music theory online : figured basslesson 18
Dr. Brian Blood

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Aside from purely technical analysis, nothing can be said about music, except when it is bad; when it is good, one can only listen and be grateful.
W. H. Auden (1907-71) English-American poet

Figured Bass :: Figured Bass Notation :: Naming Chords With Roman Numerals

Figured Bass :: top

Key words:
thorough bass
basso continuo

Figured Bass


  • Basso Continuo

    In the sixteenth century accompaniments were played on a number of musical instruments; organs, harps, lutes, chittaroni, viols or combinations of these. Sometimes the parts were fully written out but often they were simple enough for the accompanying player to fill in over a bass line using block harmony and working just from the full score.

    By the seventeenth century, the practice of accompanying upon the Thorough Bass, where the accompanist might add a varying degree of ornamentation to a simple bass line, the nature and degree depending on the occasion, meant that it was no longer possible nor indeed helpful to write out every last note; to do so would have restricted the freedom that a well-trained accompanist had, and expected to have, in order to display his extemporising skills.

    Even so, the accompanist was expected to observe the rhythmic and harmonic structure of the musical line and, for this reason, a form of 'harmonic shorthand' was developed that provided just enough information to extemporise an accompaniment but without making the part over-restrictive. This 'harmonic shorthand' is called 'figured bass' or 'thorough bass'. The first example, taken from Syntagma Musicum (1619) by Michael Praetorius, is one he gives and the realisation below it is his own. You will see that more has been 'added' than just bare block chords.

    Risolutio by Michael Praetorius (1619)

    This realisation is not particularly inspired. Arnold Dolmetsch, who quotes it in his book "The Interpretation of Music of the Seventeenth and Eighteenth Centuries" in a chapter entitled 'Thorough Bass', makes the comment "it would not get a high number of points in a musical examination". The main reason for showing it at all is that not only are the harmonies of the 'figured bass' realised but additional counterpoint is also added freely, a testament to what would have been expected from a keyboard player of the time.

    Arnold Dolmetsch tells us about Francesco Geminiani, a popular Italian-born violinist who worked in London at the same time as Handel.

    Sir John Hawkins, in his History of Music, reports that when Geminiani was asked to play some of his violin sonatas before King George I, he intimated a wish that Handel might accompany him on the harpsichord, which was granted. We can assume that Handel's realisations would not have been far removed from Geminiani's own.

    When Geminiani came to write his two volume work "The art of Accompaniment, or A new and well digested method to learn to perform the Thorough Bass on the Harpsichord with Propriety and Elegance.", Op. 11, he gave several examples of how a passage of figured bass might be realised. The range of possible realisations was explained by the need to accompany different instruments or the voice (each requiring a different approach) or to 'liven up' a less well written work. We reproduce below Geminiani's own examples; one figured bass line which he has realised in four different ways.

    Geminiani Realising Figured Bass (1755)

  • 2

    Figured Bass Notation


  • Playing from Figured Bass by Clifford Bartlett
  • Figured Bass Symbology by Robert Kelley
  • Bassus Generalis hosted and supported by the Conservatory of Geneva

    The general rules applied to figured bass are given below. It should be remembered that the figures give the contents of a chord and not their position on the stave. Thus a 5 3 chord, a chord in root position, can be written in many different arrangements. The only restriction is that the bass note is the lowest note in the chord. Any note given by the figuration, including the bass note, can be repeated in the chord and the 3rd can lie below or above the 5th.

    or no numbers at all
    root position chord: 3rd and 5th to the written note as bass
    or 6
    first inversion chord: 3rd and 6th to the written note as bass
    second inversion chord: 4th and 6th to the written note as bass
    accidental under note5 3 root position
    accidental applied to the 3rd
    line through a numberraise the note in that position one chromatic semitone
    accidental under numberapply accidental to 3rd and add note given by number to written note as bass
    accidental beside single 6
    may be placed before or after
    6 means 6
    ; apply accidental to 3rd
    accidental beside number
    may be placed before or after
    apply accidental to the note given by the number
    horizontal line after a numbernote represented by the preceding figure is to be held
    7 or 8 or 97th or 8th or 9th added to root position chord
    short for 7 5 3 or 8 5 3 or 9 5 3
    7th chord, first inversion
    short for 6 5 3 : third is understood
    7th chord, second inversion
    short for 6 4 3 : sixth is understood
    7th chord, third inversion
    short for 6 4 2 : sixth is understood
    chord is also called a 2 chord

    Accidentals are used to signify where notes are to be raised or lowered a semitone in pitch from the scale of the key-note.

    One must watch for notational errors and 'non-standard' notation in both early and modern editions. We have given above the figurings most commonly met in 'early' music.

    Baroque composers seldom marked every place where harmony might be wanted - indeed, one has to be very careful not to interpret the absence of a mark as always being a 5/3 chord, even though, more often than not, this will be the case. At all times, a keyboard player should make a tasteful realisation, a point made with great clarity by Geminiani.

