Harmony and counterpoint

Song Analysis - Mozart - Sonata 11 K331, In A, Theme

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DanelePiano

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Opening post by DanelePiano

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Studying counterpoint and composition as a self-taught student, I tried to analyze the theme of this famous composition. I wanted to share my analysis to get critical feedback (advice, errors) since I have never taken a counterpoint course but have only read a book on my own.

I thank the forum administrators and anyone who wishes to comment.

Mozart – Sonata 11, theme

In A major, tempo 6/8 and ABA metric scheme

Cantus firmus

In the first two measures with leaps of a third and then by stepwise motion, the same phrase is repeated twice: the first time with a 3°-2° ending and the second time 3°-1°. The second phrase starts on the 5th towards a climax on the 8th with a leap of a third, then closes towards the 2nd. The first phrase is repeated again.

At the beginning, there are turn notes 121 that culminate with leaps of a third; then after two measures by stepwise motion, the 32 closure is embellished with the 54 ornament; in the second repetition, the 4321 ending is harmonized with Bm rev, A rev, E rev, A rev. The second phrase begins with turn notes to reach the climax on the 8th with a leap of a third and an appoggiatura, descending to the 32 closure; it stops on the 5th which is ornamented with arpeggios 531 and 542. The first phrase is repeated again, modifying its respective closure: the ending is harmonized with a chord progression Bm rev, A rev, E-A, A rev, E7 sus 5, E5, and a closure with an ornament on the 8th climax followed by an octave leap to the 1st and a closure with 321.

Bass voice

It always follows the progression of leaps of a third and passing notes, then stepwise motion and closure, harmonizing with a sequence of chords 1545 and repetition 15451. In the second phrase, the voice stops on the 1st in counterpoint and then descends in the ending to the 5th. In the theme's closure, it leans on the octave and the sixth and seventh for the ending.

Middle voice

Always stationary on the 5th degree for almost the entire duration of the theme; in the second phrase, it moves slightly in counterpoint. It harmonizes the bass voice as mentioned above.

Harmonic analysis

The piece is in A major and is schematized on a succession of chords 1545 and 15451; the only chromaticism used is the diminution of the 5 at the closure in the second phrase. Rhythmically, the piece is schematized as SM – C; the SM part is divided into C∙SM C for the first three beats of the first two measures. In the second phrase, the chords are arpeggiated and then played in dyads at the B closure. In the final ending, the piece is harmonized to give strength to the passage from P to F.

Dynamic analysis

The piece follows a P grazioso pattern up to a slight reinforcement on phrase endings. In phrase B, the dynamics go to MF without excess, returning to the initial P. In the theme's closure, the piece reaches the highest F with the chord sequence to close in P during the cadence.

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Reply 3 by Gagaku

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I would like to have some clarification on:

DanielePiano wrote:

ABA metric schema

"metric schema" in particular... then we talk about ABA, which in reality does not indicate a tripartite structure?

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Reply 4 by thallo

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General considerations on your analysis: there is no such thing as a 'contrapuntal analysis' done that way; counterpoint has nothing to do with that composition. You must base yourself on harmony and, therefore, on harmonic analysis. That is, reason in terms of chords, not voices, unless there are very particular characteristics (which, however, remain exceptions and often struggle to emerge in piano writing). Therefore, the definitions of cantus firmus and voices are absolutely nonsensical. I can explain why later if you want.

If you analyze a theme, you can analyze it in various other ways besides performing a harmonic analysis. Certainly, the most important considerations are formal. That is, you must understand how this theme is structured formally speaking. This varies greatly from "school" to school. While macro-formal definitions are fairly common and accepted (sonata form, rondo, romance, etc.), micro-formal definitions are less standardized.

I generally use Schoenbergian terminology; for me, themes are tendentially divisible into phrases, periods, and small ternary forms. Phrases are ternary and generally have an aa'b form. This means they repeat the material immediately after the first motive and then conclude it with a cadential motive (generally the number of measures is something like 4+4+2). Periods are binary, often abab', meaning they have the motive, an open cadence, the repetition (varied or not) of the motive, and the closed cadence (generally 8+8 measures). The small ternary form is often aba, where b is often modulating.

This first theme by Mozart, in my opinion, is a small ternary form, albeit a very particular one.

We have a first section of 8 measures in A, a second modulating section of 4 measures that ends by tonicizing E, and a third section again in A of 6 measures. The first section is, in turn, constructed as a period; that is, at measure 4 we have a cadence suspended on the dominant, and from measure 5 the same material is taken up until a perfect cadence at measure 8.

The second section is suspended between the first and fourth degrees, and at the twelfth measure it concludes with a suspended cadence on the dominant E, using its seventh degree (the D# diminished chord).

The third section reprises the first part of the first section, both harmonically and melodically.

