Harmonic entropy: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2015-08-21 00:13:29 UTC</tt>.

: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2015-08-21 01:14:39 UTC</tt>.

: The original revision id was <tt>~~557087005~~</tt>.

: The original revision id was <tt>557088553</tt>.

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* The perception of partial **timbral fusion** of the chord into one complex sound

* The appearance of a **virtual fundamental** pitch in the bass

* ~~Timbral~~ **beatlessness**, compared to mistunings of the chord in the surrounding area

* Critical band effects, such as timbral **beatlessness**, compared to mistunings of the chord in the surrounding area

* The appearance of a quick fluttering effect sometimes known as **periodicity buzz**

~~These~~ effects ~~do not always appear strictly~~ in ~~tandem with one another~~. ~~For instance~~, ~~Paul Erlich has noted~~ that most ~~models for beatlessness measure 10:12:15 and 4:5:6 as being identical~~, ~~whereas~~ the ~~latter yields exhibits more timbral fusion and a more salient virtual fundamental than~~ the ~~former. However~~, ~~suppose we want~~ to ~~come up with a combined measure for how often effects such as~~ the ~~above tend to occur~~. ~~It is then useful to note that~~

There has been much research specifically on the musical implications critical band effects in the literature (e.g. Sethares's work), which are perhaps the psychoacoustic phenomena that readers are most familiar with. However, the modern xenharmonic community has displayed immense interest in exploring the other effects mentioned above as well, which have proven extremely important to the development of modern xenharmonic music.

These effects sometimes behave differently, and do not always appear strictly in tandem with one another. For instance, Paul Erlich has noted that most models for beatlessness measure 10:12:15 and 4:5:6 as being identical, whereas the latter yields exhibits more timbral fusion and a more salient virtual fundamental than the former. However, suppose we want to come up with a combined measure for how often effects such as the above tend to occur. It is then useful to note that

* effects such as these tend to appear most strongly for those chords with large subsets that correspond to simple chunks of the harmonic series

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<h1 id="toc1"><a name="Background"></a>Background</h1>

The general workings of the human auditory system lead to a plethora of well-documented and sonically interesting phenomena that can occur when a musical chord is played:

<ul><li>The perception of partial timbral fusion of the chord into one complex sound</li><li>The appearance of a virtual fundamental pitch in the bass</li><li>~~Timbral~~ beatlessness, compared to mistunings of the chord in the surrounding area</li><li>The appearance of a quick fluttering effect sometimes known as periodicity buzz</li></ul>

<ul><li>The perception of partial timbral fusion of the chord into one complex sound</li><li>The appearance of a virtual fundamental pitch in the bass</li><li>Critical band effects, such as timbral beatlessness, compared to mistunings of the chord in the surrounding area</li><li>The appearance of a quick fluttering effect sometimes known as periodicity buzz</li></ul>

~~These~~ effects ~~do not always appear strictly~~ in ~~tandem with one another~~. ~~For instance~~, ~~Paul Erlich has noted~~ that most ~~models for beatlessness measure 10:12:15 and 4:5:6 as being identical~~, ~~whereas~~ the ~~latter yields exhibits more timbral fusion and a more salient virtual fundamental than~~ the ~~former. However~~, ~~suppose we want~~ to ~~come up with a combined measure for how often effects such as~~ the ~~above tend to occur~~. ~~It is then useful to note that~~

There has been much research specifically on the musical implications critical band effects in the literature (e.g. Sethares's work), which are perhaps the psychoacoustic phenomena that readers are most familiar with. However, the modern xenharmonic community has displayed immense interest in exploring the other effects mentioned above as well, which have proven extremely important to the development of modern xenharmonic music.

These effects sometimes behave differently, and do not always appear strictly in tandem with one another. For instance, Paul Erlich has noted that most models for beatlessness measure 10:12:15 and 4:5:6 as being identical, whereas the latter yields exhibits more timbral fusion and a more salient virtual fundamental than the former. However, suppose we want to come up with a combined measure for how often effects such as the above tend to occur. It is then useful to note that

<ul><li>effects such as these tend to appear most strongly for those chords with large subsets that correspond to simple chunks of the harmonic series</li><li>the effects produced exhibit some degree of tolerance for mistuning</li></ul>

