A Dictionary of Music and Musicians/Resolution

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RESOLUTION is the process of relieving dissonance by succeeding consonance. All dissonance is irritant and cannot be indefinitely dwelt upon by the mind, but while it is heard the return to consonance is awaited. To conduct this return to consonance in such a manner that the connection between the chords may be intelligible to the hearer is the problem of resolution.

The history of the development of harmonic music shows that the separate idea of resolution in the abstract need not have been present to the earliest composers who introduced discords into their works. They discovered circumstances in which the flow of the parts, moving in connsonance with one another, might be diversified by retarding one part while the others moved on a step, and then waited for that which was left behind to catch them up. This process did not invariably produce dissonance, but it did conduce to variety in the independent motion of the parts. The result, in the end, was to establish the class of discords we call suspensions, and their resolutions were inevitably implied by the very principle on which the device is founded. Thus when Josquin diversified a simple succession of chords in what we call their first position, as follows—

\new ChoirStaff << \override Score.TimeSignature #'stencil = ##f
  \new Staff \relative d'' { \mark \markup \small "Ex. 1." \time 4/2 \partial 2
    << { d2 ^~ | d4 c c2 ^~ c4 b!8 a b2 | c1 \bar "||" } \\
       { bes2 | g a g1 | g } >> }
  \new Staff \relative f' { \clef bass
    << { f2 | e f d1 | e } \\
       { bes2 | c f, g1 | c, } >> } >>

it seems sufficiently certain that no such idea as resolving a discord was present to his mind. The motion of D to C and of C to B was predetermined, and their being retarded was mainly a happy way of obtaining variety in the flow of the parts, though it must not be ignored that the early masters had a full appreciation of the actual function and effect of the few discords they did employ.

Some time later the device of overlapping the succeeding motions of the parts was discovered, by allowing some or all of those which had gone on in front to move again while the part which had been left behind passed to its destination; as by substituting (b) for (a) in Ex. 2.

\new ChoirStaff << \override Score.TimeSignature #'stencil = ##f
  \new Staff \relative e'' { \mark \markup \small "Ex.2." \time 2/2 \partial 2
    << { e2^\markup \tiny "(a)" ~ e d \bar "||"
         \partial 2 e2^\markup \tiny "(b)" ~ e d \bar "||" } \\
       { <c g>2 <a f>1 | <c g>2 <a f> <b f> } >> }
  \new Staff \relative c { \clef bass c2 d1 c2 d g } >>

This complicated matters, and gave scope for fresh progressions and combinations, but it did not necessarily affect the question of resolution, pure and simple, because the destination of the part causing the dissonance was still predetermined. However, the gradually increasing frequency of the use of discords must have habituated hearers to their effect and to the consideration of the characteristics of different groups, and so by degrees to their classification. The first marked step in this direction was the use of the Dominant seventh without preparation, which showed at least a thorough appreciation of the fact that some discords might have a more independent individuality than others. This appears at first merely on this side, of occasionally discarding the formality of delaying the note out of a preceding chord in order to introduce the dissonance; but it led also towards the consideration of resolution in the abstract, and ultimately to greater latitude in the process of returning to consonance. Both their instinct and the particular manner in which the aspects of discords presented themselves at first led the earlier composers to pass from a discordant note to the nearest available note in the scale, wherever the nature of the retardation did not obviously imply the contrary; and this came by degrees to be accepted as a tolerably general rule. Thus the Dominant seventh is generally found to resolve on the semitone below; and this, combined with the fact that the leading note was already in the chord with the seventh, guided them to the relation of Dominant and Tonic chords; although they early realised the possibility of resolving on other harmony than that of the Tonic, on special occasions, without violating the supposed law of moving the seventh down a semitone or tone, according to the mode, and raising the leading note to what would have been the Tonic on ordinary occasions. However, the ordinary succession became by degrees so familiar that the Tonic chord grew to be regarded as a sort of resolution in a lump of the mass of any of the discords which were built on the top of a Dominant major concord, as the seventh and major or minor ninth, such as are now often called Fundamental discords. Thus we find the following passage in a Haydn Sonata in D—

