II. Counterpoint

Ground Bass

Mark Gotham

‘Ground bass’ compositions are based on a bass line that repeats throughout the piece, usually exactly, or nearly so. Many musicians have found this a compelling compositional constraints for keeping them … well … grounded!

How many musicians are we talking about? Well, this practice was highly popular in the Baroque. Purcell was a particularly keen and expert protagonist; it is even more common in popular songs of recent years (see Harmonic Schemas in Pop Music); and there are more than a few example from in between. In short, it is an extremely and enduringly popular form.

It it’s easy to confuse the ‘Ground bass’ with some other terms; the key terms to distinguish are:

  • Ostinato: any pattern that repeats throughout a long section or whole work in one voice. The motto side drum rhythm of Ravel’s Bolero is an ostinato pattern but clearly not a ground bass.
  • Ground bass is a term which can refer either to a bass line which repeats throughout a work or section, or the work itself based on that ground. A ground bass is a type of ostinato but the reverse is not true.
  • Chaconne and Passacaglia (and international variants spellings such as ‘Chacony’) refer to sub-genres of the Baroque ground bass. Among their other characteristics, both of these two are in 3-time. Again, if a piece is a Chaconne or Passacaglia then it is also a ground bass; the reverse is not true.

This chapter provides some files and instructions to help you explore some of the ways to create effective ground bass compositions. We focus on the Baroque model, and on creating variety through re-harmonising the same bass in different ways and varying the texture.

Files

  1. A cheat sheet for the many ways of re-harmonising any bass interval;
  2. Template scores based on Baroque ground bass compositions, but with only the ground bass provided so you can compose a completion of the rest;
  3. Those Baroque compositions again, but with the upper parts now included along with annotated files with Roman Numerals and more.

In all of these templates and annotated scores, there is exactly one iteration of the ground per system so you can compare equivalent moments directly (vertically).

Here are links to the files for 2. and 3.:

Template score Fully annotated
Bach Crucifixus Template Annotation
Purcell Sonata in G Minor Z 807 Template Annotation
Purcell Chacony in G Minor Z730 Template Annotation
Purcell Here the Deities Approve Template [To follow]

Multiple Harmonisations of a Given Bass

This ‘cheat sheet‘ shows how you can harmonise any bass interval in several different ways. It is organised by bass interval: both ascending and descending forms of each interval from minor seconds to tritones. This is supposed to help you work out your options – you definitely don’t need to use all of these! We’ll see below how Purcell uses just a few of these to create harmonic variety in a very long work that’s almost entirely in g minor. We’ll be especially interested in moments where Purcell avoids the main, perfect cadence at the start/end of each iteration of the ground, joining two grounds together with a subtler seam, and varying not just the harmony, but also the phrase rhythm of the piece.

Composition Exercises

These template scores allow you to try your hand at composing music based on some of the repertoire’s great ground basses.

Take a template and try to compose:

  1. A simple, predominantly diatonic harmonisation of the ground, with simple blocks chords, making sure to follow good voice-leading practice. Use this as a prototype.
  2. A set of alternative harmonizations including tonicizations of other keys and re-harmonizations of the first note in particular to vary the apparent phrase length (as discussed above in reference to the ‘cheat sheet’);
  3. Melodic parts that fit with the bass and create more interesting textures. Seek out ways of writing upper parts that can recur in another voice in imitation. We’ll see how Purcell approaches this below.
  4. Finally, combine the best of your ideas into an overall piece that balances textural and harmonic interest and charts an overall trajectory. Why not try a piece with 6 iterations of the ground, of which the first and last are simple and alike.

Analysis: Purcell’s Sonata in G Minor (Z 807)

To explore some of the options here, let’s take a look at Purcell’s Sonata in G Minor (Z 807). We’ll look at how Purcell uses (extensive) imitation and (occasional) tonicisation. All of these matters are summarized in the tables at the end of this page, and are also included on the downloadable score as text annotations at the relevant moment.

Harmony. Harmonically, the piece is resolutely in g minor almost throughout, though Purcell tonicizes several keys along the way as summarized in the second table below. Notice especially how Purcell finesses that boundary between the start/end of a ground iteration by avoid yet another perfect cadence in g. For instance, see m.16 and 106 for uses of G major as part of V42-i6 in d minor, broadly reversing tonic and dominant function, and likewise m.26 and 86 for g diminished as viio6-I in F major.

As a wider matter, notice how extensively Purcell uses 5-6 steps in the melodic parts and how this creates ambiguity in the harmony. Is the 5 or the 6 harmonic, or perhaps both? Is this consistent or does it change? This all makes it harder to pin down exactly what the harmony is and where it changes, adding ever further layers of interest to the score. It also helps set up the sequences of 7-6 suspensions such as from m.71.

Imitation. Imitation is prevalent throughout. The melodic imitations are labelled ‘D’ and ‘C’ on the score, and in the table below. This is short for ‘Dux’ and ‘Comes’ – ‘leader’ and ‘follower’. For instance, the violin 1 parts starts a melodic line in measure 1 (beat 1) which is imitated by the violin 2 entering in measure 3 (beat 1). Notice from the table how often these imitations start in the same part of the bar. This is consistent with what we discussed in the context of 16th century and 18th century imitative traditions. Visit those chapters to learn more. Entering on equivalent beats lead to temporal gaps between entries of 3 or 6 beats (beat gaps on the table). Note the many exceptions where Purcell uses closer imitation.

