View source for Figured bass

{{Short description|Musical notation}}
{{more citations needed|date=May 2012}}
[[File:Purcell diatonic chromaticism.png|thumb|400px|right|Melody from the opening of [[Henry Purcell]]'s "Thy Hand, Belinda", ''[[Dido and Aeneas]]'' (1689) with figured bass below ({{audio|Purcell diatonic chromaticism.mid|Play}}, {{audio|Purcell diatonic chromaticism fb.mid|Play}} with figured bass realization).]]

'''Figured bass''' is [[musical notation]] in which numerals and symbols appear above or below (or next to) a bass note. The numerals and symbols (often [[accidental (music)|accidentals]]) indicate [[interval (music)|intervals]], [[chord (music)|chord]]s, and [[non-chord tone]]s that a musician playing [[piano]], [[harpsichord]], [[organ (music)|organ]], or [[lute]] (or other instruments capable of playing chords) should play in relation to the bass note. Figured bass is closely associated with [[#Basso continuo|basso continuo]]: a historically improvised [[accompaniment]] used in almost all genres of music in the [[Baroque music|Baroque period]] of [[Classical music]] ({{circa}} 1600–1750), though rarely in modern music. Figured bass is also known as '''thoroughbass'''.

Other systems for [[Chord (music)#Notation|denoting or representing chords]] include<ref>{{Citation |last1=Benward |first1=Bruce |last2=Marilyn Nadine |first2=Saker |year=2003 |title=Music: In Theory and Practice, Vol. I |publisher=Mcgraw-Hill |edition=7th |location=N.Y.|page=77 |isbn=978-0-07-294262-0}}.</ref> plain [[staff notation]], used in [[classical music]]; [[Roman numeral analysis|Roman numerals]], commonly used in [[harmonic analysis (music)|harmonic analysis]];<ref>{{Citation |last=Schoenberg |first=Arnold |year=1983 |title=Structural Functions of Harmony |publisher=Mcgraw-Hill |edition=7th |location=London |pages=1–2 }}.</ref> [[chord letters]], sometimes used in modern [[musicology]]; the [[Nashville Number System]]; and various [[Chord names and symbols (jazz and pop music)|chord names and symbols]] used in [[jazz]] and [[popular music]] (e.g., [[Major chord|C Major]] or simply C; [[Minor chord|D minor]], Dm, or D&minus;; [[Dominant seventh|G<sup>7</sup>]], etc.).

==Basso continuo==
{{Main|Basso continuo}}

[[Basso continuo]] parts, most common in the [[Baroque music|Baroque]] era (1600–1750), provided the [[harmony (music)|harmonic]] structure of the music by supplying a [[bassline]] and a [[chord progression]]. The phrase is often shortened to ''continuo'', and the instrumentalists playing the continuo part are called the ''continuo group''.
[[File:Soloquartet and strings.jpg|thumb|right|200px|A harpsichordist and a bassist play continuo for a small group of singers.]]
The makeup of the continuo group is often left to the discretion of the performers (or, for a larger performance, the [[conductor (music)|conductor]]), and practice varied enormously within the Baroque period. At least one instrument capable of playing chords must be included, such as a [[piano]], [[harpsichord]], [[organ (music)|organ]], [[lute]], [[theorbo]], [[guitar]], [[Regal (instrument)|regal]], or [[harp]]. In addition,{{citation needed|date=May 2020}} any number of instruments that play in the [[bass (music)|bass]] register may be included, such as [[cello]], [[double bass]], [[viol|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 [[opera]]s, and organ  and cello for [[sacred music]]. A double bass may be added, particularly when accompanying a lower-pitched solo voice (e.g., a bass singer).

Typically performers match the [[Family (musical instruments)|instrument families]] used in the full ensemble: including bassoon when the work includes oboes or other winds, but restricting it to cello and/or{{citation needed|date=May 2020}} [[double bass]] if only strings are involved. [[Harp]]s, lutes, and other handheld instruments are more typical of early 17th-century music. Sometimes instruments are specified by the composer: in ''[[L'Orfeo]]'' (1607) [[Monteverdi]] calls for an exceptionally varied instrumentation, with multiple harpsichords and lutes with a [[bass violin]] in the pastoral scenes followed by lamenting to the accompaniment of [[Positive organ|''organo di legno'']] and ''[[chitarrone]]'', while [[Charon (mythology)|Charon]] stands watch to the sound of a regal.

