They are those that arise from the division by equal parts of the chromatic scale (temperament/ 12 notes) and in which, both ascending and descending, the form/ intervals of them are respected.
There is a large amount of symmetrical scale, however some of the most used and known in popular music (Jazz, MPB, etc …) are the Whole Tone scale and the Symmetric Diminished scale, which will be presented below.
WHOLE TONE SCALE: arises from using intervals of second majors on the chromatic scale revealing a structure of 1, 2, 3, #4, #5, b7. This scale of 6 notes is mostly used for dominant chords with augmented fifth.
DIMINISHED SCALE: arises from using intervals of major and minor second (1 | 1/2) in continuous form on the chromatic scale. There are two variations of this scale, the first using tone and semitone continuously revealing a structure of 1, 2, b3, 4, b5, b6, bb7, maj7. This is mostly used on Diminished chords.
The second variation of this scale is given beginning by half and whole step in continuous form revealing an alternative structure to the previous one of 1, b2, #2, 3, #4, 5, 6, b7. This second variation is mostly used on Dominant chords.
There is a lot of material on these scales going around different books and sites on the internet, however there is a great book that I like very much that delves into the creation of symmetrical scales entitled: “Thesaurus Of Scales And Melodic Patterns” by Nicolas Slonimsk.
Until the next post.