@@ 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:mbattaglia1|mbattaglia1]] and made on <tt>2015-08-21 00:13:29 UTC</tt>.<br>
+: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2015-08-21 01:14:39 UTC</tt>.<br>
-: The original revision id was <tt>557087005</tt>.<br>
+: The original revision id was <tt>557088553</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 17: / Line 17: @@
 * The perception of partial **timbral fusion** of the chord into one complex sound
 * The appearance of a **virtual fundamental** pitch in the bass
-* Timbral **beatlessness**, compared to mistunings of the chord in the surrounding area
+* Critical band effects, such as timbral **beatlessness**, compared to mistunings of the chord in the surrounding area
 * The appearance of a quick fluttering effect sometimes known as **periodicity buzz**
-These effects do not always appear strictly in tandem with one another. For instance, Paul Erlich has noted that most models for beatlessness measure 10:12:15 and 4:5:6 as being identical, whereas the latter yields exhibits more timbral fusion and a more salient virtual fundamental than the former. However, suppose we want to come up with a combined measure for how often effects such as the above tend to occur. It is then useful to note that
+There has been much research specifically on the musical implications critical band effects in the literature (e.g. Sethares's work), which are perhaps the psychoacoustic phenomena that readers are most familiar with. However, the modern xenharmonic community has displayed immense interest in exploring the other effects mentioned above as well, which have proven extremely important to the development of modern xenharmonic music.
+These effects sometimes behave differently, and do not always appear&lt;span style="line-height: 1.5;"&gt; strictly in tandem with one another. For instance, Paul Erlich has noted that most models for beatlessness measure 10:12:15 and 4:5:6 as being identical, whereas the latter yields exhibits more timbral fusion and a more salient virtual fundamental than the former. However, suppose we want to come up with a combined measure for how often effects such as the above tend to occur. It is then useful to note that&lt;/span&gt;
 * &lt;span style="line-height: 1.5;"&gt;effects such as these tend to appear most strongly for those chords with large subsets that correspond to simple chunks of the harmonic series&lt;/span&gt;
@@ Line 202: / Line 203: @@
 &lt;!-- ws:start:WikiTextHeadingRule:15:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Background"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:15 --&gt;Background&lt;/h1&gt;
   The general workings of the human auditory system lead to a plethora of well-documented and sonically interesting phenomena that can occur when a musical chord is played:&lt;br /&gt;
-&lt;ul&gt;&lt;li&gt;The perception of partial &lt;strong&gt;timbral fusion&lt;/strong&gt; of the chord into one complex sound&lt;/li&gt;&lt;li&gt;The appearance of a &lt;strong&gt;virtual fundamental&lt;/strong&gt; pitch in the bass&lt;/li&gt;&lt;li&gt;Timbral &lt;strong&gt;beatlessness&lt;/strong&gt;, compared to mistunings of the chord in the surrounding area&lt;/li&gt;&lt;li&gt;The appearance of a quick fluttering effect sometimes known as &lt;strong&gt;periodicity buzz&lt;/strong&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
+&lt;ul&gt;&lt;li&gt;The perception of partial &lt;strong&gt;timbral fusion&lt;/strong&gt; of the chord into one complex sound&lt;/li&gt;&lt;li&gt;The appearance of a &lt;strong&gt;virtual fundamental&lt;/strong&gt; pitch in the bass&lt;/li&gt;&lt;li&gt;Critical band effects, such as timbral &lt;strong&gt;beatlessness&lt;/strong&gt;, compared to mistunings of the chord in the surrounding area&lt;/li&gt;&lt;li&gt;The appearance of a quick fluttering effect sometimes known as &lt;strong&gt;periodicity buzz&lt;/strong&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
-These effects do not always appear strictly in tandem with one another. For instance, Paul Erlich has noted that most models for beatlessness measure 10:12:15 and 4:5:6 as being identical, whereas the latter yields exhibits more timbral fusion and a more salient virtual fundamental than the former. However, suppose we want to come up with a combined measure for how often effects such as the above tend to occur. It is then useful to note that&lt;br /&gt;
+There has been much research specifically on the musical implications critical band effects in the literature (e.g. Sethares's work), which are perhaps the psychoacoustic phenomena that readers are most familiar with. However, the modern xenharmonic community has displayed immense interest in exploring the other effects mentioned above as well, which have proven extremely important to the development of modern xenharmonic music.&lt;br /&gt;
 &lt;br /&gt;
+These effects sometimes behave differently, and do not always appear&lt;span style="line-height: 1.5;"&gt; strictly in tandem with one another. For instance, Paul Erlich has noted that most models for beatlessness measure 10:12:15 and 4:5:6 as being identical, whereas the latter yields exhibits more timbral fusion and a more salient virtual fundamental than the former. However, suppose we want to come up with a combined measure for how often effects such as the above tend to occur. It is then useful to note that&lt;/span&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;ul&gt;&lt;li&gt;&lt;span style="line-height: 1.5;"&gt;effects such as these tend to appear most strongly for those chords with large subsets that correspond to simple chunks of the harmonic series&lt;/span&gt;&lt;/li&gt;&lt;li&gt;&lt;span style="line-height: 1.5;"&gt;the effects produced exhibit some degree of tolerance for mistuning&lt;/span&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;