# 04. Erstarrung. (*Numbness*)

Modified strophic form in c minor containing five stanzas. [more]

Quantized and normalized chroma features (12 sec) which are correlated to harmonic and melodic progression. [more]

Singer: Gerhard Hüsch (Baritone), Piano: Hanns-Udo Müller. Recorded on vinyl, April-September 1933.

**Source**,
License:
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# Information about our segmentation of »04. Erstarrung«

Modified strophic form in c minor containing five stanzas.

Coarse segmentation as ternary form ABA'.

The first part consists of the segments I1, A, B, and C1 of the given fine-granular segmentation.

In this case, A and B are the first stanza of the poem and its repetition.

The instrumental introduction I1 as well as the sung part A are in c minor. Segments B and C1 are in e flat minor and g minor, respectively.

Its middle part (D in segmentation) has an instrumental prelude lasting four measures. The part itself is in A flat major, and corresponds to the third stanza of the poem.

The song's last part is a modified variant of its first part without interlude. Instead, a coda (I3) in c minor is appended.

Segments A and B following D cover the fourth stanza and its repetition. C2 is the last stanza.

**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 ℓ^{2}-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.

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.

## Literature

- 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.