Chord Progressions in Tonal Music

Following is a summary of Syntactic Structures in Music. One of the purposes of this site is to get feedback to improve the content of this book and facilitate the process of publishing. By reviewing the contents of the web site you agree to be bound by the conditions of the copyright as indicated on the copyright note. For guidelines on how to reference this site from other websites or in academic papers please refer to the guidelines page. Preface Chapter 1. The Basic Syntactic Structure Introduction Syntax in Language Syntax in Music Chapter 2. Static and Dynamic Harmony Static Harmony Dynamic Harmony Chapter 3. Non-functional Chords Introduction Auxiliary Chords Passing Chords Appoggiatura Chords Chapter 4. Linear Progressions Chapter 5. Extensions within the Basic Structure Introduction The Dominant Prolongation The Static Coda The Dynamic Introduction

Chapter 6. Extensions to the Basic Structure Chapter 7. Modulation Basics In Dynamic Harmony Using Chromatic Chords Tonic to Tonic Chapter 8. Example Musical Analyses General Introduction Schumann - Kinderszenen No 1. Brahms - St Antoni Chorale Variations Others to follow in the book Chapter 9. Example Harmonisation Chapter 10. Historical Background

Appendices A: Voice Leading Overview B: 20th Century Popular Music C: Glossary of Terms D: Glossary of Symbols Bibliography and Web Links Index of Musical Examples Ver. 2.6

CHAPTER 1

THE BASIC SYNTACTIC STRUCTURE

Introduction Conventional theories of structure in tonal music concentrate either totally on root progression patterns (Rameau. Schoenberg, etc) or totally on voice leading. (Schenker etc) This book is the first to explain how root progression patterns and voice leading work together. This book is based on a systematic analysis of root progression patterns in a large number of tonal (and tonally influenced) pieces of music and shows how chord progressions (once voice leading patterns have been addressed) create musical phrase structures similar to sentence structures in natural language. Whilst voice leading principles are fairly well understood, what is new in this book is the explanation of how root progressions work in tonal music and how they interact with voice leading. When viewed from this perspective, it is possible to demonstrate that musical phrases are constructed in ways that show similarities with the way sentences are structured in natural languages. This makes it possible to explain every chord in its context within the musical phrase rather than just in terms of the chords surrounding it. This book is about what is normally referred to as tonal music or music which is based on tonality. By tonal music I mean music that is composed in a recognisable system of scales and chord patterns as exemplified by the European classical tradition of the 18th and 19th centuries and to some extent the 20th century. Most of the music we listen to: classical, popular music, jazz, world music, etc. is constructed to some extent along tonal lines. People are often puzzled about why this system, which at first sight, is so simple just a scale of seven diatonic notes (plus 5 chromatic notes) arranged in different patterns - actually produces such a wealth of possibilities. What I hope to show is that what gives tonal music the ability to form these varied structures is, the way voice leading and root progression patterns work together and the way chord progressions are organised into musical phrase structures similar to language structures in natural languages. Some writers such as Weber, Schoenberg, McHose and Piston have described chord progressions but only in terms of tables of probabilities. These tables tell us nothing about the relationships between the chords themselves or between the chords and musical phrases. Schenker proposed a theory of musical structure based totally on voice leading but this does not adequately explain how root progressions work or how musical phrases are structured. Please refer to the Outline Thesis and the Q and A section of this site for further information on the history of such theories. A more

complete history is being prepared for inclusions as chapter 10 (Historical Background). In demonstrating the role that chord progressions have in creating syntactic structures, the author does not intend to imply that other components of music do not also play a role. Chapter 8: Full Musical Analyses shows the link between voice leading and chord progressions; the link between between voice leading and motivic and melodic structures, and the link between chord progressions and musical phrase structures. Chapter 6: Extended Musical Structures will further explore this subject. The Outline Thesis explains some of the evidence for the theory presented.

The Connection with Language Language has evolved well organised structures because it gives human beings an evolutionary advantage. It allows us to communicate: - to pass information about our environment, about the location of food and warnings of danger. It enables us to agree plans and to pass traditions, ideas and techniques from person to person and from generation to generation. Because this is so important to our survival as a species it is an ability we have evolved over tens of thousands of years. It communicates messages, feelings and emotions and we enjoy the experience. Based on the evidence collected about the patterns in chord progressions, it seems likely that the mind's innate ability to understand language structures has been transferred to the western system of music we describe as tonal music. Analysis of modal music and tonally related music shows that these musical systems (at least when harmonised) also share some of the patterns that are evidenet in tonal music. As tonal music evolved over several centuries, it seems that composers have subconsciously emulated the underlying grammatical structures which exist in language. Because the underlying structures are common to all languages, these musical structures can be understood by anyone, anywhere in the world. Hence tonal music is accessible to many cultures and the harmonic structures in tonal music have influenced the popular music of many other musical traditions. Composers have not planned things this way or designed the tonal system. It has evolved through a series of experiments and discoveries that have gradually built on each other. This was necessary as western art music developed beyond accompaniment to song or dance into a self-contained art form with internal structures of its own. Whilst Chord syntax and voice leading syntax are well documented and understood. What is missing is chord progression syntax. This

theory is the first that attempts to accurately describe chord progression syntax. By filling this gap we can more fully describe the syntax of musical language. In language, structures are formed in sentences made up of parts of speech. The joining of these parts of speech into sentences is governed by the rules of sentence syntax. For example, the basic structure of a sentence in the English language can be represented in a parsing diagram as follows:

This diagram indicates that a sentence is divided into two parts: the subject and the predicate. The predicate is itself divided up into two parts: the verb followed by the object. This represents the simplest complete sentence structure and although more complex structures are possible they all derive from this simple structure. One method of adding complexity is by further division of the branches. For example, the subject could be a noun or could be expanded into a pronoun + noun or further expanded to include a noun phrase or verb phrase. These underlying principles also apply to musical structures, There is one basic phrase structure in tonal music and all other phrase structures are derived from this basic structure.

For more on syntax in language click here

For more on the role of syntax in music click here

The Basic Musical Phrase Structure It might be assumed that the basic element of the syntactic structure in music is the chord, but in order to make the connection between the chord and the musical phrase an intermediate level is required. This is the syntactic element which is identifiable as blocks of harmony of one of two types: static harmony and dynamic

harmony. (This analysis of harmony is anticipated by Schoenberg and others but they do not make the connection with the musical phrase.) In the basic syntactic structure in music, harmony that is static is made up of only the tonic chord (elaborated by voice leading patterns) or an oscillation of the tonic chord with other structural chords. Harmony that is dynamic is made up of chord progressions. It is because chords can be formed into these two basic types of grouping that music can be formed into structures similar to language structures. The basic phrase structure in music ends with the cadence which in tonal music is normally made up of the dominant and tonic chords (chords V and I), which complete the basic musical phrase structure. In this way, the phrase in music is the equivalent of the sentence in language. The basic syntactic structure for tonal music can be represented as follows:

The basic musical phrase structure is very common and occurs at important points in compositions. For short pieces, it is sometimes the whole structure. In larger pieces, it is often the first phrase and also the last phrase in the piece and occurs at other important positions in a piece. It is so prevalent that we hear it subconsciously as the base standard that modifications are measured against. Just as there is one basic structure in language, that is modified in various ways, the basic structure in tonal music is modified in similar ways. Modified structures are not arbitrary variations, rather they are used as ways of creating shorter or larger scale structures just as subordinate clauses and phrases in language are used with the basic language sentence structure to create larger scale structures. They are important in creating form. More will be covered on these variations in Chapters 5 and 6. Abrreviations can be used if desired as follows

Where: P

=

O

=

C S.H. D.H. Cad V I

= = = = = =

Phrase Opening Section of the Phrase Closing Section of the Phrase Static Harmony Dynamic Harmony Cadence Dominant Chord Tonic Chord

The parsing diagram shows the sequence of the elements of the basic structure but it also shows the logical relationship between the static and dynamic elements and the cadence. For instance, whilst the static harmony is independent of the other two elements, the Dynamic Harmony and Cadence are shown under one heading. This is because the Dynamic Harmony and Cadence combine to create a larger dynamic harmony structure. So what is marked as Dynamic Harmony is in reality "the dynamic harmony leading to the Cadence". I only point this out to show the meaning of the hierarchy. The Cadence is shown separately because it has an important syntactic function in its own right. It determines the boundary of the phrase, anchors the static and dynamic elements in their place in the phrase and determines the key which is arrived at, at the end of the phrase. The static harmony establishes the tonic at the start of the phrase and creates the context of the music by indicating the style and introducing the main melodic elements. The dynamic harmony develops these and makes the movement to the cadence. It either supports the key established in the static harmony or it can modulate. The dynamic harmony usually elaborates on melodic elements from the static harmony. The Cadence confirms the key arrived at and indicates the end of the phrase. The most common and structurally important cadence in tonal music is the V to I "perfect cadence" or "complete close" which is why the cadence is broken down in this way. Other variations are possible but this is the

"reference standard" that other variations make reference to. For more on cadences (including modal cadences) see cadence in the glossary of terms. As a short example, of this simple structure, let us examine the following 8 bar phrase from the Scherzo of Haydn's Sonata in F major, Hob XVI: 9:

We know that this is a complete musical phrase because it starts at the beginning of the melody and ends with a perfect cadence, C major to F major (chord V to chord I). From bar 17 to bar 21, the phrase is composed of tonic harmony (F major) with just one movement to a dominant chord (C major) at bar 19 and back to the tonic at bar 20. As the harmony just oscillates around the tonic there is no overall movement and consequently the harmony is static harmony. At bars 22 to 24, in contrast, the harmony changes to a chord progression as follows: I (F major) to II (G minor) to V (C major) to I (F major). There is a clear root movement here. In chord progressions, it is the root of the chord that is important rather than the bass. The chord root rises a single step (a rising 2nd) from F to G, then rises three steps, (a rising 4th) from G to C, then rises a further rising 4th from C to F. This creates a sense of movement up to and including the V - I cadence. This is dynamic harmony. The full book will contain further example(s). There are also further examples in demos 1 and 2.

