Research design

First, a "Pop Chord Set", containing common chords found in popular music, is proposed. The Pop Chord Set functions as the core of the research material, so its structure and contents need to be thought out very carefully. For this reason, an entire subchapter (see below) is dedicated to the definition and presentation of the Pop Chord Set. Next, the interrelatedness of the chords belonging to the Pop Chord Set is studied with the chosen research method(s). The collected data is then organized and analyzed using statistical tools and methods. Eventually, the results of the study are presented, and findings discussed. Based on the findings, some preliminary components

constituting a system that may very well be called "Pop Chord Space" is proposed. Finally, the limitations of the study are acknowledged, and recommendations for further study proposed. In addition, suggestions for practical applications of the Pop Chord Space follow.

3.1.1 Pop Chord Set

In the "road map of hit song harmony", presented in Chapter 1.2, commong chord progressions were extracted from a random sample of popular music, containing hundreds of hit songs. It was found out that the majority of the chords included in the progressions could be generalized into the following three functional categories:

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1. diatonic triads,

2. secondary dominants, and 3. modal interchange chords²⁶.

For the purpose of this study, we will from now on refer to the group of chords belonging to the aforementioned categories as the "Pop Chord Set" (presented in Table 5 below).

Table 5.

The Pop Chord Set (chords presented in C major).

c d° Eb f g Ab Bb ^chord

Modal

interchange i ii° bIII iv v bVI bVII function

C d e F G a b° chord

Diatonic

triads I ii iii IV V vi vii° function

G7 A7 B7 C7 D7 E7 (N/A) ^chord

Secondary

dominants V7(/I) V7/ii V7/iii V7/IV V7/V V7/vi (N/A) function

Legend: N/A = Not available

Chords common to jazz harmony, for example, that were not found widespread in pop songs included the following:

1. substitute dominants

2. secondary subdominants, and 3. substitute subdominants.

In addition, the following chord categories, although occasionally found in pop songs, were ruled out, because they were not considered as being able to explicitly change the basic tonal function of chords presented in Table 5 above:

1. suspended chords (sus2, sus4) and chords with additional tones (add9, add11), 2. "slash chords" (triads over bass notes, most often simple triad inversions), and 3. seventh chords (other than V7/X) and chords with extensions (9, 11, and/or 13)

Finally, the few diminished chords found in pop songs were either working as secondary dominants (vii°7/X, sometimes regarded as "upper structures" of secondary dominant seventh chords, e.g.

26In this case, modal interchange refers to chords "borrowed" to a major key (C major) from the parallel natural minor key (C natural minor, or the C aeolian mode in modal terms). Some of these chords (most notably the "v" or "g" and

"bVII" or "Bb") can in some cases be regarded as modal interchange chords from the parallel mixolydian mode (C mixolydian), but since this distinction is not essential to this study, we will not let it complicate matters further.

Toward Pop Chord Space: Harmonic Hierarchy in Popular Music

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G#°7 ≈ E7) or appeared in a minor key context, rendering them beyond the scope of this study.²⁷ The rare (in pop) blues chords (such as the "IV7") were also excluded, because they come from a different genre than the one under study.

Diatonic triads

All diatonic triads (chord degrees of the prevailing key) were included in the Pop Chord Set for obvious reasons, except for the "vii°" that was not encountered – at least in strict diatonic vii°

function – in any of the chord progressions extracted. This view is supported in several respected theory textbooks (e.g. Piston, 1978) and scientific studies (e.g. Krumhansl et al., 1982).

Secondary dominants

All secondary dominant chords of the aforementioned diatonic triads were naturally included in the Pop Chord Set. Note that the V7(/I) chord ("G7" in C major), which is commonly regarded as the primary dominant (V7) of a major key, is put in the secondary dominant category in order to separate it from the diatonic V ("G" in C major) triad. Also, note that the (theoretical) "vii°" chord does not have a secondary dominant associated with it, because one of the core features of

secondary dominants is their ability to "tonicisize" diatonic chord degrees. In other words, a genuine secondary dominant chord must be able to imply the possibility of a standard dominant-to-tonic resolution between it and the diadominant-to-tonic target. Since a diminished chord, such as the "vii°", cannot function as a (temporary) tonic, the "V7/vii°" does not exist – at least in music (although on the paper it might).

Modal interchange

All modal interchange chords borrowed from the parallel natural minor key were also included in the Pop Chord Set, except for the "ii°" chord, which was excluded for similar reasons as the diatonic "vii°" chord in major was. After all, the "ii°" chord (e.g. "d°") of the parallel minor key (e.g. c minor) is actually a "vii°" in the relative major key (e.g. Eb major) of the parallel minor.

Note that the "i" chord, although never discovered from actual songs, was not removed from the Pop Chord Set, because its exclusion was neither supported nor opposed in previous studies. It was also thought that, in the end, it might be good to have a practically nonexistent "control chord"

within the set, in case its inclusion would end up contributing valuable information to the study. For a reference, Johansson (1999) reported that in the 194 Beatles songs in major keys (of a total of 210 







27For an excellent, practical presentation on diminished seventh chords in jazz, see Nettles & Graf (1997), p. 110 onwards. In short, the authors present three diatonic functions (ascending [a semitone up]), descending [a semitone down], and auxiliary [no root motion]) for diminished seventh chords, of which only the last one has a traditional dominant function.

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songs), the "bVII" chord was more frequent that the diatonic "iii" chord, for example. Other modal interchange chords found in the music of the Beatles were the "iv", "bIII", and "v". In my opinion, these findings alone are enough to support the inclusion of modal interchange chords in any study of tonal harmony in popular music.

To summarize, the Pop Chord Set was proposed to include a total of 18 chords – six diatonic triads, six secondary dominants, and six modal interchange chords.