Harmony
Entry for EPMOW by Philip Tagg
harmony: 1. (general sense) tonal polyphony, i.e. the simultaneous sounding of notes to produce chords and chord sequences; 2. the chordal and accompanimental rather than melodic or contrapuntal aspects of music (cf. counterpoint, melody, accompaniment); 3. the theoretical systematisation and study of 1. and 2.
1 Terminology; 1a History; 1b Definitions; 1.b.i Classical harmony; 1.b.ii Triads and tertial harmony.
2 Classical harmony; 2a. History; 2b Structural traits; 2.b.i Syntax, narrative, ‘function’; 2.b.ii Voice leading, the ionian mode and modulation; 2.b.iii Dissolution of classical harmony; 2c Classical harmony in popular music
3 Non-classical harmony; 3a. Non-directional tertial harmony; 3.a.i Ionian mode and barré; 3.a.ii Tertial modal harmony; 3b Quartal harmony; 3.b.i Structural definition; 3.b.ii History and usage
4 Bibliography
5 Musical references
1 Terminology
1a History
‘Harmony’ derives from Greek’s armonia (= joint or union, hence, sonically, a concord), via Latin’s harmonia (= agreement of sounds, concord or melody). In medieval Europe, harmony initially meant the simultaneous sounding of two notes only (dyads), in much the same way as a backing vocalist in popular music may be described as ‘singing harmonies’ (even though harmony, in the general sense of the term, is more likely to be provided by accompanying instruments). European theorists of the Renaissance extended the notion of harmony to the simultaneous sounding of three notes, thus accommodating the ‘common triad’, with its third as well as the fifth (see chord). Since then the concept of harmony has largely been associated with the chordal practices of music in the Central European tradition of the eighteenth and nineteenth centuries, i.e. with European art music and with styles of popular music relating to that tradition (see 2a, below). More recently the notion of harmony has been popularly applied to any music which sounds in any way chordal to the Western ear, for example, to the vocal polyphony of certain African and Eastern European traditions, or to the polyphonic instrumental practices of some Central and South-East Asian music cultures. In short, whereas popular English-language parlance may qualify as ‘harmony’ such phenomena as a melody plus drone or two voices singing in parallel homophony, conventional musicology would tend to reserve the term for chordal practices relating to the Central European classical tradition of tertial harmony (see 1b and 2, below). However, since popular music encompasses a wider range of tonal polyphonic practices than those conventionally covered by musicology, it is appropriate to qualify any type of tonal polyphony as harmony. This wider meaning of the term makes it possible to speak of a variety of harmonic practices and thus to treat harmonic idiom as one important set of traits distinguishing one style of music from another.
1b Definitions
Two main types of harmony practice are currently used in popular music: classical (see section 2) and modal (3), the latter divisible into the general subcategories tertial (3a) and quartal (3b). Since most writing on harmony deals with procedure inside only one of these categories or subcategories (e.g. classical harmony, chorale harmony, bebop jazz harmony, modal harmony), cardinal problems arise when terms conventionally used with reference to one category of harmony — usually the classical — are applied to a much wider range of practices. Two conceptual areas are in particular need of clarification: [1] classical harmony, [2] triads and tertial harmony.
1.b.i Classical harmony
Classical harmony is so called because it denotes the most common practices of tonal polyphony found in the large and globally influential body of European classical music of the eighteenth and nineteenth centuries. Such harmony is also commonly referred to as ‘triadic’ (see below), ‘diatonic’, ‘functional’, ‘tonal’ (see 2b), etc., but these qualifiers are misleading since they can each be applied to harmonic practices diverging significantly from those of the European art music canon, its immediate precursors and successors. For example, all modal harmony using three-note chords is by definition triadic. It is also diatonic if, as is often the case, its tonal material can be derived from a standard heptatonic scale containing two semitone intervals. Moreover, with the possible exception of ‘atonal’ underscores for horror scenes, all harmonic idioms in popular music are tonal and none is without function. In short, although many popular music styles throughout the world may follow the basic harmonic principles of the European art music tradition (see 2a), ‘classical harmony’ is probably the least inadequate of convenient labels to apply to those principles.
1.b.ii Triads and tertial harmony.
