Cadential Structure in Mozart's Piano Sonata K. 310, 1st Movement
RIFFS
Appendix
Cadential Structure in Mozart's Piano Sonata K. 310, 1st Movement
Lester Allyson Knibbs, Ph.D.
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Introduction


The Chaconne

Cadential Structure

Unitary & Binary Structures

Linear & Periodic Structures

Riff Modalities

Structural Counterpoint

Modular Composition

Appendices --

Afro-Americana

Mozart's K. 310

Two Liszt Etudes
Cadential structure in sonata-allegro form, and in many other examples of tonal music, does not coincide with thematic structure.  The result is structural counterpoint, dynamic tension between fundamental tendencies.  An outline of the thematic structure of the first movement of Mozart’s piano sonata in a-minor K. 310 appears below; an outline of the cadential structure follows.

THEMATIC STRUCTURE


Exposition     mm. 1 –  49

    
First Theme Group     mm. 1 –  22

          Theme I, phrase 1    
mm. 1 –  9
          Theme I, Phrase 2    
mm. 9 –  16
          Transition    
mm. 16 –  22

    
Second Theme Group     mm. 23 –  49

          Theme II    
mm. 23 –  35
          Theme II, closing phrase    
mm. 35 –  45
          Codetta    
mm. 45 –  49

Development     mm. 50 –  79

     First Section    
mm. 50 –  58
     Second Section    
mm. 58 –  70
     Third Section    
mm. 70 –  79

Recapitulation     mm. 80 –  133

    
First Theme Group     mm. 80 –  103

          Theme I, phrase 1    
mm. 80 –  88
          Theme I, Phrase 2    
mm. 88 –  97
          Transition    
mm. 97 –  103

    
Second Theme Group     mm. 104 –  133

          Theme II    
mm. 104 –  116
          Theme II, closing phrase    
mm. 116 –  129
          Codetta    
mm. 129 –  133

CADENTIAL STRUCTURE

Binary Statement of Cadence:  

     First Statement [ I – IV – V ]    
mm. 1 –  79

              
Initial Tonic [ I – ]     mm. 1 –  73

                    Initial Cadence    
mm. 1 –  9
                    Mediant Elaboration (binary)    
mm. 9 –  49
                        
[ I – IV – V ]     mm. 9 –  22
                        
[ I – IV – V – I ]     mm. 23 –  49
                    Motion to Subdominant    
mm. 50 –  70
                    Return to Tonic    
mm. 70 –  73

              
Cadential Subdominant (Spanish) [ – IV – ]     mm. 73

              
Cadential Dominant [ – V ]     mm. 74 – 79

    
Second Statement (binary)     mm. 80 –  133

          [ I – IV – V ]    
mm. 80 –  103

               Initial Tonic [ I – ]    
mm. 80 –  93

               Cadential Subdominant [ – IV – ]    
mm. 94 –  96

               Cadential Dominant [ – V ]    
mm. 97 –  103

          [ I – IV – V – I ]    
mm. 104 –  133

DISCUSSION

Exposition: First Theme Group

Measures 1-5 consist of a prolongation of the tonic over a tonic pedal-point.  In my analysis, what follows is a motion (by way of VII and VI) to the cadential subdominant of this opening phrase, the ii6 in m. 8.  Then we have the i6/4 – V7 – i in mm. 8-9.  So, harmonically, mm. 1-9 is a statement of the [I-IV-V-I] idea which is fundamental to cadential structure.

Thematically and harmonically, the second phrase starts out as a “fake” (to use basketball terminology).  Measure 9 starts strongly in a-minor, but by measure 16 a-minor has dissolved into C-major.  If we glance ahead at mm. 45-47, we see what has happened to a-minor here; it has become a motion into the subdominant area of C-najor.  In mm. 45-47, a full cadence is completed.  In mm. 9-16, we have two partial statements of the cadential idea, both using a-minor as a motion of the submediant (vi) into the subdominant (IV in m. 13, ii6 in m. 15) of C-major.  The first partial statement ends at the tonic (I) in m. 14, third beat.  I call this type of event “tying-the-knot”.  At this point, Mozart has taken a “big” a-minor tonic and dissolved it into a “little” C-major tonic; the a-minor triad has become the submediant of C-major.  The C-major tonic in m. 14 is clearly the goal of motion – melodically in the descending line of the bass, and harmonically as well.  Nevertheless, this C-major tonic is reduced in stature by three factors: (1) the sudden compression in harmonic rhythm, leading to the arrival at the tonic on the third beat of the measure instead on the first beat of the next measure; (2) the devious syncopated chromatic melodic line, which delays resolution on the tonic chord’s mediant note until after the harmony has moved to the submediant on the fourth beat; and (3) approaching the tonic by way of the V6/5 instead of the root position dominant chord.  In a sense, we perceive this phrase through the wrong end of a telescope; the arrival at the C-major tonic in m. 14 is far more important than it is made to seem, in that mm. 9-14 are a prolongation (or elaboration) of motion into this tonic.

