Figured bass

Melody from the opening of Henry Purcell's "Thy Hand, Belinda", Dido and Aeneas (1689) with figured bass below ( Play (help·info),  Play (help·info) with figured bass realization).

Figured bass, or thoroughbass, is a kind of integer musical notation used to indicate intervals, chords, and non-chord tones, in relation to a bass note. Figured bass is closely associated with basso continuo, an accompaniment used in almost all genres of music in the Baroque period, though rarely in modern music.

Other systems for denoting or representing chords include:^[1] plain staff notation, used in classical music, Roman numerals, commonly used in harmonic analysis,^[2] macro symbols, sometimes used in modern musicology, and various names and symbols used in jazz and popular music.

Basso continuo

Basso continuo parts, almost universal in the Baroque era (1600-1750), provided the harmonic structure of the music. The phrase is often shortened to continuo, and the instrumentalists playing the continuo part, if more than one, are called the continuo group. The titles of many Baroque works make mention of the continuo section, such as J. S. Bach's Concerto for 2 violins, strings and continuo in D minor.

The makeup of the continuo group is often left to the discretion of the performers, and practice varied enormously within the Baroque period. At least one instrument capable of playing chords must be included, such as a harpsichord, organ, lute, theorbo, guitar, or harp. In addition, any number of instruments which play in the bass register may be included, such as cello, double bass, bass viol, or bassoon. The most common combination, at least in modern performances, is harpsichord and cello for instrumental works and secular vocal works, such as operas, and organ for sacred music. Very rarely, however, in the Baroque period, the composer requested specifically for a certain instrument (or instruments) to play the continuo. In addition, the mere composition of certain works seems to require certain kind of instruments (for instance, Vivaldi's Stabat Mater seems to require an organ, and not a harpsichord).

The keyboard (or other chording instrument) player realizes a continuo part by playing, in addition to the indicated bass notes, upper notes to complete chords, either determined ahead of time or improvised in performance. The player can also "imitate" the soprano (which is the name for the solo instrument or singer) and elaborate on themes in the soprano musical line. The figured bass notation, described below, is a guide, but performers are also expected to use their musical judgment and the other instruments or voices as a guide. Modern editions of music usually supply a realized keyboard part, fully written out for the player, eliminating the need for improvisation. With the rise in historically informed performance, however, the number of performers who improvise their parts, as Baroque players would have done, has increased.

Basso continuo, though an essential structural and identifying element of the Baroque period, continued to be used in many works, especially sacred choral works, of the classical period (up to around 1800). An example is C. P. E. Bach's Concerto in D minor for flute, strings and basso continuo. Examples of its use in the 19th century are rarer, but they do exist: masses by Anton Bruckner, Beethoven, and Franz Schubert, for example, have a basso continuo part for an organist to play.

Figured bass notation

A part notated with figured bass consists of a bass-line notated with notes on a musical staff plus added numbers and accidentals beneath the staff to indicate what intervals above the bass notes should be played, and therefore which inversions of which chords are to be played. The phrase tasto solo indicates that only the bass line (without any upper chords) is to be played for a short period, usually until the next figure is encountered.

Composers were inconsistent in the usages described below. Especially in the 17th century, the numbers were omitted whenever the composer thought the chord was obvious. Early composers such as Claudio Monteverdi often specified the octave by the use of compound intervals such as 10, 11, and 15.

Contemporary Figured Bass as taught at university level, may be summarized as follows, for memorization.

For diatonic triads:

• root position = blank
• 1st Inversion = 6
• 2nd Inversion = 6/4

For 7th chords:

• root position = 7
• 1st Inversion = 6/5
• 2nd Inversion = 4/3
• 3rd Inversion = 4/2

Numbers

The numbers indicate the number of scale steps above the given bass-line that a note should be played. For example:

Here, the bass note is a C, and the numbers 4 and 6 indicate that notes a fourth and a sixth above it should be played, that is an F and an A. In other words, the second inversion of an F major chord is to be played.

In cases where the numbers 3 or 5 would normally be indicated, these are usually (though not always) left out, owing to the frequency these intervals occur. For example:

In this sequence, the first note has no numbers accompanying it—both the 3 and the 5 have been omitted. This means that notes a third above and a fifth above should be played—in other words, a root position chord. The next note has a 6, indicating a note a sixth above it should be played; the 3 has been omitted—in other words, this chord is in first inversion. The third note has only a 7 accompanying it; here, as in the first note, both the 3 and the 5 have been omitted—the seven indicates the chord is a seventh chord. The whole sequence is equivalent to:

although the performer may choose which octave to play the notes in and will often elaborate them in some way rather than play only chords, depending on the tempo and texture of the music.

Sometimes, other numbers are omitted: a 2 on its own or 42 indicate 642, for example.

Sometimes the figured bass number changes but the bass note itself does not. In these cases the new figures are written wherever in the bar they are meant to occur. In the following example, the top line is supposed to be a melody instrument and is given merely to indicate the rhythm (it is not part of the figured bass itself):

When the bass note changes but the notes in the chord above it are to be held, a line is drawn next to the figure or figures to indicate this:

The line extends for as long as the chord is to be held.

Accidentals

When an accidental is shown on its own without a number, it applies to the note a third above the lowest note; most commonly, this is the third of the chord. Otherwise, if a number is shown, the accidental affects the said interval. For example, this:

is equivalent to this:

Sometimes the accidental is placed after the number rather than before it.

Alternatively, a cross placed next to a number indicates that the pitch of that note should be raised by a semitone (so that if it is normally a flat it becomes a natural, and if it is normally a natural it becomes a sharp). A different way to indicate this is to draw a bar through the number itself. The following three notations, therefore, all indicate the same thing:

When sharps or flats are used with key signatures they may have a slightly different meaning, especially in 17th-century music. A sharp might be used to cancel a flat in the key signature, or vice versa, instead of a natural sign.

