User:VectorGraphics/Latitude: Difference between revisions

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{{Breadcrumb|Interval region}}'''Latitude''' is a measure of an interval's size in relation to a (possibly tempered) fifth, or another interval (the "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.

~~[[File:Imagemef.png|thumb|1305x1305px|The spectrum of medials]]~~

'''Latitude''' is a measure of an interval's size in relation to a (possibly tempered) fifth, or another interval (the "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 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 subminor third, a major 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, and supermajor, which better reflect their role.

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-{{Breadcrumb|Interval region}}
+{{Breadcrumb|Interval region}}'''Latitude''' is a measure of an interval's size in relation to a (possibly tempered) fifth, or another interval (the "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.
-[[File:Imagemef.png|thumb|1305x1305px|The spectrum of medials]]
-'''Latitude''' is a measure of an interval's size in relation to a (possibly tempered) fifth, or another interval (the "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 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 subminor third, a major 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, and supermajor, which better reflect their role.