Mixed timbre: 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:

: This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2016-02-15 22:24:24 UTC</tt>.

: This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2016-02-22 01:11:02 UTC</tt>.

: The original revision id was <tt>~~574925935~~</tt>.

: The original revision id was <tt>575446935</tt>.

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

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If other non-octave-equivalent timbres are similarly modified, it will be possible to construct a timbre around a particular temperament. Using 22edo, we should bend the overtones corresponding to the 3rd, 7th and 9th harmonics up, and those corresponding to the 5th and 11th harmonics down. We can also omit the 13th harmonic altogether (since 22edo does not deal with this harmonic well). By adapting the timbre to the temperament in this way, the tritone will sound much more consonant and will function more credibly as both 7:5 and 10:7; other intervals including the whole tone, thirds, and fifths will also sound much better.

Another tuning that would benefit a great deal from this is [[17edo]], which is superb for melody (as documented by George Secor), but whose harmonies beyond the 3-limit are rather lacking. By bending the 7th, 11th, and 13th harmonic partials down, while bending the 5th harmonic partial //way// up (assuming the sharp val for 5), we can compensate for 17edo's deficiencies and effectively convert it into a full 13-limit system, while still using timbres that don't sound //too// inharmonic. Using the flat val for 5 will result in a more xenharmonic effect since it maps both the "5:4" and "5:6" onto a neutral third.

Timbres like this are easy to synthesize on a computer, but it may also be possible to achieve this effect in physical instruments by coupling a harmonic or nearly harmonic oscillator (such as a bowed string), to a more inharmonic one such as an idiophone. String resonance (like that which naturally occurs in a piano when the damper pedal is pressed) is another option.

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If other non-octave-equivalent timbres are similarly modified, it will be possible to construct a timbre around a particular temperament. Using 22edo, we should bend the overtones corresponding to the 3rd, 7th and 9th harmonics up, and those corresponding to the 5th and 11th harmonics down. We can also omit the 13th harmonic altogether (since 22edo does not deal with this harmonic well). By adapting the timbre to the temperament in this way, the tritone will sound much more consonant and will function more credibly as both 7:5 and 10:7; other intervals including the whole tone, thirds, and fifths will also sound much better.

Another tuning that would benefit a great deal from this is <a class="wiki_link" href="/17edo">17edo</a>, which is superb for melody (as documented by George Secor), but whose harmonies beyond the 3-limit are rather lacking. By bending the 7th, 11th, and 13th harmonic partials down, while bending the 5th harmonic partial way up (assuming the sharp val for 5), we can compensate for 17edo's deficiencies and effectively convert it into a full 13-limit system, while still using timbres that don't sound too inharmonic. Using the flat val for 5 will result in a more xenharmonic effect since it maps both the &quot;5:4&quot; and &quot;5:6&quot; onto a neutral third.

Timbres like this are easy to synthesize on a computer, but it may also be possible to achieve this effect in physical instruments by coupling a harmonic or nearly harmonic oscillator (such as a bowed string), to a more inharmonic one such as an idiophone. String resonance (like that which naturally occurs in a piano when the damper pedal is pressed) is another option.

@@ 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>2016-02-15 22:24:24 UTC</tt>.<br>
+: This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2016-02-22 01:11:02 UTC</tt>.<br>
-: The original revision id was <tt>574925935</tt>.<br>
+: The original revision id was <tt>575446935</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 19: / Line 19: @@
 If other non-octave-equivalent timbres are similarly modified, it will be possible to construct a timbre around a particular temperament. Using 22edo, we should bend the overtones corresponding to the 3rd, 7th and 9th harmonics up, and those corresponding to the 5th and 11th harmonics down. We can also omit the 13th harmonic altogether (since 22edo does not deal with this harmonic well). By adapting the timbre to the temperament in this way, the tritone will sound much more consonant and will function more credibly as both 7:5 and 10:7; other intervals including the whole tone, thirds, and fifths will also sound much better.
+Another tuning that would benefit a great deal from this is [[17edo]], which is superb for melody (as documented by George Secor), but whose harmonies beyond the 3-limit are rather lacking. By bending the 7th, 11th, and 13th harmonic partials down, while bending the 5th harmonic partial //way// up (assuming the sharp val for 5), we can compensate for 17edo's deficiencies and effectively convert it into a full 13-limit system, while still using timbres that don't sound //too// inharmonic. Using the flat val for 5 will result in a more xenharmonic effect since it maps both the "5:4" and "5:6" onto a neutral third.
 Timbres like this are easy to synthesize on a computer, but it may also be possible to achieve this effect in physical instruments by coupling a harmonic or nearly harmonic oscillator (such as a bowed string), to a more inharmonic one such as an idiophone. String resonance (like that which naturally occurs in a piano when the damper pedal is pressed) is another option.
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 &lt;br /&gt;
 If other non-octave-equivalent timbres are similarly modified, it will be possible to construct a timbre around a particular temperament. Using 22edo, we should bend the overtones corresponding to the 3rd, 7th and 9th harmonics up, and those corresponding to the 5th and 11th harmonics down. We can also omit the 13th harmonic altogether (since 22edo does not deal with this harmonic well). By adapting the timbre to the temperament in this way, the tritone will sound much more consonant and will function more credibly as both 7:5 and 10:7; other intervals including the whole tone, thirds, and fifths will also sound much better.&lt;br /&gt;
+&lt;br /&gt;
+Another tuning that would benefit a great deal from this is &lt;a class="wiki_link" href="/17edo"&gt;17edo&lt;/a&gt;, which is superb for melody (as documented by George Secor), but whose harmonies beyond the 3-limit are rather lacking. By bending the 7th, 11th, and 13th harmonic partials down, while bending the 5th harmonic partial &lt;em&gt;way&lt;/em&gt; up (assuming the sharp val for 5), we can compensate for 17edo's deficiencies and effectively convert it into a full 13-limit system, while still using timbres that don't sound &lt;em&gt;too&lt;/em&gt; inharmonic. Using the flat val for 5 will result in a more xenharmonic effect since it maps both the &amp;quot;5:4&amp;quot; and &amp;quot;5:6&amp;quot; onto a neutral third.&lt;br /&gt;
 &lt;br /&gt;
 Timbres like this are easy to synthesize on a computer, but it may also be possible to achieve this effect in physical instruments by coupling a harmonic or nearly harmonic oscillator (such as a bowed string), to a more inharmonic one such as an idiophone. String resonance (like that which naturally occurs in a piano when the damper pedal is pressed) is another option.&lt;br /&gt;