\new ChoirStaff << \override Score.TimeSignature #'stencil = ##f \override Score.Rest #'style = #'classical
  \new Staff \relative e' { \key d \major \mark \markup \small "Ex. 3." \time 4/4
    e8.\( g16 fis8. a16\) g4 r | \appoggiatura { fis,16[ a] } d2 s8_"etc." }
  \new Staff \relative c' { \clef bass \key d \major
    << { cis4\( d e\) } \\ { a,2. } >> r4 | r8 cis,16\( d d,4\) s8 } >>

in which the Dominant seventh is not resolved by its passing to a near degree of the scale, but by the mass of the harmony of the Tonic following the mass of the harmony of the Dominant. Ex. 4 is an example of a similar use by him of a Dominant major ninth.

\new ChoirStaff << \override Score.Rest #'style = #'classical \override Score.TimeSignature #'stencil = ##f
  \new Staff \relative c''' { \key ees \major \time 4/4 \mark \markup \small "Ex. 4."
    << { r2 c | c\fermata } \\ { ees,4. d2 d8 ~ | d2 } >>
    r8 g32( ees16.) ees32( bes16.) bes32( g16.) |
    r8 c32( aes16.) aes32( f16.) f32( c16.)
      ees4 ~ ees16[ bes] \tuplet 3/2 { aes'16 f d } | s8_"etc." }
  \new Staff \relative a' { \key ees \major
    << { aes4 aes2 aes4 ~ aes2\fermata } \\ { c,8 bes2 bes4. ~ bes2 } >>
    \clef bass <ees, bes g>4 r | <ees c aes> r
    r8 <g bes,> q <f bes,> | s } >>

A more common way of dealing with the resolution of such chords was to make the part having the discordant note pass to another position in the same harmony before changing, and allowing another part to supply the contiguous note; as in Ex. 5, from one of Mozart's Fantasias in C minor.

\new ChoirStaff << \override Score.TimeSignature #'stencil = ##f \override Score.Rest #'style = #'classical
  \new Staff \relative b' { \key c \minor \time 4/4 \partial 2 \mark \markup \small "Ex. 5."
    b8.[ f'16 aes8. b,16] | c4 \bar "||" \mark \markup \small "Ex. 5a." \partial 4 \clef treble \key f \major des4 | e, r s }
  \new Staff \relative d { \key c \minor \clef bass
    <d f aes b>4 r <ees g c> \clef bass \key f \major
    << { bes4 bes } \\ { g g } >> r s } >>

Some theorists hold that the passage of the ninth to the third—as D♭ to E in Ex. 5a (where the root C does not appear)—is sufficient to constitute resolution. That such a form of resolution is very common is obvious from theorists having noticed it, but it ought to be understood that the mere change of position of the notes of a discord is not sufficient to constitute resolution unless a real change of harmony is implied by the elimination of the discordant note; or unless the change of position leads to fresh harmony, and thereby satisfies the conditions of intelligible connection with the discord.

A much more unusual and remarkable resolution is such as appears at the end of the first movement of Beethoven's F minor Quartet as follows—

\new ChoirStaff << \override Score.Rest #'style = #'classical \override Score.TimeSignature #'stencil = ##f
  \new Staff \relative g' { \key f \minor \time 4/4 \mark \markup \small "Ex. 6."
    << { g2.\( c4 | f,\) } \\ { bes,2. c4 | f } >> r4 r2 \bar "||" }
  \new Staff \relative e { \clef bass \key f \minor
    << { e2.\( c'4 | f,\) } \\ { r4 des,\( c c' f,\) } >> r4 r2 } >>

where the chord of the Dominant seventh contracts into the mere single note which it represents, and that proceeds to the note only of the Tonic; so that no actual harmony is heard in the movement after the seventh has been sounded. An example of treatment of an inversion of the major ninth of the Dominant, which is as unusual, is the following from Beethoven's last Quartet, in F, op. 135.

