The word says it all--
Symmetrical scales are scales that have an even amount of notes on both sides. There is no middle note like in the major/minor scales where you have a middle note and 3 notes to each side.
An example of this kind of scale is the "whole tone" scale. This is a scale that is constructed by simple whole steps. It produces 6 notes instead of the normal 7 notes found in the major/minor scale.
"Whole half"...."half whole"...."blues"...."chromatic" are some examples.
Now finding the application to these can take some experimenting. Actually that is the fun part!
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