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/ | 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 slendric systems, especially those with a flat fifth such as 16edo, the arto and tendo thirds may be widened to 1\3edf and 2\3edf. | * In slendric systems, especially those with a flat fifth such as 16edo, the arto and tendo thirds may be widened to 1\3edf and 2\3edf. | ||
** The chord produced by playing the arto and tendo thirds together is actually just the first few slendric generator steps. | ** The chord produced by playing the arto and tendo thirds together is actually just the first few slendric generator steps. | ||
* In a [[fendo]] system such as 13edo, the JI ratios for the arto and tendo thirds are equated with the suspended mediants of 9/8 and 4/3, meaning that suspended chords and arto/tendo chords | * In a [[fendo]] system such as 13edo, the JI ratios for the arto and tendo thirds are equated with the suspended mediants of 9/8 and 4/3, meaning that suspended chords and arto/tendo chords are equated. | ||
* In blackwood systems, the suspended and slendric chords (and hence a possible tuning of the extraclassical chords) are the same thing. | * In blackwood systems, the suspended and slendric chords (and hence a possible tuning of the extraclassical chords) are the same thing. | ||
* Any pair of [[List of root-3rd-P5 triads in JI|JI medials]] with a latitude around ±25 degrees. | * Any pair of [[List of root-3rd-P5 triads in JI|JI medials]] with a latitude around ±25 degrees. | ||
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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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