Due to the importance of harmonic narrative in European art music of the eighteenth and nineteenth centuries (see 2.b.ii), harmonic theory has been overwhelmingly dominated by terms suited to the description of that particular type of polyphonic practice. (An example of incongruity arising from that domination is the use of ‘suspended fourth’ in reference to quartal harmony). Similarly, terms applicable to any type of tonal polyphony (e.g. ‘triad’) have become so identified with phenomena peculiar to classical harmony and to its direct successors as to require redefinition when other harmonic idioms are discussed. Moreover, terms from pre-classical music theory have had to be resurrected and redefined to denote modern modal practices, and a few new concepts have been added to the arsenal to denote phenomena for which harmonic theory previously had no name. One such term is ‘quartal harmony’ (see 3b), so called because from the viewpoint of European art music theory its most distinctive trait appears to be chords built on fourths rather than the thirds, this latter trait requiring no accurate descriptor as long as it is considered the norm from which all other practices are seen to diverge. Such a viewpoint is clearly untenable when discussing the variety of harmonic idioms used in popular music and a general structural descriptor for harmony based on thirds becomes essential. Therefore, if harmony characterised by the use of fourths is called quartal, harmony characterised by the use of thirds will be called tertial.
The historical legacy of European classical music theory is so strong that such a common phenomenon as the triad, which occurs in several harmonic idioms, is so named as if no triads existed in modal or quartal harmony. The problem is that if ‘dyad’ (from Greek’s duo/dyo, meaning ‘two’) means, when applied to music, any chord contatining two different notes, then ‘triad’ (triada) should mean any chord containing three different notes, ‘tetrad’ four different notes, ‘pentad’ five, and so on; however, as the expression ‘common triad’ indicates, triads built on the superimposition of two adjoining thirds are literally so common in classical harmony that ‘triadic’ has come to qualify not so much chords containing three different notes as chords built on the superimposition of adjoining thirds. When discussing several harmonic idioms, including those associated with European art music of the classical period, it is necessary to use ‘triad’ and ‘triadic’ only in their original sense. Harmony based on superimposed thirds will therefore be called tertial, not triadic, and ‘triad’ will mean any chord, tertial or not, containing three different notes.
2 Classical harmony
2a. History
The tonal polyphony of European art music is generally regarded as having gradually developed into a form which by the end of the seventeenth century crystallised into a set of practices qualifiable in today’s terms as classical harmony. Its establishment is associated with the transition from contrapuntal (counterpoint) to more homophonic (homophony) types of tonal polyphony in late sixteenth and early seventeenth century Central Europe, and with the adoption of the melody-accompaniment dualism as a basic compositional device in which harmony is generally associated with instrumental or vocal accompaniment (‘background harmony’, ‘backing vocals’, ‘underlying harmonies’). Practically all European art music of the seventeenth, eighteenth and nineteenth centuries uses harmonic practices which also form the basis of tonal polyphony in such common types of popular music as operetta, parlour song, music hall, waltzes, marches, hymns, community songs, national anthems, romantic ballads, Schlager, evergreens, jazz standards, swing, bebop, etc. This broad tradition of harmony also pervades much Country music and film music.
2b Structural traits
2.b.i Syntax, narrative, ‘function’
Classical harmony is generally thought to encompass the sequential (horizontal, linear) as well as simultaneous (vertical) aspects of chords. It is in other words not just a matter of instantaneous sonority or of short, repeated chord sequences. On the contrary, one of its most salient features is the implication of tonal direction of notes within chords (shown as |, «, Æ in ex. 1-8), such horizontal linearity being instrumental in elemental processes of musical narrative (opening, continuation, change, return, closure, etc.). The importance of these syntactic functions in the European art music tradition led influential musicologists like Riemann to qualify its harmony as ‘functional’ (Funktionsharmonik). Although this nomenclature is misleading in that it falsely assumes all other harmonic practices to be without function, its insistence on syntactic function underlines important differences of expression and narrative organisation between European classical harmony and other types of tonal polyphony.
2.b.ii Voice leading, the ionian mode and modulation
In classical harmony dissonances are in principle prepared as suspensions (notes held over from a previous chord) and resolved into consonances (e.g. Csus4 Æ C or Cm, see ex. 1b), while closure is generally assumed to be effectuated by perfect cadence (V-I, e.g. G7 Æ C in C, as in ex. 1a, 1b). In such basic chord progressions the concept of voice leading is paramount in that the perfect fourth in relation to the keynote (e.g. the f of G7 in relation to C, as in ex. 1a) usually descends to the third (e in relation to c) and the major seventh (e.g. the b8 of the G or G7 chord in relation to C, as in ex. 1) usually ascends to the keynote. These rules of voice leading are not arbitrary: they derive from the fact that the most popular array of notes within an octave during the rise and hegemony of the bourgeoisie in Europe was the ionian mode (the standard major scale, e.g. c to c on the white notes of the piano).
The ionian is the only heptatonic diatonic mode to feature at the same time:
w major triads on all perfect intervals of the scale (tonic, fourth and fifth, e.g. C, F and G in C major, see table 1);
w a dominant seventh chord, containing a tritone, on the fifth degree (e.g. G7, containing f8 and b8, in C);
w semitone intervals, one ascending and one descending, which adjoin two of the tonic triad’s three constituent notes, i.e. leading note to tonic (#7 | 8, or b8 | c in C) and subdominant to mediant (4 « 3, or f « e in C).