After this brief phraseological analysis, it is interesting to note other micro-fragmentations. Melodically, we are faced with two types of material: the dotted eighth-sixteenth-eighth structure and the half note-eighth note structure. For 8 measures, only these two are used; at the ninth measure, eighth-note arpeggios enter, and until measure 17, only those three rhythmic formations are used. They themselves are developed in a very particular way. They are always generated by what comes before. The first three eighth notes of the first measure, in short, already contain everything else. The repeated E's of the second part are already present; the entire second measure is the repetition in progression one tone lower than the first measure; the A-B-C# ascent in measures 3-4 is the continuation of the progression another tone lower. The new melodic configuration at measure 9 is nothing more than the continuation of the E-A cadential arpeggio in the bass at measure 8. This generative technique is typical of Mozart and is one of the reasons why the first movement of this sonata is one of the most analyzed musical pieces in music history.

Another thing that could be noted, with a nod to those familiar with Schenkerian analysis...

Briefly, Schenkerian analysis is a reductionist madness that seeks to find original forms (Ursatz) within classical compositions. The Ursatz are composed of the Urlinie, descending melodic lines, and Bassbrechung, cadential bass arpeggios. They are primal structures reached by "eliminating" possible augmentations. Anyway, take my word for it; I can explain it to you again later if needed.

In this first movement, we can notice a fairly evident change in texture. From A3 in measure 10, we reach A2 in measure 15. In reality, the highest and most frequently played note is E4. Well, Schenker saw an Urlinie going from E descending through D, C#, B, and A, as a constant "cadential" descent. The utility of this type of analysis is questionable, and lies in the details, in recognizing certain fundamental degrees within the composition. The importance of E is beyond doubt, for example. Until measure 7 it is a true pedal, but then it remains as the melodic center of almost all the figurations.

We will see what else comes up from other interventions.

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Reply 5 by Oracolo

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thallo wrote:

The utility of this type of analysis is doubtful, and lies in the details, in recognizing certain fundamental degrees within the composition. The importance of E, for example, is beyond doubt. Up to measure 7 it is a true pedal, but then it remains as the melodic center of almost all the figurations.

... not by chance E is the dominant (precisely, it dominates) of A+. There must be a reason why it is called that. A bit like the repercussio of Gregorian modes

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Reply 6 by DanelePiano

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I thank Thallo and Oracolo very much for their contributions; in particular, I read Thallo's comment very carefully and made a few observations:

By ABA scheme, I meant the musical phrases: from measure 1 to 8 is A and from 9 to 12 is B.... and then A repeats.

I think I understand why one cannot speak of contrapuntal writing... it is not a fugue in which there are various voices that all have the same importance and are written in counterpoint (note against note), but it is a sonata composed only of a melody and an accompanying harmony. Therefore, melody and harmony would be the correction of the definition of cantus firmus and voices, if I understood correctly.

On some other things, I would like to understand better:

“It means they repeat the material immediately after the first motive and then conclude it with a cadential motive (generally the number of measures is something like 4+4+2)”…..I see the 4+4 from measure 1 to 8.... but I don't see the +2.

“The periods are binary, often abab', meaning they have the motive, an open cadence, the repetition (varied or not) of the motive and the closed cadence (generally 8+8 measures)”….I, on the other hand, see the motive with the open cadence (A), the repetition with the closed cadence (A’), and a new phrase (...so if I am not mistaken, considering also the repetition, the whole piece should be AA’B and not ABAB as you said; this is also not clear to me).

“The new melodic configuration at measure 9 is nothing more than the continuation of the mi-la cadential arpeggio in the bass of measure 8.”….at measure 9, I instead see an arpeggio of A and D seventh, and not of mi-la.

“Anyway, take my word for it, I can explain it to you again later if necessary.”….well, I don't think I have understood Schenkerian analysis very well, but I had noticed the importance of the repetition of the dominant E4.

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Reply 7 by thallo

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Before commenting on what Daniele said, I must correct myself: I spoke of E4 and A3. Being a singer, I always get confused with note numbering... so, let's reset everything. Considering Middle C as C1 and the third space C as C2, I meant that although the peak of the range was A3 (at measure 10), the high note touched most often is E3.

If it will be useful, I will delve into this discussion again.

DanielePiano wrote:

By ABA scheme I meant the musical phrases: from measure 1 to 8 A and from 9 to 12 B.... and then A repeats

which is then the structure of the small ternary form, the one that I consider the subdivision of this first theme.

