He who understands harmony must understand thorough bass, though he may not be able to perform it; while the
thorough bass player cannot even comprehend what he has to do without some knowledge of the rules of composition.
A person may compose who cannot play at all. In this sense, thorough bass differs from composition. It is the
habit of playing an extempore accompaniment to a given bass, or treble and bass, by the aid of figures ; and this art
therefore requires a command of the instrument, an eye capable of reading quickly, and a retentive memory. For the
exercise and improvement of all these, a work, consisting of a concentration of the practical rules agreeing with the
former theory, rejecting all that is foreign to this purpose, and containing a variety of practices and specimens, was
required by the author\'s pupils, and others who approve of his method. With this sole view it is now produced, and
not with the slightest intention of depreciating many excellent cotemporary works on the same subject.

The student having been taught his notes¹, may first be required to play Example 1. He must then learn to
reckon the semitones in any interval, thus from A to B are two semitones (or one tone); from B to C is one semitone,
&c. And in the latter part of the same example, from F ^ j? to C (7 is seven semitones; from C t> [? to G [j [j, seven
semitones ; and so of the rest—Ex. 1 and 2. In playing from a figured bass, the figures stand for treble notes, to be
played with the right hand, and are to be always reckoned upwards from the bass note inclusive. Thus, if the bass
note is A, the figure 2 stands for B, 3 for C, &c. as far as 9; no double figures, as 10, 11, 12, being in common use.
If the base note is B, 2 represents C, 3 D, &c. &c. A 10th is written 3, as also a 17th; and thus 4 stands for 11 and
18, 5 for 12 and 19, &c. &c.

A diatonic scale is a series of notes in alphabetical order, as the natural or white keys of the piano forte, or any
scale which resembles them, viz. all such scales as are characterized by the flats and sharps placed at the beginning
of the stave—Ex. 3. Diatonic intervals are such as can be performed on any diatonic scale, and are as follow :

A minor 2nd equal to

A major 2nd --

A minor 3rd -

A major -

A perfect 4th -

A superfluous!

or extreme V 4itn -

sharp j
An imperfect "J

or extreme y 5tn -

flat j

A perfect 5th -

A minor 6tb -

A major 6th -

A minor 7th -

A major 7th -

A perfect 8th, or octave

A minor 9th, -

A major 9th, -

1 semitone.

2 semitones.

3 semitones.

4 semitones.

5 semitones.

6 semitones.

7 semitones,

8 semitones.

9 semitones.

10 semitones.

11 semitones.

12 semitones.

13 semhones.

14 semitones.

Naturals.

Ex.4\', such as EF,orBC.

5,-CD, DE, FG, GA, and AB.

(J,-AC, BD, DF, and EG,

7 ,-CE, FA, and GB.

8 ,-CF, DG, EA, GC, AD, BE.

10,

11,-
12,-

13,-

14,-

15,

16,-

17,-

18,-

FB.

BF.

CG, DA, EB, FC, GD, AE.
BG, AF, EC.
GE, FD, DB, and CA,
■ BA, AG, GF, ED, CB.
- CB and FE.

CC, DD, &c, &c.
EFand BC.

CD, DE, FG, GA, and AB.

1 The Editor refers for every thing not fully explained in this work, to his Elements of Musical Composition and Rudiments of
Playing on the Piano Forte. The latter work contains preludes and modulations which may, it is hoped, be of some use to the
extemporaneous performer and young composer. His Rounds for the Piano Forte are intended for the use of persons learning to
play from score and clefs.

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Chromatic intervals are such as cannot be performed upon a diatonic scale without destroying the alphabetical
arrangement of the notes.

On the White Keys.

An extreme sharp 2nd is equal to 3 semitones. Ex. 19, such as AB:|;, BCx, DE#, and EFx.

--flat 3rd - 2--20, ACb, DFb, FA bb, or E# G, and GBbb or Fx A.¹

---flat 4th--4--21, CFb, FBbb, or E# A, GCb-

--sharp 5th--8--22, AE| or BbbF, BFx, or C|, Gand EBf or Fb C.

---sharp 6th--10- 23, DBff, ECx, GE#, AFx and Cb A.

--flat 7th--— 9--24,CBbb, DCb,E#D,GFb.

--flat 8ve--11-25, CCb, orB4Bt|andFFborE#Et|.

---sharp 8ve --13-— 26, EE# or FbFlq and BB# or Cb Cl:|.

--sharp 9th--15--27, AB#, &c. see extreme sharp 2nd.

Enharmonic intervals cannot be distinguished on keyed instruments.—Ex. 28.

A complete knowledge of the major and minor keys is absolutely requisite for the performer from a figured bass ;
but a long detail of them, and of the manner of forming them, is necessarily avoided in this work; and the Editor
again refers the student to his former works already mentioned, and will only insert a list of a few of the major and
minor keys, with the number of flats and sharps which characterize them.

Flats. Sharps.

76543210 1 234567
Major keys. Cb Gb Db Ab Eb Bb F C G D A E B F# C#

Flats. Sharps.

__\' .

7654 3 2101234 5 67
Minorkeys. Ab Eb Bb F C G D A E B F#C#G#D#A|

The minor keys are, in music, distinguished from the relative major keys (having a similar number of flats and
sharps) by the chromatic alterations which so frequently occur in them.

OF TRIADS.

A triad is a note accompanied by its 3rd and 6th. Thus, the triad of

A is A C and E.
thatofB —BDF.

- C — C E G.

-D—DFA.

-— E — E G B.

- F — F A C.

---- G — G B D.

These should be learnt by memory.

Consonant triads have their 5ths perfect.—Ex.29.

Dissonant triads have their 5ths extreme flat or extreme sharp.—Ex. 30.

Consonant triads are called major triads when their 3rds are major, Ex. 31; and minor triads when their Srds
are minor.—Ex. 32.

In thorough bass, triads occur so frequently, that when they are required to be played, figures are not always put,
especially to the first and most accented notes in a bar.
The 8 is added merely to enrich the effect.

1 An extreme sharp 3rd (5 semitones, as A b C #) occurs in the Adagio of Mozart\'s Sinfonia, usually called Jupiter. The C#

is a mere appoggiatura.

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RULES FOR PLAYING FROM A FIGURED BASS.

a succession of triads.
8

When no figures are placed over a bass note, play 5 with the right hand on the treble stave, avoiding the ex-

tremes of high and low, and placing any one of the three figures at the top according to circumstances.—Ex. 33.
A sharp, natural, or flat placed over the bass note, as in bars 4, 5, 6, signify that the 3rd is accordingly to be sharp,
natural, or flat. The 5th is always perfect when the 3rd is major, unless expressly specified otherwise. The 8th, 5th,

or 3rd, without any figures, also stand for 6. The 8th is only inserted to make the harmony fuller, and is more

frequently omitted than the 5th or 3rd. Indeed the 3rd should not be omitted if possible. The 8th should be omitted
in a dissonant triad by the inexperienced performer of thorough bass.—Ex. 34. In playing from a figured bass, the
rules of composition must be as strictly observed as in writing music. Hence, two consecutive perfect fifths, or octaves,
must not take place between the same parts, as in Ex. 35,36, STf. Ex. 38, 39, and 40, are correct, but less convenient
than Ex. 44, 45, 46, on account of the unnecessary motion given to the right hand, which should generally remain as
still as possible. The upper melody should repeat the same note whenever it can be done; and when that cannot be,
should move to the nearest note, excepting when by so doing it produces consecutive fifths or eighths. Such tran-
sitions, however, as Ex. 38, 39,40, must occasionally be made to recover the position of the right hand after it has got
too low or\' too high. The same 5th or 8ve repeated, is not considered as a violation of the rule—Ex. 41; nor if one
part moves while the other stands still.—Ex. 42. The imperfect 5th will be treated of hereafter. Octaves or unisons
may pervade a whole passage. The words " tasto solo" are used to prevent the performer from playing chords when
no figures are put—Ex. 43. Octaves may be played below the bass notes without violating the rule—Ex. 44. This is
only done to imitate the effect of the double bass in an orchestra, or to increase the loudness. Chords are likewise
occasionally played for the same purpose with the left hand and octaves in the right, especially on the harp. But the
student is recommended to avoid them for the present. Ex. 44, 45, 46, are respectively preferable for all general
purposes to Ex. 38, 39, 40. The student should therefore transpose Ex. 44, 45, 46, into several major and minor
keys, both writing them and playing them by memory, placing the chords in all the three positions—Ex. 47 to 60.

Ex. 61 is said to be in the major key of C, because it begins and ends in that key; but it modulates frequently
into the relative minor key of A. Where the asterisk is placed (*) in this and in several of the following examples, the
less pleasing transition is adopted, generally, for the sake of gaining a good position for the right hand. The student
should transpose this into various other major keys, writing only the bass and playing the chords according to the
foregoing rules. Ex. 62 is in A minor, and should likewise be transposed and practised in various other minor keys.
Ex. 63, 64, 65, are three different ways of accompanying the same bass, of which the latter is the best, on account of
the upper melody having the least motion. See last bar but one of Ex. 62.

OF THE CHORDS OF THE ® AND

The chord of the 6th is marked ^ or only 6, which stands for g, because 3 is always understood when 4 or 2 is not

expressed. The inexperienced performer will find it safest to perform only two notes vvith the right hand, the 6th and
the 3rd, either of them at the top, according to circumstances, but generally the 6th, The performer who has studied

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composition and can distinguish between such chords of the 6th as are inversions, and such as are not, will, in the
latter cases, add an 8th, which he must not do in the former on account of doubling that which was the 3rd note of
the triad in its original or direct position—(See Subordinate Rules in the Elements.) Ex. 66 shews the way recom-
mended to the beginner; and Ex. 67 shews how they may be accompanied when known to be inversions, by adding
another note in the right hand. Ex. 68 and 69 contain inversions, and should be transposed and practised in various
keys. Ex. 70 shews how a succession of ascending or descending 6ths should be accompanied by the beginner.
Ex. 71, 72, and 73, shew how another note may be added in the right hand without violating the stricter rules*.
6 8

^ stands for 6. Any one of the 3 notes may be at the top according to circumstances—Ex. 74. Ex. 75 to 80 should
4

be transposed and practised in all the principal major and minor keys. Ex. 81 being longer, may be transposed
into two or three only of the principal keys. Ex. 82 contains illustrations of the four sorts of cadence or termination
of passages, the knowledge of which not being essential to the mere performer from a figured bass, a reference
is made for the definition of them to the Elements of Composition.

The thorough bass player should always avail himself of the composer\'s own melody where he has an oppor-
tunity, as in chants, psalms, services, and other church music, recitatives, songs, and violin solos. In playing Ex. 83,
84, 85, he must never go above the treble or below the bass, and when these are too near together to admit of a chord
between them, he must omit the harmony as in Ex. 85. Given trebles will be found to several other examples in the
course of the work.

