Extraclassical tonality: Difference between revisions

@@ Line 163: / Line 163: @@
 [[Category:Tonality]]
 [[Category:Fendo]]
+== Arto and tendo as interval qualities ==
+By utilizing the logic of 24edo, "arto" and "tendo" can be generalized to interval qualities that follow interval arithmetic, corresponding to semi-diminished and semi-augmented, which are closer to their definition as interval regions in diatonic scales close to Pythagorean; in meantone tunings, these tend to correspond to supermajor and subminor.
+For a diatonic edo to have arto and tendo intervals by this definition, its chroma must be an even number of edosteps.
+{| class="wikitable"
+|+
+!Interval
+!24edo
+!31edo
+!17edo
+!41edo
+|-
+|Tendo unison
+|50c
+|39c
+|71c
+|59c
+|-
+|Arto second
+|50c
+|77c
+|0c
+|29c
+|-
+|Tendo second
+|250c
+|232c
+|282c
+|263c
+|-
+|Arto third
+|250c
+|271c
+|212c
+|234c
+|-
+|Tendo third
+|450c
+|426c
+|494c
+|468c
+|-
+|Arto fourth
+|450c
+|465c
+|424c
+|439c
+|-
+|Tendo fourth
+|550c
+|541c
+|565c
+|556c
+|-
+|Arto fifth
+|650c
+|659c
+|635c
+|654c
+|-
+|Tendo fifth
+|750c
+|735c
+|776c
+|761c
+|-
+|Arto sixth
+|750c
+|774c
+|706c
+|732c
+|-
+|Tendo sixth
+|950c
+|929c
+|988c
+|966c
+|-
+|Arto seventh
+|950c
+|968c
+|918c
+|937c
+|-
+|Tendo seventh
+|1150c
+|1123c
+|1200c
+|1171c
+|-
+|Arto octave
+|1150c
+|1161c
+|1129c
+|1141c
+|}
+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.