Figured bass
Encyclopedia
Figured bass, or thoroughbass, is a kind of integer musical notation
Musical notation
Music notation or musical notation is any system that represents aurally perceived music, through the use of written symbols.-History:...

 used to indicate intervals
Interval (music)
In music theory, an interval is a combination of two notes, or the ratio between their frequencies. Two-note combinations are also called dyads...

, chord
Chord (music)
A chord in music is any harmonic set of two–three or more notes that is heard as if sounding simultaneously. These need not actually be played together: arpeggios and broken chords may for many practical and theoretical purposes be understood as chords...

s, and non-chord tones, in relation to a bass note. Figured bass is closely associated with basso continuo, an accompaniment
Accompaniment
In music, accompaniment is the art of playing along with an instrumental or vocal soloist or ensemble, often known as the lead, in a supporting manner...

 used in almost all genres of music in the Baroque period
Baroque music
Baroque music describes a style of Western Classical music approximately extending from 1600 to 1760. This era follows the Renaissance and was followed in turn by the Classical era...

, though rarely in modern music.

Other systems for denoting or representing chords include:
plain staff notation, used in classical music
Classical music
Classical music is the art music produced in, or rooted in, the traditions of Western liturgical and secular music, encompassing a broad period from roughly the 11th century to present times...

, Roman numerals
Roman numeral analysis
In music, roman numeral analysis is the use of roman numeral symbols in the musical analysis of chords. In music theory related to or derived from the common practice period, arabic numerals with carets are used to designate scale degrees themselves , whereas in theory related to or derived from...

, commonly used in harmonic analysis
Harmonic analysis
Harmonic analysis is the branch of mathematics that studies the representation of functions or signals as the superposition of basic waves. It investigates and generalizes the notions of Fourier series and Fourier transforms...

,
macro symbols
Macro analysis
In music theory, macro analysis is a method of transcribing, or writing down chords that may be used along with or instead of conventional musical analysis...

, sometimes used in modern musicology
Musicology
Musicology is the scholarly study of music. The word is used in narrow, broad and intermediate senses. In the narrow sense, musicology is confined to the music history of Western culture...

, and various names and symbols
Chord names and symbols (jazz and pop music)
Various kinds of chord names and symbols are used in different contexts, to represent musical chords. In jazz and popular music, a chord name and the corresponding symbol are typically composed of one or more of the following parts:# The root note ....

 used in jazz
Jazz
Jazz is a musical style that originated at the beginning of the 20th century in African American communities in the Southern United States. It was born out of a mix of African and European music traditions. From its early development until the present, jazz has incorporated music from 19th and 20th...

 and popular music
Popular music
Popular music belongs to any of a number of musical genres "having wide appeal" and is typically distributed to large audiences through the music industry. It stands in contrast to both art music and traditional music, which are typically disseminated academically or orally to smaller, local...

.

Basso continuo

Basso continuo parts, almost universal in the Baroque
Baroque music
Baroque music describes a style of Western Classical music approximately extending from 1600 to 1760. This era follows the Renaissance and was followed in turn by the Classical era...

 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
Harpsichord
A harpsichord is a musical instrument played by means of a keyboard. It produces sound by plucking a string when a key is pressed.In the narrow sense, "harpsichord" designates only the large wing-shaped instruments in which the strings are perpendicular to the keyboard...

, organ
Organ (music)
The organ , is a keyboard instrument of one or more divisions, each played with its own keyboard operated either with the hands or with the feet. The organ is a relatively old musical instrument in the Western musical tradition, dating from the time of Ctesibius of Alexandria who is credited with...

, lute
Lute
Lute can refer generally to any plucked string instrument with a neck and a deep round back, or more specifically to an instrument from the family of European lutes....

, theorbo
Theorbo
A theorbo is a plucked string instrument. As a name, theorbo signifies a number of long-necked lutes with second pegboxes, such as the liuto attiorbato, the French théorbe des pièces, the English theorbo, the archlute, the German baroque lute, the angélique or angelica. The etymology of the name...

, guitar
Guitar
The guitar is a plucked string instrument, usually played with fingers or a pick. The guitar consists of a body with a rigid neck to which the strings, generally six in number, are attached. Guitars are traditionally constructed of various woods and strung with animal gut or, more recently, with...

