The harmonic structure is shown in a double triangle. The upper triangle corresponds to major keys, the lower triangle to minors.

Harmonics can be analyzed on different time scales. These time scales corresponds to heights in the triangle: The bottom line (for the major keys) shows the harmonics of a very short time frame, slightly above describes the chords, then successively coarser harmonic structures and local keys, up to the top showing the most dominant key in the entire song. This point is also considered as the overall tonic of the piece and defines the coloring.

The coloring of the keys is inspired by the circle of fifths where neighbor keys share similar colors:

Index (semitones) shift colormap.

Black indicates no shift (tonic key), red a shift towards the dominant key, blue towards the subdominant. The green colors are used for more distant keys. Cyan and yellow correspond to the parallel major/minor key as well.

Path enhancement

Path length:

Cutoff:

In the realm of musical form analysis, self-similarity matrices (both x- and y-axis show the temporal progression of the current song) serve as valuable tools for uncovering a song's repetitive structures.

From left to right: Musical form, self-similarity matrix, computed segmentation.

The middle image shows the optimized self-similarity matrix. Within this matrix, the main diagonal reflects moments in the song that are identical to themselves. Meanwhile, the other diagonal patterns shed light on repetitions found within the music. Colors are used to signify whether these repetitions are transposed, employing the same color scheme as the Chord Analysis tool.

The second image shows machine-recognized segmentation. In this instance, advanced mathematical techniques are applied to the matrix, leading to the identification of diagonal patterns. These patterns are then translated into segments, offering a segmented view of the song's structure. It's important to note that the color scheme in this image is randomly generated.

To tailor the self-similarity matrix analysis to the specific song at hand, you have the option to customize various parameters using the fine-tuning feature. This allows for experimentation to find the best settings that suit your analytical needs.