This switching between static harmony and dynamic harmony happens in all tonal music and the simple structure above is the basis of all chord progression syntax in tonal music. In conventional theory chords are classified in terms of their function in relation to keys. This tends to disguise underlying progressions especially when they go across key structures. This topic is further discussed throughout the remainder of the book. For further examples of simple harmonic structures then please refer to the animated demonstrations. Longer phrases will have longer static elements and/or longer dynamic harmony elements. More complex musical phrases can be explained as expansions of this basic structure by combining complete and incomplete structures in various ways and by expanding some elements of the standard structure. These extensions are summarised in Chapters 5 and 6. The reader will at this point no doubt be asking the question: 'Well, if this is so simple why has no one ever noticed it before?' One reason for this is that most theories of musical structure concentrate totally on voice leading or assume that root progressions can be explained without any reference to voice leading. In order to establish the true chord progressions, whether static or dynamic, it is necessary to determine which chords are significant (or functional) in the progression and which chords are passing in nature (non-functional). These non-functional chords arise out of voice leading patterns just as the surface detail of the music does. Whilst in many examples (including the ones above) there are no non-functional chords to muddy the waters, when they are present they can disguise the underlying static and dynamic structures so that the voice leading patterns need to be analysed clearly in order to determine which chords are significant and which are not. Some theorists argue that the analysis of root progressions is a futile exercise; that it is not always easy to determine what the correct root of a chord is, and that for some note combinations it is not possible to determine roots at all. Schenker believed that all chords arise from counterpoint and he gives particular importance to the role of linear progressions in creating chord sequences. The correct analysis of chord progressions depends on decisions about which vertical note combinations are significant in the analysis and which note combinations do not constitute structural chords. Given this necessary selection process, the suspicion may be that in finding patterns in chord progressions, the theorist has in some way selected chords and progressions that fit the theory and has rejected note combinations that do not fit the desired results. In fact, this is one of the principle objections to Schenker's Fundamental Structure - that the means of its derivation are not independent of the results themselves. (1)

To overcome this problem, the selection of note combinations must be applied in a consistent manner and in such a way that is independent of the end result. In other words, the reduction of music to an harmonic outline that lends itself to adequate root progression analysis, must be carried out by a system of rules that is as objective as possible. These are based, here, on the well established principles of voice leading (or more correctly "divisions"). This is explained more fully in Chapter 3. By working this way, it will be shown that chord progressions show clear patterns and that these patterns are similar to the grammatical structures in language. For more on Voice Leading see the Voice Leading Appendix.

Summary This theory may be summarised as follows: All phrases in tonal music are organised into syntactic structures, similar to those in language. These are constructed in three levels: The phrase, the syntactic elements (of the type static harmony or dynamic harmony) and the chords. In tonal music, complete phrases usually terminate in a perfect cadence (chord V to I) . Static harmony in the basic structure is made up of a prolongation of the tonic chord by voice leading only or by oscillations between the tonic chord and other structural chords. Dynamic harmony is made up of chord progressions constructed mainly from strong root progressions (rising 4th, falling 3rd and rising 2nd). This selection of progressions for dynamic harmony I will refer to as the polarisation of chord progressions. In order to make visible the underlying chord progression the surface voice leading must be first accounted for. This means some chords might appear to be structural but in fact arise purely out of voice leading. These are not significant in the root progression analysis. This concept can be described as functionality. Non-functional chords include passing chords and chords which do not have clear roots such as the diminished seventh chord. The basic syntactic structure may be extended by the further expansion of one of the syntactic elements in the basic structure. For example, the cadential V chord may be extended by dominant static harmony to form a dominant prolongation and the cadential I chord may be extended by tonic static harmony to form a static coda. See Chapter 5: Internal Extensions. Complete and incomplete structures may also be "conjoined" to form larger structures. In some situations incomplete structures can be embedded within complete phrase structures. Variations on the basic structure will be furhter expalined in Chapter 6: Extended Phrase Structures.

(1). Narmour, Beyond Schenkerism

CHAPTER 2 (PART 1) STATIC AND DYNAMIC HARMONY

Introduction In the last chapter, I introduced the concept of static and dynamic harmony and its importance in the construction of syntactic phrase structures. In this chapter, I will further explore the nature of static and dynamic harmony and explain how the form of these can vary according to the style and period in which the music was written. In order to retain interest throughout their execution, all temporal art forms: music, the novel, theatre, cinema etc. Must vary their degree of tension and relaxation. When you watch a play or a film, observe how the tension varies, at one moment, static: scene setting, mood establishing, character introducing and then at another moment dynamic: something happens, tension is built up, what will happen next? The mood constantly alternates between these static and dynamic states. This is necessary to maintain the interest. These states are easy to identify once you know about them. They vary in length and in the degree of tension or relaxation but they are always there. In music, these static and dynamic episodes are created by the use of different types of harmony. A prolongation of a single chord creates a sense of being stationary. I will refer to this as static harmony. Progressions of chords create a sense of moving forward. I will refer to this type of harmony as dynamic harmony. As well as varying the tension in music these episodes form the basic building blocks or syntactic elements that are necessary to make syntactic phrase structures similar to language sentence structures.

Static Harmony The simplest form of static harmony is the sustained tonic chord elaborated only by surface voice leading. In the following example, the tonic F chord is sustained for two bars:

The horizontal square bracket is used to show the extent of the tonic chord (F) and will be used to underline static harmony patterns. The tonic chord is elaborated by arpeggios, passing notes and auxiliary notes, but no new chords are introduced. The same chord may be sustained over several bars. The Prelude to Wagner's Rheingold is made up entirely of a sustained E-flat harmony which lasts for 136 bars. However, the most common type of static harmony is that made up of an oscillation between the tonic chord and other chords. Two commonly used chords for this purpose are the primary triads: chords IV and V, as follows: I - [ IV ] - I and I-[V]-I The square bracket will be used to indicate that a chord is used (in this case in conjunction with the tonic) to form static harmony. This type of chord will be referred to as an auxiliary chord by analogy with the auxiliary note. An auxiliary note is a non-harmony note that returns back to the harmony note. These are further discussed in the Voice Leading Appendix and Chapter 3 (part 2). These auxiliary chords do not create chord progressions since they return to the chord which precedes them. The example in Chapter 1. included chord V as an auxiliary chord. The following example also uses chord V as an auxiliary chord:

In this example the dominant auxiliary chords are deployed in root position and take on a role almost equal in importance to that of the tonic chord. This type of tonic-dominant oscillation is very common and is deployed in many well know melodies. The use of chord V, especially V7, as an auxiliary chord is a characteristic of classical secular music. The choice of auxiliary chord is thus an indicator of the style of the music. The extent of the static harmony is indicated by the horizontal square bracket and the auxiliary chords are show in square brackets. The figured base notation "7" is shown where a 7th is added to the dominant chord. The following example uses chord IV as an auxiliary chord:

In this example the subdominant chords are also in root position. The 4th bar of the phrase is a brief prolongation of the dominant. The horizontal square brackets indicate the extent of the prolongations. Chord IV is frequently used in sacred music and is thus an indicator of the style of the music. Chord IV as an auxiliary chord is also common in popular music underlying one of its origins

in gospel music which inherits its harmony from choral church music. The purpose of auxiliary chords is to prolong the tonic (or sometimes the dominant) harmony. They do not create a forward moving chord progression. The static harmony normally occurs at the start of the phrase, introduces the melodic ideas (motives) and establishes the key at the start of the phrase. Chord V (especially V7 ) is more generally associated with secular music and chord IV (especially in root position) is more generally associated with sacred music, as indicated in the examples above. The choice of auxiliary chord thus contributes to the style of the music. The following example demonstrates the use of both chord IV (not in root position) and V as auxiliary chords:

The appearance of the tonic chord in root position whilst the chord IV auxiliary chords are employed in second inversion emphasises the subordinate nature of the chord IV auxiliary chords in this example. In contrast, the two occurrences of the chord V are in root position, indicating the arrival of the cadence. The horizontal square bracket shows the extent of the static harmony. In this example, the static harmony encompasses the V - I cadence, and so, this brief phrase is made up of totally of static harmony. This topic will be further discussed in Chapter 6. In this example, the IV chords could be interpreted as simply the result of auxiliary notes (shown in the examples by the letter "A") and not functional chords in their own right: the G# and B of the tonic chord ascending to form the A and C# of the subdominant chords at bars 7, 8 and 9 and return immediately to the G# and B. There are thus two types of auxiliary chord:

a) Non-functional chords that arise merely as a result of auxiliary notes i.e. voice leading. b) Functional chords ( in root position) These cannot be due purely to voice leading because of the movement of the bass to a new chord therefore they are structural in their own right. In either case, theses chords create static harmony. The main difference is that the second type can take on further levels of voice leading elaboration. The type of chord used for the auxiliary chord can also be an indicator of the period of the music. In the 19th century, harmonic possibilities are extended by the use of chords ii and VI as tonic prolonging auxiliary chords. In the following example, Schubert uses chord ii7 in the minor key:

