Extraclassical tonality: Difference between revisions

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~~The~~ '''[[arto and tendo]]''' or '''extraclassical tonality ~~system~~''' ~~is a~~ tonality ~~system built from~~ ultramajor (~~called~~ "tendo") and inframinor (~~called~~ "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.

'''A[[arto and tendo|rto 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.

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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.

An arto triad results by flatting the third of a minor triad by approximately one [[quarter tone]], producing an inframinor third of ~~~250~~{{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}}.

A tendo triad results by sharping the third in a major triad by approximately one quarter tone, producing an ultramajor third of ~~~450~~{{cent}}.

A tendo triad results by sharping the third in a major triad by approximately one quarter tone, producing an ultramajor third of about 445–465{{cent}}.

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/The spectrum of mediants|medials]] of a fifth with a latitude of ~25 degrees may be considered arto and tendo thirds.

More generally, [[User:VectorGraphics/The spectrum of mediants|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.

== Notation ==

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This creates an interesting, subtle ambiguous flavor, but what's even more interesting is that the two triads still sound distinct enough to be considered separate and being played together causes a lack of resolution. This also generates the possibility that both arto and tendo chords can be used in a progression on the same root without going outside of the scale. Likewise, a melody on a tendo chord can play notes of the arto chord of the same root.

This property of arto and tendo chords is a major contributing factor to the "omniconsonant" property of [[5edo]].

== Use cases ==

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-The '''[[arto and tendo]]''' or '''extraclassical tonality system''' is a tonality system built from ultramajor (called "tendo") and inframinor (called "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.
+'''A[[arto and tendo|rto 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.
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 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.
-An arto triad results by flatting the third of a minor triad by approximately one [[quarter tone]], producing an inframinor third of ~250{{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}}.
-A tendo triad results by sharping the third in a major triad by approximately one quarter tone, producing an ultramajor third of ~450{{cent}}.
+A tendo triad results by sharping the third in a major triad by approximately one quarter tone, producing an ultramajor third of about 445–465{{cent}}.
 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/The spectrum of mediants|medials]] of a fifth with a latitude of ~25 degrees may be considered arto and tendo thirds.
+More generally, [[User:VectorGraphics/The spectrum of mediants|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.
 == Notation ==
@@ Line 27: / Line 27: @@
 This creates an interesting, subtle ambiguous flavor, but what's even more interesting is that the two triads still sound distinct enough to be considered separate and being played together causes a lack of resolution. This also generates the possibility that both arto and tendo chords can be used in a progression on the same root without going outside of the scale. Likewise, a melody on a tendo chord can play notes of the arto chord of the same root.
+This property of arto and tendo chords is a major contributing factor to the "omniconsonant" property of [[5edo]].
 == Use cases ==