Fig. 2: Two examples of scales.

The figure presents a two-note scale from a recording of the Kiowa-Apache people of the southern United States (A–C) and a triatonic scale from a recording from Ghana in west Africa (D–F). The unwrapped scale series is written to the right of the culture name, where the * indicates the tonic pitch. Pitch (fundamental frequency) traces (A, D) for selected excerpts are shown alongside the pitch-class histograms before (B, E) and after (C, F) additional filtering. Dashed grey lines and numbers on the y-axis indicate scale degrees obtained from Gaussian mixture models (GMMs) (A–F), while blue dashed lines indicate manual scale annotations (A, D). Fits to GMMs are shown as solid colored lines (C, F). In the top example, rare pitches are filtered out that correspond to non-discrete glissandi by applying a filter to the pitch-class histogram (B, red line). In the bottom example, filtering is done by time (D), selecting a short excerpt that includes all notes. This is done so that the tonic, which is heard much more often than the other notes (E), is less dominant in the filtered histogram (F), which makes it easier to fit a GMM.