This type of arrival at (usually) a tonic – “tying-the-knot” –serves as an effective jumping-off point for the next development.  In this case – and commonly so – the next development is a strong motion by way of the cadential subdominant into the cadential dominant (mm. 14-16).  This is the second partial statement of the cadential idea, again using the a-minor chord (this time clearly the submediant of C-major) as a motion into the cadential subdominant.  In this second partial statement, the subdominant moves to a strong root-position cadential dominant, completing a strong half-cadence in C-major and setting up the customary fanfare (mm. 16-22) which leads to the second theme group.

Exposition: Second Theme Group

Theme II could almost be called a “prolongation of the I6”. The prolongation of the tonic extends from m. 23 to m. 31 (beginning and ending on the I6).  The cadential subdominant extends for two measures (mm. 32-33), and the cadential dominant (I6/4-V) resolves to the concluding cadential tonic in mm. 34-35.  This process is repeated in mm. 35-40 and again in mm. 40-45.  Each time, the cadential subdominant is approached from the I6.

The codetta recalls the process that established C-major (mm. 9-16), bringing that original “half-cadence” idea to a full close on the final tonic of the exposition section.

Development: First Section

Here we have another “wrong-end-of-the-telescope”.  Our “strong” C-major dissolves into the dominant of e-minor.  I differ here with Felix Salzer (Structural Hearing, vol. I, pp. 23-25 and examples VIII and IX, vol. II, pp. 4-5), and the difference affects the overall analysis.  Harmonically, there is no C-D-E motion (m. 50 to m. 70 to m. 74), as in Salzer’s analysis.  The C-D-E is a melodic reality, a surface idea and a nice counterpoint to the underlying harmonic process in this development section.  As we see in mm. 57-58, this underlying harmonic process takes quite a different turn.  B-major harmony (V of e-minor) is the goal – C-major becoming VI of e-minor (i.e., dissolved) – and the V of e-minor itself is apparently the first stage of an escalator that leads us by way of V of a-minor and V of d-minor to the d-minor tonic in m. 70.

Now, momentarily, we have arrived somewhere.  But, where?  Let’s summarize.  In mm. 9-14, our initial a-minor tonality was dissolved into being a mere vi in C-major.  In mm. 50-58, our mighty C-major tonality was dissolved into being a mere VI moving to the V of e-minor, which led to the V of a-minor, which led to the V of d-minor, which led to our current d-minor tonic.  So, at the moment, this d-minor tonic in m. 70 is the only tonic we have.  All other tonics having dissolved, what is this tonic going to do?  Dissolve, of course, and quickly.

Do you remember mm. 6-7? – iv6/5 – VII – III6/5 – VI – interesting diatonic sound in the minor mode.  The progression in mm. 70-72 is similar, except that the appearance of b-natural kills d-minor as a tonic.  We seem to be falling headlong.  The harmonic rhythm of mm. 70-72 is eight times as fast as in mm. 58-69, with no stops.  Are we returning to C-major (V6/5 – I in mm. 70-71)?  No, we don’t stop.  We keep moving until we arrive at the a-minor tonic on the first beat of m. 73 – preceded by a clear V6/5 of a-minor.  The appearance of this tonic of a-minor “ties-the-knot”.  The opening a-minor tonality is prolonged to this point (mm. 1-73).  This is the [ I ] of a [ I-IV-V ] structure.  The [ IV ] appears in the third and fourth beat of m. 73, and the [ V ] arrives in m. 74 and is prolonged to m. 79.

This may seem extreme – a 72-and-one-half-measure prolongation of the tonic, followed by two beats of subdominant and six measures of dominant – but I believe this extreme prolongation is what gives a piece such as this such a tremendous “wind-up” in the closing measures of the development section.

To summarize, the overall harmonic structure of this movement is a [I-IV-V] in measures 1-79, the Recapitulation could be summarized as a [I-IV-V-I], the whole being – to simplify – a half cadence (mm. 1-79) followed by a full cadence (mm. 80-133).  Actually, mm. 80-133 reiterate the half cadence idea.

Not all sonata-allegro movements use this idea, so that from a structural-harmonic point of view sonata-allegro movements differ from one another in fundamental ways.

