Extraclassical tonality: Difference between revisions
"Latitude" and "medial" are idiosyncratic |
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The name "extraclassical" derives from the mediants' position outside the range of the classical and standard diatonic mediants. | The name "extraclassical" derives from the mediants' position outside the range of the classical and standard diatonic mediants. | ||
== Arto and tendo triads == | == Arto and tendo triads == | ||
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More generally, [[User:VectorGraphics/Latitude|medials]]{{idiosyncratic}} of a fifth with a latitude of ~25–30 degrees may be considered arto and tendo thirds, where the outer bound (and one of the most common tunings) is [[3edf]], corresponding to slendric. | More generally, [[User:VectorGraphics/Latitude|medials]]{{idiosyncratic}} of a fifth with a latitude of ~25–30 degrees may be considered arto and tendo thirds, where the outer bound (and one of the most common tunings) is [[3edf]], corresponding to slendric. | ||
Note: The usage of the terms "arto" and "tendo" here (derived from Latin for "compress" and "stretch") here is unrelated and not to be confused with their usage in [[Alpharabian tuning]] terminolgy, where they are used to distinguish 2.3.11 subgroup intervals separated by a [[243/242|rastma]] (such as [[11/9]] being an "artoneutral third" and [[27/22]] being an "tendoneutral third"). | |||
== Notation == | == Notation == | ||
Assuming the normal major and minor thirds are roughly 12edo or pythagorean, a tendo triad may be notated {{nowrap|{{dash|C, E{{demisharp2}}, G}}}} or {{nowrap|{{dash|A, C{{sesquisharp2}}, E}}}}, and an arto triad may be notated {{nowrap|{{dash|C, E{{sesquiflat2}}, G}}}} or {{nowrap|{{dash|A, C{{demiflat2}}, E}}}}. | Assuming the normal major and minor thirds are roughly 12edo or pythagorean, a tendo triad may be notated {{nowrap|{{dash|C, E{{demisharp2}}, G}}}} or {{nowrap|{{dash|A, C{{sesquisharp2}}, E}}}}, and an arto triad may be notated {{nowrap|{{dash|C, E{{sesquiflat2}}, G}}}} or {{nowrap|{{dash|A, C{{demiflat2}}, E}}}}. | ||
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In just intonation, the "arto" and "tendo" labels may be used for the diesis 416/405, which relates the Pythagorean and arto/tendo thirds in just intonation. | In just intonation, the "arto" and "tendo" labels may be used for the diesis 416/405, which relates the Pythagorean and arto/tendo thirds in just intonation. | ||
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