Titanium: Difference between revisions

: This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2016-07-12 21:48:16 UTC</tt>.<br>

: The original revision id was <tt>586850075</tt>.<br>

In titanium, the 7-limit tetrad has very low [[Graham complexity]] (only 3). The fact that 7:5 is also 4:3 allows a type of "tritone substitution" distinct from that which appears in [[jubilismic]] temperaments; namely, one in which the 4:3 of one chord becomes the 7:5 of the next or vice versa. This is equivalent to modulating upward or downward by a generator. The more usual type of modulation (upward or downward by fifths) is also easy since two generators make a fifth. These tetrads, despite being relatively inaccurate, are still easily recognizable and not necessarily unpleasant-sounding (though of course it depends on the timbre of the instrument they are played on).

Titanium forms enneatonic scales which may be either of the form LLsLsLsLs or ssLsLsLsL; where both step sizes are equal this simply gives [[9edo]]. An enneatonic scale has six otonal and six utonal tetrads, and just like the diatonic scale it allows a variant of the familiar "I-IV-V" type of chord progression (which, using enneatonic notation, would be I-V-VI). Titanium's enneatonic scales provide an alternative to the Erlich decatonic; they are lower in accuracy, but are also simpler and offer more freedom of modulation, and thus for some listeners they might actually be less xenharmonic.

An example of an enneatonic scale (using a generator of 271 cents) is given below. The step sizes are 116 and 155 cents. In this scale, the generator, while representing three different intervals, is quite close to a just 7:6 and thus has a rather stable sound, as does the 387-cent interval which is very close to a just 5:4. This helps compensate for the fifths and fourths being so out of tune. This is the reverse of what happens in Pythagorean scales (where the fifths are consonant and the thirds dissonant). Another thing to watch out for is that the so-called "wolf" fifth, at 697 cents, is actually quite close to just. It is a "wolf" interval only in the sense that it can't easily be used as a 10:7, unlike the other fifths, but it will certainly prove useful in other ways. This scale, in the standard major mode (i. e, the mode allowing for a I-IV-V chord progression), has the form sLsLsLssL.

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In titanium, the 7-limit tetrad has very low &lt;a class="wiki_link" href="/Graham%20complexity"&gt;Graham complexity&lt;/a&gt; (only 3). The fact that 7:5 is also 4:3 allows a type of &amp;quot;tritone substitution&amp;quot; distinct from that which appears in &lt;a class="wiki_link" href="/jubilismic"&gt;jubilismic&lt;/a&gt; temperaments; namely, one in which the 4:3 of one chord becomes the 7:5 of the next or vice versa. This is equivalent to modulating upward or downward by a generator. The more usual type of modulation (upward or downward by fifths) is also easy since two generators make a fifth. These tetrads, despite being relatively inaccurate, are still easily recognizable and not necessarily unpleasant-sounding (though of course it depends on the timbre of the instrument they are played on).&lt;br /&gt;

Titanium forms enneatonic scales which may be either of the form LLsLsLsLs or ssLsLsLsL; where both step sizes are equal this simply gives &lt;a class="wiki_link" href="/9edo"&gt;9edo&lt;/a&gt;. An enneatonic scale has six otonal and six utonal tetrads, and just like the diatonic scale it allows a variant of the familiar &amp;quot;I-IV-V&amp;quot; type of chord progression (which, using enneatonic notation, would be I-V-VI). Titanium's enneatonic scales provide an alternative to the Erlich decatonic; they are lower in accuracy, but are also simpler and offer more freedom of modulation, and thus for some listeners they might actually be less xenharmonic.&lt;br /&gt;

An example of an enneatonic scale (using a generator of 271 cents) is given below. The step sizes are 116 and 155 cents. In this scale, the generator, while representing three different intervals, is quite close to a just 7:6 and thus has a rather stable sound, as does the 387-cent interval which is very close to a just 5:4. This helps compensate for the fifths and fourths being so out of tune. This is the reverse of what happens in Pythagorean scales (where the fifths are consonant and the thirds dissonant). Another thing to watch out for is that the so-called &amp;quot;wolf&amp;quot; fifth, at 697 cents, is actually quite close to just. It is a &amp;quot;wolf&amp;quot; interval only in the sense that it can't easily be used as a 10:7, unlike the other fifths, but it will certainly prove useful in other ways. This scale, in the standard major mode (i. e, the mode allowing for a I-IV-V chord progression), has the form sLsLsLssL.&lt;br /&gt;

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