User:Aura/Aura's Ideas on Functional Harmony (Part 1): Difference between revisions
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The lack of [[Meantone]] temperament has some pretty significant implications for triadic transformations and oblique voice-leading in my theory- namely in that while all three basic [[Wikipedia: Neo-Riemannian theory|Neo-Riemannian]] transformations are available, there must be additional specifiers to distinguish the original triadic transformations from new types of triadic transformations, and, as a result of my own theories on functional harmony, certain triadic transformations need to be renamed. | The lack of [[Meantone]] temperament has some pretty significant implications for triadic transformations and oblique voice-leading in my theory- namely in that while all three basic [[Wikipedia: Neo-Riemannian theory|Neo-Riemannian]] transformations are available, there must be additional specifiers to distinguish the original triadic transformations from new types of triadic transformations, and, as a result of my own theories on functional harmony, certain triadic transformations need to be renamed. One must also keep in mind that the direction of transformation indicated doesn't necessarily result in resolution, as a number of transformations indicated can be executed one way for an increase in tension and in the other direction for a decrease in tension. | ||
'''Pythagorean Parallel''' - This transformation involves exchanging a Pythagorean triad for its Pythagorean parallel. For a Pythagorean Major triad, move the third down by an apotome, and for a Pythagorean Minor triad move the third up by an apotome. | '''Pythagorean Parallel''' - This transformation involves exchanging a Pythagorean triad for its Pythagorean parallel. For a Pythagorean Major triad, move the third down by an apotome, and for a Pythagorean Minor triad move the third up by an apotome. | ||
'''Ptolemaic Parallel''' - This transformation involves exchanging a typical Ptolemaic triad for its Ptolemaic parallel. For a Ptolemaic Major triad, move the third down by a Diptolemaic Chromatic Semitone, and for a Ptolemaic Minor triad move the third up by a Diptolemaic Chromatic Semitone. | '''Ptolemaic Parallel''' - This transformation involves exchanging a typical Ptolemaic triad for its Ptolemaic parallel. For a Ptolemaic Major triad, move the third down by a Diptolemaic Chromatic Semitone, and for a Ptolemaic Minor triad move the third up by a Diptolemaic Chromatic Semitone. | ||
'''Pythagoran-Ptolemaic Picardy''' - This transformation involves exchanging a Pythagorean triad for its Ptolemaic parallel. For a Pythagorean Major triad move the third down by a Ptolemaic Chromatic Semitone, and for a Pythagorean Minor triad move the third up by a Ptolemaic Chromatic Semitone. | |||
'''Pythagorean Relative''' - This transformation involves exchanging a Pythagorean triad for its relative of the same kind. For a Pythagorean Major triad, move the fifth up by a Pythagorean Whole Tone, and for a Pythagorean Minor triad, move the root down by a Pythagorean Whole Tone. | '''Pythagorean Relative''' - This transformation involves exchanging a Pythagorean triad for its relative of the same kind. For a Pythagorean Major triad, move the fifth up by a Pythagorean Whole Tone, and for a Pythagorean Minor triad, move the root down by a Pythagorean Whole Tone. | ||