User:Aura/Aura's Ideas on Functional Harmony (Part 1): Difference between revisions
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== Additional Composite Functions == | == Additional Composite Functions == | ||
Notes on the boundaries of functional regions have multiple functions due to occurring at the boundary between different functions, the process by which this happens is known as '''Compositing'''. As for the actual composite functions themselves, there are quite a few of them. | Notes on the boundaries of functional regions have multiple functions due to occurring at the boundary between different functions, the process by which this happens is known as '''Compositing'''. As for the actual composite functions themselves, there are quite a few of them. | ||
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The lack of [[Meantone]] temperament has some pretty significant implications for triadic transformations | 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. | ||
'''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. | |||
'''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. | |||
'''Ptolemaic Relative''' - This transformation involves exchanging a Ptolemaic triad for its relative of the same kind. For a Ptolemaic Major triad, move the fifth up by a Ptolemaic Whole Tone, and for a Ptolemaic Minor triad, move the root down by a Ptolemaic Whole Tone. | |||
'''Pythagorean Limma Exchange''' - This transformation involves exchanging a Pythagorean triad for a mostly similar triad with one note differing in pitch class by a Pythagorean Diatonic Semitone. For a Pythagorean Major triad, move the root down by a Pythagorean Diatonic Semitone, and for and Pythagorean Minor triad, move the fifth up by a Pythagorean Diatonic Semitone. | |||
'''Ptolemaic Limma Exchange''' - This transformation involves exchanging a Ptolemaic triad for a mostly similar triad with one note differing in pitch class by a Ptolemaic Diatonic Semitone. For a Ptolemaic Major triad, move the root down by a Ptolemaic Diatonic Semitone, and for and Ptolemaic Minor triad, move the fifth up by a Ptolemaic Diatonic Semitone. | |||
== References == | == References == | ||