The particular idea of this movement – prolonging the initial structural tonic to the middle of the Development section, followed by the cadential subdominant, which leads to the cadential dominant, completing a half-cadence first statement of the overall binary cadential structure of the movement – this particular idea seems to be common in the sonata-form works of Mozart and Beethoven, in particular.  Theoretically, the initial structural tonic is optional.  I don’t know of any instances where the initial tonic is omitted on the structural level [Beethoven op. 57, I].  Beethoven’s piano sonata in E-flat major op. 31 no. 3, first movement, toys with the idea on lower levels, but does not bring it up to the structural level.

The cadential subdominant is definitely optional.  In mm. 337-338 of Beethoven’s third symphony, motion is directly from the tonic to the dominant.  Paradoxically, the cadential subdominant is frequently highly elaborated on lower levels (see mm. 80-89 of Beethoven’s piano sonata op. 10 no. 1, first movement), and non-cadential subdominants are frequently highly elaborated on the structural level (see mm. 118-146 of the op. 10 no. 1 movement).

The cadential dominant is sometimes highly prolonged (as in mm. 136-155 of Beethoven’s piano sonata op. 53, first movement), but I doubt that another example can be found that is as elaborate a prolongation of the cadential dominant as mm. 338-397 of Beethoven’s third symphony, first movement.  (There is an ambiguity in this example, however.  It is possible to hear “tying-the-knot” in mm. 376-377 and the arrival of the cadential dominant in m. 378.  Beethoven is obviously toying with us, but since his “funning” starts at m. 338 – where his very serious “new” theme, with its step-wise melodies and syncopated-eighths background, drops out – I prefer to say that the cadential dominant begins with the “sea change” at m. 378.)

Other structural ideas include:

Prolongation of the initial structural tonic into the Recapitulation. Examples:  Beethoven’s piano sonata in E-flat major op. 7, first movement; Beethoven’s ninth symphony, first movement; Mozart’s piano sonata in c-minor K. 457, first movement (I think); Brahms’ third symphony, first movement.  (This is sort of a “cop-out” analysis:  If I can’t understand it, it must be prolongation of the tonic.)

Prolongation and elaborated motion to the cadential dominant (possibly by way of the cadential subdominant). Examples:  Beethoven’s piano sonata in c-minor op. 13, first movement; Beethoven’s first symphony, last movement; Brahms’ fourth symphony, first movement.  In Beethoven’s piano sonata in f-minor op. 57, first movement, the cadential dominant is arrived at in the Development, but extended through the beginning of the Recapitulation.  In Brahms’ second symphony, first movement, the cadential dominant is arrived at (in the form of a I6/4) as the Recapitulation begins.

Motion to a half-cadence in the submediant (V of vi). Mozart was fond of this Baroque holdover.  Examples in his piano sonatas:  K. 280 (first and third movements); K. 282 (third movement); K. 283 (second movement); K. 333 (first movement); K. 576 (first movement) (I think).  In most examples, there seems to be a prior return to the tonic.  See also Beethoven’s first symphony, first movement.

EXAMPLES IN BEETHOVEN’S PIANO SONATAS

The following is a list of Beethoven piano sonata movements which follow the cadential structure discussed above in the first movement of Mozart’s piano sonata K. 310:

Op. 2 No. 1 (first movement):
     Tying-the-knot:    
m. 78
     Cadential subdominant:    
mm. 79-80
     Cadential dominant:    
mm. 81-100
     Recapitulation (tonic):    
m. 101

Op. 2 No. 3 (first movement):
     Tying-the-knot:    
m. 126 (3rd and 4th beats)
     Cadential subdominant:    
mm. 127-128
     Cadential dominant:    
mm. 129-138
     Recapitulation (tonic):    
m. 139

Op. 10 No. 1 (first movement):
     Tying-the-knot:    
mm. 150-156
     Cadential subdominant:    
m. 157
     Cadential dominant:   
mm. 158-167
     Recapitulation (tonic):    
m. 168

Op. 10 No. 2 (first movement):
     Tying-the-knot:    
mm. 107-108
                               
mm. 109-130 (digression: motion to subdominant – inspired!)
     Cadential subdominant:    
mm. 131-132
     Cadential dominant:    
mm. 133-136
     Tonic of Recapitulation:    
m. 137

Op. 10 No. 3 (first movement):
     Tying-the-knot:    
mm. 163-164
     Cadential subdominant (Spanish):    
mm. 165-166
     Cadential dominant:    
mm. 167-183
     Recapitulation (tonic):    
m. 184