\new ChoirStaff << \override Score.Rest #'style = #'classical \override Score.TimeSignature #'stencil = ##f
  \new Staff \relative a' { \key d \major \time 4/4 \partial 2 \mark \markup \small "Ex. 7."
    << { a4 r | a r b r | d2 } \\
       { fis,4 s | fis s g s | fis2 s4_"etc." } >> }
  \new Staff \relative d' { \clef bass \key d \major
    d4 r | d r cis r | b2 s4 } >>

There remain to be noted a few typical devices by which resolutions are either varied or elaborated. One which was more common in early stages of harmonic music than at the present day was the use of representative progressions, which were in fact the outline of chords which would have supplied the complete succession of parts if they had been filled in. The following is a remarkable example from the Sarabande of J. S. Bach's Partita in B♭.

\new ChoirStaff << \override Score.TimeSignature #'stencil = ##f
  \new Staff \relative c'' { \key bes \major \time 3/4 \mark \markup \small "Ex.8."
    c16( ees,)\prall ees32( d ees16) a!( fis)\prall fis32( e fis16)
      ees'( b)\prall b32( a b16) | c8. c16 <c g ees c>4_"etc." \bar "||" }
  \new Staff \relative a { \clef bass \key bes \major
    << { a!4 g g ~ | g c, } \\ { fis g g, | c c, } >> } >>

which might be interpreted as follows:

\new ChoirStaff << \override Score.TimeSignature #'stencil = ##f
  \new Staff \relative c'' { \key bes \major \time 3/4 \mark \markup \small "Ex. 9."
    <c a e>4 << { <a cis> b | c } \\ { e, ~ <e g>8 <d f> | <e c>4 } >> \bar "||" }
  \new Staff \relative a { \clef bass \key bes \major
    << { a!4 g g | g } \\ { fis g g, | c } >> } >>

Another device which came early into use, and was in great favour with Bach and his sons and their contemporaries, and is yet an ever fruitful source of variety, is that of interpolating notes in the part which has what is called the discordant note, between its sounding and its final resolution, and either passing direct to the note which relieves the dissonance from the digression, or touching the dissonant note slightly again at the end of it. The simplest form of this device was the leap from a suspended note to another note belonging to the same harmony, and then back to the note which supplies the resolution, as in Ex. 10; and this form was extremely common in quite the early times of polyphonic music.

\new ChoirStaff << \override Score.TimeSignature #'stencil = ##f
  \new Staff \relative d'' { \mark \markup \small "Ex. 10." \time 2/4 \partial 8
    << { d8 ~ d g, c4 \bar "||" \partial 8 f8 ~ f g e4 \bar "||" } \\
       { f,8 e2 <g d'>8 <g c>2 } >> }
  \new Staff \relative g { \clef bass
    << { g8 ~ g2 } \\ { b,8 c2 } >> b'8 c2 } >>

But much more elaborate forms of a similar nature were made use of later. An example from J. S. Bach will be found at p. 678 of vol. i, of this Dictionary; the following example, from a Fantasia by Emanuel Bach, illustrates the same point somewhat remarkably, and serves also as an instance of enharmonic resolution.

\new ChoirStaff << \override Score.BarNumber #'break-visibility = #'#(#f #f #f) \override Score.Rest #'style = #'classical \override Score.TimeSignature #'stencil = ##f
  \new Staff \relative b' { \key c \minor \time 3/4 \partial 4 \mark \markup \small "Ex. 11."
    bes4 ~ | bes16 bes f'( e) e8( bes) bes4 ~ |
    bes16 bes bes'( aes32) g f8( e) bes4 \bar "||" \key c \major
    \cadenzaOn s4.... r64 cis,64[  \once \override TextScript.script-priority = #-100 cis32]^\markup { \sharp }\turn
    dis64[ e fis gis ais b! cis dis e fis ais gis! fis! e dis! cis! b]
    ais!4 gis!8[\turn ais!16 fis!] fis8 <dis fis b>2 }
  \new Staff \relative c { \clef bass \key c \minor
    r4 <c g c,>2. q \key c \major << { r4 r8 r16 r32 ais64[ cis] e1 } \\ { e,2 _~ e1 } >> <dis' fis b>2 } >>

The minor seventh on C in this case is ultimately resolved as if it had been an augmented sixth composed of the same identical notes according to our system of temperament, but derived from a different source and having consequently a different context. This manner of using the same group of notes in different senses is one of the most familiar devices in modern music for varying the course of resolutions and obtaining fresh aspects of harmonic combinations. [For further examples see Modulation, Change, Enharmonic.]

An inference which follows from the use of some forms of Enharmonic resolution is that the discordant note need not inevitably move to resolution, but may be brought into consonant relations by the motion of other parts, which relieve it of its characteristic dissonant effect; this is illustrated most familiarly by the freedom which is recognised in the resolution of the chord of the sixth, fifth and third on the subdominant, called sometimes the added sixth, and sometimes an inversion of the supertonic seventh, and sometimes an inversion of the eleventh of the Dominant, or even a double-rooted chord derived from Tonic and Dominant together.

It is necessary to note shortly the use of vicarious resolutions—that is, of resolutions in which one part supplies the discordant note and another the note to which under ordinary circumstances it ought to pass. This has been alluded to above as common in respect of the so-called fundamental discords, but there are instances of its occurring with less independent combinations. The Gigue of Bach's Partita in E minor is full of remarkable experiments in resolution; the following is an example which illustrates especially the point under consideration.

\new ChoirStaff << \override Score.TimeSignature #'stencil = ##f
  \new Staff \relative b' { \key e \minor \time 4/4 \mark \markup \small "Ex. 12."
    b8 cis a4 ~ a8 d, d'4 ~ | d8 b c4 ~ c8 a b4_"etc." }
  \new Staff \relative e' { \key e \minor
    << { e4. c'8 fis,4. b8 | gis4. a16 cis g4 s } \\
       { c,4. a8 b4. gis8 | fis'4. dis8 e4 s } >> } >>

The inference to be drawn from the above examples is that the possible resolutions of discords, especially of those which have an individual status, are varied, but that it takes time to discover them, as there can hardly be a severer test of a true musical instinct in relation to harmony than to make sure of such a matter. As a rule, the old easily recognisable resolutions, by motion of a single degree, or at least by interchange of parts of the chord in supplying the subsequent consonant harmony, must preponderate, and the more peculiar resolutions will be reserved for occasions when greater force and intensity are required. But as the paradoxes of one generation are often the truisms of the next, so treatment of discords such as is utterly incredible to people who do not believe in what they are not accustomed to, is felt to be obvious to all when it becomes familiar; and hence the peculiarities which are reserved for special occasions at first must often in their turn yield the palm of special interest to more complex instinctive generalisations. Such is the history of the development of musical resources in the past, and such it must be in the future. The laws of art require to be based upon the broadest and most universal generalisations; and in the detail under consideration it appears at present that the ultimate test is thorough intelligibility in the melodic progressions of the parts which constitute the chords, or in a few cases the response of the harmony representing one root to that representing another, between which, as in Examples 3 and 4, there is a recognised connection sufficient for the mind to follow without the express connection of the flow of the parts. Attempts to catalogue the various discords and their various resolutions must be futile as long as the injunction is added that such formulas only are admissible, for this is to insist upon the repetition of what has been said before; but they are of value when they are considered with sufficient generality to help us to arrive at the ultimate principles which underlie the largest circle of their multifarious varieties. The imagination can live and move freely within the bounds of comprehensive laws, but it is only choked by the accumulation of precedents.