Here, again, the static nature of the harmony is emphasised by the retention of the tonic note in the base. This is usually referred to as a tonic pedal. Note that since the ii7 chord arises as a result of the auxiliary and passing notes in the accompanying harmony, consequently the 7th of the chord is relieved of its normal obligation to resolve downward. As this piece is in the minor key chord ii is in

fact a diminished chord (in this case with an added 7th) which is why this is shown as ii°. The auxiliary and passing notes are shown in the Harmonic Outline as "A" and "P". Pedal notes are frequently used under static harmony to underline the static nature of the chord succession. Pedal notes can be deployed under any auxiliary chords regardless of whether the tonic note forms a normal part of the auxiliary harmony. In the Harmonic outline, I've introduced some of the symbols to be used throughout this book and the Full Analysis Chapter to represent the underlying structure of the music. The structural notes are represented as white note heads and the voice leading as black note heads. The figured bass notation further documents the voice leading patterns. The cadential Chord V is elaborated by two appoggiaturas which create a cadential 6 4 chord (which is chord I in inversion) However, this is shown in the harmonic outline as black notes with tails (crotchets). This is to highlight the fact that they do not alter the underlying chord succession. Non-functional chords such as these will be explained in Chapter 3. It can be seen from these examples, the choice of auxiliary chord in the static harmony contributes to the style and period of the piece of music. The full book will contain further examples of static harmony from different periods of music. The range of auxiliary chord possibilities can be further extended by the use of chromatic chords. The type of chromatic chord is a further indicator of style and period. Examples of these are given later in chapter 3

CHAPTER 2 (PART 2) STATIC AND DYNAMIC HARMONY

Dynamic Harmony The function of dynamic harmony is to provide a sense of moving forward, the change of status between static and dynamic harmony is critical in creating variety, enabling the ear to follow the phrase syntax and in creating musical form. Rather than an oscillation between chords, dynamic harmony in tonal music is made up of a succession of strong chord progressions. As roots of chords can exist on seven possible scale steps: I, II, III, IV, V, VI, VII each individual root has 6 possible roots to move to (ignoring octaves and chromatic notes). Consequently, roots may rise or fall a 2nd, rise or fall a 3rd, rise or fall a 4th. Dynamic harmony in tonal music is made up almost exclusively of three of the six possible types of root progression. These will be referred to as the three strong chord progressions and will be labeled: alpha, beta and gamma (α, β and γ) progressions, as follows: α - root progression by rising 4th (or falling 5th)

( e.g. V - I, I - IV etc.) β - root progression by falling 3rd (or rising 6th) ( e.g. I - VI, VI - IV etc. ) γ - root progression by rising 2nd (or falling 7th) (e.g. I - II, IV - V etc. )

The reversals of these progressions: α', β' and γ' are weak and are generally (but not completely) avoided in dynamic harmony in common practice tonal music. It will be observed that this classification groups together root progressions which do not involve exactly similar intervals. For instance, the root progression β could involve a descent of a major or minor third depending on which chords are involved and whether the tonality is major or minor. In practice, both major and minor descending third progressions are frequent whereas both major and minor ascending third progressions are infrequent so that this classification adequately describes the use of root progressions. This is because the use of root progressions is primarily a diatonic and not a chromatic phenomenon. Chromatic harmony serves primarily to decorate rather than create structure. For further discussion on root progressions please refer to the Thesis section on this site. The α chord progression is by far the strongest and most frequently used progression in dynamic harmony and when used to make the move from V to I at the end of a phrase it forms the perfect cadence. Of the other two progressions, the β progression is generally more common than the γ progression, in most compositions, but the relative frequency varies according to style and period of the music. Whilst the primary triads IV and V are the most common chords used in forming static patterns, in one key, there is only one dynamic pattern that can be formed (starting and ending in chord I) with these chords, using only strong progressions, as follows:

Consequently, the secondary triads are used to extend the range of possible dynamic patterns. Chords II and VI are most useful for this purpose. Following are some common (non-modulating) patterns, starting and ending on the tonic:

The following example clearly shows the use of α and γ chord progressions. Even though the texture of the music is contrapuntal, and the writing is in two parts, the dynamic harmony is nevertheless clear. It should be noted that in the baroque and classical periods, α and γ progressions are often used in preference to other progressions.

Inversions weaken the feeling of moving forward. The chord progressions which have the strongest sense of moving forward tend to be those where the chords are all presented in root position and composers use the strongest chord progressions at the position in the structure where the strongest sense of movement is required. This polarisation of chord progressions appears to have taken place gradually from around 1600 to around 1700 and is easily seen in the music of Bach and his contemporaries. Static and Dynamic harmony patterns, however, can be seen in music before that period but not with the same degree of polarisation. Techniques for strengthening progressions can be seen in the following example from Brahms:

This example deploys α and β progressions. The chords in bars 19, 21 and 22 are all dominant 7th chords since they all take on an added 7th and, in case of bar 21, the minor third is raised to form a major third. Clearly all of these dominant 7ths chords do not indicate rapid modulations to new key centres. New key centres have to be established by the presence of static harmony or a cadence in the new key. The function here is just to strengthen the harmonic movement and to add variety and interest to the harmony. No modulation is intended or heard. Bars 107 to 114 of Brandenburg Concerto No 2. could be examined at this point. Here a whole series of seven dominant 7th chords (using six α and two β progressions) are used to form a very strong chord progressions prior to the final recapitulation of the main theme. They are preceded by a tonic chord and end with a tonic chord and therefore no modulation occurs in this example. This very strong sequence is used to alert the user to the imminent end of the movement. This Final Dynamic Episode thus has a formal or structural function as well as its normal syntactic phrase function.

The harmonic outline uses the symbols to be used in the rest of this book and in the Full Analysis Chapter. The white note heads represent structural notes in structural chords and black note heads are used to represent voice leading patterns. For instance, a 7th is added to the tonic chord in bar 19 as a passing note between the Ab of the tonic chord and the F of the subdominant chord in bar 20. The passing movement is highlighted here by the notes being connected by stems and a beam for clarity. Other 7ths additions to chords are shown as black note heads. The examples given above are both from pieces in major keys. In the minor key, chords I and IV are minor, chord II is diminished and chord VI is major. However, these chords are used in a similar way to the way the same chords are used in the major key. I will include more on this topic in the full book. Whereas in the baroque and classical periods, alpha and gamma progressions are often used in preference to other progressions, in the 19th century, beta progressions are often used in preference to gamma progressions. In music prior to the tonal period and in 20th century modal music, the degree of polarisation is less evident so that the weaker progressions are used more frequently. Consequently, weak progression create a modal effect or mood. The degree of polarisation is thus a style indicator. Even in one period of music the difference in frequency of use of progressions can be observed in different types of music. For instance, in the Bach Chorale harmonisations, the degree of polarisation is less than in the Brandenburg Concertos. This is because Bach is looking back to an earlier style in the chorales. This is a fact overlooked in some studies of root progressions. Thus the choice of root progressions is an indicator of the period, style and mood of the music. For more on polarisation of progressions see the thesis section on this website. The reader is referred to Demo 2 which animates a succession of seven α progressions starting and ending in the tonic chord.

CHAPTER 3 (PART 1) NON-FUNCTIONAL CHORDS

Introduction Many theorists from Rameau to Schoenberg and Piston have attempted to analyse chord progressions by describing patterns in their root movements. However, none of these fully describes the syntax of chord progressions. Please refer to the Outline Thesis and the Q and A sections of this site for further information on the history of such theories. A more complete description is being prepared for inclusion in Chapter 10: Historical Background. Previous attempts have proven inadequate because, in order to establish clear patterns, two factors have to be taken into account in the analysis. Firstly, as explained in the last chapter, it is necessary to make a distinction between two types of harmony: static and dynamic harmony. Secondly, some vertical note combinations, whilst appearing to be independent harmonies in their own right, arise out of voice leading. These types of movement are sometimes referred to as melodic to distinguish them from movements which are genuinely harmonically based. When these are discounted from the analysis, patterns in the root progressions become clearer. Static and dynamic harmony were described in Chapter 2. In this chapter, I will deal with the second factor which I will refer to as functionality. All theories of harmony make an assumption about functionality whether explicitly or implicitly. Most theorists would accept that certain note combinations are not chords in their own right but arise due to some type of melodic or voice leading movement in one or more of the voices. They nevertheless differ in what they would consider to be significant. I hope to present a clearer and more objective way of defining what is functional and what is nonfunctional. This should overcome any suspicions that chords are being ignored simply because they do not fit the theory. The justification for taking the position explained in this chapter is based on research into patterns in chord progressions. For more information on how these patterns have been established, please refer to the outline thesis.

