# 04. Erstarrung. (*Numbness*)

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

Cyclic Fourier tempogram (8 sec) correlated to rhythm (intensity) and tempo (color). [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

# Tempogram

This feature corresponds to rhythmic properties of a musical piece as well as tempo.
A *tempogram* is computed similar to a spectrogram by short-time Fourier transform or using autocorrelation function.
It represents periodic occurances of high energy in the waveform and hence is used to estimate tempo and beat positions.
To reduce jumps between a certain tempo value and its multiples, a cyclic variant is used where we identify all tempo multiples
similar to the computation of chroma from pitch features.
Subsequently, the resulting tempo features are quantized, smoothed (in temporal direction), and normalized with respect to
the ℓ^{2}-norm.

In the spirit of the transposition-invariant chroma-based SSM, we compute something similar for cyclic tempo features also.
Although the properties of this matrix are not discovered yet, we present this representation to show that the transposition index
carries *some* meaningful information. We guess that this can be used to separate information about rhythm and tempo.
In this case, we use a standard HSV colormap.

## Literature

- Geoffroy Peeters:
*Time variable tempo detection and beat marking*, ICMC 2005. - Peter Grosche, Meinard Müller, Frank Kurth:
*Cyclic tempogram – a mid-level tempo representation for music signals*, ICASSP 2010, pp. 5522–5525. - Peter Grosche, Meinard Müller:
*Tempogram toolbox: Matlab implementations for tempo and pulse analysis of music recordings.*, ISMIR 2011.