Op. 14 No. 2 (first movement):
     Tying-the-knot:    
m. 106 (1st beat)
     Cadential subdominant (Spanish):    
m. 106 (2nd beat)
     Cadential dominant:    
mm. 107-124
     Recapitulation (tonic):    
m. 125

Op. 27 No. 2 (third movement):
     Tying-the-knot:    
m. 85
     Cadential subdominant (Spanish*):    
m. 86
     Cadential dominant:   
mm. 87-101
     Recapitulation (tonic):    
m. 102

    
or:

     Tying-the-knot:    
m. 85
                               
mm. 85-99
                                (motion to cadential subdominant by way of false cadential dominant)
     Cadential subdominant (Spanish*):    
m. 100
     Cadential dominant:    
m. 101
     Recapitulation (tonic):     
m. 102

Op. 31 No. 1 (first movement):
     Tying-the-knot:    
m. 156 (1st beat)
     Cadential subdominant (Spanish*):    
mm. 156-157
     Cadential dominant:    
mm. 158-193
     Recapitulation (tonic):    
m. 194

Op. 31 No. 2 (first movement):
     Tying-the-knot:    
mm. 117-118
     Cadential subdominant (Spanish):    
mm. 119-120
     Cadential dominant:    
mm. 121-138
     Recapitulation (begins on V6):    
m. 143

Op. 49 No. 1 (first movement):
     Tying-the-knot:    
mm. 52-53 (1st beat)
     Cadential subdominant (Spanish):    
m. 53
     Cadential dominant:    
mm. 54-63
     Recapitulation (tonic):    
m. 64

Op. 53 (first movement):
     Tying-the-knot:    
mm. 132-133
     Cadential subdominant (Neapolitan):    
mm. 134-135
     Cadential dominant:    
mm. 136-155
     Recapitulation (tonic):    
m. 156

Op. 57 (third movement):
     Tying-the-knot:    
mm. 158-163
     Cadential subdominant (Neapolitan):    
mm. 164-167
     Cadential dominant:    
mm. 168-211
     Recapitulation (tonic):    
m. 212

Op. 79 (first movement):
     Tying-the-knot:    
m. 110 (1st beat)
     Cadential subdominant (Spanish*):    
m. 110 (2nd and 3rd beats)
     Cadential dominant:    
mm. 111-122
     Recapitulation (tonic):    
m. 123

Op. 101 (third movement):
     Tying-the-knot:    
mm. 176-190, or mm. 189-190 (as rhythm suggests)
     Cadential subdominant:    
mm. 190-191 (harmony vs. rhythm)
     Cadential dominant:    
mm. 192-199
     Recapitulation (tonic):    
m. 200 (clearly!)

Op. 111 (first movement):
     Tying-the-knot:    
m. 84 (4th eighth)
     Cadential subdominant (Spanish*):    
mm. 84-85
     Cadential dominant:    
mm. 86-90
     Tonic of Recapitulation:    
m. 92

Op. 2 no. 3, op. 79, and especially op. 111 demonstrate that tying-the-knot can occur in an instant.  Op. 10 no. 1, op. 57, and perhaps also op. 101 demonstrate that it can be drawn out.
Op. 10 no. 3, op. 14 no. 2, op. 31 no. 2, and op. 49 no. 1 have the “(Spanish)” indication next to “cadential dominant” (as does Mozart’s K. 310 – see page 2 above) because the motion from the tonic to the cadential dominant is by way of the so-called “Phrygian cadence” – which, historically, is a Spanish cadence.  I propose, therefore, that we call it the “Spanish cadence”.  (Will the Phrygians object?)  Op. 27 no. 2, op. 31 no. 1, op. 79, and op. 111 have the “(Spanish*)” indication because the motion from the tonic to the cadential dominant is by way of a modified Spanish cadence.  There is a historical evolution from the Spanish cadence by way of the modified Spanish cadence to the [I-IV-V] of cadential structure.  I believe that I can demonstrate with historical examples that the Spanish cadence, arriving in the form of
diferencias and other variation techniques, was the catalyst in the development of modern tonality, the foundation of which is cadential structure.

Tonal music works, not on some “universal” theoretical basis, but on a foundation of historical development peculiar to particular times and particular places and the interactions, through war and peace, commerce and communication, between peoples and cultures.

It is fascinating how Mozart’s piano sonata in a-minor K. 310 ties East to West, Europe to Asia and to Africa.  The theme is a Turkish march – from the East – and the climactic cadential dominant arrives by way of a Spanish cadence – from the West.  This cultural expression joins Europe (Mozart), Asia (Turkish), and Africa (Spain, the land of the Moors).

February 1, 1990
May 30, 2004