1. Abstract
Theories explaining chord progressions (in particular root progressions) in tonal music have been developed by several theorists, including: Rameau, Weber, Schoenberg, McHose and Piston. There have also been some chord progression analyses by computer. Schenker's theory in contrast emphasises the importance of contrapuntal elements (voice leading) in the understanding of musical structure.
This outline thesis will demonstrate that none of the above theories accurately describes the patterns in chord progressions in tonal music. Through the systematic analysis of chord progressions, it will demonstrate that, only when the interaction between voice leading and root progression patterns are correctly accounted for can we see clear patterns in root progressions. We can then see how these create musical phrase structures that are in ways similar to grammatical structures in language. This is the first theory that correctly explains the relationship between voice leading, root progression patterns and musical phrase structures in tonal (and some tonally influenced) music.
The author believes that this represents an important contribution to the understanding of the structure of tonal music and its relationship with language. Further discussion of the link with linguistics and the role of syntax in music are included in chapter one of the book section.
The author is preparing a book Syntactic Structures in Music which is summarised on this website.
2. Introduction
The ideas presented are based on research data from the analyses of a large number of pieces of tonal (and some tonally influenced) music. A sample of analyses are recorded on a database on this website. To view this database, see later at: Comparative Root Progression Analysis.
This outline thesis will concentrate on the analysis of a single piece of music - the Mozart Piano Sonata in A Minor (KV 310 (300d)). This piece has been chosen as it demonstrates the results and issues reasonably clearly. Also, a piano piece is easily accessible to the reader and takes less time to analyse than an orchestral or chamber work.
Much constructive feedback has so far been received, and this is being used to improve the content of this web site and will be used to improve the contents of the book prior to publishing. As the author is working as an independent researcher, he feels that it is important to communicate these ideas to a large audience first in order to gain adequate feedback about the method of working and conclusions.
Following is an outline summary of the problems inherent in some previous theories of chord progressions. This is a complex subject which I've attempted to summarise briefly below. I plan to include a more detailed history of relevant theories as chapter 10 of the book summary on this site, as soon as is practical. In the mean time, please also refer to the Question and Answer Section for some further notes and refer to the bibliography and web references for related web sites and books.
My personal aims in presenting this paper are:
- To publish my ideas
- To gain some feed back on these ideas
- To use the feed back to further refine my book prior to publication.
If you wish to bypass the following historical discussion of theories of chord progression then I suggest you move on to the Next Section.
For further information on the books mentioned below, please refer to the bibliography section on this site.
Rameau's Theory of Root Progression
Rameau's theory of chord progressions evolved through his many works. The following is a summary from Génération Harmonique 1)(1737):
1. Only succession of 5ths should be used within a given mode (i.e. roots rising or falling by a 5th)
2. Successions of 3rds should be used only when changing mode (i.e. when modulating between relative major and minor keys)
3. Successions of 2nds should be used only by double employment (double emploi)
Rameau developed his third principle to explain the common progressions I - II7- V. The idea being that the the chord II7 could be simultaneously regarded as either a chord II with an added 7th or chord IV with an added 6th (hence 'added 6th chord'). This chord is thus approached by a falling 5th (I - IV6) and moves to chord V by a further falling 5th progression ( II7 - V ) the chord being reinterpreted by the ear as II7 by virtue of the double emploi.
Some problems with Rameau's theory:
- It fails to explain progressions such as the falling third progression: (e.g. I - VI). This occurs frequently in progressions such as I - VI - II - V - I without any modulation intended.- It does not explain the difference in usage between the rising and falling 5th chord progressions. Falling 5ths are more common than rising 5ths and rising 5ths tend to occur mainly when paired with falling 5th progressions as in:
I - V - I and I - IV - I
- It does not explain rising 2nd chord progressions such as:
I - II and IV to V where no added 6th or 7th is present thus making the double emploi impossible.
- It makes no account of the fact that falling third chord progressions are common but rising 3rd progressions are relatively rare.
- It makes no account of the fact that rising 2nd chord progressions are common but falling 2nd progressions are relatively rare.
Overall, not very satisfactory.
Schoenberg's Theory of Root Progression
Schoenberg's theory of chord progressions is explained in Structural Function of Harmony (1948: page 6 onwards) and may be summarised as follows:
(musical figures not included)
Structural Functions are exerted by root progressions
There are three kinds of root progressions:
(1) Strong or ascending progressions:
(a) A fourth up:
V- I , VI - II, VII - III, I - IV, etc.
(b) A third down:
I - VI, II - VII, III - I, IV - II, etc.
....These can be used without restriction...
(2) Descending progressions:
(a) a fourth down:
I - V, II - VI, III - VII, IV - I, etc.
(b) a third up:
I - III, II - IV, III - V, IV - VI, etc.