OF DISCORDS.

We begin (as in the Elements) with discords of addition, and first the dominant 7th, which is a major Srd,

perfect 5th, and minor 7th to the 5th note of the key, whether major or minor key.

8
7

When played full, ^ may be taken in the right hand, any one of the notes at the top—Ex. 86, 88, 90, and 92. The
3

same chord is transposed into the minor key—Ex, 87, 89, 91, and 93. The discordant note of all discords must fall-
here it is the 7th. This note must never be doubled. The leading note of the key should rise; this therefore should

not be doubled; the octave stands still. The 3rd and 5th both go to the same note g ^^^C

The dominant 7th, however, should only be occasionally accompanied with four notes in the right hand, as in loud
passages ; for this accompaniment, together with the bass, constitutes a harmony of five distinct parts; and as one of
four parts is considered the most clear and beautiful in composition, so in playing thorough bass, three notes are generally
sufficient iu the right hand. The 8th is the least essential note of the dominant 7th, and is most frequently omitted.

8 7

7 therefore may stand for^^; but it usually stands for 6.—See Ex. 94 in the major key of C; and 95 in A minor.

3 ^

The inversions of the dominant 7th are—-

The g (standing for 5| on the leading note of the key.—Ex. 96,97.
3\'

6 .
The 4 (sometimes written ^ J| on the second note of the key.—Ex. 98, 99.
3

6 ..
And the 4 (sometimes written „) on the fourth note of the key.—Ex. 100,101.

(4 6 X

2 only stands for 4 when the bass note falls to the note below.^ Their resolutions will be seen in the above
examples.

When the fundamental note of the dominant 7th is altogether omitted, we obtain the dissonant triad—Ex. 102,

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103, or its inversions, the ^ on the second note of the key—Ex. 104, 105; or the ^ on the 4th note of the key-
Ex. 106, 107. The best composers of the antient style of music, and some very eminent modern writers, prefer the

® on the second note of the key—Ex. 104, 105, to the 4—Ex. 98,99. On no account therefore should the S he sup-

posed to stand for 4. Indeed a fourth is never understood ; but always specified in figured basses.
3

The added 6th is resolved by making the discordant note (viz. the 5th) fall and become the 3rd to the next chord
of the fifth of the key.

Ex. 110 and 111 shew the omission of the 3rd.

Ex. 112and 113 shew the omission of the 5tb. The 8th, or bass note, is inserted in the treble, because this 6th is
not an inversion of the g, but the bass note is fundamental and may be doubled.

Ex. 114 and 115 shew the difference between the accompaniment of the 3 to F in the major key of C, where it is

not an inversion, and in the minor key of A where it is an inversion. Ex. 116 is the same in the minor key as 114.

6 6 6 7
The inversions of the S> on the 4th note of the key, are 4 on the 6th note of the key ; 4 on the key note, and 5
3 3 2 3

on the 2nd note of the key.

6 .

Ex. 117 and 118 shew the resolutions of the 4, (sometimes written^ J in the major and minor key. Ex. 119 and

120 shew the ^ with the 6th omitted, a chord not very common in the music of the great masters, as they avoided a

perfect 4th to the bass note as much as possible, unless used as a discord of suspension. The ® without the 3 was

still less tolerable, and is therefore omitted in this work. Ex. 121 and 122 shew the resolutions of the 4. Ex. 123 and

The 4 is generally used as a discord of suspension.
2

124, the Ex. 125 and 126, thej.

Ex. 127 and 128 shew the resolution of the 5 on the 2nd note of the key played with four notes in the right hand,

8 8

the 8th being added for the sake of loudness. Three are, in general, sufficient—Ex. 129, 130. The 7 or 7 mio-ht also

3 5

be occasionally used, but are omitted as being less agreeable than the 5. Two ways of resolving the „ are shewn

in Ex. 131 and 132. When the 7th is omitted, as in Ex. 133, this chord resembles the triad of the 4th note of the
minor key. When transposed into the minor key, Ex. 134, it is not so agreeable to ascend three semitones from Ffc| to
G|:, as to descend from F to an extreme flat seventh. Had the F been sharp, it would be better to ascend.—(See
Elements of Composition, note on page 51). According to the rules of contrary motion, the student would be induced
at first to conclude, that the first way of accompanying the triads, D and G in Ex. 135, was better than the 2nd; but
when he reflects, that the fundamental note of this chord is F and not D, (see Ex. 114 and 116), he will perceive that
the 2nd method is really agreeable to the laws of contrary motion. The same remarks apply to Ex. 136, (see Ele-
ments.) Ex. 137 to 141, are practices for the student who should play them in all keys, transposing Ex. 137, 139,
and 141 into other major keys, and 138 and 140 into other minor keys.

Ex. 142 contains various ways in which the added 6th and its inversions may be resolved into the dominant 7th
and its inversions; the only rule being that the discordant note (viz. the 5th), must fall. Ex. 143 is the beginning
of the same in the minor, which the student must complete. Ex. 144 is merely meant to show, that the added 6th,
when the 5th is not retained, may also be succeeded by the dominant 7th : no rule is required.

