PROLONGATION- Most simply put, extending the influence of a note by adding more notes that depart from and return to it over time.

HORIZONTALIZATION- Extending a chord overtime by converting it into a melody. One simple example would be when we arpeggiate a chord but we can also add passing tones and neighbor notes between members of the chord.

-Below we see the first 8 bars of "Ode To Joy"

-We are in the key of D. The F# is the 3rd of the D major triad. So for harmony and counterpoint purposes, we will consider this a part of the tonic harmony.

-The first measure mainly consists of CHORD TONES F# and A (scale degrees 3 and 5). But there is the NON CHORD TONE G (scale degree 4) that connects the CHORD TONES F# and A. This G note is a PASSING TONE.

-In Schenkerian analysis, this G would carry less weight then the two chord members that it passes between. This measure would be considered to be a PROLONGATION of the tonic triad (D major).

-The last two notes of meausre 4 are both the NON CHORD TONE E (scale degree 2). This section would be analyzed as more "structually" dominant then what harmonies might result from the passing tones in the previous measure. It is also a half cadence which is clearly a dominant funtion.

-The final note of this passage is the D note (scale degree 1) on beat 3 of measure 8. Schenker would "zoom" out and call these eight measures a walk down from scale degree 3 to scale degree 1, interupted by the half cadence in measure 4. Being interupted, it returns to scale degree 3 in measure five but ultimately lands on 1 in the end.

-These eight measures would be considered to be a progression of the HORIZONTALIZED chords of I - V - I.

-Below we see the first 6 measures of Mozart's Sonata 16, K545 (Andante) in the key of G major.

-In the left hand (bass clef) the first 2 measures are simply arpeggiations of the I chord (G major) with the exception of beat 3 of measure 1. In this cluster of 4 sixteenth notes we have the bass note stepping up to A, from the G in beat 2. Also, the C note in this cluster stepped up from the B in beat 2. In beat 1 of the following measure, they return to the notes that they came from.

-While these 4 notes more or less spell out a V chord in 2nd inversion, Schenker would consider this incident to be one of neighbor notes PROLONGING the tonic function.

-This PROLONGATION also occurs in measure 3. We see the B from the last measure stepping up to C while the D from the previous measure steps up to E. While these notes spell out a IV chord (C major), Schenker would consider this whole measure to be a PROLONGATION of the tonic by means of neighbor note motion because they ultimately return to the same notes in measure 4.

-Dominants contain scale degrees 2 and 7. These tendency tones have a strong imputus to resolve to the tonic.

-As seen in our previous example, sometimes this imputus is interrupted. The half cadence is where this often occurs.

-This has important inplications in counterpoint. It means that a resolution set up in one measure may not resolve until several measures later. This "end goal" thinking is fundamental to Schenkerian analysis but also the structural analysis we've been doing thus far.

-Dominants can also expanded by cadential motion, passing chords, neighbor chords or by adding 7ths to strenghen the resolve.

-Chords of predominant function, prolonged or not, serve as a connection between the prolonged I chord and the ultimate V which will resovle to I.

-They receive attention as a function because they "connect" the I chord to V, while not qualifying as a prolongation of I.

-This happens so often that we consider predominant chords to be a part of the underlying harmonic structure.

-Diatonic chords that can do this are the IV (sub dominant), II (supertonic) and VI (submediant). Chromatic chords that can do this are the Neapolitan 6 (N6) or the augmented six chord (+6). Keep in mind that "bigger picture" functioning chords tend to be diatonic and rest in the "middle ground level". Chromatic chords such as the N6 and +6 will be occuring more on the "surface level".