Dramaturgy

Aristotle's dramatic model, as formulated in his Poetics, was one of the first attempts to identify recurrent structures in stories of all sorts. His theory became widespread in various re-formulations and variations, e.g., Freytag's Pyramid for stage dramas (Freytag, 1863/2004) or Syd Fields' (1979) three-act structure for movie scripts, and even more and more normative over time (at least for Western mainstream culture). Aristotle's model divides a story in a beginning, a middle part, and an end. The beginning contains the exposition, i.e., introduces the setting (time and place) and the main protagonists of the story. Typically after an inciting incident, conflicts of various sorts arise and are built up along several turning points to a climax. After the climax is reached, conflicts are either slowly or quickly resolved, so that the story ends with either a positive (comedy), a negative (tragedy) or a mixed outcome (tragicomedy). The tension curve—or dramaturgy, as we will refer to it in the following—is thus shaped like an arch, a convex structure, moving from low to high tension and back to low tension.

Unfortunately, tension is a complex concept and its ontological location is not entirely clear, i.e., whether it can be located in the artistic object itself or in perception or in both. Most probably, tension can be seen as a certain psychological state induced in a perceiver/listener by certain elements in the dramatic action. Tension is related to expectations in a very general sense ("What happens next?") with the special case of unpleasant states, which generate desire (expectations) for relief. In the case of music, several options to generate expectations and tensions are available to a composer or an improviser, e.g., harmonic tension in Western tonal music by employing a dominant-seventh chord. One could even conceive of music as a permanent flow of expectations/tensions and releases, often at several hierarchical levels at once. However, identifying these tension-generating elements in jazz solos is not an easy task. Therefore, we will restrict ourselves mostly to proxy measures in form of related, more readily measurable concepts, such as intensity. This can be justified by the assumption that tension is partly (but not fully) generated via modal analogies and empathic coupling. Empathic coupling can, for example, occur if the perceived intensity curves are interpreted as the result of emotional states in the performer and transferred to the performance. This does not demand that these emotional states are de facto present in the performer. The sheer possibility of this interpretation is sufficient for the coupling to take place (just like an actor can project emotions without actually experiencing them). However, a high degree of displayed intensity in a performance can also be interpreted as heightened activity in conflict situations, thereby indirectly referring to and inducing tension. Right now, it cannot be decided which of these hypothetical mechanisms are actually taking place in jazz improvisation. However, all options result in the same hypothesis: Jazz solos possess distinct curves of musical parameters that are commonly associated with arousal, tension and intensity and might follow certain trends of dramatic development as, for example, arched or concave curves.

Aim and Limitations

In order to explore this hypothesis, we decided for a quantitative statistical approach, which has only recently become feasible due to the availability of a large jazz solo database (the Weimar Jazz Database; Frieler, Abeßer, Zaddach, & Pfleiderer, 2013). We designed and conducted three studies: (1) An investigation of global trends of pitch and loudness, using note-wise values, (2) an investigation of global trends of selected features related to tension, variability and intensity based on phrase-wise values, and (3) an investigation of the distribution of improvisational ideas with respect to their relative position in a solo.

The Weimar Jazz Database contains only scarce information of the backing group performance (except for beat tracks and annotated chords). This means that interactions between the soloist and the band, which might have an impact on the dramaturgy, fall out of the scope of this paper. Likewise, the overall dramaturgy of the recordings, i.e., the sequence of theme parts, interludes and solos, is not in reach of this study.

Data

We used 299 monophonic solos by 70 musicians. The solos are taken from the Weimar Jazz Database and cover a wide range of styles and performers (see Table A.1 in the Appendix for list of performers). The Weimar Jazz Database contains high-quality jazz solo transcriptions with manual annotations of chords, beat and meter, phrases, form sections, and articulation. The solos were transcribed and annotated by jazz and musicology students and were carefully cross-checked to ensure their high quality. The solos are equipped with rich metadata, such as instrument, style (TRADITIONAL, SWING, BEBOP, HARDBOP, COOL, POSTBOP, AND FREE), rhythm feel (TWO-BEAT, SWING, LATIN, FUNK, MIXED), tonality type (FUNCTIONAL, BLUES, MODAL, FREE, and COLOR, i.e. a mixture of modal and functional harmony) and tempo class (SLOW, MEDIUM SLOW, MEDIUM, MEDIUM UP, and UP).

The median number of choruses is three; the maximum number was a staggering 31 choruses (John Coltrane's 1961 solo over Impressions). One hundred eleven solos have one chorus, 83 two choruses, 36 three choruses, 21 four choruses, and 48 five or more choruses. The total number of tones is 128,078, with a median number of tones per solo of 349 (range: 49–4955 tones, SD = 380.6).

