Isoharmonic chord: 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:<br>

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-~~27 21~~:53:27 UTC</tt>.<br>

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-03 16:02:47 UTC</tt>.<br>

: The original revision id was <tt>~~597353876~~</tt>.<br>

: The original revision id was <tt>601298180</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>

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<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;white-space: pre-wrap ! important" class="old-revision-html">=isoharmonic chords=

In [[JustIntonation|just intonation]], Isoharmonic chords are ~~build~~ by successive jumps up the [[OverToneSeries|harmonic series]] by some number of steps. Since the harmonic series is arranged such that each higher step is smaller than the one before it, all isoharmonic chords have this same shape -- with diminishing step size as one ascends. All isoharmonic chords are equal-hertz chords, meaning that the frequencies of the notes are in an arithmetic sequence with an equal difference in cycles per second between successive notes. However, not all equal-hertz chords are isoharmonic chords, since the ratios between the notes need not be integers. An isoharmonic "chord" may function more like a "scale" than a chord (depending on the composition of course), but we will use the word "chord" on this page for consistency.

In [[JustIntonation|just intonation]], Isoharmonic chords are built by successive jumps up the [[OverToneSeries|harmonic series]] by some number of steps. Since the harmonic series is arranged such that each higher step is smaller than the one before it, all isoharmonic chords have this same shape -- with diminishing step size as one ascends. All isoharmonic chords are equal-hertz chords, meaning that the frequencies of the notes are in an arithmetic sequence with an equal difference in cycles per second between successive notes. However, not all equal-hertz chords are isoharmonic chords, since the ratios between the notes need not be integers. An isoharmonic "chord" may function more like a "scale" than a chord (depending on the composition of course), but we will use the word "chord" on this page for consistency.

===class i===

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<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>isoharmonic chords</title></head><body><h1 id="toc0"><a name="isoharmonic chords"></a>isoharmonic chords</h1>

<br />

In <a class="wiki_link" href="/JustIntonation">just intonation</a>, Isoharmonic chords are ~~build~~ by successive jumps up the <a class="wiki_link" href="/OverToneSeries">harmonic series</a> by some number of steps. Since the harmonic series is arranged such that each higher step is smaller than the one before it, all isoharmonic chords have this same shape -- with diminishing step size as one ascends. All isoharmonic chords are equal-hertz chords, meaning that the frequencies of the notes are in an arithmetic sequence with an equal difference in cycles per second between successive notes. However, not all equal-hertz chords are isoharmonic chords, since the ratios between the notes need not be integers. An isoharmonic &quot;chord&quot; may function more like a &quot;scale&quot; than a chord (depending on the composition of course), but we will use the word &quot;chord&quot; on this page for consistency.<br />

In <a class="wiki_link" href="/JustIntonation">just intonation</a>, Isoharmonic chords are built by successive jumps up the <a class="wiki_link" href="/OverToneSeries">harmonic series</a> by some number of steps. Since the harmonic series is arranged such that each higher step is smaller than the one before it, all isoharmonic chords have this same shape -- with diminishing step size as one ascends. All isoharmonic chords are equal-hertz chords, meaning that the frequencies of the notes are in an arithmetic sequence with an equal difference in cycles per second between successive notes. However, not all equal-hertz chords are isoharmonic chords, since the ratios between the notes need not be integers. An isoharmonic &quot;chord&quot; may function more like a &quot;scale&quot; than a chord (depending on the composition of course), but we will use the word &quot;chord&quot; on this page for consistency.<br />

<br />

<h3 id="toc1"><a name="isoharmonic chords--class i"></a>class i</h3>

@@ 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:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-27 21:53:27 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-03 16:02:47 UTC</tt>.<br>
-: The original revision id was <tt>597353876</tt>.<br>
+: The original revision id was <tt>601298180</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 8: / Line 8: @@
 <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;white-space: pre-wrap ! important" class="old-revision-html">=isoharmonic chords=
-In [[JustIntonation|just intonation]], Isoharmonic chords are build by successive jumps up the [[OverToneSeries|harmonic series]] by some number of steps. Since the harmonic series is arranged such that each higher step is smaller than the one before it, all isoharmonic chords have this same shape -- with diminishing step size as one ascends. All isoharmonic chords are equal-hertz chords, meaning that the frequencies of the notes are in an arithmetic sequence with an equal difference in cycles per second between successive notes. However, not all equal-hertz chords are isoharmonic chords, since the ratios between the notes need not be integers. An isoharmonic "chord" may function more like a "scale" than a chord (depending on the composition of course), but we will use the word "chord" on this page for consistency.
+In [[JustIntonation|just intonation]], Isoharmonic chords are built by successive jumps up the [[OverToneSeries|harmonic series]] by some number of steps. Since the harmonic series is arranged such that each higher step is smaller than the one before it, all isoharmonic chords have this same shape -- with diminishing step size as one ascends. All isoharmonic chords are equal-hertz chords, meaning that the frequencies of the notes are in an arithmetic sequence with an equal difference in cycles per second between successive notes. However, not all equal-hertz chords are isoharmonic chords, since the ratios between the notes need not be integers. An isoharmonic "chord" may function more like a "scale" than a chord (depending on the composition of course), but we will use the word "chord" on this page for consistency.
 ===class i===
@@ Line 55: / Line 55: @@
 <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">&lt;html&gt;&lt;head&gt;&lt;title&gt;isoharmonic chords&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="isoharmonic chords"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;isoharmonic chords&lt;/h1&gt;
   &lt;br /&gt;
-In &lt;a class="wiki_link" href="/JustIntonation"&gt;just intonation&lt;/a&gt;, Isoharmonic chords are build by successive jumps up the &lt;a class="wiki_link" href="/OverToneSeries"&gt;harmonic series&lt;/a&gt; by some number of steps. Since the harmonic series is arranged such that each higher step is smaller than the one before it, all isoharmonic chords have this same shape -- with diminishing step size as one ascends. All isoharmonic chords are equal-hertz chords, meaning that the frequencies of the notes are in an arithmetic sequence with an equal difference in cycles per second between successive notes. However, not all equal-hertz chords are isoharmonic chords, since the ratios between the notes need not be integers. An isoharmonic &amp;quot;chord&amp;quot; may function more like a &amp;quot;scale&amp;quot; than a chord (depending on the composition of course), but we will use the word &amp;quot;chord&amp;quot; on this page for consistency.&lt;br /&gt;
+In &lt;a class="wiki_link" href="/JustIntonation"&gt;just intonation&lt;/a&gt;, Isoharmonic chords are built by successive jumps up the &lt;a class="wiki_link" href="/OverToneSeries"&gt;harmonic series&lt;/a&gt; by some number of steps. Since the harmonic series is arranged such that each higher step is smaller than the one before it, all isoharmonic chords have this same shape -- with diminishing step size as one ascends. All isoharmonic chords are equal-hertz chords, meaning that the frequencies of the notes are in an arithmetic sequence with an equal difference in cycles per second between successive notes. However, not all equal-hertz chords are isoharmonic chords, since the ratios between the notes need not be integers. An isoharmonic &amp;quot;chord&amp;quot; may function more like a &amp;quot;scale&amp;quot; than a chord (depending on the composition of course), but we will use the word &amp;quot;chord&amp;quot; on this page for consistency.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="isoharmonic chords--class i"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;class i&lt;/h3&gt;