For a theory of functionality to be credible it is important that the principles deployed to determine functionality are clear and simple and independent of the results derived. It is important that there should be some rational reason for excluding chords from the root progression analysis. The method deployed must satisfy the following conditions: • • • •

It must be It must be It must be It must be end result

clear and unambiguous based on concrete research data applied in a consistent manner applied in such a way that it is independent of the

In other words, the reduction of music to an harmonic outline that lends itself to adequate root analysis, must be carried out by a system of rules that is as objective as possible. In other words, the method should not be normative i.e. it should not lead to predetermined results but should uncover what is in the music itself. Whilst many non-functional chords are totally diatonic, it is important to mention chromatic harmonies as these are frequently deployed as non-structural filling-in chords which decorate the underlying harmony. This is because chromatic stepwise movements lend themselves easily to the production of chromatic auxiliary notes, passing notes and appoggiaturas. These add variety and interest without causing the ear to lose track of the underlying harmony or tonality. Chords that do not contain a perfect 4th or 5th do not enable the ear to easily determine a root for the chord. Consequently, these chords are normally used as non-functional chords. These include the diminished 7th chord, the augmented 5th chord and the various forms of the augmented 6th chord*. These chords are nonfunctional due to their very nature. Other non-functional chords are note combinations that in other circumstances would be heard as functional chords. Simple triads and 7th chords can be used as nonfunctional chords when they arise from voice leading movement such as passing notes, auxiliary notes or appoggiaturas. The latter types are ones that can lead to misinterpretation as they are easy to mistake as functional harmony. * One form of the augmented 6th chord (the German 6th chord) does contain a perfect fifth, but due to the way the augmented 6th interval resolves outwards, the chord behaves like a non-functional chord except where it is reinterpreted and resolves like a dominant 7th chord in a new key. See Glossary: augmented 6th chord and Chapter 7: Modulation via Chromatic Chords and also chromaticism in the Voice Leading Appendix.

There are three types of non-functional chord that could be confused with functional chords: The Auxiliary Chord, The Passing Chord and The Appoggiatura Chord. The reason for giving these chords special names is not because they have a special significance but because they are capable of being confused with functional chords. In reality, they arise out of voice leading just as other surface voice leading patterns (passing notes, auxiliary notes etc) do. The first type was introduced in the last chapter as it is important in forming static harmony patterns. The second type occurs frequently and in many forms. The third type is significant mainly as a device for elaborating the cadence by extending the dominant (and sometimes the tonic) harmony. Before we explore each type in turn it may be useful to summarise how we can distinguish between functional and non-functional chords. By far the most important and defining factor is the first rule i.e. That non-functional chords are made up from auxiliary notes, passing notes or appoggiaturas (i.e. voice leading patterns) whereas functional chords are not. However the additional guidelines may also be helpful in correct identification. FUNCTIONAL CHORDS: The components of the chord do not arise as a result of auxiliary notes, passing notes or appoggiaturas. Other factors that may help in identification: Almost always a major or minor triad (with or without an added 7th 9th etc.) Usually on stronger beats than associated non-functional chords Likely to be in a stronger inversion than associated non-functional chords Likely to be more consonant than non-functional chords Except for alterations to the 3rd of the chord (and in cycles of 5ths), are not usually chromatic. NON-FUNCTIONAL CHORDS: The components of the chord arise as a result of auxiliary notes, passing notes or appoggiaturas. Other factors that may help in identification:

Less likely to be a major or minor triad (with or without an added 7th 9th etc.) Usually on weaker beats than associated functional chords Likely to be in a weaker inversion than associated functional chords Likely to be less consonant than functional chords Are often chromatic.

CHAPTER 3 (PART 2) NON-FUNCTIONAL CHORDS

Auxiliary Chords Auxiliary chords are formed by the stepwise movement (up or down) of one or more of the voices away from a harmony note in one chord to form a new chord. The voice(s) then return to the originals note(s) to re-form the original harmony. Normally the auxiliary chord is made up solely of notes from the original chord plus notes involved in the auxiliary movement. In this case they arise totally out of voice leading. (But see note below on auxiliary chords in root position). These auxiliary chords are non-functional whereas the tonic chords surrounding them are functional. This is because the auxiliary chord merely elaborates the main functional chord, its purpose being to prolong the functional harmony. Auxiliary chords are used extensively to prolong the tonic harmony in static harmony as explained in Chapter 2. They can also be used to extend the dominant to form a dominant prolongation. (See Chapter 5). Sometimes auxiliary chords can be used to decorate individual chords in dynamic harmony especially where this is slow moving but this is not as common. The auxiliary chord is named by analogy with the auxiliary note. The following example contains auxiliary notes marked with an "A":

The short duration of the auxiliary note does not create a feeling of a change in the harmony. An auxiliary chord, is an extension of the auxiliary note such that the duration of the auxiliary note and the way the note sounds in conjunction with the other notes of the chord, creates a sense of a change in harmony. This type of chord has its origins in 16th century polyphony. See Voice Leading Appendix: Auxiliary Notes and Linear Progressions for more details. Using the analytical symbols introduced earlier, the following harmonic outlines indicate some of the possible auxiliary chords within the diatonic major scale:

White headed notes are components of the functional chords and the black headed notes are the result of voice leading. The letter "A" indicates an auxiliary note. The examples marked a) are not very common (at least in the inversions shown) as they generate the secondary triads vi and iii. I've shown these in lower case letters to hightlight the fact that they are minor. The examples marked b) are very common since they generate the primary triads IV and V by the simultaneous auxiliary movement of two voices. The following example includes both chords of b) and also an example of the second of c), the V7 chord.

In bar 2, the lower C rises to D and returns, the higher C falls to B and returns, and the E rises to F and back. These three auxiliary notes (shown as "A") create a dominant 7th auxiliary chord. In bar 3 the E rises to F and returns to the E whilst the G rises to A and returns to G. The C major chord is thus transformed temporarily to an F major auxiliary chord. In bar 4 the E and C descend to D and B and return to E and C thus briefly creating an auxiliary dominant G chord. The melodic line in bar 4 also contains an F which forms a 7th to the dominant chord, but in this case as a descending passing note which is further elaborated by a short auxiliary note E. For simplicity this is shown an octave lower in the outline. The passing note is shown as "P". Similar auxiliary chords may be drawn up for the minor key, In this case, the 7th degree of the scale is usually sharpened to form the major chord V. The following figure shows some of the common possibilities involving chromatic harmonies:

. The examples a) and b) involve movement in one direction only. a) contains two auxiliary notes: one diatonic, E rises to F and returns to E, and one chromatic: G rises to A-flat and returns to G. The auxiliary chord formed is the minor subdominant chord which occurs naturally in the minor key. In b) all three notes of the tonic triad rise a semitone and then return to the original notes. This chord is usually referred to as the Neapolitan 6th chord and is usually deployed in first inversion to avoid the parallel 5ths that would otherwise arise. The next three auxiliary chords in c) (i), (ii), (iii) are the three possible diminished 7th chords. I've shown all three for completeness and to introduce the terminology to be used for each of these. See below. (i) and (ii) are common auxiliary formations, but (iii) is more usually deployed as a passing chord between I and II as the C - B-flat movement has a tendency to continue downward to A rather than to return to the C. (see next section - passing chords). The example c) (ii) could be shown with a D# instead of the Eb. Please see note below on naming of chromatic chords.

Example d) is an example of the "German" version of the augmented 6th chord, created by three chromatic auxiliary notes all moving a semitone and back. The Eb could also be shown as a D# auxiliary note but is usually shown as Eb in this situation. Auxiliary Chords in Root Position Sometimes auxiliary chords are used in root position (could be any triadic chord). In this situation, they are not composed entirely of voice leading (notes of the main chord plus auxiliary notes) because of the way the bass moves from one root to another and sometimes because of other voice movements. These chords will nevertheless be referred to as auxiliary chords, by analogy with the auxiliary note, because of the way the chord returns to its preceding chord and because these root position chords are also used to create static harmony. In this situation, it is possible to have, in addition, passing chords that fill in between the main chord and the auxiliary chord. So there are really two types of auxiliary chord: those that are in root position and are capable of further elaboration are really functional chords and those that arise totally out of surface voice leading which are non-functional. In either case, they can be used to create static harmony. The distinction between these two types of auxiliary chords does not normally create too much difficulty because both types are used in similar ways. In different styles of music, many different chords (diatonic and chromatic) have been used as auxiliary chords to create static harmony and in this way, the choice of auxiliary chords contributes significantly to the style and mood of the music in particular as this occurs at the start of the musical phrase. Please refer to Chapter 2 and the Full Analysis Chapter for further examples.

Description of Chromatic Chords

This is an appropriate point to introduce the terminology to be used in this book for chromatic harmonies, in particular the diminished seventh chord. The following figure demonstrates some of the possible diminished 7th chords in C major. Most books treat these as borrowed from related or unrelated minor keys or as dominant substitute chords. However as neither of these designations accurately describes the true function of the chords, I will introduce an alternative, simpler, terminology which acknowledges the voice leading rather than harmonic function of the these chords. I will use the terms: tonic leading, dominant leading and supertonic leading to describe the three possibilities regardless of the particular spelling of the chord. The tonic leading diminished seventh chord is named

in this way because it contains the leading note which leads to the tonic, the dominant leading diminished seventh chord contains the sharpened 4th degree of the scale which leads to the dominant and the supertonic leading diminished seventh chord, because it contains the sharpened tonic which leads to the supertonic note. This terminology makes identification and discussion easier and highlights the voice leading function of these chords.

In the following example, Tchaikovsky uses the tonic leading diminished 7th chord as an auxiliary chord in the static harmony in Valse Des Fleur. The static nature of the harmony is emphasised by the use of a tonic pedal which is sustained below the diminished 7th chord in spite of the dissonance between the D, C# and E.

