Symmetric scales repeat the same sequence of intervals. Being symmetric, they can be transposed to any other tone of the scale, keeping the same pattern.
The best known symmetric scale is the chromatic one, stepping from half-tone to half-tone, containing all the notes:
The Whole-Tone scale skips from tone to tone. From A:
This scale has 6 notes. The other 6 notes can be found in the Bb Whole-Tone scale:
That means that, in fact, there are only two Whole-Tone scales, one starting from A, B, C#, D#, F or G and one starting from Bb, C, D, E, Gb or Ab.
The Whole-Half scale alterns whole and half-tones. Starting from A:
The Half-Whole is the opposite:
Augmented scales altern minor thirds and half-tones:
Possible patterns for playing symmetric scales:
And the tabs, starting from A: