In flux by Tobias Andersson

In this research project, guitarist and improviser Tobias Andersson investigates compositional tools and techniques to create flexible harmonic frameworks for improvisation. In a strive for music that stays in an improvisational state the reseach project also adresses questions on the quality of coherence in the music. The research project investigates how the application of theoretical concepts associated to the 20th century western classical music and post-tonal theory can be useful when composing for improvisation. By taking a close look on the musical material itself, the author starts to compose music where all harmonic and melodic material is derived from a small original set. The results of the investigation is a series of compositions for different ensembles, spanning from solo work, via smaller settings a large ensemble of wind instruments. The compositions are analysed in regard to the initial questions of coherence and harmonic flexibility, sharing insights to how the compositional approach influenced the musical results.

Key concepts

-a very short introduction to post tonal theory

20th century harmony

The harmonic language of western classical music went through a fast development in the early 20th century. Some of the techniques that were developed in this period deal with the understanding of pitch material and how they relate to each other. These ideas on pitch material have been central when working with the music presented in this research project.

First, let us discuss the meaning of "post-tonal". Unlike tonal music, in which chords are described as functions explaining their role as a musical driving force towards a tonic, the harmony of post tonal music is largely constructed around its intervallic content. All intervals have a special character as acoustic phenomena, depending on how many overtones the sounding pitches have in common. The result is a sensation of consonance or dissonance. When only comparing two notes this characteristic is easily audible but the more notes there are to a chord its complexity quickly increases, as does the number of intervals within the chord. This leads us to one of the first important concepts, that of degree of dissonance¹. In the chart below all intervals are ordered by degree of dissonance. When studying the chart, the reader will notice that the intervals in post-tonal theory have integer names that correspond to the number of semitones².

Example 1: Intervals by degree of dissonance.

Sets and normal form

Any collection of pitches can be grouped into a ”set”,witch is then labeled by its interval content. Many pitch combinations are in fact variants of the same set in different inversions, spacings or transpositions. This is not as strange as it might sound, in tonal harmony the concept of a major or a minor chord is a kind of abstraction from the pitches involved. They are in fact also sets that can be transposed, inverted etc (interestingly the minor triad is a major triad upside down). There are of course numerous ways of ordering the pitches within a set so for that reason the set is labeled by its ”normal form” that is its most compressed form³. Normal form is written with integer numbers. As an example, a minor triad would be written (0,3,7) in normal form, the "0" beeing the root, "3" the minor third and "7" the fifth. In this way we also get at tool to see the intervallic identity of the set. In my analyses all sets are written in their normal form.

Trichords

In my research project I have worked extensively with sets of three pitches, also called trichords. Why trichords? It is really a minimal amount of material and in that regard it is interesting in relation to my question of developing a small musical cell into a bigger organism. Trichords are also the foundation for John O’Gallaghers improvising method book⁴ that has been one of my ways of combining theoretical studies with instrumental practice. Most trichords can also be played as chords och the guitar, an investigation that resulted in my trichord map for the guitar:

Examples of operations

Above I mentioned the possibility of boiling down a collection of pitches into its normal form. But what if you want to do it the other way around and expand on a set that is described in only as a group of numbers?

The most common operations consists in changing the order of the pitches within the set, turning it upside down (inversion) or playing it backwards (retrograde) or both. The set can also be rotated, in this case one can think of a brick that is turned over so that a new side is facing downwards, it is still the same brick but is properties has changed.

These operations can be done in combination with transposition, starting from a new pitch and applying the same formula of interval combination. One technique that I have used many times in this work is to use a common tone in both sets, sometimes called a ”pivot”, to make the transposition less noticeable. In the drawing below one can think of all the groups of three circles as the same trichord set that is being developed through this concept of common tone transposition.

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