The keyboard (or other chord-playing instrument) player ''[[Realization (figured bass)|realizes]]'' (adds in an improvised fashion) a continuo part by playing, in addition to the notated bass line, notes above it to complete chords, either determined ahead of time or [[Musical improvisation|improvised]] in performance. 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 (notably the lead [[melody]] and any [[accidental (music)|accidental]]s that might be present in it) as a guide. Experienced players sometimes incorporate [[Motive (music)|motives]] found in the other instrumental parts into their improvised chordal accompaniment. Modern editions of such music usually supply a realized keyboard part, fully written out in [[staff notation]] for a player, in place of improvisation. With the rise in [[historically informed performance]], however, the number of performers who are able to improvise their parts from the figures, as Baroque players would have done, has increased.{{citation needed|date=December 2015}}

Basso continuo, though an essential structural and identifying element of the Baroque period, rapidly declined in the [[Classical music era|classical]] period (up to around 1800).<ref>"[http://thegreathistoryofarts.weebly.com/classical-era.html Classical Era (1750-1820)]", ''TheGreatHistoryofArts.Weebly.com''. Accessed: 27 July 2017.</ref> A late example is [[C. P. E. Bach]]'s Concerto in D minor for flute, strings and basso continuo (1747). Examples of its use in the 19th century are rarer, but they do exist: [[mass (music)|mass]]es by [[Anton Bruckner]], [[Ludwig van Beethoven|Beethoven]], and [[Franz Schubert]], for example, have a basso continuo part that was for an organist.{{Citation needed|date=July 2016}}

==Figured bass notation==
A part notated with figured bass consists of a [[bass line]] notated with [[Musical note|note]]s on a [[musical staff]] plus added numbers and [[Accidental (music)|accidental]]s (or in some cases [[Backslash|(back)slash]]es added to a number) beneath the staff to indicate what [[interval (music)|interval]]s above the bass notes should be played, and therefore which [[Inverted chord|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. This instructs the chord-playing instrumentalist not to play any improvised chords for a period. The reason ''tasto solo'' had to be specified was because it was an accepted convention that if no figures were present in a section of otherwise figured bass line, the chord-playing performer would either assume that it was a [[root-position]] triad, or deduce from the harmonic motion that another figure was implied. For example, if a continuo part in the key of C begins with a C bass note in the first measure, which descends to a B{{music|natural}} in the second measure, even if there were no figures, the chord-playing instrumentalist would deduce that this was most likely a [[first inversion]] [[dominant chord]] (spelled B–D–G, from bottom note of the chord to the top).

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 [[interval (music)|compound intervals]] such as 10, 11, and 15.

===Numbers===

{| class="wikitable floatright"
|+Common Conventional Symbols for Figured Bass
! colspan="4" style="background: Silver" |[[Triad (music)|Triads]]
|-
! align="center" | Inversion
! align="center" | Intervals<br>above [[Bass note|bass]]
! align="center" | Symbol
! align="center" | Example
|-
|[[Root position]]
| align="center" | {{su|p=5|b=3}}
| align="center" | None
| rowspan="3" align="center" |<score lang="lilypond">
{
     \override Score.TimeSignature #'stencil = ##f
      \new PianoStaff <<
        \new Staff <<
            \relative c' {
                \clef treble \time 3/4
                <e g c>4 <c g' c> <c e g>
                }
            >>
        \new Staff <<
           \relative c {
                \clef bass \time 3/4
                c4 e g
                }
  \figures {
    < _ >4 <6> <6 4>
  }
            >>
    >> }
</score>
|-
|[[First inversion|1st inversion]]
| align="center" | {{su|p=6|b=3}}
| align="center" | {{music|6 chord}}
|-
|[[Second inversion|2nd inversion]]
| align="center" | {{su|p=6|b=4}}
| align="center" | {{music|64 chord}}
|-
! colspan="4" style="background: Silver" |[[Seventh chord]]s
|-
! align="center" | Inversion
! align="center" | Intervals<br>above bass
! align="center" | Symbol
! align="center" | Example
|-
|Root position
| align="center" | {{overset|7|{{SubSup||3|5}}}}
| align="center" | {{music|7 chord}}
| rowspan="4" align="center" |<score lang="lilypond">
    {
     \override Score.TimeSignature #'stencil = ##f
      \new PianoStaff <<
        \new Staff <<
            \relative c' {
                \clef treble \time 4/4
                <b d f>4 <g d' f> <b f' g > <b d g>
                }
            >>
        \new Staff <<
           \relative c {
                \clef bass \time 4/4
                g4 b d f
                }
  \figures {
    <7>4 <6 5> <4 3> <4 2>
  }
            >>
    >> }
</score>
|-
|1st inversion
| align="center" | {{overset|6|{{SubSup||3|5}}}}
| align="center" | {{music|65 chord}}
|-
|2nd inversion
| align="center" | {{overset|6|{{SubSup||3|4}}}}
| align="center" | {{music|43 chord}}
|-
|[[Third inversion|3rd inversion]]
| align="center" | {{overset|6|{{SubSup||2|4}}}}
| align="center" | {{music|42 chord}} or {{music|2 chord}}
|}

Contemporary figured bass abbreviations for triads and seventh chords are shown in the table to the right.

