User:MasonGreen1/Naughty and nice harmonics: 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>2015-11-23 14:52:25 UTC</tt>.

: This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2015-11-23 14:53:24 UTC</tt>.

: The original revision id was <tt>~~567516825~~</tt>.

: The original revision id was <tt>567517025</tt>.

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

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

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Because the 11 is naughty, damping or omitting the 11th harmonic partial from the sound of synthesized tones or physical instruments may result in a more pleasant timbre. Similarly, the 19th harmonic could be amplified louder than it would otherwise be.

~~Similarly, it~~ might be a good idea to use a modified [[The Riemann Zeta Function and Tuning|Z function]] when analyzing higher edos, removing the component corresponding to the 11th harmonic (thus making it a no-elevens Z function) while increasing the weighting of the component corresponding to 19. Using such a function even more firmly establishes 12edo's position as supreme among small edos, since 12edo matches the 19th harmonic very closely while avoiding the 11th.

It might be a good idea to use a modified [[The Riemann Zeta Function and Tuning|Z function]] when analyzing higher edos, removing the component corresponding to the 11th harmonic (thus making it a no-elevens Z function) while increasing the weighting of the component corresponding to 19. Using such a function even more firmly establishes 12edo's position as supreme among small edos, since 12edo matches the 19th harmonic very closely while avoiding the 11th.

Among higher edos, the one that has the most to gain is [[53edo]], which closely matches the 13 and 19, while matching the 17 less well and completely avoiding the 11.

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Because the 11 is naughty, damping or omitting the 11th harmonic partial from the sound of synthesized tones or physical instruments may result in a more pleasant timbre. Similarly, the 19th harmonic could be amplified louder than it would otherwise be.

~~Similarly, it~~ might be a good idea to use a modified <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning">Z function</a> when analyzing higher edos, removing the component corresponding to the 11th harmonic (thus making it a no-elevens Z function) while increasing the weighting of the component corresponding to 19. Using such a function even more firmly establishes 12edo's position as supreme among small edos, since 12edo matches the 19th harmonic very closely while avoiding the 11th.

It might be a good idea to use a modified <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning">Z function</a> when analyzing higher edos, removing the component corresponding to the 11th harmonic (thus making it a no-elevens Z function) while increasing the weighting of the component corresponding to 19. Using such a function even more firmly establishes 12edo's position as supreme among small edos, since 12edo matches the 19th harmonic very closely while avoiding the 11th.

Among higher edos, the one that has the most to gain is <a class="wiki_link" href="/53edo">53edo</a>, which closely matches the 13 and 19, while matching the 17 less well and completely avoiding the 11.

@@ 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>2015-11-23 14:52:25 UTC</tt>.<br>
+: This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2015-11-23 14:53:24 UTC</tt>.<br>
-: The original revision id was <tt>567516825</tt>.<br>
+: The original revision id was <tt>567517025</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 25: / Line 25: @@
 Because the 11 is naughty, damping or omitting the 11th harmonic partial from the sound of synthesized tones or physical instruments may result in a more pleasant timbre. Similarly, the 19th harmonic could be amplified louder than it would otherwise be.
-Similarly, it might be a good idea to use a modified [[The Riemann Zeta Function and Tuning|Z function]] when analyzing higher edos, removing the component corresponding to the 11th harmonic (thus making it a no-elevens Z function) while increasing the weighting of the component corresponding to 19. Using such a function even more firmly establishes 12edo's position as supreme among small edos, since 12edo matches the 19th harmonic very closely while avoiding the 11th.
+It might be a good idea to use a modified [[The Riemann Zeta Function and Tuning|Z function]] when analyzing higher edos, removing the component corresponding to the 11th harmonic (thus making it a no-elevens Z function) while increasing the weighting of the component corresponding to 19. Using such a function even more firmly establishes 12edo's position as supreme among small edos, since 12edo matches the 19th harmonic very closely while avoiding the 11th.
 Among higher edos, the one that has the most to gain is [[53edo]], which closely matches the 13 and 19, while matching the 17 less well and completely avoiding the 11.
@@ Line 52: / Line 52: @@
 Because the 11 is naughty, damping or omitting the 11th harmonic partial from the sound of synthesized tones or physical instruments may result in a more pleasant timbre. Similarly, the 19th harmonic could be amplified louder than it would otherwise be.&lt;br /&gt;
 &lt;br /&gt;
-Similarly, it might be a good idea to use a modified &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning"&gt;Z function&lt;/a&gt; when analyzing higher edos, removing the component corresponding to the 11th harmonic (thus making it a no-elevens Z function) while increasing the weighting of the component corresponding to 19. Using such a function even more firmly establishes 12edo's position as supreme among small edos, since 12edo matches the 19th harmonic very closely while avoiding the 11th.&lt;br /&gt;
+It might be a good idea to use a modified &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning"&gt;Z function&lt;/a&gt; when analyzing higher edos, removing the component corresponding to the 11th harmonic (thus making it a no-elevens Z function) while increasing the weighting of the component corresponding to 19. Using such a function even more firmly establishes 12edo's position as supreme among small edos, since 12edo matches the 19th harmonic very closely while avoiding the 11th.&lt;br /&gt;
 &lt;br /&gt;
 Among higher edos, the one that has the most to gain is &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt;, which closely matches the 13 and 19, while matching the 17 less well and completely avoiding the 11.&lt;br /&gt;