These are the geometric diagrams I have seen...
Is this a good way to understand the topic or not? If not, what's the
I suppose this is about personal preference and someone's level of aversion to staff notation. Personally, they don't help me know the shape of chords on the piano and they don't help me read notation, so I don't find them helpful. The other big problem is see is the diagram set labels 'chromatic' and 'circle of fifths' seem to confuse the harmonic difference of chromatic circle of fifths progression and a diatonic circle of fifths progression.
In the diagrams the difference is only about the order of tone going around the circle. The end result is different shapes that maintain the same symmetrical/asymmetrical qualities. But the set of diagrams labelled 'chromatic' is showing a diatonic progression. It is not harmonically a chromatic progression.
...Chromatic Circle and the [diatonic] Circle of Fifths ...What's the
I will continue explaining the harmonic difference, because this is what is important musically.
Both are harmonic sequences which is when a two chord pattern is repeated but the repeats transposed the chords up or down either diatonically or chromatically. Specifically, the circle of fifths is a two chord pattern of root progression by descending fifth which is then transposed down a step. Let's see some notation. The chords could be voiced many different ways, but here are some basic root position examples:
Diatonic Circle of Fifths
- Note that in the bass
B is an augmented fourth (inverts to a diminished fifth.) All of the root progressions are by fifths, but they are not all perfect fifths.
- No accidentals are used, all the chords come from the same key (
C major in the example)
- several chord qualities are used: major 7th, minor 7th, dominant 7th, etc.
Chromatic Circle of Fifths
- All of the bass progressions are by perfect fifth.
- Accidentals are used because 1) a bass line of all perfect fifths eventually goes out of the diatonic notes of a key. You will see the difference at the point where
F goes to
B in the bass. When it's diatonic there are no accidentals. When it's chromatic accidentals are used as
B 2) all the chords are the same quality (dominant sevenths) chords don't occur like that diatonically so we must use chromatic spellings.
- In a chromatic circle progression we do not necessarily use all dominant sevenths. It could be all minor sevenths or a variety of other chord types. The important point is that it is not the diatonic set of chords and therefore will be chromatic.
What's the difference in practice between the two circles?
With a complete diatonic circle of fifths, the harmony ends up right where it started, in some sense it is static, because it doesn't go anywhere new, it really just prolongs a phrase in the key. Here is a famous Mozart example (the
F# is used, because the music changed keys from
G major, but within
G major the chords are all diatonic and just go from
Sequences are also used to develop a motif by playing it over many harmonies. Here is one from Bach in minor where a neighbor tone figure in thirds and sixths is developed.
Another practice it to make a small chromatic change at the end of a diatonic circle to get into a new key. Here we start in
C major, but then change
D7 which takes us into the key
Of course a longer chromatic circle can be used to change key. But - changing styles from classical to jazz - it is common to see a short portion of the chromatic circle used for another purpose: the 'turnaround' at the end of a song. When a circle of fifths is inserted into other sections of a song it is sometimes called 'back cycling.'
So a re-cap of some common traits and uses is:
- chord root progression by fifths, diatonic or chromatic
- contrasting or similar chord qualities
- the full sequence or a truncated segment may be used
- can lead to a key change
- can prolong a statement in one key
- can develop a motif
- can be used for a 'turnaround' or 'back cycling' in pop or jazz