Off by 1: Mozart Counting

Le Nozze di Figaro; Opening Duet “Cinque, dieci”.

While the Mozart operas continue to enchant through their abundance of extraordinary melodic invention, another key to their durability is Mozart’s uncanny ability in determining the right length for each aria, ensemble, scene. A remarkable example of this, in that it also reveals the constructive aspect of Mozart’s mind, is the opening duet of Le Nozze di Figaro. The dramatic action (The Tiff) is simple enough-Figaro is measuring the apartment which will be his and Susannah’s future home and Susannah is trying on a hat. Figaro’s initial lack of attention to the hat  supplies the dramatic tension which must be resolved.  Mozart does this by subtle alterations in the sequence and length of  the two character’s music. He also accomplishes this by constructing jokes and games about counting. The following is a guide to the chart:

The chart is constructed in an x:y axis with x equalling Experience, that is music which has never occurred before, and y equalling Memory, music which is repeated. This is the same type of graph as the Debussy Ondine analysis.

The scene begins with an Orchestral Introduction (OI) with three components: 

Ms. 1-8      Music which will become Figaro Counting (measuring)
Ms. 9-14   Three repetitions of what will become Susannah's Hat ("how do you like it?")
Ms. 15-17 Closing Material

Total=17 measures BUT one must add 1 because Ms. 18 is an elision, both the Tonic resolution of Ms. 17's Dominant and the repetition of Ms. 1.....so 17+1! 

As Figaro begins to sing, we understand now the dramatic assignment of the OI music. Ms. 1-8 is Figaro Counting but now this music is longer, with insertions of new measures. Why? Because the music now signifies physical action. Figaro in Ms. 23 and 25 is perhaps writing down his tabulations or moving and Mozart adjusts the music, formerly physically "abstract" in the OI, to indicate its new dramatic function. This is a beautiful example of why Mozart changes the phrase lengths in his music-these changes are indications of physical or psychological adjustment. Susannah in Ms. 30-33 now indicates the dramatic function of OI Ms. 9-14. It's her asking Figaro to admire her Hat. Significantly she only asks twice, because she is not yet aware that he's not paying attention.

Ms. 18-29  Figaro Counting (measuring)
Ms. 30-33  Susannah's Hat ("how do you like it?")
Ms. 34-35  New Closing Material

Total=18 measures BUT one must add 1 because Ms. 18 is an elision, both the Tonic resolution of Ms. 17's Dominant and the repetition of Ms. 1.....so 18+1! 

How should the scene continue? Mozart has two choices. Figaro can stop counting and admire the hat or he can continue his measuring. Mozart chooses Option 2. In this Second Counting with now somewhat peeved interjections from Susannah, Figaro takes exactly the same amount of time as the OI. Why? Because his tabulations are correct, there is no need for writing down the numbers and Mozart indicates this by removing the extra measures of the First Counting. Susannah however, does not continue with her Hat Music because she is upset with Figaro's lack of attention (Ms. 44-48). Figaro's singing of the Hat Music (Ms. 49-52) fails to resolve the Tiff and Mozart indicates this in two ways: Figaro sings it in the wrong key, the Dominant, and sings it only twice-he is not ardent enough. 2 measures of Closing Material conclude the Second Counting/Hat.

Ms. 36-43  Figaro Counting for the second time 
Ms. 44-48  Susannah's Rebuke for his lack of attention
Ms. 49-52  Figaro's Failed Admiration of the Hat
Ms. 53-54  Closing Material

Total 19 Measures and without an elision because the Counting Music is over. 19! (and no +1)

Part I is now concluded. We can say this because the Counting Music is concluded. TOTAL 54 measures.
It's about the Hat.

Mozart had given us the clues to understand how the Tiff must be resolved. There are three things which must occur;
a) Figaro must sing the Hat Music in G Major
b) He must sing it three times
c) He must sing it with Susannah

Part II begins with 12 measures of new music in which the Tiff is Resolved (Ms. 55-66). This is made clear in Ms. 67-72 in which the Hat Music  is sung three times in G Major by both characters. Then we hear the Closing Material of the Counting twice, then two new measures, then one more Counting Closing material, four new measures,The OI Closing material and one final bar of Tonic Affirmation.

Ms. 55-66   The Tiff Resolved
Ms. 67-72   The Hat Music sung by Figaro and Susannah
Ms. 73-76   Counting Music Closing Material
Ms. 77-78   More Reconciliation
Ms. 79-80   Counting Music Closing Material one last time
Ms. 81-84   More Reconciliation
Ms. 85-87   OI Closing Material
Ms. 88        Tonic Affirmation

TOTAL 34 Measures

One last question remains. How did Mozart calculate the length of Part II? The joke of Part I's construction is that each of the three sections is progressively one measure longer-a representation,"off by 1", of the approximate way most people measure. But Part II cannot apply this logic as the Counting Music is banished. So Mozart uses another mathematical measurement-the Golden Mean, the Divine Proportion.

Part I  =54 measures
Part II =34 measures

TOTAL=88 measures
88 x .618=54.384

The total length of the piece is divided by Golden Section. Human Counting and Divine Counting in mutual co-existence!