All possible chord progressions (No Seriously!)

Using Simple and Complex Root Motion Sequences to Navigate the Diatonic Universe

The question, what are all the possible chord relationships?, first occurred to me when studying jazz harmony. My jazz professor had introduced me to a chord exercise in which you randomize a given chord quality or a set of given chord qualities. Let us take all half-diminished chords and fully-diminished 7th chords as but one example. You then randomize the order of all 12 half-diminished chords and all 12 fully-diminished 7th chords. The resulting chord progression might be as follows.

Gø7 –C#o7 – Dø7 – Bo7 – Eo7 – Fø7 – Go7 – Bbø7 – Aø7 – Eø7 – Abo7 – Bø7 -

Cø7 - Bbo7 – Fo7 – Ebø7 – Do7 – Co7 – C#ø7 – Ebo7 – F#ø7 - Gø7 - F#o7 – Abø7

The above exercise is great for its intended purpose which was to develop a good since of voice-leading. It helps develop an intuition for finding the shortest distance between chords or, as I like to say, the path of least resistance. However the above chordal exercise or exploration has three faults. 1.) It's not immediately musical. 2.) There is not always a sense of key. 3.) It is not pragmatic because it yields virtually unlimited possibilities.

I had also come across a second chord theory, this time from the perspective of a composer. The theory was an enumeration of all the possible relationships between two chords. The qualities of chord were restricted however to Major, minor, Dominant 7th, half-diminished 7th, minor 7th, major 7th, and Minor-major 7th. The wealth of possibilities which could be discovered through this type of restricted exploration is very beneficial to composers. While some very beautiful chord relationships are revealed to us via this process they are, again, not always innately musical, don't always convey a sense of key, and are too innumerable to have relevance to the practicing musician and the lay listener.

The two aforementioned theory-practices are both rewarding and valuable in their own rights. One for the lead-sheet/big-band chart reading pianist/improviser the other for the deep-reflective composer. In my opinion, however, they both lack a sense of internal musical-logic which brings the sound meaning and any resultant meaning is forced or happened upon by chance and luck. This isn't because there is anything inherently wrong with the previously described practices as they both provide valuable insights to the musical thinker. The shortcomings are due to lack of restrictions such as key and the musical rabbit-hole they throw listeners into. There are just too many possibilities without parallels, too much chaos and not enough order, too much rambling and not enough POETRY.

How can this musical poetry be achieved or discovered? Is it only in form, sentence, or periodic structure that gives rise to this expressive meaningful quality or can our understanding of chord-progressions/relationships help us?

My biggest breakthrough was when I re-realized that there are only 6 possible diatonic chord-root-relationships between any two chords of a key. For example in the key of C major. C can move up or down a 2nd to D or B respectfully, up or down a 3rd to E or A, and lastly up or down a 4th to F or G. The 5th, 6th, and 7th, relationships yield the same result as the 2nd, 3rd, and 4th movements so they are the same and in essence redundant! These 6 relationships are what I term simple motions. They are simple because only 2 chords are related via one motion.

The simple motions can be visualized as follows.

Chord X moves ____________ distance to chord Y.

C major moves up 4 to F major

(or simply) Up 4

All simple motions can be sequenced through a key. For instance the well-known circle of fifths (aka down by 5) is nothing more than a sequence of [Up 4, Up 4, Up 4 etc...]

(E minor) up 4 (A minor) up 4 (D minor) up 4 (G major) up 4 (C major)

One very interesting facet of simple motions is that each move in one direction has a paralleled inverse motion having the same voice-leading distances in the opposite direction.

For example the sequence of up 4, up 4, up 4 etc. is mirrored by down 4, down 4, down 4, etc. How funny that one is widely discussed and used while the other has dropped out of common usage after Beethoven. Both sequential progressions are equally valid, possible, and aesthetically pleasing. I'll leave it to the reader to try out the remaining simple motions at the piano. When practicing these motions it is best play 3 notes in the right hand against 1 note roots in the left hand. Make the right hand voice-leading as smooth as possible moving the least amount of notes possible to achieve the next desired chord. Lastly when the left hand ascends try to have the right hand descend. When the left hand descends have the right ascend. This is to help avoid parallel 5ths and 8ths.