, or harp
Harp
The harp is a multi-stringed instrument which has the plane of its strings positioned perpendicularly to the soundboard. Organologically, it is in the general category of chordophones and has its own sub category . All harps have a neck, resonator and strings...

. In addition, any number of instruments which play in the bass register may be included, such as cello
Cello
The cello is a bowed string instrument with four strings tuned in perfect fifths. It is a member of the violin family of musical instruments, which also includes the violin, viola, and double bass. Old forms of the instrument in the Baroque era are baryton and viol .A person who plays a cello is...

, double bass
Double bass
The double bass, also called the string bass, upright bass, standup bass or contrabass, is the largest and lowest-pitched bowed string instrument in the modern symphony orchestra, with strings usually tuned to E1, A1, D2 and G2...

, bass viol
Viol
The viol is any one of a family of bowed, fretted and stringed musical instruments developed in the mid-late 15th century and used primarily in the Renaissance and Baroque periods. The family is related to and descends primarily from the Renaissance vihuela, a plucked instrument that preceded the...

, or bassoon
Bassoon
The bassoon is a woodwind instrument in the double reed family that typically plays music written in the bass and tenor registers, and occasionally higher. Appearing in its modern form in the 19th century, the bassoon figures prominently in orchestral, concert band and chamber music literature...

. The most common combination, at least in modern performances, is harpsichord and cello for instrumental works and secular vocal works, such as opera
Opera
Opera is an art form in which singers and musicians perform a dramatic work combining text and musical score, usually in a theatrical setting. Opera incorporates many of the elements of spoken theatre, such as acting, scenery, and costumes and sometimes includes dance...

s, 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
Improvisation
Improvisation is the practice of acting, singing, talking and reacting, of making and creating, in the moment and in response to the stimulus of one's immediate environment and inner feelings. This can result in the invention of new thought patterns, new practices, new structures or symbols, and/or...

 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
Historically informed performance
Historically informed performance is an approach in the performance of music and theater. Within this approach, the performance adheres to state-of-the-art knowledge of the aesthetic criteria of the period in which the music or theatre work was conceived...

, 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: mass
Mass (music)
The Mass, a form of sacred musical composition, is a choral composition that sets the invariable portions of the Eucharistic liturgy to music...

es by Anton Bruckner
Anton Bruckner
Anton Bruckner was an Austrian composer known for his symphonies, masses, and motets. The first are considered emblematic of the final stage of Austro-German Romanticism because of their rich harmonic language, complex polyphony, and considerable length...

, Beethoven
Ludwig van Beethoven
Ludwig van Beethoven was a German composer and pianist. A crucial figure in the transition between the Classical and Romantic eras in Western art music, he remains one of the most famous and influential composers of all time.Born in Bonn, then the capital of the Electorate of Cologne and part of...

, and Franz Schubert
Franz Schubert
Franz Peter Schubert was an Austrian composer.Although he died at an early age, Schubert was tremendously prolific. He wrote some 600 Lieder, nine symphonies , liturgical music, operas, some incidental music, and a large body of chamber and solo piano music...

, 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 note
Note
In music, the term note has two primary meanings:#A sign used in musical notation to represent the relative duration and pitch of a sound;#A pitched sound itself....

s on a musical staff plus added numbers and accidental
Accidental (music)
In music, an accidental is a note whose pitch is not a member of a scale or mode indicated by the most recently applied key signature. In musical notation, the symbols used to mark such notes, sharps , flats , and naturals , may also be called accidentals...

s beneath the staff to indicate what interval
Interval (music)
In music theory, an interval is a combination of two notes, or the ratio between their frequencies. Two-note combinations are also called dyads...

s above the bass notes should be played, and therefore which inversions
Inversion (music)
In music theory, the word inversion has several meanings. There are inverted chords, inverted melodies, inverted intervals, and inverted voices...

 of which chords are to be played. The phrase tasto solo
Tasto solo
Tasto solo is an Italian term used in music scores, usually on the continuo part, to indicate that a note or section should be played on its own, without harmony. The phrase first appeared in music theory books in the eighteenth-century, but was used by composers such as Arcangelo Corelli before...