As the score and first table show, there is a great deal of imitation in this piece; almost every iteration of the ground is accompanied by a new imitative relationship in the upper parts (the exceptions are given in the second table, below). Perhaps the two most special and interesting cases are the:

  1. double imitation starting in m.196 and imitated with parts swapped in m.201;
  2. imitation of the ground itself in the violin 2 part at m.99/102.

The second table summaries the iterations without imitation.

Rhythm and Meter. Finally, note how Purcell continually varies the rhythmic values (metrical levels) involved, using a wide range of options. This includes introducing continuous eighth-notes (m.36), sixteenth-notes (m.81 and 146), syncopation (m.126), dotted rhythms (136), and for one passage near the end, changing the notated meter to compound time (m.166–185). This is a common device in Baroque ground bass (and other variations-style works of the time); again these changes usually (but not always) coincide with the start of a new iteration of the ground.

D. Part D. Measure D. Beat D. Pitch C. Part C. Measure C. Beat C. Pitch Beat gap Pitch interval
1 1 1.0 D5 2 3 1.0 G4 6.0 P5
1 6 1.0 G5 2 7 1.0 D5 3.0 P4
2 10 3.0 D5 1 11 3.0 D5 3.0 P1
1 20 2.0 D5 2 21 2.0 G4 3.0 P5
2 27 2.0 C5 1 29 2.0 D5 6.0 M2
2 30 2.0 D5 1 31 2.0 D5 3.0 P1
2 33 1.0 D5 1 34 1.0 C5 3.0 M2
2 36 1.0 G4 1 36 2.0 G4 1.0 P1
2 41 2.0 E-5 1 41 3.0 B-5 1.0 P5
2 46 1.0 D5 1 47 1.0 E-5 3.0 m2
2 51 1.5 G5 1 52 1.5 D5 3.0 P4
2 56 1.0 E-4 1 56 2.0 C5 1.0 M6
1 61 2.0 G4 2 62 2.0 D5 3.0 P5
1 63 1.0 G5 2 63 2.0 C5 1.0 P5
2 66 1.5 G5 1 67 1.5 D5 3.0 P4
2 71 2.0 D5 1 71 3.0 G5 1.0 P4
1 81 1.25 G5 2 82 1.25 D5 3.0 P4
1 91 1.0 B-4 2 94 1.0 D4 9.0 m6
1 95 2.0 A4 2 97 2.0 D5 6.0 P4
1 99 1.0 D5 2 102 1.0 D5 9.0 P1
1 106 1.0 E5 2 108 1.0 B-4 6.0 A4
2 111 2.0 D5 1 112 2.0 A4 3.0 P4
2 117 2.0 D5 1 118 2.0 A5 3.0 P5
2 121 1.0 G4 1 121 3.0 D5 2.0 P5
1 129 2.0 D5 2 130 2.0 A4 3.0 P4
1 133 1.5 D5 2 133 2.5 G4 1.0 P5
2 136 1.0 G4 1 137 1.0 D5 3.0 P5
2 141 1.0 G4 1 142 1.0 D5 3.0 P5
2 146 1.0 G4 1 147 1.0 D4 3.0 P4
1 151 1.0 G4 2 153 1.0 G4 6.0 P1
1 156 2.0 E-5 2 157 2.0 A-4 3.0 P5
1 161 2.0 E-5 2 162 2.0 A-4 3.0 P5
1 166 1.0 G4 2 167 1.0 D4 3.0 P4
1 171 1.0 G4 2 171 2.0 G4 1.0 P1
2 176 1.0 G5 1 177 1.0 D5 3.0 P4
2 178 1.0 E-5 1 178 2.0 E-5 1.0 P1
1 181 1.0 G5 2 181 2.0 G5 1.0 P1
1 182 1.0 D5 2 182 2.0 D5 1.0 P1
1 186 2.0 D5 2 187 2.0 A4 3.0 P4
2 196 1.0 G4 1 201 1.0 B-4 15.0 m3
1 196 1.5 G5 2 201 1.5 D5 15.0 P5
1 206 1.0 B-4 2 208 1.0 B-4 6.0 P1

 

Notes Measure Beat
Tonicization: Bb 12 3
No imitation; more homophonic 16 1
Tonicization: d 17 1
Tonicization: F 27 1
Tonicization: Bb (but deceptive cadence) 28 1
Imitation freer intervalically 31 1
Tonicization: c 33 1
Imitation freer intervalically 46 1
Cycle of 5th? But missing every other root … 71 3
Tonicization: Eb 78 1
Tonicization: F 87 1
Tonicization: Eb 88 1
Tonicization: c 93 1
Tonicization: d 107 1
Tonicization: F 117 1
Homophonic 126 1
Tonicization: c 131 2
Tonicization: c 133 1
Two notes 156 1
Tonicization: Eb 158 1
Repeat 161 1
Tonicization: Eb 163 1
Meter change 166 1
Chromatic ascents 186 1
Meter changes back 186 1
Chromatic descents 191 1
Sequences and double imitation 196 1

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Open Music Theory by Mark Gotham is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License, except where otherwise noted.

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