In simple terms, the ionian mode’s fourth is felt to be pulled down to the major third a semitone below, while its major seventh or leading note is so called because it is heard as leading up to the keynote one semitone above. This simple principle of voice leading endows the ionian mode with its unique qualities of tonal directionality.
Although this directionality is that of the V-I cadence anticlockwise round the circle of fifths (e.g. G7 Æ C), the ionian mode’s semitones can also exert a pull in the opposite direction because the third degree can rise as leading note to the fourth (e.g. e | f in C, ex. 2a) while degree one (or eight) can descend to degree seven (e.g. c « b8, ex. 2b), which also happens to be major third in a simple triad on the dominant. In the first instance (degree 3 | 4) harmonic direction remains subdominantal in that the mediant of the tonic acts as leading note to the subdominant (e | f, ex. 2a); but in the second instance the tonic acts as fourth descending to the mediant of the dominant (c « b8, ex. 2b).
Dominantal direction (clockwise round the circle of fifths, e.g. from C to G) is usually enhanced by raising the tonic’s fourth by one semitone (e.g. f to f# in the D7 chord of ex. 3a), such alteration making for a clearer direction towards the dominant by introducing a second, rising semitone (f# | g) to complement the falling semitone already mentioned (c « b8, ex. 2b, 3a). Raising the fourth by a semitone (e.g. f to f#) moves the tonic of the ionian mode to the dominant, from I to V (e.g. C Æ G), and constitutes a change of key or modulation, especially if a pivot chord is included in the progression (ex. 3a). Conversely, lowering the leading note by half a tone (e.g. from b8 to b$ in the C7 chord of ex. 3b) will introduce a descending semitone (b$ « a8) to underline the subdominantal direction of semitone rising to the keynote of the new ionian mode (e.g. e8 | f, see ex. 2a, 3b). The introduction of accidentals providing ascending or descending leading notes for V-I cadences in other keys than the tonic is an essential characteristic of classical ionian-mode harmony because such chromaticism is a precondition for the type of modulation without which the basic narrative of most European art music would be unthinkable.
2.b.iii Dissolution of classical harmony
It is generally agreed that the harmonic idiom of influential European composers of art music in the late nineteenth and early twentieth centuries (e.g. Wagner) became increasingly chromatic and modulatory to the extent that tonality, in the sense of a home key for a particular piece of new music, was no longer considered by figures like Schönberg as a valid strategy for composition (c.1910). The subsequent development of dodecaphonic and other types of ‘atonal’ music contributed to a widening of the gap between popular and art genres. Jazz harmony underwent a similar process of chromaticisation in the forties with bebop’s increasing use of chords containing two tritones, the rising augmented fourth (#4) or falling flat fifth ($5) providing yet another leading note to tertial harmony’s ascending major seventh and descending fourth (see 7$5, 9$5, etc. under lead sheet chord shorthand, see also 2.b.ii, above).
‘Tonal’ art music reactions to late Romantic chromaticism were offered by impressionism (e.g. Debussy, see ex. 22), neo-classicism (e.g. Hindemith), and influences from folk music (e.g. Bartók). Impressionism often uses chords as sonorities in themselves without the constituent notes of each chord requiring voice leading into those of the next one, while music influenced by neo-classicism and interest in folk music outside Central Europe show clear traits of modality, often using quartal harmony (see §3b, below) which abandons the leading-note fixation of classical tertial harmony in favour of chords based on the fourth and fifth. Similar developments are found in jazz with the change from bebop into modal and ‘free’ jazz forms. All these currents have been influential on some postwar popular music styles.
2c Classical harmony in popular music
2.c.i Main characteristics
Ex. 4. Mendelssohn: Oh! For the Wings of a Dove.
Ex. 5. James L Molloy: Love’s Old Sweet Song (1882).
Tertial harmony of the type used in operetta, parlour song, marches, musicals and in traditional church hymns, etc. largely follows the voice-leading practices of European art music: flat sevenths descend, sharp sevenths rise, voices may move in parallel thirds or sixths but never in parallel octaves or fifths. Dominantal modulation (changing key one step clockwise round the circle of fifths), V-I cadences and inversions of tertial triads and seventh chords are other common features in these types of popular music.
