Science Fair Project Encyclopedia
Figured bass, or thoroughbass, is a kind of integer musical notation used to indicate intervals, chords, and nonchord 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.
Basso continuo parts, almost universal in the Baroque era (1600-1750), were, as the name implies, played continuously throughout a piece, providing the harmonic structure of the music. The word is often shortened to continuo, and the instrumentalists playing the continuo part, if more than one, are called the continuo group.
The makeup of the continuo group is 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, viola da gamba, 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.
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 figured bass notation, described below, is a guide, but performers are 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 continued to be used in many works, especially sacred choral works, in the classical period (up to around 1800). 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 at 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.
The numbers indicate the number of notes 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 a first inversion. The 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:
Sometimes, other numbers are omitted: a 2 on its own or 42 indicate 642, for example.
Sometimes the figured bass 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.
When an accidental is shown on its own without a number, it applies to the third of the chord; otherwise it applies to whichever note it is shown next to. 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 though 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.
Improvised organ accompaniments for choral works was common in the late 16th century, and separate organ parts, showing only a bass line, date back to at least 1587. The earliest extant part with sharp and flat signs above the staff is a motet by Giovanni Croce from 1594. The use of numerals began with the earliest operas, composed by Cavalieri and Caccini.
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). A form of figured bass is used in notation of accordion music. 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 the bass note C in 64 figured bass would be written . The symbols can also be used with Roman numerals in analyzing functional harmony, a usage called figured Roman; see chord symbol.
- Chords that the (major) Scale Degrees (in the bass) Can Imply by Robert Kelley
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