Project Partials

Digraph depicting the central role of the partials in the sound structure.

This project investigates ways to measure the quality of a musical tone using basic structural components.

Helmholtz (1) proposed a basic taxonomy for the sound comprised by

  • intensity,
  • pitch, and
  • quality.

This is depicted in the figure above.

The basic structural COMPONENTS chosen for this project were derived from this taxonomy:

  • resonance, related to intensity;
  • intonation, related to pitch;
  • harmonicity, related to quality.

The COMPONENTS are filled with light grey in the picture above.

The action plan for this project has the following steps:

  1. produce software capable of measuring the COMPONENTS given a musical tone;
  2. obtain musical tone samples of different quality levels;
  3. measure the COMPONENTS of step 2 using the software from step 1;
  4. analyze the correlation between the COMPONENTS and the quality levels.

The strategies for each step are:

  1. produce the software in-house (Ling Ling Meter);
  2. extract the sound from practice videos of musicians with different proficiency levels (#100daysofpractice-dataset).

Steps 3 and 4 are self-explanatory.

For more details about the inspiration for this project, please continue reading.

In his seminal book, On the Sensations of Tone (1), Helmholtz proposed the characterization of a musical tone by

  • intensity,
  • pitch, and
  • quality.

This is depicted in the figure above.

These three components may be relativelly well described in terms of their partials:

  • the intensity of the sound being the sum of the individual intensities of the partials, and
  • the pitch being a function of the frequency of the fundamental and corresponding upper partials,
  • the quality encompassing other carachteristics besides intensity and pitch, e.g., deviations or conformities relative to expected individual characteristics of the partials.

Additionally,

  • resonance may increase the intensities of the partials, thus increasing the overall sound intensity
  • intonation determines the frequency of the fundamental, hence the pitch itself
  • harmonicity reflects how close the frequency of each upper partial is to the corresponding “ideal” one (the one that maximizes consonance).

References

  1. H. L. F. Helmholtz. On the Sensations of Tone as a Physiological Basis for the Theory of Music. London, 1895.


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To the extent possible under law, Bits4Waves has waived all copyright and related or neighboring rights to Project Partials.

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