The numbers indicate the number of [[Scale (music)|scale]] steps above the given bass-line that a note should be played.<ref name=":0">{{Cite web|url=http://www.colby.edu/academics_cs/courses/MU182A/upload/Figured-Bass-Notation.pdf |archive-url=https://web.archive.org/web/20151010073842/http://www.colby.edu/academics_cs/courses/MU182A/upload/Figured-Bass-Notation.pdf |archive-date=2015-10-10 |url-status=live|title=Figured Bass Notation|last=Vigil|first=R|access-date=July 14, 2018}}</ref> For example:

:<score>{ \override Score.TimeSignature #'stencil = ##f \time 6/4 \clef bass << { c1 } \figures { < 6 4 >1 } >> }</score>

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 can be realized as:

:<score>{ \override Score.TimeSignature #'stencil = ##f \time 6/4 \clef bass << { <a f c>1 } >> }</score>

In cases where the numbers 3 or 5 would normally be understood, these are usually left out. For example:

:<score>{ \override Score.TimeSignature #'stencil = ##f \clef bass << { \cadenzaOn c1 b, g, } \figures { < _ >1 < 6 > < 7 > } >> }</score>

has the same meaning as

:<score>{ \override Score.TimeSignature #'stencil = ##f \clef bass << { \cadenzaOn c1 b, g, } \figures { < 5 3 >1 < 6 3 > < 7 5 3 > } >> }</score>

and can be realized as

:<score>{ \override Score.TimeSignature #'stencil = ##f \clef bass \cadenzaOn <c e g>1 <b, d g> <g, b, d f> }</score>

although the performer may choose which octave to play the notes in and will often elaborate them in some way, such as by playing them as [[arpeggio]]s rather than as [[block chord]]s, or by adding improvised [[Ornament (music)|ornaments]], depending on the [[tempo]] and [[texture (music)|texture of the music]].

Sometimes, other numbers are omitted: a 2 on its own or {{su|b=2|p=4}} indicates {{overset|6|{{SubSup||2|4}}}}, for example. From the figured bass-writer's perspective, this bass note is obviously a [[third inversion]] [[seventh chord]], so the [[sixth interval]] is viewed as an interval that the player should automatically infer. In many cases entire figures can be left out, usually where the chord is obvious from the [[chord progression|progression]] or the melody.

Sometimes the chord changes but the bass note itself is held. In these cases the figures for the new chord are written wherever in the bar they are meant to occur.

:<score>{ \override Score.TimeSignature #'stencil = ##f \time 6/4 << { a'2 g' } \new Staff { \clef bass { c1 } } \figures { < 6 >2 < 5 > } >> }</score> can be realized as  <score>{ \override Score.TimeSignature #'stencil = ##f \time 6/4 << { a'2 g' } \new Staff { \clef bass << { <a e>2 <c' e> } \\ { c1 } >> } >> }</score>

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, for as long as the chord is to be held, to indicate this:

:<score>{ \override Score.TimeSignature #'stencil = ##f \time 6/4 \clef bass << { c2 b, } \figures { \bassFigureExtendersOn < 6 >2 < 6> } >> }</score> can be realized as  <score>{ \override Score.TimeSignature #'stencil = ##f \time 6/4 \clef bass << { <e a>1 } \\ { c2 b, }  >> }</score>

When the bass moves the chord intervals have effectively changed, in this case from {{su|b=3|p=6}} to {{su|b=4|p=7}}, but no additional numbers are written.

===Accidentals===

When an [[accidental (music)|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.<ref name=":1">{{Cite book|title=Harmony, Fifth Edition|last=Piston|first=Walter|publisher=W. W. Norton|year=1987|isbn=978-0-393-95480-7|location=New York|pages=84–86}}</ref> Otherwise, if a number is shown, the accidental affects the said interval.<ref name=":0" /> For example, this, showing the widespread default meaning of an accidental without number as applying to the third above the bass:

:<score>{ \override Score.TimeSignature #'stencil = ##f \time 4/4 \clef bass << { e1 c } \figures { < _+ >1 < 6- _- > } >> }</score> can be realized as <score>{ \override Score.TimeSignature #'stencil = ##f \time 4/4 \clef bass <e gis b>1 <c ees aes> }</score>

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 ([[augmented interval|augmented]]) by a [[semitone]] (so that if it is normally a [[flat (music)|flat]] it becomes a natural, and if it is normally a natural it becomes a [[sharp (music)|sharp]]). A different way to indicate this is to draw a [[backslash]] through the number itself.<ref name=":1" /> The following three notations, therefore, all indicate the same thing:

:<score lang="lilypond">{ \override Score.TimeSignature #'stencil = ##f \time 4/4 \key c \minor \clef bass << { c1 c c } \figures { < 6! >1 < 6\+ > <6\\> } >> }</score> can all be realized as <score lang="lilypond">{ \override Score.TimeSignature #'stencil = ##f \time 4/4 \key c \minor \clef bass << { <c ees a>1 } >> }</score>

More rarely, a [[Slash_(punctuation)|"forward" slash]] through a number indicates that a pitch is to be lowered ([[diminished interval|diminished]]) by a semitone: <ref>{{cite web | url=https://www.teoria.com/en/reference/a/alterations.php | title=Reference : Alterations in figured bass }}</ref>

:<score lang="lilypond">{ \override Score.TimeSignature #'stencil = ##f \time 4/4 \key c \minor \clef bass << { c1 c } \figures { < 5- >1 < 5/ > } >> }</score> can both be realized as  <score lang="lilypond">{ \override Score.TimeSignature #'stencil = ##f \time 4/4 \key c \minor \clef bass << { <c ees ges>1 } >> }</score>

When sharps or flats are used with [[key signature]]s, 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 in context===
:[[File:Figured bass example from BWV 443.png|left|thumb|500px|An example of figured bass in context. Taken from ''Beschränkt, ihr Weisen'', by [[J. S. Bach]] (BWV 443). {{audio|Figured bass example from BWV 443.mid|Play}}]]{{clear}}

==Contemporary uses==
In the 20th and 21st century, figured bass is also sometimes used by [[classical music]]ians as a shorthand way of indicating chords when a [[composer]] is sketching out ideas for a new piece or when a music student is [[Harmonic analysis|analyzing the harmony]] of a notated piece of music (e.g., a [[Bach chorale]] or a [[Preludes (Chopin)|Chopin piano prelude]]). Figured bass is not generally used in modern musical compositions, except for neo-Baroque pieces.  

In the 2000s, outside of professional [[Baroque ensemble]]s that specialize in the [[performance practice]] of the Baroque era, the most common use of figured bass notation is to indicate the [[inversion (music)|inversion]] in a harmonic analysis or composer's sketch context, however, often without the staff notation, using letter note names followed with the figure. For instance, if a piano piece had a C major triad in the right hand (C–E–G), with the bass note a G with the left hand, this would be a [[second inversion]] C major chord, which would be written G{{su|b=4|p=6}}. If this same C major triad had an E in the bass, it would be a [[first inversion]] chord, which would be written E{{su|b=3|p=6}} or E{{sub|6}} (this is different from the [[jazz]] notation, where a C{{sup|6}} means the [[added sixth 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 [[diatonic functionality|functional harmony]], a usage called ''figured Roman''; see [[chord symbol]].

A form of figured bass is used in notation of [[accordion]] music; another simplified form is used to notate [[guitar chord]]s.{{citation needed|date=March 2016}}

==See also==
*[[Realization (figured bass)]]
* [[Unfigured bass]]

==References==
{{reflist|25em}}

==Further reading==
*{{cite journal |last1=Schick |first1=Kyle |title=Improvisation: Performer as Co-composer |journal=Musical Offerings |date=1 January 2012 |volume=3 |issue=1 |pages=27–35 |doi=10.15385/jmo.2012.3.1.3 |doi-access=free |url=https://digitalcommons.cedarville.edu/context/musicalofferings/article/1002/viewcontent/MO_F2011_Schick_revision_3_Volume_3_Number_1_Article_3.pdf }}

==External links==
*[http://www.robertkelleyphd.com/figuredbass.htm Figured Bass Symbology] {{Webarchive|url=https://web.archive.org/web/20171120103401/http://www.robertkelleyphd.com/figuredbass.htm |date=2017-11-20 }} by Robert Kelley
*[http://www.robertkelleyphd.com/scaledegrharm.htm Chords that the (major) scale degrees (in the bass) can imply] {{Webarchive|url=https://web.archive.org/web/20171205075222/http://www.robertkelleyphd.com/scaledegrharm.htm |date=2017-12-05 }} by Robert Kelley
*[http://theoryofmusic.wordpress.com/2007/11/23/theory-and-practice-of-the-basso-continuo/ Theory and Practice of the Basso Continuo] by Barry Mitchell
*[https://web.archive.org/web/20130504200827/http://bassus-generalis.org/ Historical sources on the subject of basso continuo - Viadana, Agazzari etc]

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{{Bass (sound)}}
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