The simple motions are beautiful and poetic. They should be understood, explored, and mastered before moving onto the complex motions.

While simple motions sequence one set distance between two or more chords (ex. Down 3, down 3, down 3, down 3 etc.) complex motions alternate two distance to relate 3 chords in sequence. The following visualization will show this more clearly.

The complex motions can be visualized as follows.

Chord x moves _____ distance to chord y which moves _____ distance to chord z

C major moves down 4 to G major which moves up 2 to A minor.

(or simply) Down 4, up 2

The above progression (down 4, up 2) is actually the well-known and widely used Romanesca a voice-leading scheme used in the famous Canon in D by Pachelbel. It is a complex motion sequence. In doing a bit of math we find that there are only 12 possible complex motions many of which have been widely used throughout history. Some, however, have been neglected or forgotten. I have enumerated each simple and complex motion below for the sake of clarity. It is my hope that this serve as a practice companion to improvisers, pianists, and composer of all varieties as these progression occur everywhere in music and in music pedagogy throughout history. These sequences are termed dispositions in the Italian school of the partimento tradition by Durante, Furno, and Fenaroli. At the Paris Conservatory they were referred to as Harmonic Marches by Théodore Dubois and Luigi Cherubini. They even show up in the harmonic exercises of Anton Arensky who's pupils included Rachmaninoff and Scriabin. I have given each of them nick-names as to facilitate memorization. Although none, to my knowledge, of the aforementioned schools have exhausted, either individually or in combination, the following list they have touched upon most possibilities. Without further ado here are all possible root motions sequences.

Simple Root Motions

fauxbourdon up – up 2

fauxbourdon down – down 2

Galant cadential 3rds – down 3

Film Score 3rds – up 3

Circle of 5ths (down) – up 4

Circle of 4ths (down) – down 4

Complex Root Motions

Erocia ↓2 ↑ 4 ------ Romanesca ↓4 ↑ 2

Climb from Hell ↓3↑4 ------ Fall from Heaven ↓4↑3

Downward Skips ↓3 ↑2 ------ Upward Skips ↑3 ↓2

Beautiful Plagal Cadences ↓3 ↓4 ------ Beautiful Authentic Cadences ↑3 ↑4

Liszt Power Cadence ↓3 ↓2 ------ Classic Deceptive Cadence ↑3 ↑2

Modern regressions ↓4 ↓2 ------ Traditional Progressions ↑2 ↑4

Motions in green have the best voice-leading and the most time proven effectiveness. Motions in yellow are good but less often seen. Motions in red are not necessarily bad and oftentimes extremely beautiful. The issue is that they can lead to awkward voice-leading. They are also not seen much in the piano literature and are not really mentioned in the great partimenti tradition of the Italian and French schools. I believe the reason for leaving out the motions highlighted in red and including those in green is due to voice-leading concerns and balance. Notice how all the complex motions highlighted in green have motions in opposite directions and those in red and yellow all include motions in the same direction. Motions in the same direction can more easily lead to awkward voice-leading and issues of range. Lastly the reason for the two highlighted in yellow is because they are both smooth in their voice-leading and are both really just transpositions of an authentic cadence (5-1) when sequenced.

We have seen that given both Simple and Complex Root motions we have arrived at 16 unique and meaningful musical events within any given key. Later we shall explore how, along with a harmonization technique know as “The Rule of the Octave”, root motion sequences can be very helpful in harmonizing melody. Simple and Complex Root Motions are extremely helpful and, in fact, unavoidable in music. If practiced and learned deeply they can show the us the path from rambling noise maker to poet-musician.

Happy practicing to all you pianists and otherwise out there!

-Branden Downing

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