CHORDS, CADENCES, ETC.
196. A _chord_ is a combination of several tones sounding together and
bearing an harmonic relation to each other. The simplest chord is the
_triad_, which consists of a fundamental tone called the _root_, with
the third and fifth above it. C--E--G is a triad, as are also D--F--A,
F--A--C, and G--B--D.
197. Triads are classified as _major_, _minor_, _diminished_, or
_augmented_.
A _major triad_ has a major third and a perfect fifth, _i.e._,
it is a major third with a minor third on top of it. Ex.
C--E--G.
A _minor triad_ has a minor third and a perfect fifth, _i.e._,
it is a minor third with a major third on top of it. Ex.
C--E[flat]--G.
A _diminished triad_ has a minor third and a diminished fifth,
_i.e._, it is a minor third with another minor third on top of
it. Ex. C--E[flat]--G[flat].
An _augmented triad_ has a major third and an augmented fifth,
_i.e._, it is a major third with another major third on top of
it. Ex. C--E--G[sharp].
198. A triad may be built on any scale-tone, but those on I, IV, and V,
are used so much oftener than the others that they are often called the
_common chords_. In referring to triads the Roman numerals are used to
show on what scale-tone the triad is based, the size of the numeral
(with other signs) indicating the kind of triad found on each tone of
the scale. Thus _e.g._, the large I shows that the triad on the first
tone (in major) is a _major triad_, the small II shows that the triad
on the second tone is minor, etc. The following figure will make this
clear.
[Illustration: Fig. 65.]
The triads in the minor scale are as follows:
[Illustration]
199. A triad is said to be _in fundamental position_ when its root is
the lowest tone. It is said to be in the _first inversion_ when the
_third_ is the lowest tone, and in the _second inversion_ when the fifth
is the lowest tone. Thus _e.g._, in Fig. 66 the same chord (C--E--G) is
arranged in three different positions, at (a) in fundamental position,
at (b) in the first inversion, and at (c) in the second inversion.
[Illustration: Fig. 66.]
200. When the root is not the bass note, figures are sometimes used to
show what chord is to be played or written. Thus, _e.g._, the figure 6
over a bass note means that the note given is the _third_ of a chord,
the root being found by going up a sixth from the bass note: _i.e._, the
chord is to be sounded in its first inversion. In the same way the
figures 6/4 indicate that the note given is the _fifth_ of the chord,
the root and fifth being found by going up a sixth and a fourth from the
note given; _i.e._, the chord is to be sounded in its second inversion.
The use of these and other similar figures and signs is called _figured
bass_ (or _thorough bass_) _notation_. An example of a _figured bass_ is
given in Fig. 67.
[Illustration: Fig. 67.]
_Thorough bass notation_ was formerly used extensively in
writing accompaniments to vocal works, the accompanist having
to interpret the notes and signs given, and then to make up an
interesting accompaniment as he went along. Much of Handel's
music was written in this way, but in modern editions of these
works the chords have been printed in full and the signs
omitted.
201. A _seventh chord_ consists of a fundamental tone with its third,
fifth, and seventh. The fifth is sometimes omitted. A _ninth chord_
consists of a fundamental with its third, fifth, seventh, and ninth.
202. A _cadence_ is the close of a musical phrase: in melody it refers
to the last two tones; in harmony to the last two chords.
The word _cadence_ is derived from _cadere_, a Latin word
meaning to _fall_, the reference being to the falling of the
voice (_i.e._, the dropping to the normal pitch) at the close
of a sentence.
203. The most frequent cadence in harmony is that involving the chord on
I preceded by the chord on V. Because of its directness the cadence V--I
is called the _authentic cadence_.
204. The most satisfactory form (to the ear) of the authentic cadence is
that in which the highest voice (the soprano) of the final chord is the
_root_ of that chord. When the final chord appears in this position the
cadence is called _perfect_[36] _authentic_, and when the third or
fifth of the chord appear in the soprano, the cadence is called
_imperfect authentic_. Fig. 68 shows the chord G--B--D cadencing to
C--E--G in three different ways. The first one (a) is called a _perfect
authentic cadence_, but the last two (c) and (d) are _imperfect
authentic_.