Method

Onset, pitch, and loudness information for the tone events in the solos were collected. The pitch values of the transcriptions were coded with MIDI pitch numbers, whereas the loudness values were extracted from the audio using score-informed source separation (Abeßer, Cano, Frieler & Pfleiderer, 2014). The algorithm produces a transformed version of raw tone intensities using a rather simple psycho-acoustical model. We will use the term "loudness" (measured in dB), even though the measured loudness cannot be identified with actually perceived loudness. The median of all loudness values for a given tone was used as a reliable estimator. However, due to very short tones annotated in the Weimar Jazz Database and to inevitable errors generated by the source separation algorithm, there are occasional clear outliers in the loudness values which were filtered out by using the outlier criterion of >1.5 times the interquartile distance, as is customary for boxplots. For one solo (John Coltrane's 14 minute solo on "Impressions" from 1961) no loudness values could be obtained due to its extraordinary length. The onsets of tones (in seconds) are directly related to the transcribed and annotated solo cut of the audio recording. To facilitate comparison, we normalized onsets in regard to overall solo lengths by scaling them to the interval [0, 1]; this has no bearing on the following fitting procedure, which is scale-free.

We fitted quadratic polynomials and collected p-values and adjusted R²-values for each solo 4. Quadratic polynomials were chosen because they are easy to interpret while being able to capture linear trends as well as arch-like shapes. We initially experimented with other options, i.e., higher and dynamic degrees of polynomials, but no clear-cut criterion for choosing the polynomial order emerged. Higher order polynomials very often provide better fits, however, there is a danger of overfitting. Since we are mainly interested in global trends, we settled on quadratic polynomials as the most simple, but still informative option.

Furthermore, we measured the relative position of the minimum/maximum of the quadratic polynomial (if present) and the overall linear trend as the difference between the first and last predicted pitch/loudness value. Finally, we classified the fits into five categories: non-significant, horizontal, ascending, descending, concave and convex. Fits that did not reach a fixed significance level of α = .01 were considered non-significant. Fits reaching significance but with R²-values less than a fixed threshold of .1 were classified as horizontal. Actually, "non-significant" and "horizontal" can be grouped into one class ("flat"), since in a non-significant regression the mean of values is already the optimal fit. For both categories, values are basically oscillating around the mean. All other significant fits with R² > .1 were classified according to the presence of a minimum or a maximum as "non-flat". If no extremum was present, the fits were labelled "ascending" or "descending" dependent on their linear trend. If a maximum (minimum) was present, the fit was classified as convex (concave).

Results

Data

We used the same 299 monophonic solos as in Study 1, along with phrase information annotated by our transcribers. The total number of phrases is 7,827; the median number of phrases within a solo is 21 (range: 4–465 phrases, SD = 30.8).

Method

For the second study, we chose a set of 12 single-valued numerical features which in our view are relatable to tension, intensity, or variability (see Table 2). The features come from four different musical dimensions (events, pitch, interval, and rhythm/meter). Changes of intensity as displayed in the course of an improvised solo might be a signifier for heightened or lowered emotional states, i.e., playing more and faster notes in the higher register for high arousal, and playing less and longer notes in the low register for relaxation. Tension is likewise a very important concept in music to convey and induce emotions; direct measures of intrinsic tension are not easy to define (but cf. Egermann, Pearce, Wiggins, & McAdams (2013) for possible ideas into this direction). Consequently, in our selection only one such feature is included. It is defined as the percentage of dissonant notes according to the underlying chords, e.g., tritones, flat ninths, major thirds over minor chords, including passing and neighboring tones. This number is an indicator for the common technique of "outside" playing (i.e., playing tones not fitting to the underlying harmony) as well as for chromaticism, which can create tension that demands relief. The third category, variability, is related to the variance of various musical parameters during an improvisation, e.g., variance of the size of intervals or durations. On the one hand, variability will keep listeners' attention alive while uniformity, e.g., always playing chains of eighths with rather small interval steps, is likely to bore listeners. On the other hand, too much variability on too many dimensions at the same time might lead to a cognitive "overload" of the listener, which in turn can result in perceived intensity or tension. One would expect complex interactions between variability, intensity, and tension and their possible effects on a listener, but each of them can contribute to the overall dramaturgy of a solo.

Initially, we extracted a slightly larger set of features for each phrase, but due to the inherent correlations (by mathematical construction), we pruned the set of features using causal inference (Pearl, 2009) as an informal way to identify the most fundamental features. Principal component analysis or a similar method could have been used to remove all correlations, but this would have hampered the interpretability of the results.

Since these features are scalar and aggregating, they need to be extracted over a certain range of tone events, which we chose to be musical phrases, because phrases represent meaningful musical units and are readily available within the Weimar Jazz Database. As a proxy for time position, we used phrase numbers 6. After obtaining the feature values for each phrase in each solo, we applied the same fit of quadratic polynomials as in Study 1, while fixing the significance level to α = .01. Similar to Study 1, we classified the contours according to the shapes horizontal, ascending, descending, concave, and convex.