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
Claudio Monteverdi
Claudio Giovanni Antonio Monteverdi – 29 November 1643) was an Italian composer, gambist, and singer.Monteverdi's work, often regarded as revolutionary, marked the transition from the Renaissance style of music to that of the Baroque period. He developed two individual styles of composition – the...

 often specified the octave by the use of compound intervals
Interval (music)
In music theory, an interval is a combination of two notes, or the ratio between their frequencies. Two-note combinations are also called dyads...

 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
Tempo
In musical terminology, tempo is the speed or pace of a given piece. Tempo is a crucial element of any musical composition, as it can affect the mood and difficulty of a piece.-Measuring tempo:...

 and texture
Texture (music)
In music, texture is the way the melodic, rhythmic, and harmonic materials are combined in a composition , thus determining the overall quality of sound of a piece...

 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
Accidental (music)
In music, an accidental is a note whose pitch is not a member of a scale or mode indicated by the most recently applied key signature. In musical notation, the symbols used to mark such notes, sharps , flats , and naturals , may also be called accidentals...

 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
Semitone
A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically....

 (so that if it is normally a flat it becomes a natural, and if it is normally a natural it becomes a sharp
Sharp (music)
In music, sharp, dièse , or diesis means higher in pitch and the sharp symbol raises a note by a half tone. Intonation may be flat, sharp, or both, successively or simultaneously...

). 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 signature
Key signature
In musical notation, a key signature is a series of sharp or flat symbols placed on the staff, designating notes that are to be consistently played one semitone higher or lower than the equivalent natural notes unless otherwise altered with an accidental...

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.



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
Vatican City
Vatican City , or Vatican City State, in Italian officially Stato della Città del Vaticano , which translates literally as State of the City of the Vatican, is a landlocked sovereign city-state whose territory consists of a walled enclave within the city of Rome, Italy. It has an area of...

 Cappella Sistina
Sistine Chapel
Sistine Chapel is the best-known chapel in the Apostolic Palace, the official residence of the Pope in Vatican City. It is famous for its architecture and its decoration that was frescoed throughout by Renaissance artists including Michelangelo, Sandro Botticelli, Pietro Perugino, Pinturicchio...

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
Concertato
Concertato is a term in early Baroque music referring to either a genre or a style of music in which groups of instruments or voices share a melody, usually in alternation, and almost always over a basso continuo...

 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
Andrea Gabrieli
Andrea Gabrieli was an Italian composer and organist of the late Renaissance. The uncle of the somewhat more famous Giovanni Gabrieli, he was the first internationally renowned member of the Venetian School of composers, and was extremely influential in spreading the Venetian style in Italy as...

 and Giovanni
Giovanni Gabrieli
Giovanni Gabrieli was an Italian composer and organist. He was one of the most influential musicians of his time, and represents the culmination of the style of the Venetian School, at the time of the shift from Renaissance to Baroque idioms.-Biography:Gabrieli was born in Venice...

), Monteverdi
Claudio Monteverdi
Claudio Giovanni Antonio Monteverdi – 29 November 1643) was an Italian composer, gambist, and singer.Monteverdi's work, often regarded as revolutionary, marked the transition from the Renaissance style of music to that of the Baroque period. He developed two individual styles of composition – the...

 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 Introit
Introit
The Introit is part of the opening of the liturgical celebration of the Eucharist for many Christian denominations. In its most complete version, it consists of an antiphon, psalm verse and Gloria Patri that is spoken or sung at the beginning of the celebration...

s and Alleluia
Alleluia
The word "Alleluia" or "Hallelujah" , which at its most literal means "Praise Yah", is used in different ways in Christian liturgies....

s by the Venetian Placido Falconio
Placido Falconio
Placido Falconio, also called Falconi in some sources, was an Italian composer of the 16th century. His birth and death dates are unknown; his first publication dates from 1575, his last from 1588....

 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
Lodovico Grossi da Viadana
Lodovico Grossi da Viadana was an Italian composer, teacher, and Franciscan friar of the Order of Minor Observants...

 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
Motet
In classical music, motet is a word that is applied to a number of highly varied choral musical compositions.-Etymology:The name comes either from the Latin movere, or a Latinized version of Old French mot, "word" or "verbal utterance." The Medieval Latin for "motet" is motectum, and the Italian...

 by Giovanni Croce
Giovanni Croce
Giovanni Croce was an Italian composer of the late Renaissance, of the Venetian School...

, also from 1594.