Example of Figured Bass in context. Taken from Beschränkt, ihr Weisen, by J.S. Bach (R. 47/69).

History

The origins of basso continuo practice are somewhat unclear. Improvised organ accompaniments for choral works were common by the late 16th century, and separate organ parts showing only a bass line date back to at least 1587. In the mid-16th century, some Italian church composers began to write polychoral works. These pieces, for two or more choirs, were created in recognition of particularly festive occasions, or else to take advantage of certain architectural properties of the buildings in which they were performed. With eight or more parts to keep track of in performance, works in polychoral style required some sort of instrumental accompaniment. They were also known as cori spezzati, since the choirs were structured in musically independent or interlocking parts, and may sometimes also have been placed in physically different locations.

It is important to note that the concept of allowing two or more concurrently performing choirs to be independent structurally would or could almost certainly not have arisen had there not been an already existing practice of choral accompaniment in church. Financial and administrative records indicate the presence of organs in churches dates back to the 15th century. Although their precise use is not known, it stands to reason that it was to some degree in conjunction with singers. Indeed, there exist many first-person accounts of church services from the 15th and 16th centuries that imply organ accompaniment in some portions of the liturgy, as well as indicating that the a cappella-only practice of the Vatican's Cappella Sistina was somewhat unusual. By early in the 16th century, it seems that accompaniment by organ at least in smaller churches was commonplace, and commentators of the time lamented on occasion the declining quality of church choirs. Even more tellingly, many manuscripts, especially from the middle of the century and later, feature written-out organ accompaniments. It is this last observation which leads directly to the foundations of continuo practice, in a somewhat similar one called basso seguente or "following bass."

Written-out accompaniments are found most often in early polychoral works (those composed, obviously, before the onset of concerted style and its explicit instrumental lines), and generally consist of a complete reduction (to what would later be called the "grand staff") of one choir’s parts. In addition to this, however, for those parts of the music during which that choir rested was presented a single line consisting of the lowest note being sung at any given time, which could be in any vocal part. Even in early concerted works by the Gabrielis (Andrea and Giovanni), Monteverdi and others, the lowest part, that which modern performers colloquially call "continuo", is actually a basso seguente, though slightly different, since with separate instrumental parts the lowest note of the moment is often lower than any being sung.

The first known published instance of a basso seguente was a book of Introits and Alleluias by the Venetian Placido Falconio from 1575. What is known as "figured" continuo, which also features a bass line that because of its structural nature may differ from the lowest note in the upper parts, developed over the next quarter-century. The composer Lodovico Viadana is often credited with the first publication of such a continuo, in a 1602 collection of motets that according to his own account had been originally written in 1594. Viadana’s continuo, however, did not actually include figures. The earliest extant part with sharp and flat signs above the staff is a motet by Giovanni Croce, also from 1594.

Following and figured basses developed concurrently in secular music; such madrigal composers as Emilio de' Cavalieri and Luzzasco Luzzaschi began in the late 16th century to write works explicitly for a soloist with accompaniment, following an already standing practice of performing multi-voice madrigals this way, and also responding to the rising influence at certain courts of particularly popular individual singers. This tendency toward solo-with-accompaniment texture in secular vocal music culminated in the genre of monody, just as in sacred vocal music it resulted in the sacred concerto for various forces including few voices and even solo voices. The use of numerals to indicate accompanying sonorities began with the earliest operas, composed by Cavalieri and Giulio Caccini.

These new genres, just as the polychoral one probably was, were indeed made possible by the existence of a semi- or fully independent bass line. In turn, the separate bass line, with figures added above to indicate other chordal notes, shortly became "functional," as the sonorities became "harmonies," (see harmony and tonality), and music came to be seen in terms of a melody supported by chord progressions, rather than interlocking, equally important lines as in polyphony. The figured bass, therefore, was integral to the development of the Baroque, by extension the ”classical”, and by further extension most subsequent musical styles.

Many composers and theorists of the 16th, 17th, and 18th centuries wrote how-to guides to realizing figured bass, including Gregor Aichinger, Friedrich Erhard Niedt, Georg Philipp Telemann, C.P.E. Bach, and Michael Praetorius.

Contemporary uses

It is also sometimes used by classical musicians as a shorthand way of indicating chords (though it is not generally used in modern musical compositions, save neo-Baroque pieces). A form of figured bass is used in notation of accordion music; another simplified form is used to notate guitar chords. Today the most common use of figured bass notation is to indicate the inversion, however, often without the staff notation, using letter note names followed with the figure, for instance, if the harmony were a C major, with the bass note a G, it would be written $\mbox{C}_4^6$; with an E in the bass, it would be written C₆ (this is different than the Jazz notation, where a C6 is the chord C-E-G-A, i.e., a C major with an added 6th degree). The symbols can also be used with Roman numerals in analyzing functional harmony, a usage called figured Roman; see chord symbol.

Notes

1. ^ Benward & Saker (2003). Music: In Theory and Practice, Vol. I, p. 77. Seventh Edition. ISBN 978-0-07-294262-0.
2. ^ Arnold Schoenberg, Structural Functions of Harmony, Faber and Faber, 1983, p.1-2.

External links

• Figured Bass Symbology by Robert Kelley
• Chords that the (major) scale degrees (in the bass) can imply by Robert Kelley
• Theory and Practice of the Basso Continuo by Barry Mitchell
• Historical sources on the subject of basso continuo - Viadana, Agazzari etc