Results

Fitting 12 features to each of the 299 solos is likely to produce a lot of spurious results. For each feature we expected about three significant tests at the given significance level by chance alone. However, we were not so much interested in true significance levels than in general trends across the whole dataset. Therefore, instead of using Bonferroni correction for multiple testing, we rely on Bayes Factors of achieved vs. expected significant tests in our discussion. Following standard recommendations for Bayes Factors (though these are not true Bayes Factors), only features with a Bayes Factor larger than three, i.e., having more than three times significant tests than expected, are considered significant. The results for all features can be found in Table 3.

Table 2. List of selected features. For a thorough mathematical definition of the selected features please refer to http://jazzomat.hfm-weimar.de/commandline_tools/melfeature/melfeature_features.html.

Category	Type	Feature	Description
Events	Intensity	number_notes	Number of notes.
	Intensity	event_density	Tone events per second.
Pitch	Intensity	pitch_range	Pitch range (ambitus).
	Intensity	pitch_mean	Mean value of the pitches of all tones.
	Variability	pitch_entropy	Entropy of pitches; measures pitch variability. Smaller values mean lower variability.
	Variability	cpc_zipf	Zipf coefficient of distribution of chordal pitch classes; measures dominance of certain pitch classes with respect to underlying harmonies. Smaller values indicate higher variability.
	Tension	outside	Summed density of dissonant pitches with respect to underlying harmony (e.g., a major seventh or major third over minor-7 chord or a minor seven over a major-7 chord). Higher values indicate more dissonances.
Interval	Variability	fuzzy_int_entropy	Entropy of refined contour classes; measures variability of interval classes (repeats and steps, leaps and jumps up and down). Smaller values indicate lower variability.
	Variability	abs_int_range	Range of absolute interval sizes.
Rhythm/Meter	Variability	CV_dur	Coefficient of duration variation; measures variability of durations. Smaller values indicate lower variability.
	Variability	durclass_abs_entropy	Entropy of duration classes; measures variability of duration classes. Classes are defined with respect to absolute time reference 500 ms (very short, short, medium, long, very long). Smaller values indicate lower variability.
	Variability	mcm_entropy	Entropy of metrical positions. Measures variability of occupied metrical positions (one bar is divided into 48 bins). Smaller values indicate lower variability.

In contrast to Study 1, much fewer significant fits could be observed, which is most likely due to a much smaller number of phrases as compared to the number of notes. This is in line with the observation that 4% of solo and feature combinations did not become significant, but had an adjusted R2 > .1. The largest number of significant fits (28) could be found for pitch_mean, mostly of convex shape. This corroborates the findings of Study 1 on pitch contour. The next best feature is event_density, also with mostly convex contours, meaning that the number of notes per second, i.e., intensity, is often first rising and then falling again. The mean relative peak position for convex event densities is 0.52, hence, the maximum is often reached in the middle of a solo (this is also true for non-significant convex event densities). Next in line is fuzzyint_entropy, again mostly with convex shapes and with relative peak positions of the maxima in the middle of the solo. For CV_dur, concave shapes are prevailing. This corresponds to the convex shapes of event density and might be traced back to fast lines occurring in the middle of a solo, which result in high densities with low duration variability. This is also corroborated by the concave shapes of duration_abs_entropy, which is lower for fast, homogeneous lines, as well as the convex shapes of mcm_entropy, which is higher if subdivision positions are regularly occupied (e.g., by sixteenth notes).

Notably, most of the solos showed only significant fits for one of the features, but not on various features at the same time. Similarly, a correspondence analysis of significant fuzzy_int_entropy and CV_dur revealed that these are mostly orthogonal. This meets our expectations, since fast lines are typically moving in small intervals (steps, thirds), and thus should have low fuzzy_int_entropy. The last two features with a Bayes Factor larger than three are pitch_range with mostly convex shapes and abs_int_range with mostly ascending and concave contours. cpc_zipf and outside did not reach the BF>3 threshold, which might be due to the facts that both variables are not very good operationalizations of harmonic tension, or that harmonic tension is not an important tool in regard to dramatic strategies of jazz musicians.

Finally, we examined the number of simultaneous significant fits per solo. The results can be found in Table 4. There are some solos which show many significant fits on several features simultaneously, which cannot arise just by chance. One of these solos might deserve a closer examination in the form of a short case study.

Table 3. Significant quadratic fits of phrase-wise features. Bayes Factor (BF) here is the ratio of significant fits to expected significant fits, which is 2.99 for α = .01 and N = 299. For an explanation of the features, see Table 2.