The added 9th, is a 9th added to the dominant 7tb, and the 9th should be placed at the top whenever it is pos-
sible ; and, at all events, the 3rd should never be placed above the .9th. When the 9th is resolved into the 8th on
the same bass note, the 7tb, 5th, and 3rd have dashes placed after them, to show that these notes are to be con-
tinued, as is the case whenever dashes are put. Ex. 145 and 146 show this resolution of the added 9th. Ex. 147

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SHOWS another resolution into the triad of the key note, in which the 5th and 7th must both be resolved into the 3rd
note of the next chord, to avoid consecutive perfect 5ths to the upper melody. The same may be done in Ex. 148,^

though the 5ths are not both perfect: but this resolution is not so agreeable as that into 6 Ex. 149 and 150. But

as three notes are generally better than four in the accompaniment, the 5th of this discord may be omitted. Ex. 151.

9 ®

9 7

So that ^ may be said to stand in general for 7 or, in full music,for

^ 3

The leading 7th, (derived from the added 9th, the fundamental note being omitted), is a 7th on the leading note
of the key, whether major, as Ex. 152 and 154, or minor, Ex. 153 and 155. Three positions for the accompaniment are
here given, but that in which the 7th is at the top is best. In the minor key this discord is called the diminished 7th,
the 3rd being minor, the Sth extreme flat, and the 7th extreme flat. But one inversion of the leading 7th, is found in
the major key, (Ex. 156,) in which the 3rd should be at the top, that note being the same which was 7th to the
leading note, and 9th in the discord of the added 9th, from which it is derived. In the minor key, however, all the in-
versions are occasionally met with, and in various positions. Ex. 157.

Ex. 158 is an exercise, to be transposed and practised in various other major keys. In the 2nd bar the dissonant

triad has an 8ve, as well as a g, because the bass is not the 3rd note of the triad from which it is derived. Bars 10,

11, 12, 13, and 15, show how the ^ on the 5th of the key may be followed by the dominant 7th and its inversions.

f . 5 ^

The ^ on the 5th of the key resolved into the g or 5 is not considered as an inversion of a triad, but as a species of

discord, or double appoggiatura. (See Elements.)

Discords of suspension are accented, generally resolved on the same bass note, (as will be specified by the
figures of the thorough bass), accompanied by the same notes that usually attend the figure which follows the discord,
and the discordant note must be always prepared, viz. continued from the same note in the preceding chord or dis-
cord. Thus the discord of the 4th is followed by the 3rd on the same bass note, is accompanied by a 5th and Sth,
because these notes usually accompany a 3rd, and the discordant note must be continued from the same note in the

8 _ 8 8 — . _
preceding chord or discord; S is therefore resolved into 5; 5 — And the 4th must be prepared. . q or 4 3

4 3 4 3. ^

8 — - _
stand for 5 —. No 3 must be played with the 4. See Ex. 159; which also contains the inversion of the same dis-
4 3

cord, where the discordant note is in the bass.

Ex. 160 shows the preparation and resolution of the same discord in the minor key, the student being left
to vary the position as in Ex. 159.

This discord is sometimes resolved into the dominant 7th. Ex. 161.

A succession of these is sometimes met with, Ex. 162, 163, 164. In Ex. 162 the treble descends so rapidly,
that had the first chord in the treble been taken in a position nearer the bass, the two hands would soon have been
too close. To avoid this the 5th may ascend to the 8th, while the 4th resolves. Ex. 163 and 164. In the latter, the
4th is supposed to descend to the 3rd in each instance, the parts changing places. Ex. 163, from its clearness, is
most agreeable. Ex. 165 and 166 are to be transposed into other major and minor keys, and practised. The

ly Q _ _ 5 _

^ _ on the Sth of the key, is an inversion of the ^ ^ seldom met with, excepting in a pedale, or holding note in the

bass, as in bar 9 of Ex. 165. Ex. 166, being in triple time, the student must be careful to observe whether the resolution
of his discords falls early or late in the bar, viz. whether the 4 is succeeded by the 3 on the 3rd, or on the 2nd
note, which he may tell by the situation of the dash, 4—^3 or 43 —.

The discord of the 9lh (not the added 9th) is resolved into an 8th on the same bass note, and (because the 8th

9 8

ought to be so accompanied) is accompanied with 5 and 3. Thus 9 8 stands for 5 —. No 8 must be played with

3 —

the 9.

The 9 must be prepared from the same note in the preceding chord or discord, (see Ex. 167), which contains
most of its resolutions and preparations in the major key, as Ex. 168 does in the minor key. At the end of Ex. 168,
the manner in which the 9 is sometimes resolved into a 3 or a 6 on another bass note may be seen. Ex. 169 shews

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how the 98 and 43 may be used on alternate bass notes.—On an organ the ligatured or tied notes should be held
down; on a piano forte they may be struck or repeated¹. In the latter half of this example the 1st and 2nd parts are
supposed to cross each other, as is specified by the words 2nd part, 1st part, &c. Ex. 170 shows the same passage
in another position, less favourable for execution, and less agreeable in its upper melody than the fornaer. Ex. 171 is
still more difficult of execution and less fit for thorough bass. Ex. 169 therefore alone need be transposed and
practised.

The discord of the 7 (not the dominant or added 7th, nor that which is an inversion of the added 6th, nor yet any
which will hereafter be described) may be resolved into a 6th on the same bass note; and (as the 6th is so accom-
panied) should be accompanied only with a 3rd, and occasionally with an 8th; but not (in general) with a 5th.

7 6

76, therefore, stands for The 7 must be prepared from the same note in the preceding chord. The 3rd,

therefore, may sometimes be over the 7 : but as a succession of sixths sounds best with the 6th at the stop (Ex. 70 to
75); and as the 7th is only a species of appoggiatura, as the 5 is to the 6th, in ascending, Ex. 172, it is better that

5 6

the 7 and 5 should be at the top when followed by a 6 : hence 56 stands for g _; but no 8th, especially when there

is a succession of them.

