Extraclassical tonality: Difference between revisions

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== Basics ==

The '''[[arto and tendo]] tonality system''' is a tonality system built from 10:13:15 (tendo, or ultramajor) and 26:30:39 (arto, or inframinor) triads (or triads with thirds of a similar size). ~~The idea is that because~~ these chords share many of the same properties as major and minor triads, the arto and tendo harmonic system resembles the diatonic system in many ways, however, it also has many distinct characteristics that make it sound nothing like the diatonic scale.

The '''[[arto and tendo]] tonality system''' is a tonality system built from 10:13:15 (tendo, or ultramajor) and 26:30:39 (arto, or inframinor) triads (or triads with thirds of a similar size). Because these chords share many of the same properties as major and minor triads, the arto and tendo harmonic system resembles the diatonic system in many ways, however, it also has many distinct characteristics that make it sound nothing like the diatonic scale.

== Arto and tendo triads ==

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More generally, thirds of roughly 250 and 450 cents, or [[User:VectorGraphics/The spectrum of mediants|mediants]] of a fifth with a contrastiveness of 25-30%, may be considered arto and tendo thirds.

Assuming the normal major and minor thirds are roughly 12edo or pythagorean, a tendo triad may be notated C-E+-G or A-C#+-E, and an arto triad may be notated C-Edb-G or A-Cd-E.

For meantone/flattone or just intonation, arto and tendo may be treated as augmented and diminished intervals, for example C-E#-G or C-Ebb-G.

== Cross-tonality ==

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 == Basics ==
-The '''[[arto and tendo]] tonality system''' is a tonality system built from 10:13:15 (tendo, or ultramajor) and 26:30:39 (arto, or inframinor) triads (or triads with thirds of a similar size). The idea is that because these chords share many of the same properties as major and minor triads, the arto and tendo harmonic system resembles the diatonic system in many ways, however, it also has many distinct characteristics that make it sound nothing like the diatonic scale.
+The '''[[arto and tendo]] tonality system''' is a tonality system built from 10:13:15 (tendo, or ultramajor) and 26:30:39 (arto, or inframinor) triads (or triads with thirds of a similar size). Because these chords share many of the same properties as major and minor triads, the arto and tendo harmonic system resembles the diatonic system in many ways, however, it also has many distinct characteristics that make it sound nothing like the diatonic scale.
 == Arto and tendo triads ==
@@ Line 7: / Line 7: @@
 More generally, thirds of roughly 250 and 450 cents, or [[User:VectorGraphics/The spectrum of mediants|mediants]] of a fifth with a contrastiveness of 25-30%, may be considered arto and tendo thirds.
+Assuming the normal major and minor thirds are roughly 12edo or pythagorean, a tendo triad may be notated C-E+-G or A-C#+-E, and an arto triad may be notated C-Edb-G or A-Cd-E.
+For meantone/flattone or just intonation, arto and tendo may be treated as augmented and diminished intervals, for example C-E#-G or C-Ebb-G.
 == Cross-tonality ==