Examples 4 and 5, taken from two highly popular parlour songs, start by establishing the home key (tonic, I) by means of an ionian shuttle (I ´V, bars 1-2 E$ ´B$ in ex. 4; 1-4 F´C in ex. 5), whence they both modulate to the dominant, ex. 4 directly, using an F7 in second inversion (bar 4), ex. 5 via an initial V-I in D minor (bars 5-6), which then acts as pivot for the double dominant (G7) and a V-I cadence in C (bars 7-8). Note also the frequency of dominant seventh chords containing the ionian mode’s two leading notes a tritone apart and how the major third in those chords ascends as leading note to the next chord’s tonic (| in ex. 4-5), while the flat seventh descends to the next chord’s third («). These traits, including sometimes use of tertial chords in their inversions, form the harmonic core of a global idiom of popular music which flourished during the late nineteenth century and the first half of the twentieth century. They can be found, in varying proportions in such popular tunes as Adeste Fideles, Cocorocó, La cucaracha, The Blue Danube, Le déserteur, Giâi phóng mièn nam, Jingle Bells, the German national anthem, L’hirondelle du faubourg, the Internationale, the song of the International Brigade, Liberty Bell, Light Cavalry, the Marseillaise, Milord, Onward Christian Soldiers, Rubinstein’s Melody in F, Cielito Lindo, Sous le ciel de Paris, Sancta Lucia, The Star-Spangled Banner, Waltzing Matilda (chorus), We Shall Overcome, When The Saints, Where Have All the Flowers Gone, Workers of the World Awaken!
Voice leading the dominant seventh chord’s minor seventh and major third, dominantal modulation, subdominantal V-I directionality, the frequent occurrence of inversions etc. have in fact become so indicative of European art music that they can be inserted as genre synecdoches in a context of non-classical harmony (e.g. pop and rock) to connote, seriously or humorously, ‘high art’ rather than ‘low-brow entertainment’, ‘deep feelings’ and the ‘transcendent’ rather than the ‘superficial’ and ‘ephemeral’ (ex. 6-8).
Ex. 6. Tonic second inversion as second chord: a ‘classical’ move — outline keyboard arpeggiation structure. (a) J S Bach: Prelude in C major from Wohltemperiertes Klavier, Band I (1722); (b) Elton John: Your Song (1970, transposed to C).
Ex. 7. Inversions through descending bass in major key: (a) J S Bach: Air from Orchestral Suite in D Major (c. 1730, transposed to C); (b) Procol Harum: A Whiter Shade of Pale (1967); (c) bass common to both (a) and (b),
Ex. 8. Altered supertonic seventh chord in fourth inversion: (a) Mozart: Ave verum corpus, K618 (1791); (b) Procol Harum: Homburg (1967); Abba: Waterloo (1974).
Together with dance styles like bossa nova, Jazz has relied heavily on a sense of harmonic direction similar to that of the European classical tradition. Long and sometimes quite complex chord sequences, an increasing amount of chromaticism, and the use of modulation are all key factors in many types of jazz. The popularity of the thirty-two bar standard as basis for improvisation bears witness to the essential role of harmonic narrative in jazz. Put simply, no jazz performance will work if musicians do not know or cannot follow the changes.
Jazz harmony can be divided into four main historical idioms: those of [1] trad. jazz; [2] the swing era; [3] bebop; [4] non-tertial jazz (see 3b). With the exception of [4], all jazz harmony follows the underlying principles as European art music: flat sevenths tend to fall, sharp sevenths rise, accidentals (alterations) are used for chromatic effect or for modulation, and there is pretty strict adherence to falling, subdominantal (V-I) progressions anticlockwise round the circle of fifths. trad. jazz harmony tends to use real circle-of-fifths progressions, adding sixths or sevenths to basic triads. swing era harmony tends to favour virtual circle-of-fifths progressions with sixths, sevenths and ninths added to basic triads. bebop harmony can be regarded as a radical expansion of swing harmony: it is characterised by considerable chromatic alteration, typically through tritone substitution which includes the flat fifth as an extra (voice) leading note, and by its use of chords of the eleventh and thirteenth. Basic differences between these jazz harmony idioms are illustrated in simplified form in example 9 which shows varying treatment of the (I-) VI - II - V - I vamp sequence.
Ex. 9. Possible renditions in C of VI-II-V-I sequence in main tertial idioms of jazz harmony.
3 Non-classical harmony
3a. Non-directional tertial harmony
3.a.i Ionian mode and barré
Although sequences of common triads in the ionian mode form the essence of tonal polyphony in many postwar popular music styles, such harmonic practice — for example, as found in Latin American urban styles such as cúmbia or son, in urban African musics like high life and kwela, as well as in most pop, rock and soul music — cannot be qualified as classical for two main reasons: [1] because it rarely conforms with European art music conventions of voice leading. Indeed, any barré chord progression involves a sequence of parallel fifths and octaves (forbidden in classical harmony), for example between the triads on IV and V of the ionian La Bamba matrix (I-IV-V, see table 2, turnaround). Similarly, bottleneck performance relies entirely on chords strung together in parallel motion. It is moreover clear that such matrices consisting rarely of more than four chords function in a radically different way to progressions in the idiom of classical harmony, not least because tertial matrices of this type contain little or no chromaticism, nor do they not modulate, nor contribute extensively to the construction of musical narrative. Although such matrices may vary from one (section of a) song to another, their main function is to provide a fitting tonal dimension to underlying patterns of rhythm, metre and periodicity. Their function is not to provide long-term harmonic direction but to generate a more immediate or continuous sense of ongoing tonal movement and to act as tonally appropriate accompanimental motor.