This chord creates a colourful effect that represents the flowers in the title and is therefore a further example that demonstrates that the type of auxiliary chord used in static harmony is an indicator of the style or mood of the music. There will be further examples in the full book. There is also a description of the auxiliary note and auxiliary chords in Chapter 2 and the Voice Leading Appendix.

CHAPTER 3 (PART 3) NON-FUNCTIONAL CHORDS

Passing Chords Passing chords are formed by the stepwise movement of one or more voices from a harmony note in one chord to form an intermediate chord or chords on the way to becoming a harmony note in another chord. The stepwise movement may be a filling in by one note or may be in multiple steps. If the filling in is by multiple steps then I will refer to this as a linear progression. (See Chapter 4.) One or more voices may be involved in similar or contrary motion. This type of chord has its origins in 16th century polyphony. See the Voice Leading Appendix: Arpeggiation and Passing Notes for more details. The reason for giving these chords a special name is not because they have a special significance but because they are capable of being confused with genuine functional chords. In reality, they arise out of voice leading movements just as other surface voice leading patterns do. For a chord to be a passing chord it must normally be made up solely of notes retained from the preceding chord plus linear moving notes. The one exemption to this is that chromatic auxiliary notes are sometimes used in addition to the passing notes. This is because of the way that voice leading patterns can be combined. See Voice Leading Patterns Combined. The passing chords so formed are thus non-functional and the surrounding chords on which the movement starts and ends are functional chords. Passing chords are used in both static and dynamic harmony. The passing chord is named by analogy with the passing note. The following example contains a passing note marked with a "P":

The passing note fills in the gap between notes of adjacent chords. It sounds whilst at least one note of the proceeding chord is retained. The short duration and nature of the passing note does not create a feeling of a change of harmony. The passing note usually forms a discord with other notes of the chord, as it does here. Note: I've shown chord ii in lower case letters to highlight the fact that it is a minor chord. The passing chord is an extension of the passing note such that the duration of the passing note(s) and the way the note(s) sound, in conjunction with other notes of the chord, creates a sense of a change in harmony. Using the analytical symbols introduced earlier, the following harmonic outlines indicate some of the possibilities within the diatonic major scale:

.

All the passing chords in the figure above are made up of two types of notes: 1. notes which are retained from the preceding chord (shown here as repeated white note heads) and 2. notes that take part in the stepwise movement (shown as black note heads annotated as "P") Normally, if other notes are involved, the chord is not a passing chord. The one exemption to this is that chromatic auxiliary notes are sometimes used. These are introduced below. The curved brackets are used to indicate that the chords within them are passing chords. The lower case letters indicate that the chord is minor.

The examples moving from chord I to chord IV are common in both static and dynamic harmony and the examples moving form chord I to chord VI are common in dynamic harmony, in which case the progression is a β (beta) chord progression. All the examples above start with chord I. However, the patterns may be transposed so that they start on other scale steps. For example, I ( iii ) IV could be transposed to ii ( IV ) V etc. It is not the actual scale steps involved that matter but the succession of scale steps. Similar patterns may also be derived for the minor key. The following is an example of a) (i):

The white note heads indicate notes from functional chords and the black note heads indicate the passing notes involved in voice leading. The note combination highlighted by an * appears at first sight to be a chord iii in root position. However, the chord iii arises as a result of a passing note in the melody between chord I and chord IV. The F# is a stepwise filling in note between the G in chord I and the E in chord IV. The bass note B arises as an arpeggiation of the G major chord in the bass. As the chord iii is the result of a passing note and an arpeggiation, it will be referred to as a passing chord. The chord iii is thus the result of a voice leading movement rather than an harmonic movement. As this is a passing chord I've shown the iii in round brackets in this outline. I've shown the bass arpeggiation with a slur to show the two notes belong to the same structural chord. I've shown the descending passing note connected to the notes it fills in between with stems and a beam to highlight

this passing motion because of its particular interest here. In this example, I've also followed the convention that I will follow in the full analysis chapter, that is that I have not shown the notes repeated form the preceding chord as new white notes in the passing chord. The assumption is that where these notes do not move they are still in force whilst the bass arpeggiates and the melody moves to the passing note. The ascending passing note between E and G, I've just shown as "P". This descending passing note pattern also occurs frequently with the passing note in the bass. In this example, it is fairly easy to see the voice leading nature of the passing chord. However, it is not always so easy to establish which chords in a progression arise from voice leading and which are harmonic. Chords that at first sight appear to be functional may arise as the result of arpeggios, auxiliary notes, passing notes or appoggiaturas. For the harmony and syntactic structures to be correctly understood it is necessary to correctly identify and separate these non-functional chords from the underlying progression. The following is an example of b) (ii) This example has a slower harmonic rhythm:

So far, we have only considered diatonic passing chords. However, the number of possibilities for chromatic passing notes is much greater. Any two notes separated by a tone in two successive

functional chords can be elaborated by a stepwise chromatic filling in note. For example, C# can fill in the gap between C and D. Chromatic passing notes are even possible between two notes a minor third apart. For example, the space between the descending C to A interval, in C major, can be filled in by a B-flat in place of the diatonic B-natural. When you consider that these chromatic notes can be combined in many ways, the number of possibilities is enormous. The resulting chromatic harmonies add variety and interest to the underlying diatonic harmonies but do not usually imply a change in key. The following table shows single voice only movements:

The following is an example of (ii). The augmented 5th chord arises from the filling in of the interval between chord I and chord IV:

Note: There is a further description of the passing note and passing chords in the Voice Leading Appendix.

CHAPTER 3 (PART 4) NON-FUNCTIONAL CHORDS

Appoggiatura Chords The appoggiatura chord is named by analogy with the appoggiatura note. An appoggiatura is a note, not normally part of a chord, which displaces a normal note of a chord. The appoggiatura resolves onto the displaced note whilst the chord is still sounding. An appoggiatura, usually (but not always) creates a dissonance with the normal notes of the chord. More than one appoggiatura may be deployed in a chord concurrently. The following example contains appoggiaturas as indicated at *1 and at 2*:

At *1 in bar 10, the two appoggiaturas form discords with the normal notes of the chord and then resolve onto consonant notes of the chord. The C appoggiatura is a compound ninth discord against the B-flat bass and resolves onto a B-flat. This is shown as 9 - 8 in the figured bass under the harmonic outline. The E-flat appoggiatura is a dissonant 7th above the F of the chord and a 4th above the bass. This resolves onto the consonant D. This is shown as 4 -3 in the figured bass.

An appoggiatura note does not create a sense of a change in harmony. However, an appoggiatura chord is an extension of the appoggiatura such that the the way the notes sound in conjunction with the other notes of the chord create an impression of a change in harmony. Appoggiatura chords are non-functional and the chords onto which they resolve are functional. This is because appoggiatura chords merely elaborate the functional harmony. Their purpose is to prolong the functional chord. Appoggiatura chords are used most commonly to decorate and extend the cadence. The reason for giving these chords a special name is because they are capable of being confused with genuine functional chords. In reality, they arise out of voice leading movements just as other surface voice leading patterns do. At *2 in bar 9 (in the above example) the two appoggiaturas: B-flat and D take over from the normal notes of the chord (A and C) and here form a new chord - the tonic chord in second inversion. This is normally referred to as the cadential 6 4 chord because the upper notes are a (compound) 6th and 4th above the bass of the dominant chord of the cadence. This is the most common type of appoggiatura chord. The appoggiatura chord is shown here as black note heads with a stem. I've shown them this way because cadential 6 4 chords are frequently elaborated by further levels of voice leading and this will enable us to distinguish the levels. See Voice Leading Patterns Combined in the Voice Leading Appendix for more on this. Note that in the example above, the appoggiatura chord in bar 9. is of shorter duration than the appoggiatura notes in bar 10. Duration is not the main consideration for this type of voice leading elaboration. There are three main types of the appoggiatura chord as indicated in the following harmonic outlines: These are all mostly associated with the elaboration of cadential dominant and tonic chords (but not exclusively). They are used extensively as means of emphasising that the chords are part of the cadence.

The chord marked as *2 in the example above is an example of Figure 7 a). Cadential 6 4 chords, with or without further elaboration are very common and the reader will find further examples very easily. Examples of the appoggiatura chord b) are not as common as the cadential 6 4. However, they are are sometimes used to decorate a dominant seventh chord at the cadence or in a chord progression or as a melodic device. In the following strong chord progression the Aflat decorates the dominant 7th chord at bar 112 to form a temporary diminished 7th appoggiatura chord:

This same chord progression can also be seen in Beethoven: Pathetique Sonata: Grave, bars 7 to 9 and in the first prelude of Bach's 48 Preludes and Fugues. It is important at this stage to emphasis the difference between a passing chord and an appoggiatura chord. A passing chord is made up of passing notes plus notes from the preceding chord. An appoggiatura chord is made up of one or more appoggiaturas plus notes from the following chord. In the last example, the A-flat is an appoggiatura and the remaining notes are notes from the following (G7) chord. The passing chord moves away from a chord and the appoggiatura chord leads into and decorates the following chord. The following is an example of c) in which the appoggiatura chord decorates the cadential tonic chord. Note that the appoggiatura chord appears in root position (if we take the lowest note of of the arpeggiated bass line) suggesting its status as an independent chord. It is, nevertheless made up of two appoggiaturas plus notes from the following tonic chord and is consequently a non-functional chord: The downward movement of one of the appoggiaturas is further elaborated by a chromatic passing note as indicated in the harmonic outline. This highlights the reason for showing the appoggiatura chord notes with stems as explained above.