...Sometimes appear as 'mere interchange' or (I - V - I etc.) or used in combination of three chords resulting in strong combinations....
(I - V - VI or I - III - VI )
(3) Superstrong Progressions:
a) One step up:
I - II, II - III, III - IV, IV - V, etc.
b) One step down:
II - I, III - II, IV - III, etc.
Often appear as deceptive progressions e.g. V - VI .. may be considered too strong for continuous use.
This improves on Rameau in that it makes the distinction between the rising and falling 5th chord progressions.
It also makes the distinction between the common falling 3rd chord progression and the relatively rare rising 3rd progression.
It highlights the use of descending progressions in passing combinations as shown above. This concept will be further developed later.
Some problems with Schoenberg's theory:
- it makes no clear distinction between the common rising 2nd chord progression and the relatively rare falling 2nd progression.
- it does not highlight the use of paired rising and falling 2nd chord progressions in oscillations similar to those with rising and falling 4th progressions.
- in grouping rising 4th and falling 3rd progressions within one group Schoenberg does not acknowledge the greater importance of the rising 4th progression which is the basis of the perfect cadence.
- Schoenberg does not attempt to fully explain root progressions when chromatic chords or modulation are involved.
- He does not make the link between the use of chord progressions with the position of the chords within the musical phrase. i.e. his theory is not context sensitive and therefore does provide an adequate description of the syntax of the musical phrase.
Schenker's Theory
Schenker's discussions of musical structures emphasises the importance of contrapuntal elements in building musical structures.
In Der freie Satz (1935) the main devices for creating chord progressions are in the middleground. The process is described as the linear filling in or prolongation of the rising bass arpeggiation: I - V. As the bass rises from I to V the progression is prolonged by interposing one or more of the following notes: II - III - IV in the bass. These can result in root position or 1st inversion chords. Please refer to bibliography and links section for books detailing Schenker's theory.
However, this gives equal importance to the progressions I - II -V ( very common) and I - III - V (very uncommon). Chord progressions can also be generated by filling in the descending I - V progression thus predicting uncommon progressions such as I - VI - V and I - VII - V. This process does not limit the possible progressions sufficiently to predict actual usage and therefor cannot be considered a theory of chord progression.
The techniques used on this site involve the removal of voice leading surface detail to uncover the root progressions beneath. Whilst this process has some similarities to the foreground reduction process in a Schenkerian analysis, it must be emphasised that this reduction process is not exactly the same and the results and conclusions are different. I will include a more detailed comparison of the two as soon as is practical. But readers familiar with Schenkerian models should be able to see the differences. In summary, My reduction process involves only traditional voice leading patterns (or "divisions") not the extended voice leading patterns invented by Schenker. The reduction process used here, thus ceases once traditional voice leading has been exhausted and consequently reveals patterns in root progression that are missed in conventional Schenkerian Analysis. These root progression patterns at then shown to create patterns in musical phrase structures similar to those in language. See also the notes in the preface to the book section. In a Schenkerian Analysis the traditional principles of voice leading are extended and distorted in order to derive "middleground" and "background" structures which exist in Schenker's normative model and not in the music itself.
Weber, McHose, Piston
Later, writers such as Weber, Schoenberg, McHose and Goetschius described chord progressions in tables showing the probabilities of chords on each degree of the musical scale moving to chords on other degrees of the musical scale. These varied from one writer to another but culminated in the chord progression table of Piston/Devoto (Harmony: Page 21) as follows:
I is followed by IV or V , sometimes by VI, less often II or III.
II is followed by V, sometimes IV or VI, less often I or III.
III is followed by VI, sometimes IV, less often I, II or V.
and so on.
Tables of chord progression probabilities have also been used in the computer analysis of musical style and composer identification.
This paradigm leaves open many questions. For example:
ˇ What does it say about the functions of chords within the context of a phrase?
ˇ Are these probability functions the same for chords in different places in the musical phrase?
ˇ How are non-structural chords accounted for? (for example passing chords?)
ˇ what about modulating passages? - chords may not be clearly I or II or III
ˇ What about chromatic chords? how do they fit into the table?
The tables are quite unsatisfactory far harmonising a melody. Knowing that a chord is more or less likely tells you nothing about which chord is right for the situation.
There is also something unsatisfactory about a theory which is just a tabular description of observed data. A theory is meant to tell you something about the underlying principles. At least Rameau attempted to present a simple set of rules and understood that chord progressions might be about movements between chords independently of their position in the musical scale.
In demonstrating the role that chord progressions have in the production of structures in music, the author does not intend to imply that other components of music do not also play an important role. Syntactic Structures in Music includes examples that demonstrate the connection between voice leading, motivic and melodic structures, root progression patterns musical phrase structures and formal structures. This thesis concentrates mainly on the role of chord progressions. However, this analysis suggests that chord progressions play a major if not defining role.