The 7 6 in the cadences Ex. 173 is sometimes accompanied as in Ex. 174; but in this case the writer of the
thorough bass should express it in the figures Ex. 175, and the performer must be careful to remove the §th when
he plays the 6th.
7

The 5 on the fourth note of the key is peculiar to ancient music. It is generally resolved into the added 6 or
3

5; the 5th, or 5th and 3rd, being expressed m the figures, Ex. 176 and 177. Ex. 178 shews how discords of
3

addition may be prepared, or used as discords of suspension.

Ex. 179 shows what a variety of figures may be used as discords of suspension on a pedale or holding note in
the bass. The performer of thorough bass is recommended not to insert any additional note not expressed in the
figures, which he might imagine would complete the harmony, as he cannot always be certain of the composer\'s in-
tentions.

Hence on the same bass note must not have a third added, but is an exception to a general rule. Hence,

Q __C

also, ^ g ; indeed, g should never have an additional note given to it. The 4th is sometimes understood, but

the effect is not generally improved by its insertion.

Many passages of great simplicity, when accompanying their usual basses, are rendered extremely difficult by
being reckoned from a pedale or holding note, usually on the 5th of the key, or sometimes on the key note, as in Ex.
180. The 4 3 is sometimes found with the dominant 7th and the added 9th. Ex. 181.

Two or more notes prepared and resolved together are called double discords. Ex. 182, 184, and 185. The

7 8 9 8

5 — 7
discord of the ^ on the key note may be written ^^ _. Ex. 183.

2 3 4 3

When the major or sharp 7th on the key note is followed by an 8ve, it is always understood to mean the

2 ^

above discord, and should be accompanied, with Ex.186,

Ex. 187 and 188 must be transposed and practised in various keys. Wherever the asterisk (*) is put, the treble
hand ascends, on account of the tendency which melody, (especially when replete with discords), has to descend.
The omission of the 5th at the end of bar 3r<|, and of the 8th at the beginning of bar the 4th (Ex. 187), is immaterial.

1 The Editor having mentioned this quality of protracting or sustaining sounds, so characteristic of the organ, cannot resist the
opportunity it affords him, of entering his protest against the abuse of this noble instrument, so frequent among organists, who,
because it may well be denominated a " vocal frame," on which they may add " length to solemn sounds," will never suffer you to
have a short note, a rest, a pause, or a passage that is mezzo staccato, or that has any animation, or resemblance to the effect which
the same passage would have performed elsewhere. Let the chant, the service, the anthem, the psalm, the organ fugue, &c. be
played in the genuine organ style ; but, if a spirited chorus or overture be adopted as a voluntary, let the performer imitate the
effect it would have in a fidl band, and not reduce it« brilliancy into an unvaried drawl.

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In bar tbe 9th, the 5th is inserted with the dominant 7th to prepare the next discord ; and this constitutes a most difficult
part of thorough bass. In bar 13 the parts are supposed to change places, the 7th of the first discord falling, and
the 5th rising to the 3d of the next discord. In bar 15 the added 6th is accompanied with an Stb, to prepare the next
discord. The last chord of bar 4, Ex. 188, has an 8th added to prepare the next discord. At the end of bar 5 a 3rd
is inserted, as this note should not be omitted.

Discords of transition consist of notes not belonging to tbe preceding chord (whether discordant notes or not),
passing diatonically up or down the scale while some note is held. They are accompanied the same as the preceding

note from which they pass. Thus a 7 following an 8 on the same bass note (Ex. 189) is accompanied with the ^ which

belonged to the 8, and the 7 must fall to the note below in the next chord, because it is a descending passing note.

8 7

Hence 8 7 stands for 5 — ; but it will not be always practicable to insert both the 5th and the 3rd, on account
3 —

of the stricter rules.

The 5 following a 6 may be accompanied by a 3, or a 6 and 3. The 5 is a descending passing note. Ex. 190. At

6 .

the end of bar 12 3 the bass note is the passing note, and is sometimes figured 4, ^ j oi" 2, or merely with dashes, as in

bar 2 and 3.

A 6 following a 5 is an ascending passing note. The 4 following a 3 is the same. Ex.191. In Ex. 192 the
nature of ascending and descending passing notes is shown, while the whole triad, or part of it, is held by other parts.
These, in thorough bass, produce a variety of figures ; but the use of dashes will render the performance easier. The

principal discords of transition are the g aiid its inversions the ^ and

2 preceded and followed by ^ on the same bass note, must not be accompanied by a 6th, (as in Ex. 121 and 122.)

Ex. 193; but it may occasionally have a 5 or an 8, as in Ex. 194.

Ex. 195 and 196 are inversions of the g? and the superiority of the dash, where it can be used instead of new

figures, for the repetition of the same note, will be readily perceived. In 197 and 200, the discords, or passing notes,
are in the bass.

In Ex. 198 and 199, the manner of adding a third part in the accompaniment may be seen.

Under the head of discords of transition may also be classed a succession of sixes on a pedale, descending or
ascending. Ex.200. Also discords of addition on a pedale, unprepared (Ex.202), in which the manner proposed
by some writers, of figuring the dominant 7th, added 9th, and leading 7tb, on a pedale, is shown. In playing the

7 6

6 and the ^ on the key note, the 6th note should always be placed in the upper melody. Ex. 203 is to be transposed

and practised.