This progression is of particular interest to readers studying harmony in popular music as it forms the basis of the standard cadential pattern for the 12 bar blues progression. This normally has the 7th added to each of the chords as follows but the chord progression is the same: V 7 - IV 7 - I 7 For more information on this then please refer to Appendix A: The Blues Progression Puccini's aria Nessun Dorma ends with the same cadential pattern, showing the influence of the blues on this early 20th century piece. Note: There is more information on the appoggiatura and appoggiatura chords in the Voice Leading Appendix.

CHAPTER 4 LINEAR PROGRESSIONS Where a chord progression arises out of a step by step movement in one or more voices rather than by root progression, I will refer to these progressions as 'linear progressions'. Those readers who are familiar with Schenker's theory should note that the use of the term 'linear progression' in this book is similar to, but not exactly the same as that by Schenker. In this book, the term is used more in line with 16th century polyphony and the traditional rules of voice leading, rather than in the extended way used by Schenker. By limiting its use in this way, the relationship between root progressions and voice leading can be more clearly described than in pure Schenkerian theory. In the last chapter, the passing chords were created by passing notes in one or more voices resulting in a single chord filling in between two functional chords. An important extension of this pattern is a series of chords created by a step by step movement in one or more voices. I will refer to this as a linear progression. The succession of filling in chords is neither recognisable as static harmony nor as dynamic harmony. This does not mean, however, that the linear progression is a third type of movement. This is because linear progressions are always incorporated within static or dynamic patterns. The chord succession results out of the linear movement of one or more voices rather than a root movement. A linear progression may be either diatonic or chromatic or a mixture of both and may involve more than one voice in parallel motion or in contrary motion. Where there are concurrent linear progressions these may sometimes move at different rates. This type of movement has its origins in 16th century polyphony. (See Auxiliary Notes and Linear Progressions in the Voice Leading Appendix) The reason for giving this type of movement a special name is not because it has a special significance but because it is capable of being confused with a genuine functional root progression. In reality, it arises out of voice leading movement just as other surface voice leading patterns do. The only real difference with other types of voice leading patterns is that linear progressions can operate over a longer duration. The stepwise movement is always contiguous. If there is a break in the step wise movement then the progression is not a linear progression. In general, the same rules as for passing chords are apparent: The passing chords in the linear progression are made up mainly (if not completely) of notes retained from the starting chord and linear moving notes. Occasionally, chromatic auxiliary notes are

also deployed. This is because of the way that voice leading patterns can be combined. See Combined Species.

Linear Progressions in Static Harmony Linear progressions in static harmony can link successive tonic chords or link the tonic chord to an auxiliary chord involved in the static harmony, in which case the auxiliary chord behaves as a functional chord and is normally in root position. The following example contains just about the simplest kind of linear progression possible. It is totally diatonic, it is created by a linear movement between two successive tonic chords and is not extended by any further elaboration other than surface arpeggios and passing notes.

It may seam at first sight that this is a I - V - IV - I progression but on further examination it is clear that the succession is driven by a linear descending bass pattern: D - C# - B - A, linking the D in the tonic chord in the upbeat bar to the A in the tonic chord in bar 2. As well as this linear movement there is a parallel downward stepwise movement: F# - E - D and also: A - G - F#. Although, neither of these linear movements stays in the same voice and both are

effectively just passing note patterns as there is only one note between successive structural notes. Note that the common properties normally observed in linear progressions are present: The chords involved in the linear progression are made up of the notes of the starting chord and notes which are moving (i.e. taking part in the linear progressions). Hence, the A (first beat, bar 1) and the D (first beat bar 2) are retained as starting chord harmonies against the other notes that are involved in the movement. This is a voice leading movement rather than a chord progression. The static harmony then continues for several bars. The harmonic outline shows the structural notes as white note heads and the voice leading filling in notes as black note heads. The beam is used to connect the notes involved in the linear movement. Slurs are used to connect notes arpeggiated within the structural tonic chord. The two passing chords created by the linear progression are shown in brackets to highlight the fact that they are not structural chords. See Voice Leading Appendix. Chromatic linear progressions are more common than diatonic linear progressions as there are more possibilities. Following is an example of a chromatic linear progression within static harmony. Like the previous example, the bass voice descends from the tonic note to the dominant but this time by 5 semitone steps. A middle voice follows the linear progression in parallel minor thirds, whilst a further voice decorates with a chromatic auxiliary note. The minor third, or the compound interval of the minor 10th or its inversion, the major 6th, are the most common intervals for chromatic linear progressions moving in parallel motion. The linear movement is accompanied by notes sustained from the staring chord (A minor): E and A, as is normal for linear progressions. In this instance, the harmonic movement is from Chord I to chord V. Note: This piece is in D minor (hence the D minor key signature) but this section is in A minor.

At bar 26, in the same composition, Mozart employs a combination of diatonic and chromatic linear progressions in contrary motion. There are three linear progressions in all: two rising in parallel thirds and one descending. In spite of this complexity the harmonies produced make perfect sense. However, it is important to note that the preparation and resolution of the discords are governed here by the rules that apply to linear progressions rather than the rules that would normally apply to structural chords. This fact underscores the voice leading nature of this and other voice leading progressions. The progression is again within static harmony and starts and ends on the tonic chord.

The descending line is in semitones apart from one tone (from G to F) and the ascending scales are diatonic apart from an augmented 2nd from F to G#.

Linear Progressions in Dynamic Harmony The following example includes a linear progression moving chromatically from the dominant chord to the tonic. The underlying harmony is dynamic as the dominant is preceded by chord II and the tonic followed by chord IV. The purpose of the linear progression is to temporarily delay and extend the movement of the dynamic harmony. Whilst diatonic linear progressions are deployed most frequently in the bass and sometimes also in the melody, chromatic linear progressions are sometimes used in a middle voice, as here. The linear progression is driven by the the line which descends: B , Bb , A - Ab - G in the tenor voice . The G from the starting chord is retained in bar 12 in the bass but then forms a passing note F which descends to the E in the ending chord. It involves: two diminished 7th chords (one supertonic leading; one tonic leading) and one triad (the supertonic). The normal rules about linear progressions are followed. The chords in bars 13 and 14 retain the D form the starting chord even though this is temporarily displaced in bar 12 by the C# and E auxiliary notes.

Linear Progressions Elaborating Dominant Harmony The third area where linear progressions are important is in the prolongation of the dominant chord. This is similar to the use of linear progressions in tonic static harmony. However, as we have not yet examined the prolongation of the dominant harmony, I will leave this subject until Chapter 5. There is also a description of the linear progression in the Voice Leading Appendix at: Auxiliary Notes and Linear Progressions and Chromatic Linear Progressions. CHAPTER 5 (PART 1) EXTENSIONS WITHIN THE BASIC STRUCTURE

Introduction All harmonic structures in tonal music derive from the basic phrase structure as explained in Chapter 1. The basic syntactic structure can be extended in various ways, just as sentence structures in language can be. In this chapter we will consider extensions within the basic phrase structure and in the next chapter extensions outside of the basic structure. There are three types of extension possible within the basic musical phrase structure: 1. The dominant chord of the cadence can be prolonged by static harmony in a similar way to the way the tonic chord is prolonged in the static harmony in the opening section. This has the effect of extending the cadence. I will refer to this as a dominant prolongation. This extension is very common. 2. The tonic chord of the cadence can be prolonged by static harmony. This has the effect of delaying the end of the phrase. This I will refer to as a static coda. This is also a common extension to the basic structure. 3. The opening section, can be subdivided into two sections. In this case, the initial static harmony is preceded by a dynamic element that I will refer to as a dynamic introduction. This is a kind of extended upbeat or lead-in to the static harmony. This occurs less frequently than the previous two types but is an important way of extending the opening section harmony. The following diagram shows all three types of extension in place in the syntactic structure. They may be present individually or in any combination. This diagram shows the most complete form of the syntactic structure without external extensions:

CHAPTER 5 (PART 2) EXTENSIONS WITHIN THE BASIC STRUCTURE

The Dominant Prolongation The dominant prolongation is the most common type of internal extension to the basic syntactic structure. Here, the dominant chord of the cadence is prolonged by the use of static harmony in a similar way to the way the tonic chord is prolonged in the opening section of the musical phrase. All the techniques explained in the previous chapters for prolonging the tonic can be applied to the dominant chord. These are:

• • • • •

Combinations of voice leading elaborations. Static harmony deploying auxiliary chords that fill in between dominant chords The use of a dominant pedal note underscoring the static harmony. The use of passing chords filling in between the dominant and auxiliary chords. The use of linear progressions filling in between the dominant and auxiliary chords or successive dominants.

