Chapter 13.

Interval treatment

Tendency tones, counterpoint, resolutions

It would behove us to examine some specifics of interval treatment used in TONL.  Since we are using the 12-tone method in a way that bounces between using serialism and using a more traditional harmonic scheme we need to address how interval treatment works particularly in these traditionally tonal sections. 

Leading tones and tritones
When we discuss tendency tones we have to also consider how rhythmic gesture affects these pitches’ pull towards a certain resolution.  By disrupting the traditional harmonic forward motion and involving serialised passages these tendency tones are also affected.  We have already discussed the need to avoid ultra-traditional harmonic cadential resolutions.  Here we will concern ourselves with borrowing some but not all of these cadential figure’s characteristics.  First we must take note of how rhythm alone can provide a cadential feeling to a passage of music. 

In the first example we will see a scalar figure move to a leading tone.

In the following passage we find ourselves in a situation whereby a scalar passage seems to take us to a necessary resolution.  Observe the figure below.  Regardless of what comes before the C#, this C# feels like it is pulling towards D.  This is because the preceding notes are of shorter, regular rhythmic value than the C#, and the C# feels like the first part of a cadence. Take note that I have purposefully avoided writing any kind of A7 chord.  This would simply make this feeling of cadential resolution even stronger.  For our intents and purposes a lone C# will suffice.

If we look at figure 2, I have changed the notes before the C#.  They offer none of the pitches one might expect to lead to D but the rhythmic impetus provided by these moving 16th notes and the quarter notes in the bass all still seem to point us to a resolution of the C#.

This short passage doesn’t use any of the obvious cadential tropes of baroque or classical era music, but our ear is still drawn to this C#’s need for resolution.

To illustrate the power of this rhythmic impetus regardless of the pitches given, I have written another cadence, showing the same rhythmic gesture, but with a different resolution, this time to F.  You’ll note that not all of these three examples are equal in their pull towards resolution, but the point is made that this final longer note value always feels like the first part of a cadence. 

Perhaps doing this once in a piece could come off as cheeky, or cute, but repeated use of this resolution quickly becomes cliche.  What was once a strong ending to a musical gesture in our new context seems weak, and trite.   

Of course we can borrow this simple form of resolution in TONL, but it’s over usage can quickly become boring, and pasticche.  To counteract this phenomenon we can decide to resolve these leading tones only occasionally.  In other words we change the listener’s expectations.  We build new cadential figures, and give tones new tendencies.

We can also borrow a strategy from Charles Seeger’s dissonant counterpoint method. If we are going to have a resolution of a leading tone as mentioned above we can equip this resolution with a non-resolving tone elsewhere in the texture.  This can sometimes imply a bi-tonal texture, but doesn’t have to.