Something I’m working on for future projects…
Musical Intervals as an analogy for the essential link between quantitative and qualitative data
Not only the distance between two notes, but also the relationship between them.
Take the interval of a Fifth as an example. Quantitatively, the distance between the two notes is a Fifth, which can be broken down in terms of half-steps. A Fifth may be 7 half-steps, or 6, or 8. This is a Quantitative description of the interval, the exact distance between the notes.
Qualitatively, the interval also describes the relationship between the two notes. A Fifth may be Perfect, Diminished, or Augmented. These descriptions are quantitatively defined by the number of half-steps between the notes, but are, more importantly, a qualitative description of the relationship: how the interval sounds, what is its character, what is its quality, how will it function within the larger structure of a composition, how will it function within a chord, etc.
A musical interval describes inseparable quantitative and qualitative data describing the relationship of two notes. The two types of data cannot be separated. Thus, research and analysis of music depends on a combination of quantitative and qualitative data.
In this way, Musical Intervals serve as an ideal example and analogy of combined quantitative and qualitative data and research.