3.a.ii Tertial modal harmony
By modal harmony is generally meant the use of chords that follow the tonal vocabulary of any church mode (see modality) except the ionian (see 2, above) and locrian (the latter excluded because its tonic triad is diminished, rather than, as in all other cases, either major or minor). It is the five remaining modes — dorian, phrygian, lydian, mixolydian and aeolian (see tables 1 and 2) — that give rise to modal harmony in the popular sense of the term.
Characteristic differences in tertial modal harmony derive from the unique tonal relationship between the keynote and major triads of each mode. Table 1 shows that each mode contains three major triads (C, F, G on the white notes of the piano). It also shows that the minor modes (dorian, phrygian, aeolian) all have a major triad on the flat third degree ($III), that the phrygian is alone with a major triad on the flat supertonic ($II), that a major triad on the unaltered supertonic (II) is unique to the lydian mode, that the mixolydian is the only major mode with a major triad on the flat seventh ($VII), that the dorian is the only minor mode with a major triad on the fourth (IV), etc.
Table 1: Major triad positions in church modes
I $II II $III IV V $VI $VII
ionian a a a
dorian a a a
phrygian a a a
lydian a a a
mixolydian a a a
aeolian a a a
The basic principles of tertial modal harmony can be simply grasped using only the white notes of a piano keyboard instrument. Playing the major triads of F, G and C, as well as the relevant tonic triad (if it is not based on f, g or c), while at the same time holding down the keynote of the relevant mode in the bass (c for ionian, d for dorian, e for phrygian and so on) will produce familiar but distinctive patterns of modal harmony. This procedure can then be transposed to any of the octave’s black or white notes.
It should be noted that the most common alteration in tertial modal harmony is to raise the third of tonic triads in minor modes. Such alteration can be understood in terms of a tierce de Picardie used consistently throughout a piece of music as substitute for the tonic minor triad, not just as alteration of the final chord. This major triad substitution practice was commonly used in the modal harmony of Elizabethan popular song and dance (ex. 10, 12; see also Farnaby’s Dreame, Dowland’s King of Denmark’s Galliard, etc.).
Ex. 10. Farnaby: Loth to Depart (c.1610): aeolian triads with major tonic triad (I iv $III iv [$VI $VII])
Ex. 11. Darling Corey (USA Trad., Doc Watson 1963): major tonic triad for minor mode tune
Major third substitution in the tonic triad is widespread in much blues and in some Country music where minor or blues thirds are sung or played to the accompaniment of major triads (ex. 11), or when barré techniques are used to progress between I $III and IV, as in the well-known dorian-mode riff of Green Onions or Smoke On The Water. Dorian harmonies are in other words suited to the accompaniment of minor pentatonic melody (1 $3 4 5 $7) because, with alteration of the tonic, major triads occur on four of five pitches (I $III IV $VII).
The fifth degree triad of minor modes was also often altered to major in European polyphonic music during the ascendancy of the ionian mode, typically to introduce V-I cadences containing dominant sevenths and their double leading notes (see §2.b.ii). Example 12 (bars 1-2) shows a dorian (I IV $III) and a mixolydian progression (I IV $VII, bars 4-5), each followed by the standard V7-I cadence of classical harmony.
Ex. 12. Weelkes: Hark, All Ye Lovely Saints (c.1610).
Alteration of minor dominant also occurs in blues-related styles, especially when barré, slide and bottleneck techniques are used on guitar. In these cases, however, such alteration relates to tuning and playing practices, not to any predilection for the ionian mode or perfect cadences, as is evident from the absence of V-I changes (B Æ E) in example 13.
Ex. 13. Slide guitar chords (opening tuning E) for Vigilante Man (Guthrie), adapted from Cooder (1971).
Table 2 shows the major triads, including, where applicable, the altered tonic (in square brackets), of each mode. (The lydian and locrian modes are excluded because they are uncommon in most forms of popular music.) Table 2 also presents each mode’s major triads as they would occur ‘in C’ (no sharps, no flats) and ‘in E’ (four sharps), along with references to examples of popular music in which each relevant modal tertial harmony can be heard.
