Appendix D: Commentary on the Analysis
Summary
The movement is in Sonata Form. This analysis clearly reveals segmentation into static harmony and dynamic harmony. The movement contains complete (static/dynamic) phrases; phrases extended by dominant prolongations and incomplete phrases made up of dynamic harmony only. Phrases are incomplete or overlap except at key points: The end of the exposition and at the end of the piece. This piece does not include other types of phrase extension (the static coda or dynamic introduction) - see Chapter 5.
Detail Commentary
This phrase (the first subject melody) shows the basic syntactic phrase structure: static harmony opening section followed by dynamic harmony closing section. See demo No 2.
The first four bars are made up of an alternation between the tonic (A minor) chord and the auxiliary chord made up of the E major dominant 7th chord suspended over a tonic pedal. The tonic pedal re-enforces the static character of the chord oscillation. Bars 5 to 8, in contrast, consist of a succession of 7 rising 4th root progressions. This forms a complete cycle starting at the tonic a minor chord and takes in all degrees of the scale. In order for the cycle to complete diatonically on the V to I cadence the rising augmented 4th progression is deployed in the progression from F to b° at bars 7 to 8. At bar 8 the A minor chord in second inversion is not counted in the root progression as it forms an appoggiatura chord that decorates the E dominant chord at the end of the bar. The dominant E chord forms a perfect cadence with the A minor chord which starts a repetition of the first phrase at bar 9.
This phrase (an extended repeat of the first subject melody) shows the basic syntactic phrase structure extended by a dominant prolongation (bars 16 to 22). This phrase ends without resolution of the dominant chord and consequently is incomplete.
Bars 9 to 11 are static harmony based on the tonic chord with a single occurrence of the auxiliary G# diminished 7th chord. The C dominant 7th chord at bar 12 acts as a passing chord between the a minor chord in bar 11 and the F major chord in bar 13. This starts off the dynamic harmony that extends to bar 15. The D minor chord in bar 13 is briefly elongated by the auxiliary A chord. As the total span of the d harmony here is less than one bar it does not form a separate static element but is a single step in the dynamic chord progression. Removing the passing C7 chord and auxiliary A chord from the progression reveals two falling 3rd progressions and four rising 4th progressions. The dynamic harmony is modulating as it ends on a G chord which is the dominant of the relative major key. The dominant chord is prolonged by a repeated V - [ I ] - V static harmony for 7 bars.
This phrase represents the second subject and is made up entirely of dynamic harmony deploying all three types of strong chord progression. This is an incomplete phrase made up of dynamic harmony only and ends on a dominant chord. The tonic resolution overlaps with the next phrase.
Bars 23 to 25 is dynamic harmony with one chord per bar harmonic rhythm. At bar 26 the tonic chord continues for two bars, briefly slowing the dynamic movement. However, this picks up speed at two chords per bar in bars 28 to 30. It would be possible to interpret the bar 28 to 30 harmony as a single D minor chord elaborated by E and G passing notes. This would not alter the interpretation as dynamic harmony. The progression would just move at a slower harmonic rhythm. However, there are reasons for taking the first interpretation as the correct one, as follows:
- The D of the D minor chord arrives too late in the bar to be taken as a root of the chord;
- The repetition of this section at bars 109 to 111 cannot be interpreted as a single chord elaborated by passing notes as the initial B flat is subsequently replaced by a B natural and the corresponding notes do not function as passing notes in the same way. Consistency of interpretation supports the view that bars 28 to 30 should be interpreted as a dynamic chord progression.
The C chord at bar 31 is elaborated by D and F passing notes. This non-functional auxiliary chord does not challenge the underlying dynamic movement. The final G dominant chord of phrase 3 is elaborated by an appoggiatura cadential 6 4 chord.
This brief phrase is the first part of the codetta section and is a simple static/dynamic phrase with a tonic chord overlapping to the next phrase.
Bars 35 to 37 are made up of a static oscillation of the tonic chord with the dominant. Bars 38 to 39 are dynamic harmony leading to an extended repetition in the form of phrase 5. The final dominant chord of phrase 4 is elaborated by a brief cadential 6 4 chord.
This phrase repeats phrase 4 but with a an extended dynamic harmony and a completed cadence. This is the first completed cadence in the movement. This cadence occurs at the end of the Exposition. Incomplete phrases 1 to 4 are thus completed finally by phrase 5. The whole of the exposition is thus made up syntactically of one extended phrase.
Bar 40 to start of bar 42 are static harmony made up of the oscillation of tonic with dominant harmonies as in phrase 4. At bar 42 the dynamic harmony starts off with a complete cycle of falling 3rd progressions extending from C to C. It could be argued that this is not a cycle of root progressions but consists of harmony arising out of a linear progression descending from the C at the start of the second beat in bar 42 to the low E at the start of bar 44. Arguing against this interpretation is the fact that the harmony in these bars does not follow the normal rules for a linear progression (see Chapter 4) i.e. that all the passing chords should be made up of notes either involved in the linear movement or sustained form the starting chord (the chromatic auxiliary note is a possible exception). Also, linear progressions usually move one step in the progression for each identifiable chord. This is not the case in this example. The dynamic harmony continues to the dominant chord at bar 48 which resolves on to the tonic chord in bar 49. This forms the first non-overlapping perfect cadence in the piece.
The whole of the development section consists of one single syntactic phrase. This starts with tonic static harmony followed by an extended modulating dynamic harmony and concludes with 6 bars of dominant prolongation.
Bars 50 to 57 consists of static harmony based on a C major chord alternating with G major, E diminished 7th and C# diminished 7th chords (the last too being enharmonically the same). At bar 57 the B-flat of the C7 chord is re-spelt as A#. The chord is thus explicitly re-interpreted as a dominant leading augmented 6th chord in E minor and resolves according to expectation onto the ensuing B major chord. This serves to facilitate the modulation and is the explanation for the use of the falling second progression. For further discussion of the use of this progression in modulation please refer to the discussion in Chapter 7 in the book section and to Chapter 7 in general for a discussion of modulation.
Bars 58 to 72 consists of an extended dynamic progression leading the harmony back to the dominant chord of the tonic key. This section is characterised by the use of a succession of chord progressions over long pedal notes. For consistency with the remaining root analysis I've ignored the pedals. This interpretation results in dynamic harmony interspersed with short static prolongations at the start of each pedal note. An alternative interpretation would be to consider each pedal note to represent a single step in the harmonic movement. The dynamic harmony would then consist of a slow moving rising 4th progression as follows:
B - E - A - d
This is then followed by the faster moving dynamic harmony up to the start of the dominant prolongation at bar 72. Based on experience of analysis of other pieces, I would say this second interpretation was the correct one. A full discussion of the relevance of pedal notes in the context of root progressions and syntactic structures is beyond the scope of this thesis. Which ever interpretation is taken does not make a material difference to the results of the analysis.
At the last beat of bar 72 starts a dominant prolongation extending over 6 bars. This is made up of the common oscillation of dominant chord with the tonic and resolves on to the tonic chord which forms the start of the recapitulation at bar 80. At bar 73 the [ I ] - V movement is elaborated by a linear progression moving step by step from A to E creating passing chords as follows: [ a ] - ( e ) - (f#°) - (F+6) - E. The A minor to E movement from bar 75 to 76 is elaborated by a passing D# diminished 7th chord. As is the progression from bar 77 to 78. This dominant prolongation leads back to the recapitulation at bar 80 via an overlapping cadence.
This is a repeat of phrase 1.
This phrase is an extended and developed version of phrase 2. It also shows the basic syntactic phrase structure extended by a dominant prolongation. This phrase ends without resolution of the dominant chord and is similarly incomplete.
