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14. Der greise Kopf. (The Grey Head)

feature RHOMBPLOT representation


14. Der greise Kopf

Variiertes Strophenlied in c-Moll mit drei Strophen. [more]

Musical aspect/feature:

harmony/key (relative)

Hierarchical representation of most likely key. Upper triangle describes major keys, lower minor. Meaning of the colors is similar to transpose-inv. CENS features. [more]


Gardner Museum: Scarlata, 2006

Singer: Randall Scarlata (Baritone), Piano: Jeremy Denk. Recording of a performance at the Isabella Stewart Gardner Museum, Boston.

Source, License: CC BY-NC-ND 2.0

Information about our segmentation of »14. Der greise Kopf«

Variiertes Strophenlied in c-Moll mit drei Strophen.
Dreiteilige Form: ABA' (I1 A I2 B1 | C | A I2 B2 I2 in der Feinsegmentierung);
Das Lied hat ein instrumentales Vorspiel I1, zwei instrumentale Zwischenspiele I2 und ein Nachspiel I2, das mit den Zwischenspielen identisch ist.
Der erste Teil umfasst das Vorspiel I1, das Segment A, ein Zwischenspiel I2 sowie das Segment B1 und stellt die Vertonung der ersten Textstrophe dar.
A und B1 weisen sowohl in der Harmonik als auch in der Melodik starke Unterschiede auf, sind sich rhythmisch jedoch sehr ähnlich.
Der Mittelteil (C in der Feinsegmentierung) hat ebenfalls rhythmische Ähnlichkeit mit A und B1. Hier wird die zweite Strophe des Gedichts vertont.
Der letzte Teil ist im Wesentlichen mit dem ersten Teil identisch, wobei B2 eine Variation (melodischer Art) von B1 ist. Dieser Teil entspricht der dritten Textstrophe.

Lyrics: Project Gutenberg

CENS (Chroma energy normalized statistics)

This feature corresponds to harmonic and melodic properties of a musical piece. Chroma features like CENS are computed by a window-wise subband decomposition of the audio file into semitones (pitches). For each pitch of an octave (C, C♯, D, ..., B), the corresponding pitch energies are summarized up, which reduces the influence of overtones. Subsequently, the resulting chroma features are quantized, smoothed (in temporal direction), and normalized with respect to the ℓ2-norm.

For transposition-invariant similarity, we compute a similarity matrix of the CENS feature sequence with a shifted version of it instead of the usual self-similarity matrix of the feature sequence with itself. Thus, we get 12 similarity matrices (one for each shift) and take the point-wise maximum afterwards. The brightness of the resulting matrix indicates this maximal similarity along all shifts, and the color indicates the index of the used shift. In the following figure the colormap of these shifts is shown.

Colormap for chroma features Circle of fifths
Index (semitones) shift colormap for CENS features.
Left: Linear shift scale from 0 to 11, Right: »Circle of fifths« notation.

One can see that our colormap is inspired by the circle of fifths where neighbor keys share similar colors. Black indicates no shift, red a shift towards the dominant key, blue towards the subdominant. The green colors are used for more distant keys. Note, that cyan and yellow correspond to the parallel major/minor key as well.


  • Emilia Gómez: Tonal Description of Music Audio Signals, PhD thesis, UPF Barcelona, 2006.
  • Anssi Klapuri: Multipitch Analysis of Polyphonic Music and Speech Signals using an Auditory Model, IEEE TASLP 2008, pp. 255–266.
  • Meinard Müller: Information Retrieval for Music and Motion, Springer 2007, Section 3.3.
  • Meinard Müller, Michael Clausen: Transposition-Invariant Self-Similarity Matrices, ISMIR 2007, pp. 47–50.
  • Gregory H Wakefield: Mathematical representation of joint time-chroma distributions, ISOP 1999, pp. 637–645.