Armodue harmony: Difference between revisions
Wikispaces>hstraub **Imported revision 166960327 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
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==The supremacy of the fifth and the seventh harmonic in Armodue== | ==The supremacy of the fifth 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 | 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 tradition - the cycle 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. | 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. | ||
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<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Two theses supporting the system-The supremacy of the fifth and the seventh harmonic in Armodue"></a><!-- ws:end:WikiTextHeadingRule:2 -->The supremacy of the fifth and the seventh harmonic in Armodue</h2> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Two theses supporting the system-The supremacy of the fifth and the seventh harmonic in Armodue"></a><!-- ws:end:WikiTextHeadingRule:2 -->The supremacy of the fifth and the seventh harmonic in Armodue</h2> | ||
<br /> | <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 | 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 tradition - the cycle of fifths - is based on the perfect fifth and hence on the same frequency ratio 3:2.<br /> | ||
<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 /> | 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 /> | ||