The Figures 97, whether placed under the Dominant, or under anyother Degree of the Scale, indicate a Chord of the Ninth, taken by direct percussion. Should the Ninth be accompanied by other Intervals than the Seventh, Fifth, or Third, such Intervals must be separately noticed. Should it appear in the form of a Suspension, its figuring will be subject to certain modifications, of which we shall speak more particularly when describing the figuring of Suspensions generally.
The formulæ 742 and 974 are used to denote the chord of the Eleventh—i.e. the chord of the Dominant Seventh, taken upon the Tonic Bass. The chord of the Thirteenth—or chord of the Dominant Ninth upon the Tonic Bass is repretented by 764 or 9764 or 7642. In these cases, the 4 represents the Eleventh, and the 6 the Thirteenth: for it is a rule with modern Composers to use no higher numeral than 9; though in the older Figured Basses such as those given in Peri's 'Euridice,' and Ernilio del Cavaliere's 'La Rappresentazione dell' anima e del corpo,' the numerals, 10, 11, 12, 13, and 14, are constantly used to indicate reduplications of the Third, Fourth, Fifth, Sixth, and Seventh, in the Octave above.
Accidental Sharps, Flats, and Naturals are expressed in three different ways. A ♯, ♭, or ♮ used alone—that is to say, without the insertion of a numeral on its own level—indicates that the Third of the Chord is to be raised or depressed a Semitone, as the case may be. This arrangement is entirely independent of other numerals placed above or below the Accidental Sign, since these can only refer to other Intervals in the Chord. Thus, a Bass-note with a single ♭ beneath it, must be accompanied by a Common Chord, with a flattened Third. One marked 65♭ must be accompanied by the First Inversion of the Chord of the Seventh, with its Third flattened. It is true that, in some Thoroughbasses of the last century, we find the forms ♯3, ♭3, or ♮3; but the Figure is not really necessary.
A dash drawn through a 6̸, or 4̸, indicates that the Sixth or Fourth above the Bass-note, must be raised a Semitone. In some of Handel's Thoroughbasses, the raised Fifth is indicated by 5̷; but this form is not now in use.
In all cases except those already mentioned, the necessary Accidental Sign must be placed before the numeral to which it is intended that it should apply; as ♭6, ♯7, ♮5, ♭9, ♭4, ♮4, ♮6, etc.; or, when two or more Intervals are to be altered, ♭6♭4, ♭6♭, ♭7♭5♭, etc.; the Figure 3 being always suppressed in modern Thoroughbasses, and the Accidental Sign alone inserted in its place when the Third of the Chord is to be altered.
By means of these formulæ, the Chord of the Augmented Sixth is easily expressed, either in its Italian, French, or German form. For instance, with the Signature of G major, and E♭ for a Bassnote, the Italian Sixth would be indicated by 6, the French by 642, the German by 6♭53, or 6♭5.
The employment of Passing-Notes, Appoggiaturas, Suspensions, Organ-Points, and other passages of like character, gives rise, sometimes, to very complicated Figuring, which, however, may be simplified by means of certain formulæ, which save much trouble, both to the Composer and the Accompanyist.
A horizontal line following a Figure, on the same level, indicates that the note to which the previous Figure refers is to be continued, in one of the upper Parts, over the new Bass-note, whatever may be the Harmony to which its retention gives rise. Two or more such lines indicate that two or more notes are to be so continued; and, in this manner, an entire Chord may frequently be expressed, without the employment of a new Figure. This expedient is especially useful in the case of Suspensions, as in Example 4, the full Figuring of which is shown above the Continue, and, beneath it, the more simple form, abbreviated by means of the horizontal lines, the arrangement of which has, in some places, involved a departure from the numerical order of the Figures.
Any series of Suspended Dissonances may be expressed on this principle—purposely exaggerated in the example—though certain very common Suspensions are denoted by special formulæ which very rarely vary. For instance, 4 3 is always understood to mean 54 53 the Common Chord, with its Third delayed by a suspended Fourth—in contradistinction to 64 53 already mentioned; 9 8 means the Suspended Ninth resolving into the Octave of the Common Chord; 94 83 indicates the Double Suspension of the Ninth and Fourth, resolving into the Octave and Third; etc.
In the case of Appoggiaturas, the horizontal lines are useful only in the Parts which accompany the Discord. In the Part which actually contains the Appoggiatura, the absence of the Concord of Preparation renders them inadmissible, as at (a) in Example 5.
Passing-Notes, in the upper Parts, are not often noticed in the Figuring, since it is rarely necessary that they should be introduced into the Organ or Harpsichord Accompaniment; unless, indeed, they should be very slow, in which case they are very easily figured, in the manner shown at (b) in Example 5.
