Extraclassical tonality: Difference between revisions
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== 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 [[ | 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 ~250{{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/The spectrum of mediants| | 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. | ||
== Notation == | == Notation == | ||
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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. | ||
* Any pair of [[List of root-3rd-P5 triads in JI|JI | * 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 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. | |||
* In terms of [[fractional monzo]]s, the arto and tendo thirds may be tuned as {{nowrap|1\2edf ± 1\2ed(9/8)}}. | * In terms of [[fractional monzo]]s, the arto and tendo thirds may be tuned as {{nowrap|1\2edf ± 1\2ed(9/8)}}. | ||
[[Category:19edo]] | [[Category:19edo]] | ||