Mozart Viennese Sonatina No. 1 in C-major, Movement 1

Click on the thumbnail images below to view larger versions of the pictures.

The Music

This sonatina movement is in C major. There are 5 key regions in the piece given below which are also marked in color in the score on the left.

C major -- first half of the first page.
G major -- first half of the first page. (Dominant of C)
D minor -- for first phrase on second page. (Dominant of G; Relative Minor of F)
F major -- for next two phrases on second page. (Subdominant of C)
C major -- rest of page 2.

Color

The following images use color to indicate pitch/chord roots/keys. Pitches are arranged so that a fifth relationship exists between the adjacent color as shown to the right. Chromatic alterations of the diatonic pitches are related to the color of their unaltered form (e.g.: C# = slightly blue-green). Although this does not relate the distant relation between the keys if E and E-flat for example, this color mapping is most useful for seeing the relationship between keys in a tonal context (such as tonic-dominant key relations).

E Red

B Orange

F Yellow

C Green

G Blue

D Indigo

A Violet

Primary Analysis

The following picture relates chords and keys on various time scales in the movement. The x-axis represent time. The start of the movement is on the left-hand side, and the end of the movement is on the right-hand side.

The y-axis represents the scale of the analysis. The top of the picture represent the entire piece analysized as a single unit. The next line represents two analyses: one for the first half of the movement, and another for the second half of the movement. The movement is subsequently subdivided into more and more pieces until the bottom of the graph which divides the movement into one-beat units.

Therefore, the bottom of the picture shows the chord root, while the top of the picture shows the overall key of the movement. The intermediate regions are where modulations and tonicizations occur.

The y-axis is on a logarithmic scale. A linear version is shown further below, but it over-emphasizes the chord roots rather than giving a balanced view of chords/keys. Click on the picture below to see more detail.

Good Features:

Jagged edge between C major and G major keys indicates the region of modulation where the chords are common to both C and G majors.
The brief modulation into D minor shows up a vertical band of purple towards the center of the movement.
The movement is clearly in C major, since the top right and left sides of the picture are predominantly green.
There is a distiction between the F modulation near the middle of the piece (yellow=F) and the temporary modulation (tonicization) of F closer to the end of the piece. The tonicization does not extend towards the top of the pieces as well as the true modulation.

Problems:

The key of F near the center of the movement does not show up as well as it should. This is due to the Dominant chord in F major (which has a root on C).
The key of G has an unusual extension over the second half of the piece. Perhaps this is an averaging effect. There are a lot of G chords in the second half of the piece, but they do not show any strength as keys until the top level subdivision of the movement.

The following pictures are alternative continuous key pictures currently being developed:

Linear scale analysis.

Slight log scaling of the above image.

Image processing on primary analysis

These images are processed versions of the above picture. In particular, the second picture uses filtering to identify major regions of modulations in the piece.

This is a blurred version of the primary analysis to give an overview of the larger scale features in the picture.

This is a sharpened version of the blurred image above. Note in the enlarged view of this picture that there is a dark line surrounding the G major section. I claim that this line is an indication of modulation in the composition. The modulation in/out of the key of F is more transient, and this modulation was not detected in this picture.

Instantaneous Key

The following images blur the vertical axis of the primary analysis picture. These pictures probably represent the instantaneous key perception of the movement.

Vertical blurring of the primary analysis picture.

A blurring of the above picture to bringout the large-scale features. The key regions of G and D are clearly visible. The key region of F right after D minor, is present, but does not show up well.

Linear vertical scale

These pictures feature a linear scale on the y-axis. This doesn't look as nice to me because the difference between subdivisions towards the bottom of the pictures do not change very fast. As a result, these pictures examine the chord structure of the movement well, but do not show the key relations well.

Linear scale analysis.

Blurred version of the above image.

Sharped edges of the above blurred image.

	Linear scale analysis.
	Slight log scaling of the above image.

	This is a blurred version of the primary analysis to give an overview of the larger scale features in the picture.
	This is a sharpened version of the blurred image above. Note in the enlarged view of this picture that there is a dark line surrounding the G major section. I claim that this line is an indication of modulation in the composition. The modulation in/out of the key of F is more transient, and this modulation was not detected in this picture.

	Vertical blurring of the primary analysis picture.
	A blurring of the above picture to bringout the large-scale features. The key regions of G and D are clearly visible. The key region of F right after D minor, is present, but does not show up well.

	Linear scale analysis.
	Blurred version of the above image.
	Sharped edges of the above blurred image.