Symmetric scales are some of the most interesting scales in theory. These are scales that have limited modes, limited transpositions, and an even number of notes. There are four main symmetric scales, and each of the four have their own distinct sound.
The Chromatic Scale
Chromatic Scale.mp3 Chromatic Scale
This is the symmetric scale that most musicians are familiar with. It is one of the scales you become associated with in the first years of taking theory. The chromatic scale is, simply, all of the notes available in western harmony that exist between an octave- 12 notes in all. The chromatic scale only has one mode. That is to say, you cannot produce a unique arrangement of notes before the scale begins to repeat itself, there will only be half steps from beginning to end. The chromatic scale cannot be transposed, any transposition lands back in the same repeating scale.
The Whole Tone Scale
Whole Tone Scales.mp3 Whole Tone Scale
This another more familiar symmetric scale. The whole-tone scale is comprised of all whole steps that fit within an octave, resulting in a 6 note scale. A whole-tone scale, essentially, splits the chromatic scale evenly in half. The whole-tone scale also only has one mode; its notes cannot be rearranged to make any other unique scale, there will always be whole steps. Contrary to the chromatic scale, however, the whole-tone scale has one transposition.
The Diminished Scale (or octatonic scale)
Diminished Scales.mp3 Diminished Scales
Now we’re getting to the meat of the symmetric scales. While the first two were fairly straight forward, this scale has a bit more substance. There are several ways to look at this scale. First, it is comprised of a repeating pattern of whole-step/ half-step. Second, it is two fully diminished 7th chords a whole-step apart, superimposed. Third, it can be viewed as two minor tetra-chords a tri-tone apart. As you can see, there are several different ways to look at this scale. The diminished scale can be transposed three times before it begins to repeat itself.
Also, this scale has one mode. This mode is as important to understand as the scale itself, so I’ll describe it below:
Aux Diminished Scales.mp3 Auxiliary Diminished Scales
This mode of the diminished scale is occasionally called by the names “auxiliary diminished scale”, and “half-whole diminished scale”. It can be thought about several different ways as well. First, as two fully diminished 7th chords a half-step apart, superimposed. Second, a sequence of half-whole intervals repeating.
Also, this scale is incredibly interesting because of what it contains (the regular diminished scale also contains these thing, but they are much easier to “see” in the half-whole diminished scale). Remember one thing before we dive into the content: if you can find something once in the diminished scale, you can always find it four more times, moving in minor thirds. This is because of the symmetric nature of the scale. We can find 4 major triads in minor thirds, 4 minor triads in minor thirds, 4 dominant 7th chords in minor thirds, 4 half-diminished chords in minor thirds- and the list continues, with minor 7th chords, several atypical 7th chords.
This scale is used often in more modern classical music. Remember we touched on Stravinsky’s Petrushka ballet when we talked about poly-tonality? Well, the Petrushka Chord is an extension of the diminished scale, two triads (C and Gb) separated by a tri-tone. Tri-tones and minor thirds are the backbone of the symmetric nature of this scale. So, while Petrushka was a landmark bout of poly-tonality, it was also a great example of the chordal nature of the diminished scale. The diminished scaled has also been used quite a bit by composers like Bela Bartok, Claude Debussy, and Oliver Messiaen.
In jazz harmony, we associated this scale with a specific functional chord:
Diminished Dominant.mp3 Diminished Dominant
This chord bears a close relationship to Altered, with one important distinguishing trait: the 13th. In the Altered 7th chord, there is a b13, where in what is often referred to as the “diminished-dominant” 7th chord, there is a natural 13 chord. One jazz musician who is outstanding at using the diminished sound is Chick Corea. In fact, I would contend he chooses to play a diminished sound on most of his dominant chords and even some of his minor and major chords!
The Augmented Scale
Augmented Scales.mp3 Augmented Scales
Finally, the augmented scale. Perhaps the most famous example of an “augmented” sound is that of John Coltrane’s “Giant Steps”, where the chord progression moves down and up in major thirds, the crux of the augmented scale. As minor thirds often equal the diminished scale, major thirds are associated with the augmented scale. Though, this scale was also used by notable classical musicians like Bartok.
The augmented scale is a symmetric scale with 4 transpositions and one mode. It can be looked at in several different ways and also contains a fair amount of harmonic weight: a repeating pattern of an augmented second (minor third) and a half-step, two augmented triads an augmented second apart superimposed, major triads moving in major thirds, minor triads moving in major thirds, augmented triads moving in major thirds, major 7th chords moving in major thirds, minor-major chords moving in major thirds. Anything you can find once in the augmented scale, you can find two more times moving in major thirds. It’s also important to note the lack of a dominant chord in this scale, though it often sounds good to use pieces of this scale over dominant chords (for example, using the first five notes as a sort of augmented pentatonic and eschewing the major 7th).
Symmetric scales carry a great deal of musical theory. Basically, what we’ve covered are four mathematically even ways to divide the octave. To repeat, symmetric scales depart from traditional scales by having limited transpositions, limited modes, and an even number of notes.