Discords of syncopation are successions of 7ths on each note (Ex. 204), or on the alternate notes (Ex. 205) of a

bass, which continually falls 6ths, or rises 4ths, or does so alternately. They may be accompanied with 5 (Ex. 204

5 8

and 205), for fulness, or with Only 3 or g . The discordant notes must all be prepared like discords of suspension,
and resolved by falling to the note below in the next chord.

There are no inversions of a succession of 7ths on each bass note; but there are two inversions of the 7ths on
alternate bass notes. Ex. 206 and 207. Ex. 208 must be transposed and^practised as usual.

f t

Chromatic harmony consists of chords, in which the alteration of flats and sharps does not change the key. Ex.
209 consists of chromatic passing notes, ascending and descending. Ex. 210, 211, 212, and 213, are discords of
transition rendered chromatic. Ex. 211. The extreme flat 3rd to the 4th note of the key sharpened (called Fa sharp
in the Elements) was, the last adopted, because, perhaps, the least agreeable.

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The foregoing- examples (209 to 213) are in the mfijor key of C; and they cannot all be transposed into the minor.
Ex. 214 contains the principal. Ex.215 is the minor 9th introduced into the major key of C ; also tlie diminished
7th and one of its inversions. Ex. 216 shews how the 4th of the key, sharpened, (fa sharp), may be accompanied
and resolved in the major key of C. In Ex. 217, the 3rd to this chromatic note, in the minor key must be sharpened.
The student may transpose the rest of Ex. 216 into the minor key of A Ex.218 shows how some writers used the 6th
sharpened on this bass note, instead of the 7th flattened, as in Ex. 216. This can only be done when the 6th ascends.
It cannot be transposed into the minor key, as the 2iid note of the minor key cannot be made extreme sharp.

The extreme sharp 6th in the minor key is occasioned by the 4th of the key being sharpened when it is in

the accompaniment. It is called the Italian 6th, when accompanied only by a 3rd, (see Ex. 219). In the minor key

of A, (Ex. 220); in the major key of C, in which the bass is flattened, as well as the treble sharpened, or they

would not constitute an extreme sharp 6th. The extreme sharp 6lh, when accompanied by a Sth as well as 3rd, is

called the German 6th. Ex. 221, in the minor key of A. and Ex. 222, in the major key of C. This discord should

5 0 4-

not be resolved into a g, but into a to avoid consecutive 5ths. When accompanied with a ^ the extreme sharp

6th is called the French 6th. Ex. 223, 224. The Neapolitan 6th in the minor key is simply the 6th to the fourth note
of the key, flattened, and sliould generally be placed at the top. Ex. 225. In the major key, the Srd as well as the
6th, is flattened, so that this chord is the same in both keys. Ex. 226. A passage peculiar to church music may be
seen, Ex. 227, 228. A flat 7th to the key note not followed by any other alterations of the flats and sharps, may
be considered as a chromatic licence. Ex. 229. Of the same nature seems to be the second bass note of Ex. 2.30.
The student should transpose and practise Ex. 231, 232; the former, in the minor key, is put first, as being most simple.
The upper notes are given, and some of the chords; but in transposing them they may be left out.

For the study of the unessential notes of melody, the composition of music in parts, and the various kinds of
time, the reader is unavoidably referred to the Elements of Composition. Modulation is also, indeed, as much a
peculiar branch of composition as they are; and the thorough bass player, finding the modulations already made for
him, is not under the necessityof understanding them : but as it is hoped that the playing thorough bass will not
generally be separated, as hitherto, from a knowledge of composition, we shall proceed to oflTer some examples of
what is contained in the work already referred to, on this subject.

Diatonic modulation changes the key from the major to the relative minor, and the reverse, without any altera-
tion of flats and sharps; Ex. 233. Chromatic modulation is a change of key, together with an alteration of the flats
and sharps, as in all the following examples of modulation. Natural modulation is when the keys, into which the
changes are made, are those most immediately related to the original key, viz. the dominant key, the subdominant,
the relative, its dominant and its subdominant; or, in other words, keys that have the same number of flats or sharps,
or only one flat or sharp more or less than the original key has. Thus, from C major the natural modulations are
into G major, F major, A minor, E minor, and D minor ; and from G minor into D minor, C minor, Bl? major, F major,
and Eb major. Modulations from C major into D major, Bt> major, C minor, &c. would be unnatural or extra-
neous, and produce a more unexpected effect. Gradual modulation is effected by doubtful chords, viz. by such as
belong to both keys, and therefore render the transition imperceptible, as from C to G, Ex. 235, where the first
triad of the second bar belongs to both (!) and G. (Similar modulations to this, as from F to C, may be made by trans-
position). From G to C, (Ex. 236), where the middle triad of the second bar is the doubtful chord. In modulatif^j,
from F to G and from G to F, if C major or A minor is the original key, the modulation is natural, but if G or F
major, or E or D minor are the original keys, the modulation is unnatural. In Ex. 237,238, the modulation is gradual,
the triad, common to both keys, being that of C. In passing to the relative minor, or the reverse, the doubtful chords
may be the added 6th, (the 5th being omitted), the dissonant triad, and the leading 7th, Ex. 239 to 243. In Ex.
244, the Neapolitan 6th, and other discords, are common to both keys; some of the modulations are natural and
others extraneous. Ex. 245 is a specimen of natural and gradual modulation, though various discords are used.
Ex. 246 is a specimen of natural, but sudden modulation, the precise moment of the change of key being percepti-
ble. For the order and duration of modulations, see Elements, page 8.9. Ex. 247 shows the manner of modulating
by a succession of discords of syncopation. Ex. 248 is a modulation by dominant 7ths, in succession. Ex. 249 is
modulation by diminished 7ths, alternately inverted on a bass of descending semitones. Ex. 250 is the same on an
ascending bass, and is of more modern invention.

