I have read about a different approach to music, the symmetrical approach of analyzing, that was after I listened to a the jazz standard Giant Steps and heard that the technique that is used in the song is also used as a special technique in jazz improvisation.

The piece have a lot of "weird" chord changes it almost has no specific scale. After digging here and there in Google I have found that this is a symmetrical approach rather a tonal one.

Apparently I and most of us use the "tonal" approach to analyse music and play.

Can someone explain for me the tonal and symmetrical analysis approach? and how they apply to the "Giant Steps" Jazz standard analysis.

Here is a quote from the site:

The new territory Giant Steps brought to the jazz tradition came from its rigorous exploration of basic jazz building blocks - ii-V-I chord progressions. However, in Giant Steps ii-V-I chord progressions articulate symmetry rather than tonality.

  • Not my field, but look this over: thinkingmusic.ca/analyses/coltrane
    – user16935
    Commented Jun 22, 2015 at 0:21
  • The system Coltrane used is referred to as a multi-tonic system. See my answer to this question, I think it addresses your question too: music.stackexchange.com/questions/20800/… Commented Jun 22, 2015 at 4:42
  • Two other kinds of symmetry may interest you - symmetrical scales like the octatonic, and negative harmony which looks at inverted chords like dominant seventh inverted to half-diminished. Commented Jul 22, 2019 at 16:26

3 Answers 3


The chromatic scale is made of 12 semitones. When you consider this in a non tonal way, there are several ways to evenly split these 12 semitones:

  • 12 semitones, the chomatic scale
  • 6 tones e.g. C D E F# G# A#, the tone scales
  • 4 minor thirds e.g. C Eb Gb A, the diminished chord
  • 3 major thirds, e.g. C E G#, the augmented chord.

These divisions are related to the modes of limited transposition, and when plotted on a circle of 5th or on a chromatic circle produce nice symmetrical figures.

The first part of the theme on the other hand is based on the "Coltrane Changes":

| BM7 D7 | GM7 Bb7 | EbM7 |

You get 3 M7 chords separated by descending major thirds (BM7 GM7 Eb7) with a "traditional" V7 IM7 progression.

The second section of Giant Steps is based on | II-7 V7 | IM7 |changes separated by ascending major thirds:

| Fm7 Bb7 | EbM7 | Am7 D7 | GM7 | C#m7 F#7 | BM7 | Fm7 Bb7 | EbM7 |

My view (as a keyboardist) of the symmetric approach to Giant Steps is closely related to the circle of 5th / chromatic circle: I stop considering notes as tonal functions, and rather view them as intervals to a center which I mentally place at the top of the circle. This translates as patterns on the circle (or on the keyboard, but the keyboard looses the visual symmetries). Then rotating the circle by 1 major thirds gives a new set notes, but the symmetries are preserved.


A jazz sax friend of mine would have said that in tonal progressions such as ii V I has to do with the ii leads to the V and the V leads to the I with I being the key. He would explain that the difference with symmetry is that the chords won't necessarily lead to other chords, i.e. ii doesn't necessarily lead to V and V doesn't necessarily lead to I. That is why it may seem like "weird" chord changes without a specific scale. (I would say key)

  • Okay that gives some information,but I still need a more formal answer. Commented Jun 21, 2015 at 23:32
  • In symmetry the ii chord is in relation to all other chords, even out of key chords. In tonal the ii chord is only in relation to the tonic, the I chord. The way of dealing with chord symmetrically is not with jazz. In symmetry the ii chord could proceed any chord and its relevance is based on how far apart that chord is tonally. The farthest away would be the tritone, but the tritone compared to it, i.e. in the key of C major the ii is d min. and the farthest away from it is the tritone g#, the chord based with g# as its root.
    – user21079
    Commented Jun 22, 2015 at 1:23
  • read: not just in jazz.
    – user21079
    Commented Jun 22, 2015 at 1:24

I found an alternative to “tonal” progressions is to move by major or minor thirds leaps from and to major or minor chords. In a grid app like chordpolypad you can construct symmetrical chord layouts and experiment.


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