Following and figured basses developed concurrently in secular music; such madrigal composers as Emilio de' Cavalieri
Emilio de' Cavalieri
Emilio de' Cavalieri was an Italian composer, producer, organist, diplomat, choreographer and dancer at the end of the Renaissance era. His work, along with that of other composers active in Rome, Florence and Venice, was critical in defining the beginning of the musical Baroque era...

 and Luzzasco Luzzaschi
Luzzasco Luzzaschi
Luzzasco Luzzaschi was an Italian composer, organist, and teacher of the late Renaissance. He was born and died in Ferrara, and despite evidence of travels to Rome it is assumed that Luzzaschi spent the majority of his life in his native city.As a pupil of Cipriano de Rore, Luzzaschi developed...

 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
Monody
In poetry, the term monody has become specialized to refer to a poem in which one person laments another's death....

, 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 opera
Opera
Opera is an art form in which singers and musicians perform a dramatic work combining text and musical score, usually in a theatrical setting. Opera incorporates many of the elements of spoken theatre, such as acting, scenery, and costumes and sometimes includes dance...

s, composed by Cavalieri and Giulio Caccini
Giulio Caccini
Giulio Caccini , also known as Giulio Romano, was an Italian composer, teacher, singer, instrumentalist and writer of the very late Renaissance and early Baroque eras. He was one of the founders of the genre of opera, and one of the single most influential creators of the new Baroque style...

.

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
Harmony
In music, harmony is the use of simultaneous pitches , or chords. The study of harmony involves chords and their construction and chord progressions and the principles of connection that govern them. Harmony is often said to refer to the "vertical" aspect of music, as distinguished from melodic...

 and tonality
Tonality
Tonality is a system of music in which specific hierarchical pitch relationships are based on a key "center", or tonic. The term tonalité originated with Alexandre-Étienne Choron and was borrowed by François-Joseph Fétis in 1840...

), and music came to be seen in terms of a melody supported by chord progressions, rather than interlocking, equally important lines as in polyphony
Polyphony
In music, polyphony is a texture consisting of two or more independent melodic voices, as opposed to music with just one voice or music with one dominant melodic voice accompanied by chords ....

. The figured bass, therefore, was integral to the development of the Baroque
Baroque music
Baroque music describes a style of Western Classical music approximately extending from 1600 to 1760. This era follows the Renaissance and was followed in turn by the Classical era...

, 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
Gregor Aichinger
Gregor Aichinger was a German composer.He was organist to the Fugger family of Augsburg in 1584. In 1599 he went for a two year visit to Rome for musical, rather than religious reasons, although he had taken religious orders before his appointment under the Fugger. Proske, in the preface to vol...

, Friedrich Erhard Niedt
Friedrich Erhard Niedt
Friedrich Erhard Niedt was a German jurist, music theorist, and composer.Niedt enrolled at the University of Jena in 1694, where he is thought to have studied law...

, Georg Philipp Telemann
Georg Philipp Telemann
Georg Philipp Telemann was a German Baroque composer and multi-instrumentalist. Almost completely self-taught in music, he became a composer against his family's wishes. After studying in Magdeburg, Zellerfeld, and Hildesheim, Telemann entered the University of Leipzig to study law, but eventually...

, C.P.E. Bach
Carl Philipp Emanuel Bach
right|250pxCarl Philipp Emanuel Bach was a German Classical period musician and composer, the fifth child and second son of Johann Sebastian Bach and Maria Barbara Bach...

, and Michael Praetorius
Michael Praetorius
Michael Praetorius was a German composer, organist, and music theorist. He was one of the most versatile composers of his age, being particularly significant in the development of musical forms based on Protestant hymns, many of which reflect an effort to make better the relationship between...

.

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
Accordion
The accordion is a box-shaped musical instrument of the bellows-driven free-reed aerophone family, sometimes referred to as a squeezebox. A person who plays the accordion is called an accordionist....

 music; another simplified form is used to notate guitar chord
Guitar chord
In music, a guitar chord is a chord, or collection of tones usually sounded together at once, played on a guitar. It can be composed of notes played on adjacent or separate strings or all the strings together...

s. Today the most common use of figured bass notation is to indicate the inversion
Inversion (music)
In music theory, the word inversion has several meanings. There are inverted chords, inverted melodies, inverted intervals, and inverted voices...

, 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 ; with an E in the bass, it would be written (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.

External links

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