Tetractys

Remanaging Riemann: A Modal View on Harmonic Functions
Karst de Jong and Thomas Noll Esmuc - Barcelona

[Put a sound example with the complete Prelude (copyright)] Please listen carefully to the prelude Op. 28 No.7 in A-major prelude by Frederic Chopin. Is there any specific moment of tension in the piece that attracts your attention? To our mind the F#-dominant seventh chord in bar 12 isparticularly ear-catching. There are various reasons for this. First of all the chord features the highest melodic note of the piece. This climactic moment is furthermore anticipated by a crescendo and through the high C#6 as part of the previous Amajor chord. The very moment even seems to question the regular hypermetric accent of the Mazurka rhythm on the downbeats of the odd bar numbers. However,the most important attraction of this moment may be due to harmonic factors. But how? To begin with a simple observation, unlike the previous harmonies, this chord is the first to be neither tonic nor dominant in A major. A salient element in this ear-catching let's not use ear-catching twice (just leave out?) harmony is the tone A#, the leading tone to the B, which is the supporting fundament ofthe harmony in bar 13. But this alone cannot explain the effect, as there are two other occurrences of the foreign tone A#, which are loaded with more tension from a contrapuntal point of view: the primary augmented fourth E-A# in bar 5 outweights the secondary augmented fourth E-A# within the F#-dominant seventh chord. The major seventh B-A# in bar 13 is a primary dissonance as well, while the A#in bar 12 enjoys consonant support of the F# in the bass. Apart from the inner dissonance of the dominant-seventh chord as a vertical sonority, there is a deeper 'harmonic tension' at work which seems to be related to the overall harmonic design of the piece. In our point of view this is related to an explanation of the fundamental bass F# in the tonality of A major. I find the following toocomplicating in this stage. Maybe it could come back later? Please listen to a modified version of the piece, where the A# in bar 12 is replaced by A. Although the F# minor-seventh chords sounds less dazzling than the dominant-seventh chord, there is still a 'harmonic tension' between the fundaments F# and A, which resolves under the falling fifths progressions F# - B - E - A. It is the aim of thepresent article to revisit the interdependency between fundament progressions and harmonic tonality.

Rameau-Dominant vs. Riemann.Dominant Although there are no principle objections against recursion in an analytical language, it is curious that roman numeral analysis needs seven symbols, and barely uses all of them frequently, while using recursion already on a very basic tonal level. Chains ofembedded dominants might be an artifact of confusion between Riemann and Rameau dominants. Becomes insensitive to harmonic functions of voice leading, and focuses on the harmonic function of the fundamental bass. (Which is not to say that voice leading issues can not be brought in in a later stage.)

1 Introduction Adapt the arguments to the simplified introduction [1] This study places theprogression of the fundamental bass in common practice tonal music into the center of investigation. It is driven by the assumption that the fundamental bass – as a virtual melody – deserves the status of an autonomous level of musical description. Although not being independent from other levels of description, such as chord taxonomy, counterpoint and voice leading, it is not entirely depending onthese other levels. Downplaying the fundamental bass to a mere shadow of the so called 'upper structures', i.e. chords and voice leading, would be a theoretical misjudgement, as we think. In support of our thesis we wish to investigate the aforementioned autonomy through principles, which are capable of explaining the constitution of typical fundament progressions. [2] The discourse on musical...