The tertial harmony of each mode is often related to the frequency with which it is (assumed to be) used in particular types of music. Hence, dorian harmony is a trait of some blues-based styles (ex. 13), while phrygian chord changes are often regarded, at least by non-Hispanics, as distinctive of Hispanic popular music styles (ex. 14). Tertial phrygian harmony is also used extensively in popular music from Greece, Turkey, the Balkans and the Near East, mostly in accompaniment to melody in the Hijaz mode (e.g. Misirlou, a.k.a. the theme from Pulp Fiction).
Mixolydian harmonies are often linked with British and Irish or Anglo-American folk music (ex. 21), with some forms of rock and Country, as well as in music for Western adventures (ex. 15). One particular trait of mixolydian harmony, the ‘cowboy half cadence’, from $VII to an altered major triad on V, is familiar enough to have become an object of both pastiche (ex. 16a) and parody (ex. 16b).
Aeolian harmony seems to have acquired two main functions in pop and rock music: [i] connoting, by means of the ‘aeolian pendulum’, notions of the ominous, fateful or implacable (Björnberg 1995); [ii] substituting standard IV-I or V-I cadences with the more colourful and dramatic $VI-$VII-I aeolian cadence, easily performed as barré chords on guitar.
Ex. 14. Phrygian harmony: (a) popular Malagueña figure; (b) Puebla: Hasta siempre
Table 2: Major triads in tertial modal harmony
relative positions on white notes with four sharps examples
ionian I IV V C F G E A B La bamba, Twist and Shout [D-G-A in D]; Guantanamera [F-B$-C in F]; Pata Pata [F-B$-F-C].
dorian [I] $III IV $VII [D] F G C [E] G
A D Green Onions, Smoke on the Water [E-G-A in E]; ex. 10, 12-13
phrygian [I] $II $III $VII [E] F C G [E] F
C G See ex. 14, verse of E viva España, start of Rodriguez’ Concierto de Aranjuez. Misirlou.
mixolydian I IV $VII G C F E A D Sweet Home Alabama [D-C-G in D]; Hey Jude [G-F-C-G]; The Magnificent Seven [E$-A$-E$-D$ in E$]; ex. 15-21
aeolian [I] $III $VI $VII [A] C F G [E] G
C D All Along the Watchtower [A-G-F-G in A], Flashdance [G-F-E$-F in G]. Cadences in Lady Madonna [F-G-A], PS I Love You [B$-C-D], SOS [D$-E$-F], Brown Sugar [A$-B$-C].
Ex. 15. Mixolydian shuttles: (a) Tiomkin: Duel in the Sun (1947); (b) Mancini: Cade’s County (1971).
Ex. 16. Cowboy half cadences: (a) The Shadows: Dakota (1963); (b) Brooks: Blazing Saddles (1974).
3b Quartal harmony
3.b.i Structural definition
Quartal harmony is so called because it is based on the fourth and on its octave complement, the fifth. Unlike its tertial counterpart, quartal harmony it is not based on thirds, nor on the ionian mode, nor do its basic chords contain tritones whose constituent notes demand voice leading by semitone steps. The structural elements of quartal harmony are set out in example 17.
The first line (a) of example 17 shows: (1) c at the centre of a pile of fourths (d g c f b$); (2) the pentatonic scale resulting from that pile of fourths (1-2-4-5-$7 or c d f g b$); (3) c at the centre of a pile of fifths containing exactly the same tonal material as (a1) and (a2): whether the notes be piled in fourths or fifths, they still constitute a run of five consecutive positions round the circle of fifths. Lines (b) and (c) show (2) the resultant pentatonic scales when c is shifted subdominantally to position 2 or, dominantally, to position 4 in the pile of fourths (ex. 17b1, c1), and to position 4 or 2 respectively in the equivalent pile of fifths (ex. 17b3, c3). Note [i] that the quartal notes of C in central position (ex. 17a) are the same as those of the G minor or B$ major anhemitonic pentatonic modes; [ii] that those of C in dominantal position (ex. 17b) tally with the pentatonic scales of D minor and F major; [iii] that those of C in subdominantal position (ex. 17c) coincide with C minor and E$ major pentatonic scales. Simple triads and tetrads resulting from C in central quartal position (ex. 17a) are presented in example 18 and are transposable to any of equal tone tuning’s eleven other pitches.
Ex. 18. Basic quartal triads and tetrads in C (central position)
Each note of the pile of fourths (or fifths, or of the relevant pentatonic scale) can be used as bass for chords consisting of the same tonal vocabulary. Moreover, all of the chords tabulated can be sounded with any pitch from the relevant pentatonic material as bass note. This procedure occasionally produces tertial chords (in ex. 18 Gm and B$, marked in black) which, in a consistently quartal idiom, are usually supplied with a bass note foreign to the tertial chord in question. For example, with c in the bass, Gm(7) and B$(6) produce variants of C11, a chord which even in a tertial context contains a fourth and is sounded without third (see lead sheet chord shorthand). Most of the chords in ex. 18 are, however, unequivocally quartal.
