Extraclassical tonality: Difference between revisions
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{{Idiosyncratic terms}} | |||
'''[[Arto and tendo]]''' or '''extraclassical tonality''' refers to tonality that uses ultramajor (or "tendo") and inframinor (or "arto") triads. Because these chords share many of the same properties as major and minor triads, the extraclassical harmonic system resembles the conventional diatonic system in many ways, however, it also has many distinct characteristics that make it sound nothing like normal major and minor chords. | '''[[Arto and tendo]]''' or '''extraclassical tonality''' refers to tonality that uses ultramajor (or "tendo") and inframinor (or "arto") triads. Because these chords share many of the same properties as major and minor triads, the extraclassical harmonic system resembles the conventional diatonic system in many ways, however, it also has many distinct characteristics that make it sound nothing like normal major and minor chords. | ||
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 == | ||
Arto and tendo triads are the same shape as minor and major triads, but with a more extreme difference between the thirds. This can be characterized in terms of interval [[latitude]] with respect to the perfect fifth, wherein arto and tendo have latitudes more extreme than major and minor. | Arto and tendo triads are the same shape as minor and major triads, but with a more extreme difference between the thirds. This can be characterized in terms of interval [[User:VectorGraphics/Latitude|latitude]]{{idiosyncratic}} with respect to the perfect fifth, wherein arto and tendo have latitudes more extreme than major and minor. | ||
An arto triad results by flatting the third of a minor triad by approximately one [[quarter tone]], producing an inframinor third of about 235–255{{cent}}. | An arto triad results by flatting the third of a minor triad by approximately one [[quarter tone]], producing an inframinor third of about 235–255{{cent}}. | ||
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The tendo chord is considered to be more consonant than the arto chord, just as the major chord is considered more consonant (if only slightly) than the minor chord. Also, both chords are only slightly more dissonant than the normal major and minor chords. | The tendo chord is considered to be more consonant than the arto chord, just as the major chord is considered more consonant (if only slightly) than the minor chord. Also, both chords are only slightly more dissonant than the normal major and minor chords. | ||
More generally, [[User:VectorGraphics/Latitude|medials]] 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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