In addition the dominant cadential harmony may be extended in two ways not usually deployed in opening section static harmony: • •

The cadential 6 4 (see Chapter 3 (part 4)) with or without further elaboration. Cadenzas which are long melodic elaborations used at the ends of some movements

Dominant prolongations are very common and are used in some form or other in most pieces of music. They vary from short elaborations just deploying a cadential 6 4 chord to long prolongations and cadenzas that extend over many bars. The more structurally important the position in the music, the longer and more elaborate the dominant prolongation may be. Dominant chords involved in the dominant prolongations often contain added 7ths and sometimes added 9ths. Even short cadential dominant chords normally contain some kind of elaboration such as a cadential 6 4 elaboration or a suspension to highlight the fact that it is the dominant chord of the cadence. Dominant prolongations are prolongations of the cadential dominant chord and form a syntactic function in the phrase. Non-cadential dominant chords are not normally prolonged in this way. The following figure shows the form of a complete phrase extended by a dominant prolongation: a) The dominant Prolongation

When considering the structure of the musical phrase (static harmony, dynamic harmony, cadence) bear in mind that it is important to distinguish between tonic static harmony and dominant static harmony. The first starts off the phrase and establishes the key. The dominant static harmony, if it exists in the phrase, is part of the cadence and delays the end of the phrase and so each is anchored in the phrase in different positions in relation to the cadence. Dominant prolongations can be distinguished from tonic prolongations by a combination of context (position in relation to the cadence) and the fact that dominant prolongations are likely to have 7ths in the main structural chords (i.e. dominant 7th chords) whereas in tonic prolongations, the 7ths (if present) are more likely to be on the auxiliary chords. (However, sometimes the tonic takes on a minor 7th when moving to an auxiliary chord IV. See also section on the blues). The following eight bar dominant prolongation from the Bach: First Prelude (see below) is based on a simple oscillation between dominant and tonic. The dominant and tonic chords here exchange roles in comparison with their roles in an opening section static harmony. That is to say, in this dominant prolongation the tonic chord acts as an auxiliary chord to the repeated occurrences of the dominant chord which is being prolonged. The tonic auxiliary chords are shown in square brackets in the harmonic outline. At bar 27 to 29 the movement from chord V to auxiliary chord I is further elaborated by chromatic passing notes in parallel 10ths. (D moves to E-flat and then E-natural in the tenor voice and F moves to F# and then G in the soprano voice). The chromatic passing notes, along with two auxiliary notes, result in a dominant leading diminished 7th chord in bar 28. At bars 26 and 30 the harmony is further elaborated by suspensions. These suspensions are shown as black notes with stems in the harmonic outline. The whole prolongation is underscored and delimited by a dominant pedal.

The dominant prolongation shown above is preceded by 23 bars of dynamic harmony and followed by a 4 bar static coda (see later). This means that the whole prelude is syntactically in the form of a closing section only. The following example from Elgar: Enigma Variations shows a dominant prolongation in context. It is preceded by I - II - dynamic harmony and followed by the tonic chord. As in the previous example, the dominant prolongation uses chord I as the auxiliary chord and the prolongation is underpinned by a dominant pedal. As can be seen from the harmonic outline, the dominant is prolonged by a combination of:

• • • •

an auxiliary chord I in bar 10, in second inversion (auxiliary 6 4) arpeggiation of the dominant chord along with passing notes in bars 9 and 10, shown by slurs and black note heads a passing 7th, in the tenor voice in bar 9 and in the top voice in bar 10, each highlighted with stems and beams. a passing 9th in the last beat of bar 9, in parallel 10ths with the 7th in the tenor.

These are shown in the harmonic outline. The horizontal square bracket indicates the extent of the dominant prolongation.

The dominant cadential harmony may be extended in two ways not usually deployed in opening section static harmony. These are the cadential 6 4 appoggiatura chord (discussed in chapter 3 (part 4)) and the cadenza. The cadenza can be anything from a simple short elaboration of the dominant chord to many bars of improvisational music. When these are used in combination, the elaboration starts

during the 6 4 harmony and continues into the dominant harmony. Whatever the nature and length of the cadenza, the function is to prolong the dominant cadential harmony, thus delaying the completion of the cadence whilst at the same time highlighting the end of the phrase, section or movement. The following example illustrates a brief cadenza that elaborates the underlying cadential 6 4 and dominant harmony:

For a full phrase example containing a dominant prolongation which extends over 7 whole bars see Appendix B of the Thesis section of this site which includes further explanation of how to delimit the phrase boundaries. You can see the full explanation at: details of the analysis.

CHAPTER 5 (PART 3) EXTENSIONS WITHIN THE BASIC STRUCTURE

The Static Coda The tonic chord of the cadence can also be prolonged by the use of static harmony. This has the effect of extending the end of the musical phrase. This I will refer to this as a static coda. All the techniques explained in the previous chapters for prolonging the tonic in the opening section static harmony can be applied to the prolongation of the tonic chord in the cadence. These are: • • • • •

Any combination of voice leading elaborations. Static harmony deploying a variety of auxiliary chords, interspersed between tonic chords. The use of a tonic pedal note underscoring the static harmony. The use of passing chords filling in between the tonic and auxiliary chords. The use of linear progressions filling in between the tonic and auxiliary chords or successive tonic chords.

Whilst similar to the static harmony in the opening section of the syntactic structure, in practice, static codas are often simple oscillations such as I [ V ] I or I [ IV ] I. Static Codas are very common but occur most frequently at the ends of main sections in a piece of music. The following figure shows the form of a complete phrase extended by a static coda:

b) The Static Coda

The static coda is similar to the static harmony of the opening section of the standard phrase structure but is part of the cadence and therefore performs a different function. It often reprises melodic ideas from opening section static harmony. As for opening section static harmony, in the static coda the tonic sometimes takes on a minor 7th when moving to an auxiliary chord IV. In the following example from the Mozart: Sonata K545, the final chord I is prolonged by a simple I [ V ] I chord oscillation. This is a common type of static coda, especially in the classical period.

Following is a full description of this phrase:

The figure above shows the syntactic structure for this phrase. It forms the repeat of the second subject in the recapitulation from the first movement of the Sonata. 1. Bars 59. To 63: Opening Section static harmony: I [ V ] I, repeated. The extent of the static harmony is indicated by the horizontal bracket. 2. Bars 63 to 68: Closing Section dynamic harmony. This completes a full cycle of 7 α progressions followed by I - II - V (one γ and one α progression) The II to V ( D minor to G

dominant) (α) progression is elaborated by a diminished 7th chromatic passing chord as indicated in the analysis. The chromatic movement is F - F # - G in parallel with D - E-flat E-natural. 3. Bars 69 and 70: The dominant chord is prolonged by a full bar cadential 6 4 appoggiatura chord. We could indicate this as a (short) dominant prolongation in the chart, in this example, the cadential 6 4 chord is indicated by a horizontal line preceding the dominant chord onto which it resolves.. 4. Bars 71 to 73: Cadential chord I is prolonged by a three bar static coda made up of I [ V ] I static harmony repeated. The extent of the Static Coda is indicated by the horizontal bracket. See the thesis for how to determine the phrase boundaries. Static codas based on I [ IV ] I static harmony are also very common, especially in church music. As for the opening section static harmony, auxiliary chord V suggests secular music and IV suggests sacred music. A good example of this is the last few bars of Handel: Hallelujah Chorus. This example contains a brief dominant prolongation of one bar duration followed by a static coda of 7 bars involving 8 repeats of the I [ IV ] I pattern.

The IV to I chord succession (repeated 8 times in this example) is sometimes referred to as a plagal or amen cadence. However, this is not in reality a cadence, merely the result of the I [IV] I static harmony prolonging the cadential tonic chord. The true cadence in this example is the movement from the last chord of the brief dominant prolongation in bar 87 to the first chord of the static coda starting in bar 88. A true plagal cadence only occurs when the syntactic V - I is replaced by IV - I. To avoid any confusion it should be made clear that there is no relationship between a static coda and a formal coda. A static coda is a syntactic element and performs a syntactic function in a musical phrase. The only purpose of the expression static coda is to explain

the syntax of the musical phrase. A formal coda may contain a whole syntactic phrase or more. CHAPTER 5 (PART 4) EXTENSIONS WITHIN THE BASIC STRUCTURE

The Dynamic Introduction Sometimes the opening section of the musical phrase is subdivided into two syntactic elements. The initial static harmony is then preceded by a dynamic chord progression that I will refer to as a dynamic introduction. This is a kind of extended upbeat or lead-in to the static harmony. It can be present in the first phrase of a piece of music or any subsequent phrase. This type of phrase extension is less common than the previous two types explained above. All the techniques explained in chapter 2 for creating dynamic harmony can be applied. These are: • • • •

The use of strong α, β, and γ chord progressions, The addition of essential sevenths and sharpening of minor 3rds to strengthen the harmonic movement. The use of passing notes and passing chords filling in between functional chords. The use of linear progressions filling in between functional chords.

