Letters to a Young Lady (Czerny)/Letter 8

Letters to a Young Lady
by Carl Czerny, translated by James Alexander Hamilton



You will already have discovered, Miss, that, among intervals, many sound agreeably, and many others very much the reverse. For this reason, intervals are divided into such as are consonant (or agreeable to the ear), and dissonant (or disagreeable to the ear).

Consonant intervals are:

(a.) The perfect unison;

(b.) The major and minor third;

(c.) The perfect fifth;

(d.) The major and minor sixth;

(e.) The perfect octave;

(f.) The major and minor tenth.

All others are dissonant.

Consonant intervals are still further divided into perfect and imperfect.

The perfect are: the perfect fifth and perfect octave.

The imperfect are: the major and minor third, and the major and minor sixth.

Concords are distinguished from discords, among other properties, by the latter requiring a resolution; that is to say, that the dissonant interval must be resolved into a consonant one; and this resolution must therefore naturally at last take place on a concord.

Among all the chords practicable in music, there is only one in each key which is called the perfect common chord, or perfect triad. It consists of a bass note or root, its third, its fifth, and when in four parts, the perfect octave also: viz.

\new PianoStaff << \new Staff { \override Score.TimeSignature #'stencil = ##f <e' g' c''>1 \bar ".." } \new Staff { \clef bass c' } >>
\new PianoStaff << \new Staff { \override Score.TimeSignature #'stencil = ##f <e' c''>1 \bar ".." } \new Staff { \clef bass <c g> } >>

The third may be either major or minor, according as the key is major or minor; but the fifth and octave must be perfect.

I must once more remind you that all the intervals in each chord are always computed and sought for from the lowest note upwards.

In the two preceding examples the octave is the highest part. But as the third or the fifth may also be the highest part, it follows that the perfect common chord admits of three positions, which are named according to the interval which occurs at the top or highest part. Ex.
\new PianoStaff << \new Staff \relative { \time 4/4 \override Score.TimeSignature #'stencil = ##f <e' g c>1^\markup { \teeny { Octave position. } } \bar ".." <g c e>^\markup { \teeny { Third position. } } \bar ".." <c e g>^\markup { \teeny { Fifth position. } } \bar ".." } \new Staff { \clef bass c c c } >>


\new PianoStaff << \new Staff \relative { \time 4/4 \override Score.TimeSignature #'stencil = ##f <e' c'>1^\markup { \teeny { Octave position. } } \bar ".." <g e'>^\markup { \teeny { Third position. } } \bar ".." <e' g>^\markup { \teeny { Fifth position. } } \bar ".." } \new Staff \relative { \clef bass<c g'> <c c'> <c c'> } >>

For the different changes or duplications of the middle parts do not, in any way, change the chord.

All this also occurs in the minor mode; that is, when the minor third is taken in place of the major third.

But the perfect common chord admits also of two inversions, by which two less perfect, though still consonant chords originate.

The inversion of a chord occurs when the bass, instead of the root, takes one of the other notes of which the chord consists. For example,

\new PianoStaff << \new Staff \relative { \time 4/4 \override Score.TimeSignature #'stencil = ##f <e' g c>1 \bar ".." <e g c>^\markup { \teeny { First inversion. } } \bar ".." <e g c>^\markup { \teeny { Second inversion. } } \bar ".." } \new Staff { \clef bass c^\markup { \teeny { Perfect common chord. } } e^\markup { \teeny { Chord of the Sixth. } } g^\markup { \overlay { \teeny "Chord of the Sixth" \translate #'(3 . -1.5)\teeny "and fourth." } } } >>
The chord of the sixth, so called because its principal interval is the sixth, has also its three positions, like the perfect common chord. Example:
\new PianoStaff << \new Staff \relative { \time 4/4 \override Score.TimeSignature #'stencil = ##f <c' g' c>1 \bar ".." <g' c e> \bar ".." <g c g'> \bar ".." } \new Staff { \clef bass e^\markup { \teeny { Sixth position. } } e^\markup { \teeny { Octave position. } } e^\markup { \teeny { Third position. } } } >>

Just so it is with the chord of the sixth and fourth, which derives its name from its containing those intervals. Ex.

\new PianoStaff << \new Staff \relative { \time 4/4 \override Score.TimeSignature #'stencil = ##f <e' g c>1 \bar ".." <e c' e> \bar ".." <e c' g'> \bar ".." } \new Staff { \clef bass g^\markup { \teeny { Fourth position. } } g^\markup { \teeny { Sixth position. } } g^\markup { \teeny { Octave position. } } } >>

It is very necessary to know all these chords readily in their different forms.

All this equally applies to minor keys, if, instead of E♮, we every where take E♭.

These two chords are less perfect than the common chord, because, although they are tolerably agreeable, they do not sound so satisfactorily as to enable us to make a close or cadence by means of them.

Although the perfect common chord may occur on each degree of the diatonic scale (though, however, on the seventh degree it appears with an imperfect fifth), it is nevertheless most important, when placed on the first degree of the key in which we are playing, as it alone can establish and determine the key.

We now come to the second principal chord in thorough-bass; namely, the chord of the minor or dominant seventh.

It consists of a bass note, its major third, perfect fifth, and minor seventh, and consequently of four essential parts; so that it requires no duplication of notes to be in four parts.

It takes place on the fifth degree, or dominant note of every scale; and therefore, in C major or minor, it falls upon G. Ex.

