Analysis

Defining difficulty

Most lists of solo repertoire group pieces into levels, based on measure of difficulty. The lists do not explicitly define what pieces in each level have in common or how pieces within a level relate to one another.

Because I feel that these missing details lead to confusion, I have set out to define what aspects of a piece make it difficult. By defining how difficult pieces and works are they can be directly compared, sorted by difficulty, and understood in terms of the components which lead to that assestment. In this way, students can more systematically progress through the repertoire.

Categories and Components

The difficulty of a piece or work can be defined by the following seven categories. The components within each category are either quantaitative measures, such as the number of pitches in the piece, or qualitative assessments, such as the difficulty of the articulation present.

1. Tessitura of the Work
2. Range: highest pitch, lowest pitch, distance between the two, part of the range containing the highest pitch, part of the range containing the lowest pitch
3. Rhythmic Complexity: number of unique rhythmic values, number of 16th notes, smallest-written-rhythm, number of smallest-written-rhythms, shortest-played-rhythm, length of shortest-played-rhythm in minutes
4. Structure of Work: number of notes, length of the work in minutes, length of horn part in minutes, number of notes per minute, number of bars in the piece, number of bars the horn plays, notes per bar
5. Notation Issues: the most difficult key signature, the most difficult time signature
6. Musical Issues: ensemble difficulty, musical difficulty
7. Technical Issues: articulations, chromaticism, extended techniques, general technical difficulty, specific techniques, tonality

Combining the Categories

The relationship of the components, their relative wieght, was determined through linear regression. First, all of the components were evaluated for the works in the A and B levels of the Wisconsin 2005-06 list. The second value needed was a relative ranking of all of the works. This ranking was developed by taking an average of the rankings assigned to a work by all of the lists that include the work, along with my own subjective assessment of the works reative difficulty. The A and B levels were selected because those pieces offer the greatest comparison to other lists, while most of the C level pieces do not appear on other lists.

The linear regression was processed on each category seperately, so as to have a high ratio of sample data to variables being solved for. Once each category's wieght was determined, the factors were combined into a final equation. The relative weights are still being evaluated to see that they reflect my opinion for how that factor should relate to the overall difficulty of the piece.