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'''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. | '''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. | ||
The latitude can be calculated using the formula ''ℓ = (s - a/2)/(a/2)*90°'', where ''s'' is the size of the interval in cents and ''a'' is the size of the axis in cents. For example, to calculate the latitude of the classic major third 5/4 relative to the perfect fifth 3/2, one first calculates the cent sizes of 5/4 (''log<sub>2</sub>(5/4)*1200 = 386.31 ¢'') and of 3/2 (''log<sub>2</sub>(3/2)*1200 = 701.955 ¢).'' Plugging 386.31 ¢ for ''s'' and 701.955 ¢ for ''a'' into the formula, we get ''ℓ = (386.31 - 701.955/2)/(701.955/2)*90° = (386.31 - 350.9775)/(350.9775)*90° = 9.06°.'' | |||
Latitude allows the characterization of, i.e. different "flavors" of thirds, with respect to a fifth that might be tempered, as opposed to in terms of absolute interval ranges that may be misaligned with the intervals' harmonic function. For example, one might describe 3\13, 4\13, and 5\13 in [[13edo]] based on their size as a [[minor third|subminor third]], a [[major third|submajor third]], and an ultramajor third, but that doesn't reflect their function in [[triadic harmony]] in 13edo. Using latitude, one can see that their latitudes are -22.5°, 0°, and 22.5°, and from that they may be assigned the labels subminor, [[neutral third|neutral]], and supermajor, which better reflect their role. | Latitude allows the characterization of, i.e. different "flavors" of thirds, with respect to a fifth that might be tempered, as opposed to in terms of absolute interval ranges that may be misaligned with the intervals' harmonic function. For example, one might describe 3\13, 4\13, and 5\13 in [[13edo]] based on their size as a [[minor third|subminor third]], a [[major third|submajor third]], and an ultramajor third, but that doesn't reflect their function in [[triadic harmony]] in 13edo. Using latitude, one can see that their latitudes are -22.5°, 0°, and 22.5°, and from that they may be assigned the labels subminor, [[neutral third|neutral]], and supermajor, which better reflect their role. | ||