When a mode of a scale produces the same type of scale as the original, the scale is symmetric. Thus, the chromatic scale is symmetric, because every single mode of it is another chromatic scale. (Whichever note you start from, you get a chromatic scale).

The three most important symmetric scales are (in Western Music):

  1. The Chromatic Scale
  2. The Whole Tone Scale
  3. The Diminished Scales
For the first two, every mode produces the same scale, while for the latter, every other instance produces the same diminished scale.

There are two types of diminished scales, half step whole step (HW) and whole step half step (WH), and when deriving modes from either, the scales alternate.

For example, take C HW diminished: C, C#, D#, E, F#, G, A, A#.
Start from C# (second mode), and you get C#, D#, E, F#, G, A, A#, C, which is the C# WH diminished.
Start from D# (third mode), and you get D# HW, again the same type of scale as the original.