The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree.
Tiger! Tiger! burning bright / In the forests of the night, / What immortal hand or eye / Could frame thy fearful symmetry?
~ William Blake
The most symmetrical scale (at least in Western music) is the chromatic scale. With a half step between each note, it’s an infinitely adaptable scale. It can be used in any key signature, and most especially in improvisation, either free or otherwise. Some genres of improvisation, like Gypsy Jazz, use it more than others, but it pretty much crops up everywhere. Adapting the scale all depends on where you put the emphasis. Or, as my English teacher Dave Estrum used to say, you have to put the emphasis on the right sylable. Too bad that doesn’t translate to writing well. Anyway, to play a chromatic scale, simply play every consecutive note on a piano keyboard. You instrument probably isn’t as intuitive as the piano keyboard (which is why it’s such a good tool to have). For guitarists, it’s every consecutive fret on a single string. Here is a free PDF of the piano keyboard and the guitar fretboard that I’ve put together. It has other info too. The chromatic scale is the least interesting of the symmetrical scales. Hear one from C to shining C here.
More interesting are the diminished scales and whole tone scales. The first interesting thing about symmetrical scales is that there aren’t 12 of them as there are with the Major, minor, blues, etc. scales. Let’s start w/ the whole tone scale.
The whole tone scale is constructed, just like it sounds, around whole tones, also known as whole steps. There is one whole step (2 half steps) between each note of the scale. They have an interesting sound to them. Kind of floaty, or unsecured, or non-committal. One of reasons we have music is that its way of conveying information isn’t easily translated into words. Otherwise we’d just talk about it, right. Try some whole tone scales and you’ll hear what I mean. Also try the augmented chords associated with the scale. See below.
In the case of the whole tone scale, there are really only 2 sets of notes and playing a particular whole tone scale depends on where you stop or start. Here are the two sets of notes:
Now is where enharmonic notes make things confusing. Play the two scales above and you’ve played all 12 tones between octaves. Here is that free PDF of the piano keyboard and the guitar fretboard if you haven’t gotten it yet. You can check.
I’ve shown the C whole tone scale and the Cb whole tone scale, but these series of notes encompass all notes in every whole tone scales. For example, the whole tone scale starting on D has the same notes as that of the written scale, C. In fact, start on any note of each of the above scales, play the same notes for an octave, and you’ve got a whole tone scale. So, the whole tone scales associated with the first group of tones are (including enharmonic tones):
And using the second set of whole tones, we can create the following whole tone scales:
Each of these whole tone scales is, of course, associated with a chord, the augmented chord. To hear D augmented, click here. The augmented chord is found in most western music, both classical, jazz, and pop, though it’s relatively rare compared to some other naturally occurring chords like the ii or the V7, or the I. because it’s a chord that creates some tension, it’s often found in turnarounds, or modulations or other places where such an affect is needed. They’re good to practice along with the associated scale.
So, the chromatic and whole tone scales are really useful to have under your fingers and in your ears. If you don’t know either, practice the chromatic scale first, as it’s the most useful.
Good luck and have fun with your practice!