The main item of harmonic interest in this phrase is the extended linear progression from bar 88 to bar 93. This section takes melodic material from the first subject static harmony, deploys this in the bass against harmony which arises from linear downward movement extending form the A of the starting chord down diatonically through almost an entire octave to the B of the E minor chord in bar 93. In parallel there is a linear progression moving from the C of the starting chord downward to E of the E minor chord. This latter movement takes in a chromatic note at bar 89 and the two linear progressions move out of step with each other to create the familiar repeating 7 - 6 - 7 - 6 counterpoint. (Usually referred to as fourth species) The E minor chord is the ending chord for this linear progression as this is the point at which these linear progressions complete and new (shorter) linear progressions commence: G - F# - F-natural - E in the bass and E - D# - D-natural - C# - C-natural - B in the top part. This creates a long range a - [ e ] - a static harmony from bar 88 - 94 followed by further A - [ b° ] - A - [ d ] - A static harmony to bar 95.
The dynamic harmony (bar 96) is brief and is made up of two α and one β progressions. The dynamic harmony in this repeat does not modulate but serves as a link to the 7 bar dominant prolongation at bar 97 to bar 103. This ends on an E major chord which is the dominant of the tonic key.
This phrase is based on phrase 3 from the exposition. It is the second subject and is made up entirely of dynamic harmony deploying all three types of strong chord progression. This is consequently an incomplete phrase and ends on a dominant chord. The tonic resolution overlaps onto the next phrase.
The analysis of the harmony is similar to that of phrase 3. There is an initial slow harmonic rhythm of one chord per bar. The auxiliary note formations in bars 104, 105 and 106 (forming a g#º, c#º and bº) are not sufficiently significant in length or strength to be considered as forming static harmony. They function as short term auxiliary elaboration of the underlying dynamic movement. After two bars of the tonic chord the harmonic rhythm accelerates to two chords per bar. In comparison with phrase 3 an alternative interpretation of bars 109 to 111 is not possible. (See note about phrase 3.) A brief augmentation of the dominant at bars 111 to 112 is not sufficiently lengthy to form a syntactic element in its own right and consequently is considered to be part of the background dynamic harmony. The final dominant chord is briefly elaborated by a cadential appoggiatura chord.
This phrase is based on phrase 4 from the exposition and is the first part of the codetta phrase. It is a static/dynamic phrase with a tonic chord overlapping to the next phrase.
Bars 116 to 118 are made up of a static oscillation of the tonic chord with the dominant. Bar 119 to the start of bar 120 deploys a chromatic B-flat chord as the auxiliary chord further elaborated by the passing G# diminished 7th chord at bar 119. Bar 120 is a brief dynamic harmony leading in to an extended repetition in the form of phrase 11. The final dominant chord is again elaborated by a brief cadential 6 4 chord.
This phrase repeats phrase 10 but with a shorter static harmony and an extended dynamic harmony. This phrase is based on phrase 5 of the exposition but ends with dominant prolongation that overlaps into phrase 12.
Bar 121 to the start of bar 123 are static harmony made up of an oscillation of tonic with dominant harmonies as at the start of phrase 10 but it lasts just over 2 bars. At bar 123 the dynamic harmony starts off with a cycle of falling 3rd progressions but this is shorter than the corresponding progression in phrase 5. It could be argued that this is not a cycle of root progressions but consists of harmony arising out of a linear progression descending from the A at the start of the second beat in bar 123 to the low E in bar 124. Arguing against this interpretation is the fact that the harmony in these bars does not follow the normal rules for a linear progression (see Syntactic Structures in Music) i.e. That all the passing chords should be made up of notes either involved in the linear movement or sustained form the starting chord (the chromatic auxiliary note is a possible exception). Also, linear progressions usually move one step in the progression for each identifiable chord. This is not the case in this example. The dynamic harmony continues to the dominant chord at bar 125. The dominant chord is then prolonged by a linear progression made up of two diminished 7th passing chords elaborating a basic V [ I ] V dominant prolongation. This resolves on to the tonic chord in bar 129 which is the first chord of phrase 12.
This phrase is made up of the last 5 bars of phrase 5 in the exposition. It is an incomplete phrase made up only of dynamic harmony leading from the dominant prolongation of the previous phrase to the final cadence of the movement.
The dynamic harmony is made up of 5 α and 2 β progressions. The phrase is incomplete in its own right but phrases 11 and 12 combine to form a complete unit. Phrase 11 gives the appearance of ending after the dominant prolongation but the tonic chord starts a further dynamic harmony which continues for a further 4 bars before the final cadence.