Armodue harmony
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[[toc]] =**Armodue: basic elements of harmony**= This is a translation of an article by Luca Attanasio. Original page in italian: [[http://www.armodue.com/armonia.htm]] //Note: This is a preliminary tranlsation. Parts that are still "under construction" are marked with "XXX".// = ---- = =Chapter 1: Two theses supporting the system= ==The supremacy of the fifth and and the seventh harmonic in Armodue== The twelve note system that has been ruling for several centuries is based on the third harmonic of the overtone series, which forms a perfect twelfth (octave-reducible to a perfect fifth) with the first harmonic or fundamental. Also, the pythagorean tradion - the cicle of fifths - is based on the perfect fifth and hence on the same frequency ratio 3:2. But, if in the twelve note system the pitch of the third harmonic - hence the perfect fourth and the perfect fifth - are almost perfectly respected (the tempered fourth and fifth differ only of the fiftieth part of a semitone from the natural fifth and fourth), this cannot be said about the odd harmonics (even harmonics are not counted because they are simply duplicates in the octave of odd harmonics) immediately above the third one: the fifth and seventh harmonic. XXX =Chapter 2: The interval table= XXX =Chapter 3: Creating scales with Armodue: modal systems= XXX =Chapter 4: "Geometric" harmonic constructions with Armodue= XXX =Chapter 5: "elastic" chords= XXX
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<html><head><title>Armodue armonia</title></head><body><!-- ws:start:WikiTextTocRule:14:<img id="wikitext@@toc@@normal" class="WikiMedia WikiMediaToc" title="Table of Contents" src="/site/embedthumbnail/toc/normal?w=225&h=100"/> --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --><div style="margin-left: 1em;"><a href="#Armodue: basic elements of harmony">Armodue: basic elements of harmony</a></div> <!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --><div style="margin-left: 1em;"><a href="#Chapter 1: Two theses supporting the system">Chapter 1: Two theses supporting the system</a></div> <!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --><div style="margin-left: 2em;"><a href="#Chapter 1: Two theses supporting the system-The supremacy of the fifth and and the seventh harmonic in Armodue">The supremacy of the fifth and and the seventh harmonic in Armodue</a></div> <!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --><div style="margin-left: 1em;"><a href="#Chapter 2: The interval table">Chapter 2: The interval table</a></div> <!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --><div style="margin-left: 1em;"><a href="#Chapter 3: Creating scales with Armodue: modal systems">Chapter 3: Creating scales with Armodue: modal systems</a></div> <!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --><div style="margin-left: 1em;"><a href="#Chapter 4: "Geometric" harmonic constructions with Armodue">Chapter 4: "Geometric" harmonic constructions with Armodue</a></div> <!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --><div style="margin-left: 1em;"><a href="#Chapter 5: "elastic" chords">Chapter 5: "elastic" chords</a></div> <!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --></div> <!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Armodue: basic elements of harmony"></a><!-- ws:end:WikiTextHeadingRule:0 --><strong>Armodue: basic elements of harmony</strong></h1> This is a translation of an article by Luca Attanasio. Original page in italian: <a class="wiki_link_ext" href="http://www.armodue.com/armonia.htm" rel="nofollow">http://www.armodue.com/armonia.htm</a><br /> <em>Note: This is a preliminary tranlsation. Parts that are still "under construction" are marked with "XXX".</em><br /> <br /> <br /> =<br /> <hr /> = <br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Chapter 1: Two theses supporting the system"></a><!-- ws:end:WikiTextHeadingRule:2 -->Chapter 1: Two theses supporting the system</h1> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="Chapter 1: Two theses supporting the system-The supremacy of the fifth and and the seventh harmonic in Armodue"></a><!-- ws:end:WikiTextHeadingRule:4 -->The supremacy of the fifth and and the seventh harmonic in Armodue</h2> <br /> The twelve note system that has been ruling for several centuries is based on the third harmonic of the overtone series, which forms a perfect twelfth (octave-reducible to a perfect fifth) with the first harmonic or fundamental. Also, the pythagorean tradion - the cicle of fifths - is based on the perfect fifth and hence on the same frequency ratio 3:2.<br /> <br /> But, if in the twelve note system the pitch of the third harmonic - hence the perfect fourth and the perfect fifth - are almost perfectly respected (the tempered fourth and fifth differ only of the fiftieth part of a semitone from the natural fifth and fourth), this cannot be said about the odd harmonics (even harmonics are not counted because they are simply duplicates in the octave of odd harmonics) immediately above the third one: the fifth and seventh harmonic.<br /> <br /> XXX<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="Chapter 2: The interval table"></a><!-- ws:end:WikiTextHeadingRule:6 -->Chapter 2: The interval table</h1> <br /> XXX<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h1> --><h1 id="toc4"><a name="Chapter 3: Creating scales with Armodue: modal systems"></a><!-- ws:end:WikiTextHeadingRule:8 -->Chapter 3: Creating scales with Armodue: modal systems</h1> <br /> XXX<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h1> --><h1 id="toc5"><a name="Chapter 4: "Geometric" harmonic constructions with Armodue"></a><!-- ws:end:WikiTextHeadingRule:10 -->Chapter 4: "Geometric" harmonic constructions with Armodue</h1> <br /> XXX<br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h1> --><h1 id="toc6"><a name="Chapter 5: "elastic" chords"></a><!-- ws:end:WikiTextHeadingRule:12 -->Chapter 5: "elastic" chords</h1> <br /> XXX</body></html>