Titanium: Difference between revisions
Wikispaces>MasonGreen1 **Imported revision 586853999 - Original comment: ** |
Wikispaces>MasonGreen1 **Imported revision 586854029 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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>2016-07-13 00: | : This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2016-07-13 00:12:44 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>586854029</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> | ||
| Line 30: | Line 30: | ||
While pajara temperament and Paul Erlich's scales are closely related to Indian music theory (pajara temperament can be used to construct a 22-note MODMOS that easily represents the sruti system), titanium temperament and its enneatonic scales have a natural kinship with Indonesian music, being related to both slendro (via tempering out 49:48, and in fact the enneatonic scale can be considered a sort of extended slendro), and pelog scales (via the presence of the flat fifths; the complete pelog scale does not however occur as a subset of the enneatonic, but does occur as a subset of the 13- and 14-note "chromatic" titanium scales. Moreover, pelog scales are sometimes described as approximating a 7-note subset of 9edo, and 9edo falls within the titanium temperament's tuning range). | While pajara temperament and Paul Erlich's scales are closely related to Indian music theory (pajara temperament can be used to construct a 22-note MODMOS that easily represents the sruti system), titanium temperament and its enneatonic scales have a natural kinship with Indonesian music, being related to both slendro (via tempering out 49:48, and in fact the enneatonic scale can be considered a sort of extended slendro), and pelog scales (via the presence of the flat fifths; the complete pelog scale does not however occur as a subset of the enneatonic, but does occur as a subset of the 13- and 14-note "chromatic" titanium scales. Moreover, pelog scales are sometimes described as approximating a 7-note subset of 9edo, and 9edo falls within the titanium temperament's tuning range). | ||
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. 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> | 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> | <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). 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 /> | ||
| Line 56: | Line 56: | ||
While pajara temperament and Paul Erlich's scales are closely related to Indian music theory (pajara temperament can be used to construct a 22-note MODMOS that easily represents the sruti system), titanium temperament and its enneatonic scales have a natural kinship with Indonesian music, being related to both slendro (via tempering out 49:48, and in fact the enneatonic scale can be considered a sort of extended slendro), and pelog scales (via the presence of the flat fifths; the complete pelog scale does not however occur as a subset of the enneatonic, but does occur as a subset of the 13- and 14-note &quot;chromatic&quot; titanium scales. Moreover, pelog scales are sometimes described as approximating a 7-note subset of 9edo, and 9edo falls within the titanium temperament's tuning range).<br /> | While pajara temperament and Paul Erlich's scales are closely related to Indian music theory (pajara temperament can be used to construct a 22-note MODMOS that easily represents the sruti system), titanium temperament and its enneatonic scales have a natural kinship with Indonesian music, being related to both slendro (via tempering out 49:48, and in fact the enneatonic scale can be considered a sort of extended slendro), and pelog scales (via the presence of the flat fifths; the complete pelog scale does not however occur as a subset of the enneatonic, but does occur as a subset of the 13- and 14-note &quot;chromatic&quot; titanium scales. Moreover, pelog scales are sometimes described as approximating a 7-note subset of 9edo, and 9edo falls within the titanium temperament's tuning range).<br /> | ||
<br /> | <br /> | ||
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. 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.</body></html></pre></div> | 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.</body></html></pre></div> | ||