[Footnote 36: Many theorists (including Durand in his monumental
"Treatise on Harmony") consider the V--I cadence to be the only one
which may legitimately be called _perfect_, but the majority of writers
seem to take the view that either authentic or plagal cadence may be
either perfect or imperfect, depending upon the soprano tone, as noted
above.]
[Illustration: Fig. 68.]
205. A _plagal cadence_ is one in which the tonic chord is preceded by
the sub-dominant chord (IV--I). The _plagal cadence_ (sometimes called
the _church cadence_, or _amen cadence_), like the authentic, is
described as being _perfect_ when the soprano of the tonic chord is the
root of that chord, and _imperfect_ when the soprano of the final chord
is the third or fifth of that chord. Fig. 69 shows the chord F--A--C
cadencing to C--E--G in three ways. The first one (a) is called a
_perfect plagal cadence_, the last two are _imperfect plagal_.
[Illustration: Fig. 69.]
206. A _half-cadence_ occurs when the dominant chord is used as the
final chord of a phrase, and is immediately preceded by the tonic chord.
This form is used to give variety in the course of a composition, but is
not available at the end because it does not give a definite close in
the tonic key. Fig. 70 shows the use of the _half-cadence_ at the close
of such a phrase.
[Illustration: Fig. 70. BACH]
207. A _deceptive cadence_ is the progression of the dominant chord to
some other chord than the tonic, the word _deceptive_ implying that the
ear expects to hear V resolve to I and is deceived when it does not do
so. The most common form of _deceptive cadence_ is that in which V (or
V^7) resolves to VI. It is used to give variety, but as in the case of
the half-cadence, is not available at the end of a composition. Fig. 71
gives an example.
[Illustration: Fig. 71. WM. MATHER]
208. A _sequence_ is a succession of similar harmonic progressions,
these resulting from a typical or symmetrical movement of the bass part.
See Fig. 72.
[Illustration: Fig. 72.]
The word _sequence_ is also applied to a succession of similar melodic
progressions, as in Fig. 73.
[Illustration: Fig. 73.]
209. _Modulation_ is a change of key without any break in the continuity
of chords or melody tones. _Harmonic modulations_ are usually effected
through the medium of a chord, some or all of whose tones are common to
both keys. Examples of both _harmonic_ and _melodic modulations_ are
shown in Figs. 74 and 75.
[Illustration: Fig. 74.]
The chord most frequently used in modulating is the _dominant seventh_,
_i.e._, a seventh chord (see Sec. 201) on the dominant tone of the key.
In the key of C this chord is G--B--D--F; in the key of D it is
A--C[sharp]--E--G; in the key of A[flat] it is E[flat]--G--B[flat]--D[flat],
etc.
[Illustration: Fig. 75.]
210. A _suspension_ is the temporary substitution of a tone a degree
higher than the regular chord-tone, this temporary tone being later
replaced by the regular chord-tone. See Fig. 76 (_a_).
[Illustration: Fig. 76.]
211. A _retardation_ is the temporary substitution of a tone a degree
lower than the regular tone, this tone (as in the case of the
suspension) being later replaced by the regular chord tone. See Fig. 77
(_a_).
[Illustration: Fig. 77.]
The "regular chord tone" to which both suspension and retardation
resolve is called the _tone of resolution_.
212. The _anticipation_ is a chord-tone introduced just before the rest
of the chord to which it belongs is sounded. See Fig. 78 (_a_).
[Illustration: Fig. 78.]
213. A _pedal point_ (or _organ point_) is a tone sustained through a
succession of harmonic progressions, to the chords of some of which it
usually belongs. The term _pedal point_ originated in organ playing,
(where the foot on a pedal can sustain a tone while the hands are
playing a succession of harmonies), but as now used it may be applied to
any kind of music. The dominant and tonic are the tones most often used
in this way. See Fig. 79.
[Illustration: Fig. 79. SCHUMANN]
214. When the upper three voices of a four-voice composition are written
close together (the soprano and tenor never appearing more than an
octave apart), the term _close position_ is applied. But when the upper
voices are not written close together, the term _open position_ is
applied.
215. By _transposition_ is meant playing, singing, or writing a piece of
music in some other key than the original. Thus _e.g._, if a song
written in the key of G is too high in range for a soloist, the
accompanist sometimes _transposes_ it to a lower key (as F or E), thus
causing all tones to sound a second or a third lower than they did when
the same song was played in the original key.