    It will perhaps be said, that the following Examples are arbitrary Compositions on the Bass; and it may be asked how this arbitrary manner of accompanying can agree with the Intention and Stile of all sorts of Compositions. Moreover, a fine Singer or Player, when he finds himself accompanied in this Manner, will perhaps complain that he is interrupted, and the Beauties of his Performance thereby obscured and deprived of their Effect. To this I answer that a good Accompanyer ought to possess the Faculty of playing all sorts of Basses in different Manner, so as to be able, on proper occasions, to enliven the Composition, and delight the Singer or Player. But he is to exercise this Faculty with Judgment, Taste, and Discretion, agreeable to the Stile of the Composition, and the Manner and Intention of the Performer. If an Accompanyer thinks nothing else but the satisfying of his own Whim and Caprice, he may perhaps be said to play well, but will certainly be said to accompany ill.

    The example below (one supplied with the Sibelius score writing program) shows how a good modern realisation adds considerably to the musical interest in a piece of music. In particular, note the way that neighbouring chords are 'voiced' (that is, their notes are arranged) to produce interesting polyphonic detail within the keyboard accompaniment.

  • Figured Bass :: top

    Key words:
    Roman notation

    Naming Chords With Roman Numerals

    We saw earlier that the degrees of the scale may be named using Roman numerals. This convention is widely used in theory books and we should spend a little time examining the conventions adopted in this form of 'figured bass'. Straight away, it should be pointed out that much is common between Roman numeral figuring and the early form of figured bass set out above.

    A chord name should tell us what a chord is; a Roman numeral should tell us what the chord does. In other words, a Roman numeral is contextual (based on key) while a chord name is not.

    The triad C - E - G can always be named C (C major) whatever the context or key. But it would be I in the key of C, or IV in the key of G, or V/V in the key of Bb.

    The seventh chord B - D - F - Ab can always be named B°7 regardless of the tonal context. But it might function as a vii°7 in the key of C, vii°7/V in the key of F, and a host of other chords in a host of other keys. Of course, depending on context, the same chord might be a passing chord or some other type of nonfunctional sonority, for which a Roman numeral label would be inaccurate and misleading. In that case, the chord name alone, B°7, would be the appropriate and best label.

    We discuss chords of the form V/V and vii°7/V in chapter 31.

    The quality of the chord is shown by whether the Roman numeral is upper or lower case. Upper case identifies a major or augmented chord (in fact it is identifying the fact that both have a major third) while lower case identifies a minor or diminished chord (which is because both have a minor third). With seventh chords, the case of the Roman numeral is determine by the quality of the triad to which the seventh has been added.

    Figured bass, with or without Roman numerals, identifies the notes above the actual bass note by the interval between that note and the actual bass note. Do not make the mistake of working from the chord root, which may not always be the bass note (e.g. with inversions)

    Root position triads are left unmarked; the first inversion triad has only a 6 usually, not the more complete 63.

    Augmented chords are marked with a plus (+) sign and an upper case Roman numeral, e.g. I+.

    Diminished chords are marked with the degree (°) sign and a lower case Roman numeral, e.g. vii°.

    Inversions are always indicated when using Roman numeral notation although generally in a more sophisticated way than that we have met earlier when naming inverted triads.

    For the seventh chord and its inversions the Roman numeral convention is: root position, V7; first inversion, V65; second inversion, V43; and third inversion, V42.

    Roman numerals can be used to indicated non-diatonic chords notes too.

    If the diatonic note is lowered or raised by a semitone (half step) a flat or sharp is written in front of the figure. A slash may be used in place of a sharp. If the root of the chord is raised or lowered a sharp or flat will be placed in front of the relevant Roman numeral.

    If the chord is non-diatonic, in other words it does not arise from the key of the work, accidentals may not always be necessary. A minor tonic triad in a major key will be shown with i. The flat third is shown by the lower case of the numeral. Similarly, the major triad on the third scale degree (e.g. E major triad in C major) is simply labeled III, here the upper case showing that the third has been sharpened.

    When comparing Roman numeral notation with the figured bass set out in an previous section of this lesson, notice that in the absence of Roman numerals, accidentals must be shown. Thus, the minor tonic triad in a major key, i with a Roman numeral, would be marked with a flat sign in figured bass, the flat sign referring to the lowered third in the triad. Occasionally, 'courtesy accidentals' are used to reinforce information already indicated by the case of the Roman numeral under the chord. Other accidentals may be used to show that a note is 'raised' (using a sharp) or 'lowered' (using a flat) when there is actually no sharp or flat in the chord.

    So, for example, a II#64 chord which might have no sharp in the chord indicates that a normally occurring flat has been sharpened to a natural.

    When there is a change of key it is not unusual to see the chord names in the new key on a second level under the staff. The name of the new key will be clearly marked and also on any subsequent staff. It is not unusual to show the Roman numeral appropriate to both the original and the new key, one above the other during the modulation sequence, or on a particular pivot chord.

    Particular chords, some we will meet later, are also specifically indicated by their own letters:

    N6 for a Neapolitan sixth

    It.6 for an Italian sixth

    Fr.6 or F6 for a French sixth

    Ger.6 or G6 for a German sixth, and so on.

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