Enharmonic modulation is the adoption of some other note in a chord, which, on a keyed instrument, sound»

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the same as one we have, or inio\'ht have, as by taking E #, where we have, or might have, F kj, &c. The first chord in
each bar of Ex. 251 and 252 sounds the same on a piano forte, viz.

Ab G# G# Ab
F F E# F
D D D D
B B B Cb

In Ex. 251 these are resolved into four minor and four major keys; and Ex. 252 into four other minor and major
keys. The Italian and German 6ths may be used in enharmonic modulations, Ex.253, 254. All the examlpes, from
233 to 254, should be transposed and practised. Ex. 291 also contains enharmonic modulations.

OF ACCOMPANYING THE SCALE.

As (he thorough bass player is sometimes expected to play an accompaniment to the major and minor scales,
ascending and descending, in the bass or treble, he will find one of each, Ex.255 and 2-56. Those which are gene-
rally taught contain modulations, and are sometimes incorrect. But the chief objection to them is that they are gene-
rally given him to perform by rote, before he has learnt the meaning of either discords or modulation; and what the
utility of this can be, the author is unable to inform his reader. There is in fact no accompaniment peculiar to such
a scale. Ex. 257 and 2S8 contain several varieties, which might be very considerably augmented.

A SHORT RECAPITULATION OF THE RULES RELATING TO THE CHORDS AND

DISCORDS MOST FREQUENTLY USED.

When no figures are put, play 5.

8, 5, or 3 with no other figures, stands for 5.

In a dissonant triad add no 8 in general, especially if it doubles the 3rd note of the chord from which it is derived.
A ff, b, or tl, (not placed against a figure, but under them, or by themselves), shows that the Srd is accordingly
to be made I, b, or tj. In old music, b means a minor 3rd and I a major.

When the 3rd is major, the 5th must always be made perfect, unless the contrary is specified.
In playing a succession of triads, avoid consecutive perfect 5ths and 8ves between any two of the parts.
Make the upper part stand still, if the same note occurs in the next triad ; if not, make it move as little as possible.
Exceptions may be made to this rule, when the right hand is too high or too low.

6 stands for g. When this chord is the inversion of a triad, the 3rd or the 6th may be doubled. But the 8ve should

only be added when it does not double the 3rd note of the triad from which it is derived. It is generally best, and
especially in a succession of 6ths, to place the 6th note at the top.

A tj, or b, before any figure, makes it, accordingly, fc], or b, as | 2, # 8, fl 4, b : but 6, 4, or 5, with a line

drawn through them, stand also for a sharpened 6th and 4th. Amongst flats this mark makes the 6th or 4th natural.
If already sharp, it would make them double sharp. The b in old music is used to contradict the f, and is then equiva-
lent to our bi- 5, with a line drawn through it, is used by some writers for the extreme flat 5th.
\'8

^ stands for 6, except in the inversions of the dissonant triad, when the 8th is better omitted.

When ^ is followed by on the same bass note, always make 6 goto 5, and 4 to 3.

7 ®

7 stands for 3; or, in full passages, for

5 3

The discordant note in all discords, (excepting some of transition), must fall.
6 . ® .

^ stands tor 5 , a 3rd being always understood with any figure, where 4 or 2 is not expressed. An exception
to this is the ^^ followed by ^ on the same bass note, which must have no 3.

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A ^

o stands for 4.

2 stands for 4 when the bass note falls afterwards one note: but on a pedale or holding note in the bass g

have no 6th, but rather an 8 or 5.

9 Q

5 7

y stands for ^ or for 7. The 9th should always be placed at the top:—hence,
3 ^

In the leading 7th, the 7th should always be at the top. And
6

In the 4 on the 4th note of the key, the .3rd should always be at the top.

A dash (—) placed after a figure, shows the retention or repetition of the note represented by the preceding figure.
6 6 6

g J" means ^ When the composer uses no dashes, the performer must understand them as well as he can.
All discords of suspension must be prepared.
5-

4 3 and . o stands for 5 —.

2 may have the 5 or the 2 doubled, but must not have an 8.
9 8

9 8 stands for 5 —.

3 —

7 6 stands for g

6 6 stands for ^ ^ .

„ fj 7 6

f. stands for 5 — .
^ ~ 3 -

^ g must have no S with the 6.

Q _ 7 6 —

7 6 6 5 5 4?\' added,

«should have no note added, except the 8th.

7 8 on the key note stands for 4 or^ and is sometimes written 7 or^ _.

8 7

8 7 stands for 5 —

3 —

«7 13

7 g 6 11

6 or . or 5 on a holding key note, should have the 6th note at the top. This discord has been written 9
4 J 4 7

^ 2 • 5

The student may now encounter the difficulties of thorough bass contained in the selection which follows of the
music of various ages and different styles. These difficulties are occasioned by the circumstance of figures having
been originally intended merely as hints to experienced professors presiding in the orchestras of the oratorio, opera, or
concert, and not as a perfect substitution for notes to be performed equally by those who have or have not studied
composition.

In the choice of position he will find much difficulty, as it is not possible to play some passages in more than one
position, without making consecutive fifths or octaves.

The preparation of suspended discords is likewise difficult.