\new PianoStaff << \new Staff { \time 4/4 \override Score.TimeSignature #'stencil = ##f <b' d'' f''>1 \bar ".." } \new Staff { \clef bass g \bar ".." } >>
\new PianoStaff << \new Staff { \time 4/4 \override Score.TimeSignature #'stencil = ##f <b' f''>1 \bar ".." } \new Staff { \clef bass <g d'> } >>

You are already conversant with this chord, from the scale-exercises in my Pianoforte School, where it serves to form the passage or transition from one key to another.

It has the property of requiring a natural, and to the ear desirable, resolution into the perfect common chord. Ex.

\new PianoStaff << \new Staff \relative { \time 4/4 \override Score.TimeSignature #'stencil = ##f \override Staff.Rest.style = #'classical <b' d f>2(<g c e>4) r \bar ".." } \new Staff { \clef bass \override Staff.Rest.style = #'classical g2 c'4 r } >>
\new PianoStaff << \new Staff \relative { \time 4/4 \override Score.TimeSignature #'stencil = ##f \override Staff.Rest.style = #'classical <b' f'>2 <c e>4 r \bar ".." } \new Staff { \clef bass \override Staff.Rest.style = #'classical <g d'>2 c'4 r } >>

It has four different positions; viz.

\new PianoStaff << \new Staff \relative { \time 4/4 \override Score.TimeSignature #'stencil = ##f <g b d f>1^\markup { \teeny { First position. } } \bar ".." <b d f g>^\markup { \teeny { Second position. } } \bar ".." <d f g b>^\markup { \teeny { Third position. } } \bar ".." <f g b d>^\markup { \teeny { Fourth position. } } \bar ".." } \new Staff { \clef bass g, g, g, g, } >>

In all these positions, it always remains the same chord of the seventh.

In addition to this, it has also three inversions, by which three different chords originate, namely, the chord of the fifth and sixth, that of the sixth, fourth, and third, and the chord of the second.

\new PianoStaff << \new Staff \relative { \time 4/4 \override Score.TimeSignature #'stencil = ##f <b' d f>1 \bar ".." <g d' f>^\markup { \teeny { First inversion. } } \bar ".." <g b f'> \bar ".." <g b d> \bar ".." } \new Staff { \clef bass g^\markup { \overlay { \teeny "Chord of the" \translate #'(1 . -1.5)\teeny "seventh." } } b^\markup { \overlay { \teeny "Chord of the" \translate #'(-1 . -1.5)\teeny "sixth and fifth." } } d'^\markup { \overlay { \teeny "Chord of the sixth," \translate #'(.5 . -1.5)\teeny "fourth, and third." } } f'^\markup { \overlay { \teeny "Chord of the" \translate #'(1 . -1.5)\teeny "second." } } } >>
Each of these new chords has also its different positions. Ex.
\new PianoStaff << \new Staff \relative { \time 4/4 \override Score.TimeSignature #'stencil = ##f <g' d' f>2 <d' f g> <f g d'>1 \bar ".." <g, b f'>2 <b f' g> <f' g b>1 \bar ".." <g, b d>2 <b d g> <d g b>1 \bar ".." } \new Staff { \clef bass b2^\markup { \teeny First, }_\markup { \teeny { Chord of the sixth and fifth. } } b^\markup { \teeny second, } b1^\markup { \teeny { third position. } } d'2^\markup { \teeny First, }_\markup { \teeny { Chord of the sixth, fourth, and third. } } d'^\markup { \teeny second, } d'1^\markup { \teeny { third position. } } f'2^\markup { \teeny First, }_\markup { \teeny { Chord of the second. } } f'^\markup { \teeny second, } f'1^\markup { \teeny { third position. } } } >>

The natural resolution of these chords is also into the perfect common chord. The chord of the second, however, is resolved by one of the inversions of that chord. Ex.

\new PianoStaff << \new Staff \relative { \time 4/4 \override Score.TimeSignature #'stencil = ##f \override Staff.Rest.style = #'classical <g' d' f>2 <g c e>4 r \bar ".." <g b f'>2 <g c e>4 r \bar ".." <g b d>2 <g c>4 r \bar ".." } \new Staff { \clef bass \override Staff.Rest.style = #'classical b2 c'4 r d'2 c'4 r f'2 e'4 r } >>

In the chord of the second, you will observe, Miss, that the discord of the second, though rather harsh in itself, sounds pleasingly enough in this application of it.

When the chord of the seventh is played on other degrees of the scale, it is very dissonant, though still capable of being employed. Ex.

\new Staff \relative { \time 4/4 \override Score.TimeSignature #'stencil = ##f <c' e g b>1 <d f a c> <e g b d> <f a c e> \bar ".." }

If, in the first of these four chords, we were to make the seventh minor, it would certainly sound much better; but it would no longer be in C major, but in F. Ex.

\new PianoStaff << \new Staff \relative { \time 4/4 \override Score.TimeSignature #'stencil = ##f \override Staff.Rest.style = #'classical <c' e g bes>2 <c f a>4 r \bar ".." } \new Staff { \clef bass \override Staff.Rest.style = #'classical c2 f4 r } >>

I have already made you acquainted with seven chords. If you give yourself the trouble to transpose them into the other keys, you will speedily be able to trace them out in every composition, under whatever forms they may occasionally be hidden. We will, in our next, learn the remaining chords; and till then believe me, &c.