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Symmetrical scales

(starting with A)
 
Half step/whole step
half step/whole step scale for guitars (intervals)
  roman numerals I to XV
 
Whole step/half step
whole step/half step scale for guitars (intervals)
  roman numerals I to XV
 
Whole tone
whole tone scale for guitars (intervals)
  roman numerals I to XV
 
Diminished
diminished scale for guitars (intervals)
  roman numerals I to XV
 
Augmented
augmented scale for guitars (intervals)
  roman numerals I to XV
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Intervals of the Symmetrical Scale

Scales are called to be symmetrical if a strictly regular structure regarding their intervals can be established. This applies to the following scales:

Half step/whole step   continuous alternation of semitone/whole tone intervals
Whole step/half step continuous alternation of whole tone/semitone intervals
Whole tone exclusively intervals of a whole tone
Diminished exclusively intervals of a minor third
Augmented exclusively intervals of a major third