Feature	#sig.	BF	horizontal	ascending	descending	concave	convex
pitch_mean	28	9.4	1	3	0	4	20
event_density	21	7.0	0	3	0	1	17
fuzzyint_entropy	18	6.0	1	2	1	2	12
CV_dur	17	5.7	1	2	1	12	1
mcm_entropy	14	4.7	1	1	0	0	12
pitch_entropy	13	4.3	1	1	0	0	11
durclass_abs_entropy	12	4.0	1	1	1	6	3
number_notes	10	3.3	1	3	0	1	5
pitch_range	10	3.3	1	2	0	2	5
abs_int_range	9	3.0	2	3	0	3	1
cpc_zipf	7	2.3	1	0	2	0	4
outside	6	2.0	1	1	0	2	2

Table 4. Common occurrence of significant quadratic feature fits. The expected number of significant fits was determined using the binomial distribution. Bayes Factor was calculated as number of expected significant tests divided by the number of observed significant tests with α = .01.

# significant fits	Frequency	Expected	Bayes Factor
1	47	32.1	1.46
2	15	1.78	8.4
3	5	0.06	83.2
4	2	<0.001	1,464
5	1	<0.001	4.5⋅104
7	5	<0.001	2.2⋅109
9	1	<0.001	1.6⋅1013

Data

In the third study, a subset of 116 solos by 55 soloists from the Weimar Jazz Database was used, which had the necessary midlevel annotations.

Method

Midlevel analysis is a recently developed qualitative method (Frieler & Lothwesen, 2012; Schütz, 2015) that segments solos into non-overlapping and exhaustive sequences of midlevel units (MLU). These midlevel units are classified into nine main categories (cf. Table 5) with 18 sub- and 38 sub-subcategories (Frieler, Pfleiderer, Abeßer & Zaddach, 2016). The categories were originally developed and condensed from the data until the system was saturated and a code book could be written. The annotation of MLUs was done by four expert annotators. Special care was taken to achieve high inter-rater reliability, which is about 80% for segment borders and around 60% for categories; the most often confused categories are lines and licks (Frieler et al., 2016). For this study, we used the midlevel annotations to examine the differences in relative position of the various midlevel unit categories within a solo. To this end, we devised the relative starting position of a MLU as the normalized tone position of the starting tone of that MLU within a certain solo.

With respect to dramatic intensity, we are particularly interested in the two main categories, expressive and rhythm, since these two seem to have the highest intensity. Expressive units are defined as units where expressivity rather than melodic or rhythmic principles is in the foreground, often comprising aspects of timbre, too, which are not captured in the representation of tone events in the Weimar Jazz Database. Similarly, rhythm units can convey a feeling of urge and intensity due to the mostly insistent repetition of a small set of pitches. On the other hand, the categories void (intentionally playing nothing), fragment (short particles or errors) and lick (rather short melodic cells) can be related to more relaxed states, since these leave more space in the musical texture.

Table 5. Midlevel analysis categories.

Main type	Subtypes	Description
line	ascending, descending, wavy, interwoven, "tick lines"	Melodic sequence with strong directionality, rhythmically rather uniform.
lick	blues lick, bebop lick	Rather short melodic motif, rhythmically and tonally diverse, succinct ("prägnant") gestalt.
melody		Clear, melodic character, "cantabile", theme-like.
rhythm	single/multi-note, regular/irregular	Rhythm prevails over pitch aspects.
expressive		Expressive aspects are in the foreground, e.g., long tones, "screams", "honks"
void		Deliberate non-playing, overlong breaks.
theme		Reference to the theme of the song.
quote		Quotation from other music.
fragment		Short particles, errors.

Results

There were 4,412 MLUs in total, with a median of 34.5 MLUs per solo (range: 7–163, SD = 22.3). The most common category is lick, comprising 44.3% of all MLUs, followed by line (33.5%), melody (7.0%), expressive (4.9%) and rhythm (4.9%). All other categories occur less than 2% each. Mean duration of all MLUs is 2.26 sec with a mean length of 12.1 tones.

The relative positions of the main categories differ significantly (F(8, 4403) = 8.618, p < 0.001). On the one hand, theme (median relative position = .22), quote (.33), and void (.38) occur earlier (see Figure 4), indicating a tendency toward relaxed beginnings of jazz solos. On the other hand, the expressive types expressive (.63) and rhythm (.62) tend to occur later in a solo. This hints at the fact that climaxes can be found more often in the second half of a solo and concurs with the findings from Study 1 and 2. Interestingly, lick and melody show a tendency to bi- or even tri-modality, with peaks both at the beginning or the end, and occasionally in the middle of a solo. This hints at additional dramaturgical devices besides tension and intensity curves connected with the semantics of the different types of MLUs. For example, a short blues lick conveys a different meaning or emotionality than a long and virtuosic bebop line.