Dynamic introductions end with a dominant chord that moves to the initial tonic chord of the static harmony. The final dominant chord can be extended into a dominant prolongation. Thus the form of dynamic introduction is similar to a structure of a complete closing section but with the final tonic chord overlapping with the first tonic chord of the static harmony. For dynamic harmony at the start of a phrase to be a Dynamic Introduction it must be fully integrated or internal to the phrase. Dynamic harmony may also exist as independent lead-ins to phrases either as introductions or as linking passages. In the latter case the dynamic introduction is an incomplete phrase and is external to the complete phrase. (See Chapter 6.) The following figure shows the form of a complete phrase extended by a dynamic introduction:

The first subject of the Beethoven Piano Sonata, Opus 31 No. 3. starts with a dynamic introduction:

This dynamic introduction is based on a simple II - V - I progression. This is elaborated by a cadential 6 4 appoggiatura chord and a passing dominant leading diminished seventh chord. After an ascending scale passage, the dynamic introduction repeats and the static harmony starts at bar 17 and continues to bar 27 where the

dynamic harmony of the closing section starts. The dynamic introduction belongs to the same phrase as the static harmony in bars 17 to 27 as both syntactic elements contain the similar motivic material (the descending 5th dotted figure) and are both part of the first subject. In this example, the dynamic introduction is an integral part of the syntactic phrase. To avoid any confusion it should be made clear that there is no relationship between a dynamic introduction and a formal introduction. A dynamic introduction is a syntactic element and performs a syntactic function in a musical phrase. The only purpose of the expression dynamic introduction is to explain how the harmony functions in relation to the musical phrase. It can exist at the start of any phrase in a piece of music not necessarily the first phrase. A formal introduction may contain whole syntactic phrases. Sometimes a dynamic introduction may precede a phrase without being integrated within the phrase. This type of external phrase extension will be dealt with in Chapter 6. Demo 3 is an example of a full phrase containing a dynamic introduction although the dynamic introduction here consists of only a single dominant chord extended over two bars. The full book will contain further examples of the dynamic introduction.

CHAPTER 7 (PART 1) MODULATION In this chapter we will consider how modulation works in the context of a theory of chord progressions and syntactic structures. For a description of some basics on modulation, click here.

Modulation by Dynamic Harmony As modulation is a process of moving from one tonal center to another and dynamic harmony is a movement of chord progressions linking one static element to another, dynamic harmony and modulation often go hand in hand. In the first example, we'll consider an instance where a common chord is in evidence and in the second example where the modulation is carried out by a direct movement to the dominant of the new key. Please refer to the basics of modulation section for more details of these methods. The following theme from Haydn's Sonata in D major contains two phrases. The first contains dynamic harmony which modulates from the tonic key to the dominant key and the second phrase contains dynamic harmony which modulates back to the tonic key:

. The first phrase is a complete phrase ending in the dominant key (bars 1 to 8). The modulation to the dominant takes place in the dynamic harmony of the closing section where the progression moves the tonality from the tonic D to the cadence in the dominant key of A major. We can describe the modulation from D major to A major by saying that the B minor chord in bar 6 acts as a common chord (or pivot chord) between the two keys. It would thus function as chord VI in D major and simultaneously as chord II in A major. An alternative interpretation is to say that the modulation is carried out by the dynamic harmony which moves the tonality forward from D major to the A major cadence via the chord progression made up of one β progression and one α progression. The third of the E chord is made major so that it can function correctly as the dominant chord in the cadence. The second phrase is a complete phrase returning to the home tonality. It starts with a dynamic introduction which is responsible for the modulation back to the home key. For this key change, it is not possible to identify a common chord, because, rather than use the B minor chord as a common chord to smooth the movement, Haydn heightens the chromatic effect by using the B7 chord which is not a diatonic chord in either key. A more satisfactory explanation is

that the modulation is facilitated by a chord progression constructed by dynamic harmony made up of one γ and two α progressions, as indicated in the example. The third of the B chord is made major just as any diatonic minor chord can be made major to strengthen the sense of dynamic movement. It creates a 'transient cadence' in E minor but this key is not established as a new tonal base by any static harmony in E minor. In the following example from the development section of the first movement of the Mozart K545 sonata, two static elements are connected by a short dynamic element made up of one γ and one α progression. The G minor static harmony of bars 29 to 31 is thus smoothly joined to the D minor static harmony of bars 33 to 35:

The dynamic harmony is constructed just as it would be if it were non-modulating. The third of the A chord in bar 32 is sharpened just as it might be in non-modulating dynamic harmony but in this case the A chord is the dominant chord in the new key. Again, no diatonic common chord is used. In this instance the movement is direct to the new key's dominant chord. As can be seen from the examples above it is not an individual chord that defines the key but the arrival of the dynamic harmony at a stable tonal position as defined by static harmony or a perfect cadence. Thus, the B7 chord in Example 7.1., at bar 9, does not signify a modulation to E minor since the E minor tonality is not confirmed by static harmony and it is not the end of a phrase. It merely functions as part of the dynamic harmony that carries the

movement forward. The A7 chord at bar 11, in contrast, does signify a modulation to D major since the home key is confirmed by 6 ½ bars of static harmony. A modulation 'direct to the new dominant' is possible for a modulation to any key. This is carried out either by a secondary dominant (a minor or diminished chord converted to a dominant 7th) or via a German augmented 6th chord which is reinterpreted as the dominant 7th chord of the new key. Either method normally takes place within an episode of dynamic harmony. One important example of 'direct to dominant' modulation is the modulation from a minor key to its relative major. In this instance, the chord progression used is a falling second progression. i.e. a γ' progression. This is a frequent key change in the classical and romantic periods and accounts almost exclusively for the use of this progression in dynamic harmony.

. This use of this (otherwise uncommon) progression supports the view that modulation functions as a conscious process whereas syntax is largely subconscious. Please refer to the thesis section for further discussion of this. The book will give more details about 'direct to dominant' modulations. Here we will concentrate on the more common types of modulation.

CHAPTER 7 (PART 2) MODULATION

Modulation via Chromatic Chords German 6th chords can be created on all chromatic and diatonic notes within the scale. As these are the same, enharmonically, as dominant seventh chords, they can be reinterpretation as dominant 7th chords in all keys. However, this is really just a form of "direct to dominant" modulation. A more common method of modulation is for a chromatic chord to move onto the new dominant rather than becoming the dominant itself. The diminished 7th and augmented 6th chords are the chords most commonly used for this purpose. These progressions normally take place within an episode of dynamic harmony. The movement to a new key is thus made by the use of a musical 'pun'. The chord progressions used can be summarised in the following table:

The chromatic chord is moved to as a passing chord from the tonic of the old key and is immediately reinterpreted as dominant leading in the new key. It then moves on as a passing chord to the new dominant chord with or without an intervening cadential 6 4 appoggiatura chord. The diminished seventh chord and augmented 6th chords are the most useful and common ways of making this type of modulation. They act as chromatic pivot chords. Here, the composer is using a 'trick of the trade' by reinterpreting the meaning of a chromatic chord. Consequently, the normal strong root progression between functional chords is broken and the two functional chords may be related by a weak chord progression. The

composer is using a consciously learned process which is overriding the normal subconscious use of strong chord progressions. These progressions are normally used, nevertheless as part of a dynamic harmony episode. Following are two examples:

In this example, bar 51 ends in C minor. The C minor chord is immediately followed by a passing diminished 7th chord which is dominant leading in C minor. This is reinterpreted as dominant leading in the new key of E-flat major. The diminished 7th chord is followed by the B-flat dominant chord of E-flat. This brief dynamic harmony acts as link passage from the first subject in C minor to the second subject in E-flat. The progression from the C minor chord to the B-flat chord would normally be too weak a progression to use in dynamic harmony but the modulation makes the chord progression acceptable. The modulation and harmony support the background syntactic structure.

In this example, the closing section of the phrase has arrived at a perfect cadence in C major. The C major chord moves onto the augmented 6th chord by linear movement. This is immediately reinterpreted as a dominant leading chord in the new key of A minor. The augmented 6th chord is followed by a cadential 6 4 chord and then the E major dominant harmony. This starts off a dominant prolongation that extends for a further 9 bars. The dynamic harmony thus includes a progression from a functional C chord to a functional E chord. This rising third progression would normally be too weak a progression to use in dynamic harmony but the needs of the modulation override the expected strong chord progression. However, the syntactic structures remain clear.

CHAPTER 7 (PART 3) MODULATION

Tonic to Tonic Modulation By far the most common type of modulation is modulation during dynamic harmony as indicated in the last two sections. However, composers occasionally modulate by juxtaposing two keys directly next to each other. This can be by two static harmony elements in different keys joined to form one static harmony element or can be one phrase following another directly in a different key without any dynamic harmony to facilitate the modulation.. The first has its origins in the contrapuntal writing of fugue. In the following fugal example, the need to bring the second voice in at the dominant pitch requires that the initial C minor static harmony be repeated one fifth higher with no intervening dynamic harmony. Thus two static elements are immediately juxtaposed in different keys forming a single static syntactic element. The falling 4th progression from the C minor chord to the G major chord is too weak to be interpreted as dynamic harmony.

When analysing examples of contrapuntal writing, as here, some interpretation is required to determine what harmony is implied by the single or two part writing. The interpretation can often be tested by making a comparison with a similar passage elsewhere in the

piece with fuller part writing. For instance, the interpretation of the third beat as chord IV is supported by the fuller harmonisation later in bar 7. However, whether this beat should be interpreted as auxiliary chord IV or some other auxiliary chord or just plain auxiliary notes does not make any difference. Whatever the implied harmony is, bars 1 - 2 are a static prolongation of the C minor tonic chord. Since the second voice enters with the answer to the fugal subject one fifth higher, static harmony on G starts immediately. At bar 5, the first fugal 'episode' starts. This is a rising sequence based on dynamic harmony using α and β progressions. Following is an example of modulation, 'tonic to tonic' in a noncontrapuntal context:

Here the end of one phrase in C major is immediately followed by a new phrase in the unrelated key of A-flat with no intervening dynamic harmony. The only connection is the common note C.

The full book will contain a further example from Brahms of modulation within static harmony in a non-contrapuntal context.