Visible Humour — Seeing P.D.Q. Bach's Musical Humour Devices in The Short-Tempered Clavier on the Spiral Array Space

Abstract: We explore the use of the Spiral Array spatial visualization of tonal evolution through time for the visual analysis of P.D.Q. Bach's The Short-Tempered Clavier. In particular, we analyze situations in which we can see some of the humour devices abstracted in an earlier study by David Huron. We conclude that although we can see a good number of Schickele's humour devices — such as incongruent styles, musically improbable tonality and harmony shifts, and excessive repetition — we do not yet have sufficient information to form a robust computer-based method for detecting musical humour.

Introduction: We explore the use of the Spiral Array spatial visualization of pitches, chords, and keys, and the tracking of their dynamic evolution through time for the visual analysis of musical humour. We visually analyze, using the Music on the Spiral Array . Real-Time (MuSA.RT) system [2], pieces from The Short-Tempered Clavier — Preludes and Fugues in All the Major and Minor Keys Except the Really Hard Ones (S. 3.14159, easy as) [5], composed by P.D.Q. Bach, a.k.a. Peter Schickele. In particular, we focus on the points of departure from musical expectation (and good taste), and determine if these strategies for violating expectation and thus eliciting laughter can be traced visibly in MuSA.RT.

The study is inspired by Huron's work on music-engendered laughter [4], where he systematically identifies and classifies laughter-eliciting musical devices in P.D.Q. Bach's music each involving expectation violation. P.D.Q. Bach is Peter Schickele, a classically trained contemporary composer who has built a career on writing laughter-eliciting musical compositions under his pseudonym. Huron's article presents the results of a study of 629 instances of laughter-eliciting music by Schickele. Huron states that, unlike most musical humourists, "beyond the visual gags and language-based humor, most of Schickele's humour devices are to be found in the core musical domains of pitch, time, and timbre." Excluding visual and language-based comedy, he proceeds to identify nine categories of musical devices that elicit laughter: (1,2) incongruity of instrumental sounds and of musical genres, (3,4) musically improbable tonality and metric shifts, (5,6) implausible delays and excessive repetition, (7) incompetence cues, and (8,9) incongruous quotations and misquotations.

The tool we use for our explorations is MuSA.RT, an interactive music analysis and visualization system, based on Chew's Spiral Array mathematical model for tonality [1], that is capable of tracking and displaying the trajectory of the tonal content and context of music in real-time during a live performance. The Spiral Array is a geometric representation of tonal entities (pitches, chords, and keys) in three-dimensional space. In MuSA.RT Opus 2.6, a silver helix shows the outermost spiral on which the pitch classes reside, and the inner and intertwined blue and red helices denote the spirals on which the minor and major keys are represented, respectively. The closest major or minor triad (shown as a triangle) is highlighted in pink or blue, and its name colored and indicated by a sphere of the same color. The closest major or minor key appears as a sphere on the corresponding major or minor key spiral, and a sphere of the appropriate color marks the letter name of the key.

MuSA.RT maps musical performances to distinctive spatio-temporal paths and patterns inside the Spiral Array that are characteristic of the piece, and of the particular interpretation. It provides a means of visualizing not only pitch clusters, and key finding and chord tracking algorithms and their results, but also the unfolding and history of the patterns over time. The chords and keys are determined via the centers of effect (c.e.'s) generated by the notes in the piece, which are mapped their respective pitch class representations in the Spiral Array using a pitch spelling algorithm. In MuSA.RT, each c.e. is located at the aggregate position of the notes present and in the recent past, where the effect of notes past are decreasing according to a linear decay function. A violet trail traces the history of the key c.e., and a purple trail that of the chord c.e.

Here, we show the visual counterparts of some of the humour-evoking devices catalogued by Huron, particularly the ones based on pitch and time, using examples from The Short-Tempered Clavier.

Style Differences: We show, by the example of the Prelude No. 5 in D minor from The Short-Tempered Clavier the differences visible when the same theme is repeated in multiple styles (or genres). The screenshots below shows the complete history of Prelude No. 5 in D minor (view from left, center view, view from right).

Prelude No. 5 in D minor: variations (in different styles) on a theme

Next, we segment the piece into its three stylistic sections, and visualize each part independently. The initial arpeggiated chords that present the theme create relatively smooth trajectories around D minor, as shown in the screenshots below.

Prelude No. 5 in D minor: theme (arpeggiated chords)

The middle section with its staccato walking bass and interplay of groupings of two against three traces a more jagged version of the initial trails outlined by the first section — see the next row of screenshots.

Prelude No. 5 in D minor: variation i (eighth note walking bass, two-against-three rhythm)

The final section with the boogie bass, in a faster triplet rhythm, again outlines the same tonal regions, but results in a tangled mess, as shown in the final row of screenshots.

Prelude No. 5 in D minor: variation ii (boogie bass)

Expectations Violated (Jazz Ending): Schickele frequently switches from baroque/classical to jazz sporadically, and particularly at the ends of pieces. For example, the Prelude No. 1 in C, a parody of J. S. Bach's Prelude No. 1 in C, occasionally slips from the classical triadic treatment to a jazzy minor seventh chord, with a definitive next-to-last measure switch to the C minor seventh chord, before ending on the C major triad, evoking a tierce picarde-like effect. This shift towards the jazz genre toward the end is visible as a southward swing of the trajectory of the piece, a departure from the tightly wound main cluster, shown below.

Prelude No. 1 in C major (jazz ending creates downward dip in trajectory)

Schickele employs a similar strategy in Prelude No. 8 in G minor, where the entry into the last measure veers sharply from G minor, using the F-sharp major triad to step chromatically into the G major ending. Again, the resulting and unexpected tonal shift is visible in the views of the trajectories of the piece, shown in Figure 6; the trajectories travel north sharply to end in the G major triad, giving this tierce de picarde a jazzy twist:

Prelude No. 8 in G minor (tierce de picarde with jazzy twist)

Expectations Violated (Improbable Harmonies): Another technique employed by Schickele is the insertion of musically improbable harmonies (chords) and tonality shifts, which typically map to distant locations in the Spiral Array space.

In the Fugue No. 2 in C minor, beginning in measure 26, Schickele begins building towards, and preparing for, a climax in C minor, only to land on a cheerful and triumphant C major in measure 34. This is visible in the c.e. trails for the piece shown in Figure 7, where the trajectories meander around the Bb region, only to shoot up toward the E-natural pitch class in a rather acrobatic fashion at measure 34:

Fugue No. 2 in C minor (return of theme in wrong key creates upward leap in trajectory)

In Fugue No. 6 in E-flat major, the composer inserts an jarring chord based on stacked Perfect fourths (E-natural, A-natural, D) in the last four measures of the piece. This departure from expectation is visible as the large upward swoop in the c.e. trails for the piece shown below:

Fugue No. 6 in Eb major (jarring chord, improbable harmonies, create upward swoop in the

Expectations Violated (Excessive Repetition): One of the Schickele's comedic strategies most easy to identify is that of excessive repetition. Typically, a figure is repeated three times. Anything beyond this level of repetition, unless it is an intentional ostinato, can be deemed to be in bad taste. The screenshots below show an example of a ludicrous and awkward amount of repetition in Prelude No. 10 in A major.

Prelude No. 10 in A major (excessive repetition)

Conclusion: We are able to see stylistic changes, improbable tonal and harmonic shifts, and incessant repeats, some of the laughter-eliciting devices uncovered by Huron in Schickele's music. However, not all expectation-violating events would result in humourous situations. For example, Pachelbel's Canon in D, and Ravel's Bolero all exhibit fairly large numbers of repeats, but most listeners do not find either of these pieces funny. In much post-tonal music, tonal (key) and harmonic (chord) progressions that may have been previously deemed to be improbable in earlier genres, are frequently invoked in practice.

While we can see a good number of Schickele's humour devices, we concede that musical humour cannot be reduced to simple musical features. There are aspects that may not be visible in the pitch and time structures of the music, such as the cultural context. Humour results from a complex combination of stimulants, and we do not yet have a robust way of automatically detecting musical humour.

References

[1] E. Chew. Towards A Mathematical Model of Tonality. PhD thesis, Massachusetts Institute of Technology, Cambridge, MA, 2000.

[2] E. Chew and A. R. J. François. Interactive multi-scale visualizations of tonal evolution in MuSA.RT Opus 2. Computers in Entertainment, 3(4):1-16, October, 2005.

[3] A. R. J. François. A hybrid architectural style for distributed parallel processing of generic data streams. In Proc. International Conference on Software Engineering, pages 367-376, Edinburgh, Scotland, UK, May 2004.

[4] D. Huron. Music-engendered laughter: An analysis of humor devices in PDQ Bach. In Proc. of the Intl. Conf. on Music Perception and Cognition, pages 93-95, 2004.

[5] P. Schickele. The Short-Tempered Clavier — Preludes and Fugues in All the Major and Minor Keys Except for the Really Hard Ones. Theodore Pressor Company, Bryn Mawr, PA 19010, S. 3.14159, easy as edition, 1807-1742?