== | |||
If using brittle titanium (23cd, 14edo, etc.), one might want to consider using this as a guideline. With this spectrum, no partials are more than 25 cents above or below their perfectly harmonic values, and when using 14edo, no intervals will be more than 26 cents out of tune. This is only a guideline, and only with synthesized tones would it be possible to achieve this perfectly. With physical idiophones (celestas, gamelans, etc.) it should still be possible to get a great approximation using CAD (or trial and error). | |||
Fundamental (1st): just | |||
Octave (2nd): just | |||
3rd: -12.5 | |||
4th: just | |||
5th: +25 | |||
6th: -12.5 cents | |||
7th: -25 cents | |||
8th: just | |||
9th: -25 cents | |||
10th: +25 cents | |||
11th: -25 cents | |||
12th: -12.5 cents | |||
13th: +15 cents | |||
14th: -25 cents | |||
15th: +12.5 cents | |||
16th: just</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>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 (<a class="wiki_link" href="/21_20">21:20</a>), 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, <a class="wiki_link" href="/6_5">6:5</a>, <a class="wiki_link" href="/7_6">7:6</a>, and <a class="wiki_link" href="/8_7">8:7</a> 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 <a class="wiki_link" href="/7_5">7:5</a>). 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. It also tempers out 27:25 and is part of the <a class="wiki_link" href="/bug%20family">bug</a> family, and in fact &quot;brittle&quot; titanium (see below) is essentially the same as bug's 7-limit extension beep; because of this, the generator also functions as <a class="wiki_link" href="/9">10:9</a> (meaning this tuning has a <em>negative</em> syntonic comma). 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 (<a class="wiki_link" href="/21_20">21:20</a>), 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, <a class="wiki_link" href="/6_5">6:5</a>, <a class="wiki_link" href="/7_6">7:6</a>, and <a class="wiki_link" href="/8_7">8:7</a> 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 <a class="wiki_link" href="/7_5">7:5</a>). 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. It also tempers out 27:25 and is part of the <a class="wiki_link" href="/bug%20family">bug</a> family, and in fact &quot;brittle&quot; titanium (see below) is essentially the same as bug's 7-limit extension beep; because of this, the generator also functions as <a class="wiki_link" href="/9">10:9</a> (meaning this tuning has a <em>negative</em> syntonic comma). 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 /> | ||
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Ductile 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.<br /> | Ductile 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.<br /> | ||
<br /> | <br /> | ||
A good example of brittle titanium comes from using the <a class="wiki_link" href="/23edo">23cd</a> val, where the generator is about 261 cents and the fifths about 678 cents. The &quot;5:4&quot; is significantly sharp in this case and is actually very close to a just 14:11, making this situation akin to <a class="wiki_link" href="/fudging">fudging</a>. The 7:4 and 3:2 are both more accurate, but the 7:5 less so. The 11th harmonic is flatter than in ductile titanium, and the 13th harmonic is not matched well at all. <a class="wiki_link" href="/14edo">14edo</a>'s patent val gives a more expressive version of brittle titanium.</body></html></pre></div> | A good example of brittle titanium comes from using the <a class="wiki_link" href="/23edo">23cd</a> val, where the generator is about 261 cents and the fifths about 678 cents. The &quot;5:4&quot; is significantly sharp in this case and is actually very close to a just 14:11, making this situation akin to <a class="wiki_link" href="/fudging">fudging</a>. The 7:4 and 3:2 are both more accurate, but the 7:5 less so. The 11th harmonic is flatter than in ductile titanium, and the 13th harmonic is not matched well at all. <a class="wiki_link" href="/14edo">14edo</a>'s patent val gives a more expressive version of brittle titanium.<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h3&gt; --><h3 id="toc0"><a name="x--Suggested timbre"></a><!-- ws:end:WikiTextHeadingRule:0 -->Suggested timbre</h3> | |||
If using brittle titanium (23cd, 14edo, etc.), one might want to consider using this as a guideline. With this spectrum, no partials are more than 25 cents above or below their perfectly harmonic values, and when using 14edo, no intervals will be more than 26 cents out of tune. This is only a guideline, and only with synthesized tones would it be possible to achieve this perfectly. With physical idiophones (celestas, gamelans, etc.) it should still be possible to get a great approximation using CAD (or trial and error).<br /> | |||
<br /> | |||
Fundamental (1st): just<br /> | |||
Octave (2nd): just<br /> | |||
3rd: -12.5<br /> | |||
4th: just<br /> | |||
5th: +25<br /> | |||
6th: -12.5 cents<br /> | |||
7th: -25 cents<br /> | |||
8th: just<br /> | |||
9th: -25 cents<br /> | |||
10th: +25 cents<br /> | |||
11th: -25 cents<br /> | |||
12th: -12.5 cents<br /> | |||
13th: +15 cents<br /> | |||
14th: -25 cents<br /> | |||
15th: +12.5 cents<br /> | |||
16th: just</body></html></pre></div> | |||