In jazz and pop circles quartal chords are sometimes referred to as suspensions. However, although chord C¡ in ex. 18 might, for example, be labelled Csus4, it is apparent from examples 22-25 that quartal chords are consonances in their own right, not suspensions requiring resolution as in example 1b. Similarly, the chord marked ‘C6/9’ in the sheet music version of Sting’s Seven Days (ex. 25) is neither a C6 chord, nor a C9 nor a C9add6, nor C6/9 (see lead sheet chord shorthand), but a 1-2-5-6 quartal chord (C in dominantal position, see ex. 17b2) that constitutes the main keynote sonority of the whole song.
3.b.ii History and usage
Open fourths and fifths, as well as quartal chords, start to appear in modern urban Western music in the folk-influenced work of composers living on the fringes of Europe.
Ex. 19. Borodin: (a) Song of the Dark Forest (1868); (b) The Sleeping Princess (1867).
Russians like Mussorgsky and Borodin (ex. 19) are followed much later by composers of the Spanish school (ex. 20, bar 2), but tertial modal harmony was for some time the most common approach to the problem of harmonising music outside with the Central European classical idiom (e.g. Dvorák, Grieg, Rimsky-Korsakov, Vaughan Williams).
However, the attitude of classically trained European musicians to music outside the canon did change during the nineteenth century. Whereas the Czech-German symphonist Carl Stamitz had in 1798 deemed Irish tunes incapable of bearing any harmony (Hamm 1979: 50), Herbert Hughes, in his preface to Irish Country Songs (vol. 1, London, 1909: iv), expressed the need for a radical and unacademic approach when dealing with such material, championing the work of ‘M. Claude Debussy’ who, he claimed, had set the trend ‘to break the bonds of this old slave-driver’ [classical tonality, etc.] ‘and return to the freedom of primitive scales’. Indeed, Hughes’s accompaniment to the mixolydian ballad She Moved Through the Fair (popularised by Simple Minds as Belfast Child) resolves its chains of open fifths and tertial triads into a final quartal chord (ex. 21).
Debussy is one of the first to use quartal harmony in modern Western music. Although whole sections of La cathédrale engloutie (1910), also as arranged by John Carpenter and Alan Howarth in Escape from New York, move in layered parallel fifths, Debussy’s use of quartal chords is generally limited to short passages providing contrasting harmonic colour to other sonorities, such as the whole-tone scale and tertial chords of the sixth, seventh and ninth. Example 22 shows the first three bars of one such brief passage.
Ex. 22. Debussy: ‘Sarabande’ from Pour le piano (1901): start of 5-bar quartal passage
The tertial aspects of Debussy’s harmonic language were adopted by prewar US composers of popular song (e.g. Gershwin, Kern). However, the type of quartal harmony just cited, and practised more widely by Bartók or Hindemith (see musical references), first found its way into the popular mainstream through composers associated with film or the stage, for example Copland (e.g. Billy The Kid, 1938; Fanfare for the Common Man, 1942, the latter used as title music for the Apollo-Soyuz broadcasts and in a General Motors commercial), Rózsa (e.g. scores for The Jungle Book, 1942; Quo Vadis, 1950), Leonard Bernstein (e.g. On the Waterfront, 1955), Elmer Bernstein (e.g. The Carpetbaggers, 1964).
Ex. 23. Miles Davis: So What (1959)
Ex. 24. Freddie Hubbard: Red Clay (1970), cited in Ingelf (1974).
Quartal harmony was slower to enter the world of jazz. The 1959 Miles Davis album Kind of Blue is often seen as a turning point when the tertial constraints of bebop harmony were abandoned in favour of quartal chords (ex. 23). Among jazz musicians to follow in Davis’s modal footsteps in the sixties and seventies were McCoy Tyner and Freddie Hubbard (ex. 24).
Pentatonic improvisation and quartal chords became a cornerstone of jazz fusion harmony (e.g. John McLaughlin, Chick Corea, not to mention Davis’s 1970 Bitches Brew album), surfacing also as music for TV (e.g. Goldenberg’s Kojak theme) and later in recordings by jazz-influenced pop artists such as King Crimson and Sting (ex. 25).
