Illuminating the space of tonal options

A plea for a precise tonality analysis

Functional analysis is an excellent instrument to explore the cosmos of classical harmony. It is based on the pattern of a tonal center. Referring to this center, the space of tonality is measured and explored. Height and depth, closeness and distance, joy and sadness, fulfillment and failed expectation, incisions and unforeseen new-found interrelations can be impressively visualized in appropriate harmonic developments. The model of a tonic and its orbit reflects a social order that was exposed to considerable pressure in the late 18th century. Mozart’s opera Le nozze di Figaro (1786) displays the centrifugal forces, but claims to believe in the final reconciliation. A little later, in Mozart’s Don Giovanni (1787), this persuasion was lost. The French Revolution began less than two years after its premiere.

In the 19th century, norms and structures of the 18th were challenged by individual concepts and actions. This conflict shapes the further development of harmony. The results of the functional analysis detect the individual part as an irritation or as a violation of norms. Thus, the unique quality is marked, but the content is not captured. This requires an additional analytical access. This is made possible by the antagonistic approach of ci analysis.

With regard to 19th century compositions, a combination of the two analytical approaches can be used to reveal characteristic, aesthetically motivated strategies. Perhaps the most significant is the masking of a still existing tonal target. There is no explicitly seeking for it, but by leaving out the ci of its K structure, the harmonic progression moves towards it. The beginning of Frédéric Chopin’s waltz in C sharp minor, op. 64 \ 2 turns flexibly towards several directions, sketching never gained targets, languishing chromatically. Meanwhile, the tonal path persists in the structure of the basic key and its parallel. Claude Debussy refines the technique, for example in his Prélude La fille aux cheveux de lin, by leaving first two tonal paths open, then closing one of them while crossing a pentatonic zone, perceived as tonally undirected. When arriving in the gently shining major sphere, you are unconscious about the path you have taken. Finally, Arnold Schönberg systematically secures the integrity of the tonal path: As long as the hexachords of his complementary series remain separate in the composition, no ci of the basic K structure can be generated, even in complex six-tone chords.

The beginning of the prelude of Richard Wagner’s opera Tristan und Isolde bundles tonal masking techniques: in addition to the shifting of the entrance motif, the tritone transposition of function representatives is used. Added to this is the absence of ci inside the short sound units: their frames seem impregnated with a subtle tonal reference, enclosing each a tonally undirected area like a transparent membrane. Even here we can uncover an almost imperceptible tonal path.

When noting the absence of a tonal path, an area is entered that can be described as atonal with a certain justification. But  both the locking up all K structures due to appropriate ci concentration, and the absence of tonal orientation due to a lack of ci then belong to the category atonal. In fact, both constellations are opposed to each other in terms of their effect and their options. A classification (as atonal) only makes sense here when considering the respective scope of possibilities. Furthermore it is necessary to ask what importance tonally undirected chords or chord sequences have in the overall system. In the Tristan prelude, they evoke moments of detachment in a tonal context. In Schönberg’s Piano Concerto op. 42, brief tonal sections shape a motivated contrast to a largely non-tonal score. To label such a composition as tonal or atonal merely prevents insight. Understanding solely results from grasping the changes of state between the poles tonal and atonal.