The utility of the dash must have heen obvious from the foregoing examples: but as al! writers do not use this
sisrn, the student must do without it as much as possible, and may therefore leave it out in his transpositions:

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for even those writers who have adopted this mark to slow bass notes, omit it to tliose which are rapid. Thus, in Ex.
274, bar 3 must be played like bar 1, and bar 6 like bar 5.

Many difficulties arise from inaccuracy, some from inconsistency, and others from the invention being in its
infancy, when the best methods of writing figures were not known. By comparing the bass part of Corelli\'s Concertos
with Dr. Pepusch\'s score, a difference in the manner of figuring the same passages will often be found, as in Ex. 275^
the fourth Concerto.

When the same bass note is repeated, the same accompaniment is to be understood. The student must not
imagine any changes of chord or key that he does not see expressed, or may infer from the bass itself. In short, if the
performer fancies a dash over every note where there are no figures, excepting the first note and the principal accented
notes in each bar, he will find the whole tolerably easy. In the first bar of the 2nd part of the vivace, the [> 5 means
that the # is to be flattened, or made natural, and so of the|j 4 in the next bar: but this method is now obsolete. The
last note in bars 9 and 10, are to be like the 1st. In bars 9 and 11 of the 2nd part of the allegro, the 3rd to E# must
be G though not specified, as also in bars 15, 16, 18, and 20.

The 8th concerto of Corelli (Ex.276) is figured from the score, and here, instead of#6 and |4, we find 6 and 4
with lines drawn through them. Still a flat signifies a natural, where it is put to contradict a sharp. The principal key
of the piece is G minor, but only one flat is placed at the beginning of the stave. So the 2nd concerto in C minor has
only two flats. The 5th and the 11th in B i, major have but one flat. In Handel\'s earlier productions, three sharps or
flats were put when four were required ; and the last movement of the concerto before us is in the key of G major,
though no sharp is putat the beginning of the stave. The 5th bar of the first movement is to be played as in Ex. 277.
In bar 11 of the movement marked grave, the sharp over D implies that the 5th A must be natural, though there was A |>
put before. In the next two adagios, the figures placed over the semiquaver rests must be reckoned from the following
notes. Bar 9, in the2nd of these adagios, would have been easier to read if written as in Ex. 278. In the vivace, dashes
must be understood to all but the first notes of each bar.

Near the conclusion of the allegro, two bars, having no figures at the beginning of line 2, page 31, may be played
as in Ex. 279. In the pastorale, the 5th and 6th bars may be played as in Ex. 280; as also in similar places. The
succession of 7 6 bar 14, &c. is tobe played as in Ex.281. A dash between the 7 and the 6 would have made it clearer.
Ex. 282 and 283 are from Corelli\'s Trios or Sonatas, for two violins and violoncello. His Sonatas for the violin are better
known by the name of Solos. In accompanying the latter, as the performer has an opportunity of availing himself of
the composer\'s melody,where he plays from the original work, he will take it in general (when it does not go too high)
as a given melody. In Ex. 284 the violin part is inserted with such an accompaniment as the Editor recommends. In
Ex. 285 and 286, the figures over the rests are reckoned from the preceding notes. In accompanying recitatives or
songs, the upper note of the harmony should be made to coincide with the voice part as much as possible, as it not
only assists the singer, but avoids consecutive octaves. In Ex. 287, (the song usually called Mad Bess, by Purcell), this
is elucidated. The thorough bass is frequently omitted in Purcell\'s music. Ex. 288 shows the style of recitative in
Handel\'s time ; and it has not received much alteration since. Bar 4 is to be played as in Ex. 289, and the last bar as
in Ex. 290, and so in all similar places. The time of a recitative is not strict, but all ad libitum for the singer. The
performer must be guided in striking the chords, by the arrival of the voice at the corresponding note in the melody.
Some persons hold the chords, some play them arpeggio, and .some make them staccato even when marked to be held ;
and each of these methods are occasionally good, the object of the performer being ever to assist, but not overpower
the singer. Ex.291 is given-as a specimen of enharmonic modulation from Handel. Ex. 292 is an ingenious and
elaborate harmony on a ground bass, by Sebastian Bach. Ex. 293 is a beautiful chorus in Iphigenie by Glück.
Ex. 294 is the concluding part of a slow movement, from a Sinfonia, by Haydn, the treble of which is given as a fine
specimen of double counterpoint, or two parts changing places with each other, as is the case with the violins and
basses in the theme, and all the variations which precede this fragment.

Lastly, the student is recommended, while performing the above selection from classical works arranged in chrono-
logical order, to observe the gradual increase of the various discords and modulations, and the application of them
to different styles and effects. Let him notice the simple sublimity of the church style, the chaste beauty of the
madrigal, and the varied expression of the cantata, with the invention of the ornamental style, so appropriate to in-
strumental music. By thus arranging his ideas, he will form his taste, and learn to appreciate real excellence of various
kinds, without expecting or wishing to see these styles confounded, as they too often are by composers of the present
day, who improve church music and madrigals on the same principles that the ecclesiastics of earlier times improved
our Gothic cathedrals, by adding screens, stalls, and altar pieces of Grecian architecture. The taste of this nation has
acknowledged, and is quickly remedying these barbarities. Let then our lovers of music also endeavour to
understand the characteristic merits of each style. So we may hope that our composers will not be tempted to
follow the example of the continent, in mingling sacred, secular, vocal, and instrumental music into one »con-
gruous whole.

FINIS.

[Printed by J. Mallett, Wardour Street, Soho. J

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