I think I understand why one cannot speak of contrapuntal writing... it is not a fugue in which there are various voices that all have the same importance and are written in counterpoint (note against note), but it is a sonata composed only of a melody and an accompanying harmony. So, melody and harmony would be the correction of the definition of cantus firmus and voices if I understood correctly.

more generally, counterpoint is not just a style but a theoretical framework of reference. Briefly, until the 17th century, one wrote in autonomous lines, not just "note against note" but line against line. The concept of a chord did not exist; there was a more generic concept of polyphony. Regardless of more precise historical definitions, this means that you can only analyze contrapuntally compositions written up to approximately the 17th century. Even Bach poses some problems, given that the integration of a contrapuntal analysis with a harmonic one is now common (Bach writes in the 1700s, a period in which harmonic sensibility was already very common). If you also wanted to analyze a fugue written in the 1800s (and there are many), you would have to integrate counterpoint with harmony, i.e., reason in terms of chords or, better yet, harmonic functions (tonic, dominant, leading tone, etc., concepts that do not exist in counterpoint).

On some other things I would like to understand better:

“It means they repeat the material immediately after the first motive and then conclude it with a cadential motive (generally the number of measures is something like 4+4+2)”…..4+4 I see from measure 1 to 8.... but I don't see the +2.

when I said that the phraseological terminology I use involves the existence of phrases, periods, and small ternary forms, I did not mean to say that all three are present in this sonata; I was explaining the phrase in a general way, but there is no phrase in this sonata

“Periods are binary, often abab, meaning they have the motive, an open cadence, the repetition (varied or not) of the motive and the closed cadence (generally 8+8 measures)”.... I instead see the motive with the open cadence (A), the repetition with the closed cadence (A’), and a new phrase (…so if I am not mistaken, considering also the repetition, the whole piece should be AA’B and not ABAB as you said; this is also not clear to me.

repeating again that I was explaining in a general way what a period is: in this sonata there is a period, of 4+4 measures, and it is the first part of the small ternary form, namely the section from measure 1 to 8. At meas. 4 you have the suspended cadence on the dominant and at measure 8 the cadence on the tonic. The thematic material presented, then, is the same and repeated. Calling the melodic material "a" and the cadences "b", you have for instance ab (meas. 1-4)-ab' (meas. 5-8).

“The new melodic configuration at measure 9 is nothing other than the continuation of the cadential arpeggio E-A in the bass of measure 8.”.... at measure 9 I instead see an arpeggio of A and inverted D, and not of E-A.

Look at the melodic configuration of the arpeggio in the bass at meas. 8: E1-E0-A0. That is, descending octave and ascending fourth. Immediately after, at meas. 9, you have an ascending octave jump, from A0 we arrive at A1, and the arpeggio A1-C#1-E2 is the logical consequence of E0-A0. You could remove the eighth rest at the end of meas. 8, shorten the A0 and melodically fill the distance by making a large arpeggio E0-A0-C#0-E1-A1-C#1-E2.

“Anyway, believe me on my word, I will explain it to you again later if necessary.”.... well, I don't think I understood Schenkerian analysis very well, but I had noticed the importance of the repetition of the dominant E4.

there, here I repeat that I was talking about E3 as the melodic peak. More generally, E is an omnipresent dominant pedal in the theme. But for the purposes of Schenkerian analysis, it is the E3 at the peak that is important. To make you understand it well, I would have to make a Schenkerian diagram, which is not exactly easy... but let's see if I can make you understand some principles.

Imagine that this score has, both in a melodic and harmonic sense, more important notes and

less important notes, structural notes and accessory notes. Let's take, for now, only the melodic structure as an example. Which would be the most important notes? In a first step, I would identify the notes of the ascending progression. Imagine rewriting the melody using only the notes I tell you; I will put them in parentheses as if there were one measure in each parenthesis: (Do#-Mi) (Si-Re) (La-Si) (Do#-Si) (Do#-Mi) (Si-Re) (La-Do#) (Si-La) || (Mi-Fa#) (La-Mi) (Mi-Mi) (Mi-Si) || (Do#-Mi) (Si-Re) (La-Do#) (Do#-Si) (Do#-Mi) (La-La). This reduction made by me is a bit brutal; Schenkerian scores are much more subtle, making very interesting melodic and harmonic considerations by trying to divide the notes and harmonic entities into structural and, let's say, ornamental ones. But the importance I was trying to give to that Mi3, for example, jumps out at you already in this my scheme. In the melodic structure, that Mi is even more present than the La, the tonic. From this reduction we discover how the third intervals have great importance in the conformation of this melody and the same third degree of the scale, Do#, is one of the most present notes. This will be FUNDAMENTAL in the development of the variations, because the third variation of the sonata is in A minor, so the Do is natural, and this will be noticed immediately in the melody (which, not by chance, begins precisely with Do).

Anyway, this is a taste of Schenkerian technique; interesting considerations could be made by going deeper, noting, indeed, how the nature of the first theme is manipulated in the variations. It would make us understand how good Mozart was at discovering those micro-fragmentations I was originally talking about and in making them the basis for new melodic ideas.

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