In Anglo-US commercial music, early use of bare fourths and fifths resembling quartal chords can be found in Nowhere To Run (Martha and the Vandellas, 1965), in Carole King’s Road To Nowhere (1966) and Manfred Mann’s I’m Your Kingpin (1964, ex. 26). While the first two are both modal tunes, their thirdless chords are attributable to word painting the emptiness of ‘nowhere’ rather than to consistent use of a new harmonic idiom. Mann, a jazz pianist, on the other hand, uses quartal harmony throughout Kingpin in conjunction with minor blues pentatonicism in both melody and bass. Quartal harmony in pop is in fact most often found together with tunes in the dorian, aeolian or minor pentatonic mode, for example in many a track by Steeleye Span or the Albion Country Band.
It is probable that the use of quartal harmony in pop and rock, including its occasional appearance in such Rolling Stones hits as Jumpin’ Jack Flash and Gimme Shelter (1969), derives partly from old rural forms of polyphony (blues, folksong, etc.). For example, Clarence Ashley’s open-string banjo accompaniment to the minor pentatonic tune Coo-Coo Bird is entirely quartal and qualified by the Folkways liner notes (1963) as archaic. Similarly, the thirdless harmonies of minor-mode shape-note hymns like Hauser’s Wondrous Love (1835) bear more resemblance to the polyphony of Heinrich Isaac (died 1517) than to their urbane contemporaries. Indeed, during tertial harmony’s global hegemony (c.1650-c.1950), polyphony based on fourths or fifths was regarded as either archaic or primitive to the extent that Hollywood stereotypes for almost any place or time felt to be distant enough from ‘our own’ was provided with some kind of thirdless polyphony. Ancient Egypt, Greece and Rome, pre-Renaissance Europe, the Chinese, the Arabs and Native Americans were often harmonically indistinguishable.
From this perspective it might seem as if modal and quartal harmony constitute no more than a return to pre-classical polyphony. There is, however, little doubt that classical harmony will survive as just one polyphonic idiom among several. It has also left an indelible impression worldwide on practices of tonal polyphony. Its imprint on quartal harmony can be seen in the need to develop means of ‘changing key’ inside a tonal idiom which in earlier times contained no modulation. Quartal key changes occur in examples 22 (from C#4-5-$7 to E4-5-$7), 23 (from Dm11 to E$m11) and 24 (a riff whose two poles are [i] Dm11 and A4-5-$7 and [ii] Cm11, E$11, G$/f). Moreover, the Kojak theme changes between Cm11 and E$m11, and much of the dynamic in Bartók’s harmonic language derives from tension between quartal chords a tritone apart (Lendvai 1971). In short, it is possible to change quartal key by introducing a chord whose constituent notes are as different as possible to those in the previous one. The most usual key changes from a quartal sonority in central position (1-2-4-5-$7, see ex. 17) are therefore those to a quartal chord situated a minor third above or below, or to a quartal chord at a tritone’s interval, or to a quartal chord on either degree IV or V in relation to those three other pitches, i.e. to any note in the quartal tonic’s diminished seventh chord, or to either IV or V in relation to those other three pitches. For example a quartal key change from C can move to E$, F#/G$ or A8, or to [i] A$ (IV in relation to E$), [ii] or B or C#/D$ (IV or V in relation to F#/G$), or [iii] E (V in relation to A). Put simply, a 1-4-5 chord can only ‘change key’ to a 1-4-5 triad on a note at least three positions away in the circle of fifths (C to E$, A$, D$, G$/F#, B, E, A) but it cannot ‘change key’ to B$, F, G or D because these notes are already contained within its own tonal vocabulary (1-2-4-5-$7, see ex. 17).
It is impossible to tell if developments in tonal polyphony during the twentieth century will survive as long as those of the classical tradition, or whether the tonal constraints of quartal and modal tonality will end up in the same sort of cul-de-sac as tertial chromaticism. It is more likely that harmony might be superseded, not least for technological reasons, by another compositional dynamic: that of sampling, MIDI-looping and the juxtaposition of pre-existent musical and paramusical sounds. Whatever the future holds, it is clear that harmony, and whatever, if anything, supersedes it is just as much an ideological as technical or theoretical matter.
4 Bibliography
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Ex. 2. (a) (b)
Ex. 3. (a) (b)
(a)
Ex. 17. Basis of quartal harmony in C
(a)
(b)
(a)
(b)
(a) trad. jazz.
(b) swing era: [1] standard, [2] chromatic.
(c) bebop: [1] standard,
[2] tritone substitution
(a)
(b1)
(b2)
(c1)
(c2)
(b)
Ex. 20. De Falla: Farruca from El sombrero de tres picos (1919).
Ex. 25. Sting: Seven Days (1993).
Ex. 26. Manfred Mann: I’m Your Kingpin (1964): bass and piano riff
Ex. 21. Irish Trad., arr. Hughes: She Moved Through The Fair (final chords in accompaniment).
