A symmetrical scale is basically one that results from the equal division of an octave. I will only be approaching the most common but there are many other ways to divide the octave. This symmetry is also usually present even when you mirror many of these scales.
The whole-tone scale has six notes and thus, it’s a hexatonic scale. The scale is built by dividing the octave in six equal steps, like so:
The Half-Whole Diminished Scale
As the name implies, this scale is built by dividing the octave in sets of alternated halves with whole steps. There are eight notes in total so, this is an octatonic scale that is also known as the dominant diminished scale:
The Whole-Half Diminished Scale
This scale also divides the octave in eight notes but this time it does so by alternating whole with half step. These two scales are very similar in the way they are built. In fact, this scale can be considered as the second mode of the previous one:
As we will see in other posts, these scales can be potentially used in both similar and distinct harmonic contexts due to enharmonic occurrences. When mirrored, these scales aren’t like the others I will be showing here but they point to one another – the mirrored W-H diminished scale becomes the H-W diminished scale, and vice-versa.
The Tritone Scale
As the name suggests, this scale is built by combining the notes from two major chords, one based on root of the scale – in C we will get the notes C E and G; and the other major triad is built on Gb, the tritone above the root – a diminished 5th with 3 steps with the notes Gb Bb and Db. In order, we get the scale below:
The Augmented Scale
This scale is built in a similar way as the previous one, but instead we use two augmented chords, a minor third apart. One of the chords is based on root of the scale – in C we will get the notes C E and G#; and the other augmented triad is built on Eb, the minor 3rd above the root with the notes Eb G and B. In order, we get the scale below:
The Chromatic Scale
The final symmetrical scale I’ll be introducing is the chromatic scale that divides the octave in twelve half-steps and thus, containing all the possible notes used in western music. This scale can also be built if you stack perfect 5th intervals until we complete the circle, like so: C – G – D – A – E – B – F# – C# – G# – D# – A# – E# (F enharmonic) and C. Put in order, we get the scale below:
Pay special attention to how each of these scales sound, its inner quality and how they can be related to other sonorities and modes. It may be useful for going from one scale material to another seamlessly; to create contrasts and/or embellish a musical passage or to explore alternative scales material.
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