The first study in scale theory are the most fundamental type of scales, called symmetrical scales – they are referred to as symmetrical because they are tonally proportional and that more than one note could be considered the root. The reason for this is simply because the intervals are singularly fixed or alternately balanced.
The first example of a symmetrical scale is a whole tone scale. Its formula is its own namesake – the interval composition is all whole tones. As you will notice, the C whole tone scale has the same intervals as the D and E whole tone scales being that F, G, and A are all sharpened and the roots of C, D, and E remain natural. Of course, one could as easily assume the roots to be either F♯, G♯, or A♯. And, if you continue to apply this formula to the four remaining natural notes of F, G, A, or B, you will again see that the notes sharpened are the same for these natural roots C♯, D♯, E♯. Therefore, whether beginning with F, G, A, or B, as the root, C, D, and E will remain sharpened. Likewise, if displacing the root to C♯, D♯, or E♯, the remaining intervals of F, G A, and B will stay natural. Consequently, the root may be placed on any note whether sharp or flat and the intervals will remain the same (i.e. C♭ is the same as B, and F♭ is the same as E).
The next type of symmetrical scale is the chromatic scale, whose formula is comprised of all semitones or half steps. Just as with the whole tone scale, any note in the scale may be considered the root. No matter where you displace the beginning of the scale, the intervals never change.
These scales are not unique to any genre because of their very nature – however, they are not a crux for any genre in which they might appear for the same reason they do appear. (A strong bit of circular logic occurs here because these scales are made up of all the Western notes, which makes them simultaneously unique and common – considering practically every song incorporates all, or most of those notes). Aside from the confusion, these scales are actually worthwhile to practice because they help to build a better sense of tone and pitch. They also help to reinforce the familiarity of the fretboard.
Diminished scales are symmetrical scales, and as with the others, more than one note may be considered the root. The diminished scale is actually a hybrid formula of the whole tone and chromatic scales alternating between a whole tone, and a semitone. Because of the interval formula, displacing the starting point from the root to every other degree also yields three duplicate scales. Consequently, what is “naturally” considered a C Diminished could also be said to be an E♭, G♭, or an A. In addition, jazz musicians, in-particular, play half-whole scales, which means the first interval is a semitone the formula remains the same, however.
An altered scale, is a combination of a diminished and whole tone scale. The first tetrachord is comprised of a diminished formula, and the second tetrachord is comprised of a whole tone scale.