Latitude: Difference between revisions

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~~[[File:Imagemeeeeeeenememe.png|thumb|Image]]~~

'''Latitude''' is a measure of an [[interval]]'s size in relation to a (possibly tempered) [[perfect fifth|fifth]], or another interval (the "axis of polarity" or just "axis") serving the same function in another harmonic system. An interval as defined by its latitude may be called a "medial" and always has an axis complement. Latitude ranges from 90 degrees Minor (-90°) to 90 degrees Major (90°), corresponding to 180edA where A is the axis. "Low-latitude" means close to 0 degrees, "high-latitude" means close to ±90 degrees.

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Medial pairs with a higher latitude than ±45° tend to sound more dissonant against the axis or root than lower-latitude medials, and extremely low-latitude interval pairs may not sound distinct from each other. Higher latitude enables "cross-tonality", where both intervals in the pair can be played at once in the same chord, as in suspended or [[extraclassical tonality|arto/tendo]] chords.

[[File:Imagemeeeeeeenememe.png|thumb|A depiction of the medial intervals ("formal thirds") of fifth-bounded triads by latitude]]

Here is a table of the latitude of medials up to ±30° in various EDOs, with respect to their fifth as the axis:

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 {{Breadcrumb|Interval region}}
-[[File:Imagemeeeeeeenememe.png|thumb|Image]]
 '''Latitude''' is a measure of an [[interval]]'s size in relation to a (possibly tempered) [[perfect fifth|fifth]], or another interval (the "axis of polarity" or just "axis") serving the same function in another harmonic system. An interval as defined by its latitude may be called a "medial" and always has an axis complement. Latitude ranges from 90 degrees Minor (-90°) to 90 degrees Major (90°), corresponding to 180edA where A is the axis. "Low-latitude" means close to 0 degrees, "high-latitude" means close to ±90 degrees.
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 Medial pairs with a higher latitude than ±45° tend to sound more dissonant against the axis or root than lower-latitude medials, and extremely low-latitude interval pairs may not sound distinct from each other. Higher latitude enables "cross-tonality", where both intervals in the pair can be played at once in the same chord, as in suspended or [[extraclassical tonality|arto/tendo]] chords.
+[[File:Imagemeeeeeeenememe.png|thumb|A depiction of the medial intervals ("formal thirds") of fifth-bounded triads by latitude]]
 Here is a table of the latitude of medials up to ±30° in various EDOs, with respect to their fifth as the axis: