# Figured bass

Allegory of Friendship by Johannes Voorhout (1674):
This painting combines three instruments that are important for performing the figured bass: the harpsichord, played by Johann Adam Reincken , the viol, played by Dieterich Buxtehude and the lute, played by the allegorical musica .
3rd movement ( Siciliana ) from Georg Friedrich Handel's sonata op. 1, 11 for flute, oboe or violin and figured bass in two-part, numbered notation

The figured bass or basso continuo ( Italian for "continuous, uninterrupted bass "; short: continuo ) forms the foundation and harmonic framework in music from around 1600 to around 1800, especially in baroque music . Because of the great importance of the figured bass at this time, this epoch is also called the figured bass age after Hugo Riemann .

The figured bass consists of the lowest instrumental part ( bass line ) in conjunction with the chords that match the melody and the musical sequence . These are the basso font not advertised, but indicated by numbers and other symbols above or below the notes are written the basso voice ( figuring ). Not infrequently, however, a number is missing or only a few numbers are given, in this case the chords result from the rules of figured bass and counterpoint and from the context of the piece. The realization of the harmonies is left to the player and is often improvised . This form, in which only the course of the bass is given, then led to the name "figured bass". Modern sheet music editions, however, often contain a possible realization of the chords in musical notation (exposed figured bass) prepared by the editor .

## Instruments

Pietro Domenico Oliviero: The Teatro Regio in Turin (detail), approx. 1752. In the orchestra front left and right you can see two continuo groups, each with a harpsichord - typical for 18th century opera.

For the execution of the bass line including chords, harmony instruments such as B. Organ , positive organ , harpsichord , shelf (only in early baroque, it later went out of fashion), spinet , lute , theorbo , chitarrone , guitar or harp ; From around the middle of the 18th century the fortepiano was also used for chamber music . The bass voice itself is usually amplified by a linear bass instrument such as viola da gamba , violoncello , bassoon , bass dulcian . String instruments such as lira da gamba , viola da gamba or cello can also be used as chords. In larger ensembles, the trombone or serpent (especially in church music) and an instrument with an octave lower part such as the violone were used. In larger ensembles, several chord and bass instruments can be used alternatively or simultaneously. B. two harpsichords usual and at least one lute and theorbo. Which instruments play the figured bass is up to the performer; the choice depends on the time of origin, the place of origin, the structure and character of the piece of music, its remaining (fixed) line-up and, last but not least, the available musicians (see historical performance practice ).

## history

### Beginning of the continuo practice in the early baroque

#### monody

Jacopo Peri : Prologue from Le musiche sopra l'Euridice

The figured bass developed as an accompaniment to the monody from around 1600 and in the course of efforts, especially in the theater, to revive the drama and music of the ancient Greeks (see: Camerata fiorentina ). The polyphonic vocal music of the previous epochs , the so-called prima pratica , was not very suitable for this purpose . The opposite practice began, the monody or seconda pratica , which was based on the linguistic style and, above all, the dramaturgy of the textual statement. Monody was so more flexible and lively than the old polyphony; the harmony of the figured bass tied the individual voices into a musical context. It was only through these fundamental, revolutionary innovations that the genre of opera , which was to find its real language in monody and the musical forms that later emerged from it, was made possible.

This practice was only with the increasing independence of instrumental music over the vocal music from the transition from the Renaissance to the early Baroque become conceivable. It developed from the basso pro organo of the 16th century, which, as basso seguente, amplified the lowest currently sounding voice of a composition and also made the remaining voices of the composition accessible on the basis of various schematized interval constellations.

#### Previous training for performing musicians

The performing musicians of the Renaissance were expected not only to perform and decorate their voices impromptu , but also to improvise any other voices in mock counterpoint ( contrapunto alla mente ). The voices extemporized in this way had to use mainly consonant intervals for the bass; the execution of such voices was the subject of extensive instruction and was u. A. described by Adriano Banchieri in his Essempio di Componere Varie Voci Sopra un Basso di Canto Fermo (1614). At that time it was not yet necessary for the composer to quantify the bass, as the intervals to be added were self-evident within a narrow, modal framework and according to the laws of counterpoint and voice guidance.

#### Intavolations of polyphonic motets

In addition, one began to transfer pure vocal compositions to instruments for the purpose of better support. This intavolation or subtraction of a score (i.e. the summarization in an organ or lute tablature without numbers such as the Wroclaw tablature book ) remained common for a long time, especially for polyphonic contrapuntal movements. In the early baroque period, this procedure initially enabled the organ , harpsichord , lute and theorbo to play along (in extracts) in order to support the singers or to replace missing vocal parts. This also gave rise to the choir practice and the colla parte practice. In addition, the vocal works adapted to the technical conditions of the individual instruments were also used for solo instrumental play without any involvement of singers and form an important root of virtuoso instrumental play.

In 1602, Lodovico Grossi da Viadana published his 100 Concerti ecclesiastici, which were revolutionary in this respect, the first documented solo compositions in the history of church music, which do not derive their harmony from the coexistence of different, contrapuntal solo parts, but rather are supported by a keyboard or plucked instrument . The middle parts of this movement are no longer noted, but are still subject to the rules that would have applied to the middle parts of a written vocal composition. Technically, these works, written in a new style, do not yet depart too far from the imitating vocal movements of the previous epoch, but they do bring about a new awareness of vertical relationships between the individual voices in the music.

#### Development of numbering

Aniello Falcone : The Concert , approx. 1630–50

Numbers were used by early opera composers such as Peri and Giulio Caccini . They also appear in Caccini's solo adrigals and arias in his collection Le Nuove musiche from 1601.

Also Agostino Agazzari spoke in 1607 of the notation of the bass part with added digits. This became necessary above all because the corresponding compositions were more and more detached from a course that grew out of the voice guidance within a narrow modal framework and they were now based on a blueprint constructed from the theory of harmony . The so-called basso continuo spread rapidly from Italy across Europe.

#### Different schools and styles

Throughout the entire era of the thoroughbass age, styles changed depending on the country and epoch. Various types of accompaniment have also been developed for the various instruments such as harpsichord, lute, arch lute or guitar, depending on the possibilities.

Giovanni Gabrieli , a main master of the Venetian polychoir , who also trained the German Heinrich Schütz , recognized the new possibilities offered by the figured bass early on and made extensive use of them. The choir arrangements he developed and refined supported each of the spatially separated choirs with figured bass instruments. Viadana also documents an exemplary choral arrangement of this kind in the preface to his Salmi a 4 cori per cantare e concertare (Venice 1612).

In 1607 Gregor Aichinger was probably the first German composer (after study trips to Venice and Rome) to refer to his model Viadana in the preface to his Cantiones ecclesiasticae . 1619 - at the same time as Michael Praetorius ' Syntagma musicum - the Psalms of David (op. 2) by Heinrich Schütz "with added basso continovo, in front of the organ / lute / chitaron etc."

Little is known about the early Baroque continuo style, but one generally assumes a harmonization that is still strongly influenced by contrapuntal. Presumably through the development of Italian opera and solo instrumental music (especially for violin), a lush, rustling and glittering continuo style developed in Italy, especially for the harpsichord, which is characterized by richly broken arpeggios with acciaccatures and typical of the high and late baroque Continuo playing is also used in other countries.

The continuo apparently came relatively late to France, at least Henri Dumont claimed in his Cantica sacra of 1652 that he was the first to introduce the basso continuo in French music (in sacred music, motets ), or at least to write it down explicitly with the help of numbers. The French continuo style was generally more moderate and less free than the Italian - except for d'Anglebert , who took part in Lully's operas and who also passed on rich acciaccatures.

The German continuo style in the high and late baroque was primarily based on Italian models. Examples by Georg Muffat are very contrapuntal and show a very fine and melodically beautiful voice leading, which are also characteristic of later examples from the environment of Bach or Handel.

### Execution of the figured bass in high baroque

#### Andreas Werckmeister

J. S. Bach: Symbolum Nicenum from the B minor Mass,
figuring above and below the bass

In 1702, at the height of the basso continuo practice from 1650 to 1750, Andreas Werckmeister paraphrased one of their principles with the words that it should be played "without much drive and squirrel" ; he preferred arpeggios as ornaments. The bass had to take over the continuous direction with a constant flow of sound. According to Johann Friedrich Daube , this variety is "... useful when the two voices are accompanied by equally valid but slow tones or notes: ... in this sense it corresponds to the accompaniment of the theorbo or lute." (1756)

#### Johann Sebastian Bach's rules as well as contemporary information on his execution of the bc

Johann Sebastian Bach put it in his figured bass teaching (1738) as follows: "His name is Bassus Continuus or, after the Italian ending, Basso contin [u] o, because it continues playing because the other parts pause now and then ..." and lead further from:

“The general bass is the perfect foundation of music which is played with both hands in such a way that the left hand plays the prescribed notes, but the right hand plays con and dissonants so that this gives a brilliant harmony to the glory of God and permissible delight of the mind and should like all music, including that of the general bass finis and end-cause, nothing else than just for God's honor and recreation of the mind. Where this is not taken into account, there is no actual music, but a devilish Geplerr and Geleyer. "

- Johann Sebastian Bach : Regulations and principles for four-part playing of the general bass or Accompagnement 1738

Bach expressly refers his rules in the title to a four-part version of the numbering. This type of figured bass is predominant as the one standardized in Germany and Italy in the 18th century. B. Bachs and Johann Matthesons as well as Johann David Heinichens testify.

One year later , Lorenz Christoph Mizler judged Bach's figured bass playing :

“Anyone who wants to hear the delicacy in the general bass and what really means to accompany it must endeavor to hear our Herr Bach here, who accompagnies every general bass to a solo in such a way that one thinks it is one Concert, and if the melody, if he made it with the right hand, had been set beforehand. "

- Lorenz Mizler : Newly opened musical library , Leipzig 1739

Another testimony to Bach's sovereign way of performing figured bass can be found in Johann Friedrich Daube; he wrote that Bach had mastered the artful way of playing the figured bass to the highest degree,

“The upper voice had to shine through him. He gave her life through his skilled accompaniment when she didn't have one. He knew how to imitate her so skilfully either with his right or left hand, or he could unexpectedly add a counter-topic that the listener had to swear that it had been set so diligently. The ordinary Accompagnement was shortened very little. In general, his accompaniment was always like one worked out with the greatest diligence, and the upper part in a concerting voice, where at the right time the upper part had to shine. This right was then left to the bass without harm to the upper voice. Enough! Anyone who does not hear him has not heard a lot. "

- Johann Friedrich Daube : thoroughbass in three chords, founded according to the rules of the old and new authors , Leipzig 1756

#### Full part; Johann David Heinichen

Marco Ricci : An opera rehearsal , around 1709. In the center of the picture the continuo group with harpsichord, theorbo, gamba and violone.

The described, so-called full-part movement was occasionally expanded to include five parts and even beyond, above all in order to achieve a stable, full and splendidly rustling sound on the harpsichord. Heinichen, who had still taught the performance of the figured bass in four-part setting in 1711, after his stay in Italy in the years 1710–1717 turned more and more to a full-gripping style of playing, in which of course the rigor of the movement inevitably takes a back seat to the fullness of the sound must kick. Regarding this new way of performing the figured bass, he remarks that it is known

“That the old world trailed the General Bass with a very weak voice after its first invention, and was still a three-part accompaniment in the last years of the faded Seculi, because now the right hand, now the left hand alone has a voice, the other hand the two other voices led, not too rare. In the following times [...] the 4th part Accompagnement became more fashionable, which was initially divided equally in front of both hands, namely two voices in the right and two in the left hand [...]. But because this type was not applicable everywhere, and especially with the use of very fast basses introduced afterwards [...]: so this 4th-part accompaniment in front of the hands was divided unequally: namely, three voices in front of the right hand, and the single bass- Voice in front of the left hand. "

- Johann David Heinichen : The General Bass in the composition 1728

According to Heinichen, this type of execution of the numbering is the most common one, which one is

“Teaches all beginners [...]. But those who are all ready to practice in the art generally seek (especially on the Clavecins) to strengthen the harmony even more, and to accompany with the left hand just as fully as with the right hand, from which, if the opportunity arises, the application of both hands results in a 6.7 . Up to 8th part Accompagnement is created. [...] The more full-voiced you accompany on the clavecins with both hands, the more harmonious it turns out. On the other hand, on organs (especially with weak music and except for the tutti) one must not fall too much in love with the all-too-full accompaniment of the left hand, because the constant murmuring of so many deep tones is unpleasant to the ear and not to the performing singer or instrumentist seldom arduously falls. The Judicium must do its best here. "

- Johann David Heinichen : The General Bass in the composition 1728

#### Rameau's theory of harmony

The awareness of the harmonic relationships between the individual chords led to the first formulation of a theory of harmony by Jean-Philippe Rameau in the 18th century . In it, the theory of the various possible chord inversions, formulated previously by Johannes Lippius (1613) and Henricus Baryphonus (1630), but with no consequences for them, was expanded to the idea of ​​the lower fondamental , on which the harmoniously related intervals are built. If the music of the Renaissance was mainly shaped by neighboring chords, chords that were related to one another in fifths were now mainly used. Despite the groundbreaking new formulation of the changing understanding of harmony, the Rameau system has argumentative weaknesses, which are primarily based on the fact that Rameau systematically tries to develop both the formation of the chords and the melody of the lower fondamental to the nucleus of the third and fifth due to which different progressions are difficult to explain or even theoretically impossible.

#### Instruments used and their specific conditions

J. B. Lully :
Air des Espagnoles from
Le Bourgeois Gentilhomme

In addition to the organ and harpsichord, which formed the backbone of the figured bass for almost two hundred years, plucked instruments such as the lute, theorbo or chitarrone, guitar , and occasionally even the harp , were used to reinforce the bass part with violone , trombone , dulzian or occasionally the Serpent is also used.

The fact that at the time of Bach obviously violons in 8 'and 16' registers were in use raises problems with the instrumentation of Bach's continuo parts. According to the current state of research in Weimar, the violone was used as an eight-foot instrument. It was only in Leipzig that Bach used the 16 'violone that his predecessor in office as Thomaskantor Johann Kuhnau had acquired. The question of the extent to which the use of the respective instruments was only due to the existing instruments must be decided on a case-by-case basis, taking artistic aspects into account; Similar to the registration of the pedal in Bach's organ trio sonatas , it is the responsibility of the performing musician to choose an 8- or 16-foot bass lead. Objective criteria for this are the question of whether incorrect progressions in the voice leading result from doing without the bass octave, as well as sound reasons. The addition of a bass instrument to the continuo group was not absolutely necessary under all circumstances; so there is e.g. E.g. in the violoncello, violon and bassoon parts of the cantata Gott ist mein König, BWV 71 , the instruction tacet , while a singer sings with organ accompaniment, which proves the flexibility of the continuo line-up in detail.

Gradually it became the rule that the figured bass was mostly performed by organ or harpsichord and violone (comparable to today's double bass); According to H. C. Robbins Landon , the figured bass section consisted of violon, bassoon, violoncello and organ or harpsichord. There is a controversial debate as to whether the figured bass must be performed by the organ in sacred music; but it is at least certain that Bach also had a harpsichord available in the Thomaskirche, as was also customary in many other German churches. According to Arnold Schering's assessment , the harpsichord was not used in the performances of the cantatas, but rather it was used at the weekly worship services together with a bass violin to support the mottette singing, which was performed from the Florilegium Portense collection . Ton Koopman, on the other hand, suspects that Bach could at least occasionally have directed his orchestra from this harpsichord and points out the advantages of performing the continuo part together with the organ and harpsichord: “The organ was able to provide load-bearing capacity in the church and the harpsichord for the Rhythm in the choir and orchestra. ”He also points out that Bach“ used the normal church organ with registers that were not too loud ”instead of the chest organ that is in use today. The organist's solo participation sounded much more pleasant [due to the larger pipe scale] and, above all, was much more dominant than is now the case with our little eyelets. "

Each of the chord instruments mentioned, however, also requires special ways of performing the chords due to its own playing style; Also with regard to the handling of the harpsichord, subtle national peculiarities developed due to the tonal properties of the respective instruments (e.g. the more direct Italian harpsichords compared to the softer French instruments).

Late baroque musicians performing a trio sonata for violin, oboe and b. c., the figuration is realized by the harpsichord, the bass part is amplified by a cello and a bassoon.
A. Corelli : Sonata da camera in E flat major op.2 No. 11

In the case of chamber music ensembles, there was and still is a certain freedom in the use of the mostly unspecified instruments that amplify the bass voice, which makes it possible and necessary to adapt them to the type of melody instruments used; For example, in a sonata for two violins and bc the figured bass can also be taken over by a string instrument, while in a sonata for two oboes it can be done by a bassoon.

A. Corelli: Concerto grosso in G minor, Op. 6 No. 8, " fatto per la notte di natale "

In the case of larger, orchestral ensembles, a correspondingly larger ensemble of figured bass was used; Gradually, a preferred line- up of the baroque orchestra is establishing itself , according to which certain, sonically complementary instruments are placed in a balanced relationship with one another. The rustling sound of the harpsichord performing the figured bass is one of the most striking features of orchestral music of this time.

### The second half of the 18th century

#### Differentiated lack of voices, Carl Philipp Emanuel Bach

CPE Bach: Sonata for Flute & bc in B flat major, Wq. 125
Adolph Friedrich Erdmann von Menzel : Flute concert of Frederick the Great in Sanssouci . In this famous painting Friedrich II can be seen in the circle of his court orchestra, on the right in the foreground the figured bass group with C. P. E. Bach on the harpsichord.

The full-voiced, chord-oriented and splendid movement of the late baroque allowed a very refined treatment of dissonances. The transparent three-part playing was only common with solo or small ensembles, and special attention was paid to the melody of the individual parts. Due to the changes in contemporary music, especially with regard to dynamics and instrumentation, Bach's son Carl Philipp Emanuel Bach wrote in the second part of his attempt in 1762 about the true way of playing the piano about the need to accompany not only polyphonically in a single orchestral work, but alternate with three, two or even one-part playing, depending on the volume and tone of the music. In solo music, too, one should subordinate the accompaniment to the dominant voice and react accordingly to changing expression and piano parts.

#### Extinction of the basso continuo in the late 18th century

Unquoted recitative from Paisiello's opera L'Astuzie Amorose (1775)

In the last quarter of the 18th century the figured bass gradually went out of fashion. One reason was the stylistic change towards the classic. Most chord instruments went out of fashion by 1740, especially lute and theorbo. Apart from the organ in the area of ​​church music, initially only the harpsichord remained. In chamber music and solo works (such as arias, flute sonatas, etc.), Carl Philipp Emanuel Bach also recommends the sonically more delicate fortepiano, which is capable of dynamic shades, as a continuo instrument. On the other hand, composers from the Mannheim School , Boccherini and Joseph Haydn brought chamber music ensembles without continuo into fashion from the 1760s, such as string quartets , trios and quintets in particular , but also works with mixed ensembles with winds.

In the age of enlightenment and reason there was occasional criticism of the imprecise notation of the figured bass and the possibility of interpreting a chord in different ways. Was z. B. Heinichen managed to get by with twelve signatures in 1711, Jean-Philippe Rameau showed as early as 1732 that 62 different numbers were in use for 30 chords. Again and again there were no or inadequately figured figured bass parts from the performers, not least from CPE Bach.

#### Use in the classical and romantic periods

The last bars written down by Mozart's hand: The sketched beginning of the “Lacrymosa” of the Requiem, strings, choir parts and the figured bass (not numbered here) have already been performed

Although the harpsichord went out of fashion as a solo instrument between around 1775 and 1790, the practice of figured bass in orchestral music, opera and church music (organ) persisted into the early 19th century. Of this u. a. also the lively interest in figured bass schools. For example, D. Kellner's figured bass school (Hamburg 1732) experienced nine regular new editions up to 1796. And Daniel G. Türk's Brief Instructions on figured bass playing (Leipzig / Halle 1791) appeared five times up to 1841.

There is also no doubt that Joseph Haydn (e.g. London Symphonies, Creation ) and Mozart (e.g. Così fan tutte , Magic Flute ) led the orchestra from the harpsichord until the end of their lives. The fortepiano was also popular as a continuo instrument in small chamber music , but it was too quiet as a “conducting instrument” with a large orchestra. It is known, however, that Mozart played continuo in his piano concertos with orchestral passages.

The early divertimenti of Mozart and Haydn are still numbered with figured bass. Until the 1820s, the recitatives of operas by Mozart, Rossini (e.g. Tancredi or Barbier von Sevilla from 1816), Meyerbeer (still in Il crociato in Egitto from 1824) and their contemporaries were accompanied by the harpsichord. Nevertheless, the figured bass had already outlived itself by 1800. Beethoven already wrote that he was born with an “obligatory accompaniment”. Only in the organ part of church music did the tradition of numbering last well into the 19th century; Anton Bruckner used them until around 1856. The figured bass notation was still one of the foundations of organist training. Other composers of this time sometimes still used the numbering to quickly write down the harmonic progression in composition sketches, such as Johannes Brahms .

The figured bass came more and more out of fashion in performance practice, but continued to play an important role in music education, especially in the partimento tradition that began in Italy . Even Ferdinand Hiller used in its exercises to the study of harmony and counterpoint (Cologne 1860) figured bass exercises, including u. a. Partimenti by Fedele Fenaroli .

#### Today's meaning of figured bass notation

In the course of the rediscovery of early music, the figured bass is increasingly being taken up again and is also being taught at conservatoires or is a prerequisite (e.g. in musicology). It is also the subject of often more specialized musicological research. There are separate courses in figured bass, and figured bass playing has always been part of the training of church musicians , albeit mostly without reference to historical types of exposure and more as a theoretical construct .

## Instructions and notes regarding organ registration for continuo playing

Special instructions for the accompaniment in the figured bass coincide with general considerations: Hans Klotz recommends that since neither the organist nor the choir can decide whether the accompaniment registers fit, someone should go to the ship or ask a music-savvy listener (also in the ship). In principle, basic registers are used for organ accompaniment (principal 8 ′). Individual obligatory motifs (this depends on the abilities of the player in the figured bass) can be emphasized by similar but somewhat stronger registers. If the voices are completely performed, an unobtrusive mix of solo registers is used on the Rückpositiv, if necessary. That then depends on the character of the piece, whether it is more of a spiritual song with an independent melody or a chorale in which the upper part of the accompaniment and the singing part go together. In case of doubt you have to accompany female and male voices that have different registers at the same time. Then you have to decide how much ornate play-arounds of the singing voice, if they are available, you want to participate, the recommendation is rather less to participate.

• Claudio Monteverdi (1612): For his Magnificat of 1610, Monteverdi prescribes the register Principale (8 ') for the instrumentation of seven vocal and six instrumental parts for the continuo . For the “Fecit Potentiam” he requires the register Fiffaro ò Voci umane . The first movement (“Magnificat”) calls for the organist to increase from Principale to Ottava to Quintadecima and the final movement a pieno .
• In 1618 Michael Praetorius recommends a Principal 8 'to accompany motets and a “gentle, lovely and gentle set or some other gentle, quiet flute work” for the “Concertat parts”. For the “Plenus Chorus” he gives a sharp register in work or positive but “nevertheless not the full work”. Elsewhere he also mentions the “whole work in the organ” “for full-part music”.
• Matthew Hertels recommendation of 1660 for doppelchörige motets : Topside: principal 8, coarse Covered 8, Rückpositiv: Quintadena 8 ', Klein Covered 4', pedal: sub-bass open and covered 16 ', principal 8'.
• In a disposition draft for the organ of the Divi Blasii Church in Mühlhausen , which was rebuilt in 1708 , Bach suggests: “As far as the new breast positive gene is concerned, the following voices could come into it - as: 7th silent act 8 feet, so there perfect accorded to the music ”.
• Friedrich Erhard Niedt recommends to the organist in his manual on variation how to vary the figured bass and the numbers placed above it & make similar inventions about it (1721): “If only one or two voices are singing or playing, all he needs in the manual is the Gedact 8 feet, and no pedal anywhere. "
• In 1726 Johann Friedrich Walther describes the organ of the Garrison Church in Berlin and teaches about the suitability of the registers for accompanying a "music". The principal 8 'sounds "pure and pleasant under the tutti of a music". The Gedackt 8 'is "nice to use for music". For the bass, a bassoon 16 ', a principal 16' and a violon 16 'are mentioned.
• Jakob Adlungs's instructions for playing the figured bass from 1758 note a "silent eight-footed voice" for the right hand, and quintades 16 'or drone 16' with principal 8 'or principal 16', viola da gamba 8 'and salizett for the bass of the left hand 4 '.

## Execution of the figured bass

The numbering consists of one or more digits, which today are usually arranged vertically below the bass note. The numbering is usually at the top of the old originals. They mean ladder-specific intervals between the bass or the lowest note and other notes of the chord in question. As a rule, only deviations from the ladder's own triad above the bass note are quantified. The intervals are played either in their natural size or with an octave shift upwards.

A triad required over an unquantified bass note is called a so-called basic triad . It consists of the bass note with the ladder's own third (3, not numbered) and the fifth (5, not numbered). A sixth (6, numbered) or a fourth (4, numbered) replace the fifth or third, unless otherwise specified. A 2 alone is always an abbreviation for , or, misleadingly, also denotes a bass lead . All other digits serve as a supplement to the triad, so that a notated 7 is interpreted as a four-note note , third, fifth and seventh . ${\ displaystyle {\ begin {smallmatrix} 6 \\ 4 \\ 2 \ end {smallmatrix}}}$${\ displaystyle {\ begin {smallmatrix} 5 \\ 2 \ end {smallmatrix}}}$

Exact location designation in
C. PE Bach's attempt on the true way of playing the piano

Countermovement of the 2nd and 3rd chord in relation to the bass to avoid octave and fifth parallels

The numbering usually does not provide any information about the position , i.e. the arrangement of the corresponding tones in the chord and thus also not about the respective top tone of the same, but only about its so-called inversion . In individual cases such as B. after Carl Philipp Emanuel Bach's attempt on the true way of playing the piano, second part (1762), the figured bass for a three-part accompaniment in the gallant style - similar to the monody - is sometimes provided with exact location names. The numbers 1 to 12 are used.

A skilful combination of the different chords and their individual voice guidance is otherwise at the discretion of the player, who designs the numbering bound to the musical rules of composition , but at the same time following the spontaneous idea and here extensive freedom with regard to the melodic and rhythmic form as well as the ornamentation of execution. Since the figured bass is generally used to accompany a melody, the reproduction of the chords must harmonize with it and, if necessary, be subordinate to it; it is the task of the companion to ensure this by adequately performing his game.

It must also be noted that there is or has not been a completely uniform, binding spelling and no generally applicable comprehensive set of rules; rather, the composers using this shorthand assumed a deep insight into the theory of harmony and performance practice on the part of the performers , through which the dubious connections were mostly revealed can be.

Example of a figured bass notation: bass line, numbering and suggestion for chord formation (light)
(listen) ? / i

(Here using the example of C major). You always have to form the intervals from the bass note.

• No numbering: third and fifth (C – E – G) , the third of the chord is generally assumed for every chord, unless it is the resolution of a lead or a dissonant tone.
• ${\ displaystyle {\ begin {smallmatrix} 6 \ end {smallmatrix}}}$: Third and sixth (E – G – C) , sixth chord , corresponds to the first inversion . It is always abbreviated instead of   The chord third is usually not doubled in the upper parts. Exceptions to this are the Neapolitan sixth chord , in which the third is usually doubled, or they result from the necessity of leading in sixth chord chains (see also Errors and Sources of Errors).${\ displaystyle {\ begin {smallmatrix} 6 \ end {smallmatrix}}}$${\ displaystyle {\ begin {smallmatrix} 6 \\ 3 \ end {smallmatrix}}}$

The objective of a voice leading as fluently as possible can also require that voices meet on the same note and that a three-part voice is created at this moment (see example).

• ${\ displaystyle {\ begin {smallmatrix} 6 \\ 4 \ end {smallmatrix}}}$: Fourth and sixth (G – C – E) , sixth fourth chord , corresponds to the second inversion (since this chord is a typical lead sound, a corresponding example can be found there).

### Typical four notes

• ${\ displaystyle {\ begin {smallmatrix} 7 \ ​​end {smallmatrix}}}$: Third, fifth, seventh (G – B – D – F) . It always takes place . Used, among other things, for dominant seventh chords (in example 1 that of C major)${\ displaystyle {\ begin {smallmatrix} 7 \ ​​end {smallmatrix}}}$${\ displaystyle {\ begin {smallmatrix} 7 \\ 5 \\ 3 \ end {smallmatrix}}}$
• ${\ displaystyle {\ begin {smallmatrix} 6 \\ 5 \ end {smallmatrix}}}$: Third, fifth and sixth (H – D – F – G) , designation: fifth chord . It always takes place . Used for (subdominant) chords with sixth ajoutée (example 1)${\ displaystyle {\ begin {smallmatrix} 6 \\ 5 \ end {smallmatrix}}}$${\ displaystyle {\ begin {smallmatrix} 6 \\ 5 \\ 3 \ end {smallmatrix}}}$
• ${\ displaystyle {\ begin {smallmatrix} 4 \\ 3 \ end {smallmatrix}}}$: Third, fourth, sixth (D – F – G – H) , designation: third fourth chord . It always takes place .${\ displaystyle {\ begin {smallmatrix} 4 \\ 3 \ end {smallmatrix}}}$${\ displaystyle {\ begin {smallmatrix} 6 \\ 4 \\ 3 \ end {smallmatrix}}}$
• ${\ displaystyle {\ begin {smallmatrix} 2 \ end {smallmatrix}}}$: Second, fourth, sixth (F – G – H – D) , designation: second chord . It stands or instead of partly also takes place . (All "instead of" information) (see example 2)${\ displaystyle {\ begin {smallmatrix} 2 \ end {smallmatrix}}}$ ${\ displaystyle {\ begin {smallmatrix} 4 \\ 2 \ end {smallmatrix}}}$${\ displaystyle {\ begin {smallmatrix} 6 \\ 4 \\ 2 \ end {smallmatrix}}}$${\ displaystyle {\ begin {smallmatrix} 5 \\ 2 \ end {smallmatrix}}}$

### Typical reservations

• ${\ displaystyle {\ begin {smallmatrix} 4 \ 3 \ end {smallmatrix}}}$: The fourth is held in front of the third, the fourth is played first and then resolved to the third in the same chord (C – F – G → C – E – G) (see example)
• ${\ displaystyle {\ begin {smallmatrix} 6 \ 5 \ end {smallmatrix}}}$: The sixth is held in front of the fifth (C – E – A → C – E – G) (see example)
• ${\ displaystyle {\ begin {smallmatrix} 7 \ ​​6 \ end {smallmatrix}}}$: The seventh is held before the sixth (F – A – E → F – A – D) (see example)
• ${\ displaystyle {\ begin {smallmatrix} 9 \ 8 \ end {smallmatrix}}}$: The ninth is held in front of the octave. This results in a four-tone; the root note is doubled in resolution by the octave (C – E – G – D → C – E – G – C) . (see example)
• ${\ displaystyle {\ begin {smallmatrix} 6 \ 5 \\ 4 \ 3 \ end {smallmatrix}}}$: The fourth and the sixth are held in front of the third and the fifth (C – F – A → C – E – G) . (see example)

### Alterations

The figured bass is basically based on the ladder's own tones. In one piece, which is listed in C major, this results in the following supply of tones: C, D, E, F, G, A, H .

Since a larger set of notes was already used in the Baroque era, there are notations with which the alteration of a ladder's own tone to another tone is displayed. Examples:

• , , : Individual accidentals refer to the third; The basic triad is thus performed here with the third altered third from the ladder and thus possibly also in the opposite tone gender. In the early days of figured bass, usually stands for humiliation, for elevation (instead of ); the diminished fifth was often referred to as when it was a ladder.
• 7 : The seventh chord is executed with the major seventh that is not part of the ladder instead of the ladder's own minor seventh. This should not be confused with where the alteration relates to the third.${\ displaystyle {\ begin {smallmatrix} 7 \\\ sharp \ end {smallmatrix}}}$
• Abbreviated instead of 6 is : increased The sixth as a leading tone, is recorded diagonally crossed, just as for other numbers, it will also set mainly in 4 and 5 for clarity slash behind this .${\ displaystyle {\ begin {smallmatrix} 6 \! \! \! / \ end {smallmatrix}}}$${\ displaystyle {\ begin {smallmatrix} 4 \ \! \! \! / \ end {smallmatrix}}}$
• In , the slash forms a “+” with a move of the 6, for example the other way around with the neck at the top (see fig.), Which is why 6+ is used synonymously. Since ♮ was not always used, this sometimes simply means the resolution of a . (see example)${\ displaystyle {\ begin {smallmatrix} 6 \! \! \! / \ end {smallmatrix}}}$
• For alterations, omitted numbers must then be added again, for example the 4 or 6 in the second chord.

### Tendencies towards dissolution of individual intervals

• Sevenths always resolve downwards.
• "Leading tones" always dissolve upwards.

### Voice Guiding Conventions

• Tones common to two consecutive chords are played or left in the same register both times.
• In the case of moving voices, the aim is to reach the individual tones of the respective voice as quickly as possible from the previous tone.
• Overall, attention should be paid to countermovement, especially between the soprano and bass of the movement.

### Others

• A horizontal line for a few notes indicates that the numbering continues, the following notes are not harmonized.
• Short diagonal lines a few notes long indicate that the numbering is repeated.
• “Tasto Solo”, “ts” or “0” is the instruction to play only the corresponding note without suspension.
• Digits under a pause indicate that the harmony is proposing, the bass is following.
• Passages and alternating notes in the bass, especially in small note values, are not numbered and are not suspended.

### Errors and sources of error

The general rule is: The realization of the figured bass should be pure in itself in any case, i.e. without forbidden progressions such as octave and fifth parallels. Parallels between the solo part (s) and the accompanying instrument can be tolerated under certain circumstances, but should, if possible, be included in the middle parts. Exceptions apply to playing with more than four voices (almost exclusively on the harpsichord). For example, Georg Muffat's tract “Regolae concentuum partiturae” (1699) contains up to eight-part exposures, some with open fifths and octaves and the note “allowed in harpsichord”.

• In the case of sequences of sixth chords, the third must be doubled alternately, and then another note (root note or fifth) must be doubled for the next chord, since the doubling of the same note in the same position in two consecutive chords by definition causes parallels.
• Short notes, for example eighth notes, have to be suspended if they are harmonically important, for example dissolve a lead.

### Further examples

• The figured bass to the first bars of the “Lamentos” from the Capriccio BWV 992 by Johann Sebastian Bach, in which the use of figured bass notation within a solo piano piece is documented as musical shorthand, shows the seldom found exact location of triads. The single 5 means fifth position, the single 3 third position:
Cantata BWV 140, recitative No. 2

## Limits of figured bass notation

The concept of the ladder's own tones practically limits the figured bass notation to music that remains harmoniously in the immediate vicinity of the fundamental key (see circle of fifths ), since modulations to keys that are further away lead to an excess of alterations and impair the legibility of the notation.

By Padre Stanislao Mattei (1750-1825), however, in Pratica d'accompagnamente sopra bassi nomerati there are practicable modulations from the example key of C major to all major and minor keys.

This makes the figured bass suitable for almost all baroque music. The following epochs opened up larger harmonic relationships and further developed the tonal differentiation in the sound body, so that from the Viennese classical period it is no longer a matter of course that the bassoon and cellos play the same part, or that the harmonic structure is supported by a polyphonic instrument.

As a result, different notations ( obligatory Accompagnement , i.e. a full score written out in all the necessary parts ) and a different understanding of harmony (level theory , later function theory ) became necessary.

## literature

• Johann David Heinichen : The general bass in the composition. Self-published, Dresden 1728 (2nd reprint. Olms, Hildesheim et al. 1994, ISBN 3-487-09824-5 ).
• Georg Philipp Telemann : Singing, playing and thorough bass exercises . Hamburg 1733/34. New edition by Max Seiffert . Bärenreiter, Kassel 1920.
• Johann Sebastian Bach : Rules and principles for four-part playing of the general bass or accompaniment for his scholars in music. Leipzig 1738 (English: J. S. Bach's Precepts and principles for playing the thorough-bass or accompanying in four parts. Leipzig 1738 [= Early music series . 16]. Translated with facsimiles, introduction and explanatory notes by Pamela L. Poulin. Clarendon Press, Oxford 1994, ISBN 0-19-816225-1 ).
• Johann Philipp Kirnberger : Principles of the figured bass as the first lines to the composition. Hummel, Berlin 1781 ( digitized version ).
• Daniel Gottlob Türk : Instructions for playing general bass. At the expense of the author on commission from Schwickert u. a., Leipzig a. a. 1800 (Facsimile. Introduced by Rainer Bayreuther. Laaber-Verlag, Laaber 2005, ISBN 3-89007-601-7 (= Laaber-Reprint 6)).
• Carl Gottlieb Hering : New, very facilitated, practical thoroughbass school for young musicians, at the same time as a necessary aid for those who want to learn the thoroughbass easily in a short time without oral lessons. Self-published, Oschatz and Leipzig 1805.
• August Eberhard Müller : Great Fortepiano School. Eighth edition, with many new examples and a complete appendix from the figured bass by Carl Czerny . Peters, Leipzig 1825.
• Johann Georg Albrechtsberger : All writings on basso continuo, harmony theory and the art of composing music. 3 volumes. 2nd carefully revised edition. Haslinger, Vienna 1837.
• Matthäus Zeheter, Max Winkler: Complete theoretical-practical basso continuo and harmony teaching . For young musicians in general, but especially for organ students, school seminarians, school apprentices. And for self-teaching. 2 volumes (volume 1: harmony theory ; volume 2: figured bass theory ). Beck, Nördlingen 1845-1847.
• Hugo Riemann : Instructions for playing basso continuo (harmony exercises on the piano) . = Handbook of figured bass playing (= Max Hesse's illustrated handbooks , 10, ZDB -ID 777229-4 ). 3. Edition. Hesse, Leipzig 1909.
• Max Schneider : The beginnings of the basso continuo and its numbering . Breitkopf & Härtel, Leipzig 1918, archive.org .
• Franck Thomas Arnold: The Art of Accompaniment from a Thorough-Bass as practiced in the XVIIth & XVIIIth Centuries . Oxford University Press, Oxford 1931. Reprint in 2 volumes: Dover Publications, Mineola (New York) 1965, 2nd edition 2003, ISBN 0-486-43188-6 (volume 1), ISBN 0-486-43195-9 (volume 2).
• Hermann Keller : School of figured bass. Bärenreiter, Kassel 1931 (5th edition there 1955).
• Walter Leib: Exercises in basso continuo (= exercises on music theory , 3, ZDB -ID 2299418-X ). Hochstein, Heidelberg 1947.
• Gerhard Kirchner: The thoroughbass with Heinrich Schütz (= musicological work 18, ZDB -ID 504891-6 ). Bärenreiter, Kassel u. a. 1960 (at the same time: Freiburg (Breisgau), Univ., Diss., 1957).
• Nigel North : Continuo Playing on the Lute, Archlute and Theorbo. Indiana University Press, Bloomington 1987.
• Ulrich Michels: dtv atlas of music. Boards and texts. Volume 1: Systematic Part, Historical Part: From the Beginnings to the Renaissance. 16th edition, 391–405. Thousand Bärenreiter-Verlag u. a., Kassel u. a. 1995, ISBN 3-7618-3022-X , p. 100.
• Irmtraut Freiberg: The early Italian figured bass presented on the basis of sources from 1595 to 1655. 2 volumes (volume 1: treatises and forewords ; volume 2: musical examples ). Olms, Hildesheim 2004, ISBN 3-487-12689-3 (Volume 1), ISBN 3-487-12690-7 (Volume 2).
• Siegbert Rampe: thorough bass practice 1600–1800. Laaber-Verlag, Laaber 2014, ISBN 978-3-89007-829-8 .

Wiktionary: figured bass  - explanations of meanings, word origins, synonyms, translations

## Individual evidence

1. Handbuch der Musikgeschichte , 2 volumes in 5 parts, Volume 2, Part 2: The age of figured bass . Leipzig, 1912
2. Laurence Decobert: Henri Dumont (1610-1684): maistre et compositeur de la musique de la Chapelle du Roy et de la Reyne (online as Googlebook ), Editions Mardaga, 2011, p. 190 (excerpt from the preface in the facsimile)
3. CD booklet on Henri Dumont - Motets pour la Chapelle du Roy, with La Chapelle Royale & Philippe Herreweghe, harmonia mundi. P. 7
4. ^ Jean-Henry d'Anglebert: "Principes de l'Accompagnement", in: Pièces de clavecin - Édition de 1689 , Facsimile, publ. sous la dir. de J. Saint-Arroman, Courlay: Édition JM Fuzeau, 1999, pp. 123–128.
5. H. Keller, school of figured bass playing
6. ^ Jean-Philippe Rameau: Traité de l'harmonie réduite à ses principes naturels , Paris 1722
7. Laurence Dreyfus: Bach's Continuo group , ISBN 978-0-674-06030-2 .
8. ^ Johann Gottfried Walther , Musical Lexicon or Musicalische Bibliothek ... , Leipzig (with Wolffgang Deer) 1732, new print, ed. by Richard Schaal, Kassel 1953 and 4th ed. Kassel and Basel 1986.
9. ^ Ton Koopman : Aspects of performance practice . In: The world of Bach cantatas . Joint edition of the publishers JB Metzler, Stuttgart / Weimar and Bärenreiter, Kassel, 1996, volume 1, p. 217
10. ^ Arnold Schering: Johann Sebastian Bach's Leipzig Church Music , Leipzig 1954.
11. ^ Ton Koopman : Aspects of performance practice . In: The world of Bach cantatas . Joint edition of the publishers JB Metzler, Stuttgart / Weimar and Bärenreiter, Kassel, 1996, volume 1, p. 213 f.
12. CPE Bach: Attempt on the true way of playing the piano ; Part 1, Berlin 1753; Part 2, Berlin 1762 (edited by Wolfgang Horn). Facsimile edition, Bärenreiter, Kassel, 1994. Part 2, Introduction, pp. 4-7.
13. ↑ Lutenists were employed in the famous Mannheim orchestra until 1742. Bärbel Pelker: "The electoral court music in Mannheim and Schwetzingen (1720-1778)". In: Silke Leopold, B. Pelker (eds.): South German court chapels in the 18th century , pp. 297–298
14. Michel Corrette writes in 1753 in Le maître de clavecin pour l'accompagnement that only the harpsichord is left “as the soul of harmony, support and honor of music”; D. Kellner in the 1767 edition of his figured bass school states that at this time the “clavier” (harpsichord or fortepiano) was the main continuo instrument. See Peter Williams: Figured Bass-Accompaniment , University Press, Edinburgh, 1970/1987, p. 27
15. ↑ In 1762 he complained in detail about unquantified basses, and wrote an entire chapter about it. In: CPE Bach: An attempt on the true way of playing the piano ; Part 1, Berlin 1753; Part 2, Berlin 1762 (edited by Wolfgang Horn). Facsimile edition, Bärenreiter, Kassel, 1994. Part 2, Cap. 35, pp. 298-301. ( Digitized version and full text in the German text archive ; online version )
16. On the use of the harpsichord as an orchestral and continuo instrument around 1802, Koch writes in his Musikalischen Lexicon , Frankfurt 1802 , under the heading “wing, clavicimbel” (pp. 586–588; wing = harpsichord): “ […] The other genres of these Clavierart, namely the spinet and the clavicytherium , have fallen completely out of use; The grand piano is still used in most of the large orchestras, partly to support the singer with the recitative , partly and mainly to fill in the harmony by means of the figured bass ... Its strong, penetrating tone makes it the fulfillment of the full-voiced music All very clever; therefore it will probably maintain the rank of a very useful orchestral instrument in large opera houses and with numerous casts of voices until another instrument of the same strength but more mildness or flexibility of tone is invented, which is also used for performing the figured bass is sent. […] In clay pieces according to the taste of the time, especially with a weak cast of the voices, […] one has begun for some time now to swap the grand piano with the weaker, but softer fortepiano . "
17. Original title: Faithful teaching in general bass. See: Peter Williams: Figured Bass-Accompaniment , University Press, Edinburgh, 1970/1987, p. 110.
18. Williams names the following editions by Kellner: 1732, 1737 (with foreword by Telemann ), 1743, 1754, 1767, 1773, 1782, 1787, 1796. In: Peter Williams: Figured Bass-Accompaniment , University Press, Edinburgh, 1970 / 1987, p. 110.
19. Türk appeared in editions: 1791, 1800 (expanded), 1816, 1822 (Vienna), 1824, 1842. See: Peter Williams: Figured Bass-Accompaniment , University Press, Edinburgh, 1970/1987, p. 114.
20. "[...] in clay pieces according to the taste of the time, especially with a weak cast of the voices, [...] one has begun for some time  to weaken the grand piano (= harpsichord !, Author's note) with the weaker, but softer to swap fortepiano . "Excerpt from:" Flügel, Clavicimbel ", Koch's Musical Lexicon , Frankfurt 1802 , p. 588
21. ^ Hans Klotz : The book of the organ , Bärenreiter, Kassel 2000, ISBN 3-7618-0826-7 .
22. www.walkerstiftung.de
23. Hans Klotz : Organ Art of the Gothic Renaissance and Baroque. Kassel 1975
24. ^ Hans Klotz: The organ art of the Gothic, the Renaissance and the Baroque 1975; Pp. 137, 231
25. lehrklaenge.de - The figured bass . Retrieved September 22, 2018