Extraclassical tonality: Difference between revisions

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'''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.

'''[[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.

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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.

** 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.

* Any pair of [[List of root-3rd-P5 triads in JI|JI medials]] with a latitude around ±25 degrees.

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-'''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.
+'''[[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.
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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.
 ** 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.
 * Any pair of [[List of root-3rd-P5 triads in JI|JI medials]] with a latitude around ±25 degrees.