A pianist friend of mine says that the 2-part Inventions are merely ‘steep hills’ but that the 3-part Sinfonias are ‘craggy mountains whose paths have lots of twists and turns’. Having lived with these pieces most of my life, I have to agree.” — Lee Ridgway, harpsichordist, BEMF 2011 Fringe Recital.
H arpsichordist Lee Ridgway performed all 15 of J.S. Bach’s 2-part Inventions and all 15 of the 3-part Sinfonias yesterday, in one of the ‘fringe’ recitals at the Boston Early Music Festival. He performed them in the sequence in which they originally appeared in W.F. Bach’s clavier-büchlein. His masterful and sensitive treatment of each provoked a number of reveries for me, for which I am grateful.
A mong these was a reflection on how the moment-to-moment agogic metric accents might be analyzed with mathematical and statistical signal processing and spectrum-analytic methods similar to those that have been applied over the past 20 years in cardiology, to understand heart rate variability (HRV) and develop predictive models of cardiac disorders. The pulse quickens; the pulse also slows! Quantitative details of small-scale dispersion of meter—and the abnormal, motoric diminution of HRV that occurs in stress and in disease states—can tell us so much! Just to see what interesting things may turn up, I begin with one of the simplest ‘variability’ measures—the root-mean-square standard deviation, RMSSD:
I look in the music theory literature and recent doctoral dissertations, and so far I am unable to find anybody who has pursued this sort of thing. If I am wrong, please email me or add a comment below.
O vernight, I download some MP3s of others’ performances of the 2-part Inventions and begin to run some analyses using the MATLAB signal processing toolbox software—the same modules that I use for analyzing digital electrocardiograms. I pick off beat-by-beat interbeat intervals in the left-hand part and the right-hand part. I exclude marked ritardando/accelerando bars; also exclude fermatas.
T here is more or less constant variation in articulation and timing... successive notes are crafted with varying durations—this is especially true on harpsichord more than other keyboard instruments, but it would be true as well for winds, voice, any instrument. The plot above is a composite across 2-part variations—a quick exploratory ‘look’ only; not what we would do for a proper analysis.
D etached releases ranging from ‘sharp’ ones to ‘lingering’ ones… this all shows up in the RMSSD and other time-domain variability measures. It also shows up in frequency-domain power-spectrum and other FFT- and wavelet-transform-based measures.
A nd, naturally, the variability and rhythmic power-spectrum measures change throughout the course of each piece. The power spectrum has ‘shoulders’ on it, on both the left (slower, longer IBI) and right (faster, shorter IBI) side of the median interbeat interval or rhythmic frequency. In principle, we would watch and measure the time-evolution of the power-spectrum from the beginning of a piece to the end of a piece—look at these evolutions or trajectories for different performers whose interpretations and styles differ. Then we would be better able to account objectively and quantitatively for how they do what they do!
L inkages across the bar-line are frequent, often involving small melodic voice-leading in one part (hand). These were particularly prominent in Ridgway’s accounts of the C-major, F-major, G-major, and C-minor 2-part variations. Beautiful, truly.
T hrough thoughtful, passionate application of agogic variations in small-scale timing, we get an acute sense of tension between (1) propulsion from ordinary and extraordinary accents in the metric frame and (2) propulsion from motivic and other phrase units. It is a major source of musical drama and beauty—not just in Bach but, I think, in all music. It was simply Ridgway’s fantastic playing yesterday that makes me think of these mathematical ways of explaining and understanding how it works.
R idgway is a solo organ and harpsichord performer, has performed for more than 40 years throughout North America and Europe. A native of Oklahoma, he received his Bachelor of Arts from the University of Oklahoma and Master of Arts from New England Conservatory of Music. Presently the organist and choir director at St. Chrysostom[s Episcopal Church in Quincy, MA, he is also Dean of the Boston Chapter of the American Guild of Organists. The instrument on which he performed yesterday at Emmanuel Church is one made by Boston’s Allan Winkler, a 2-manual adaptation of a 1716 design by Carl Conrad Fleischer… gorgeous sound.
B eyond their pedagogical applications, the Inventions and Sinfonias offer us wonderful, individual pieces of music… The similarities or contrasts between pieces in the same key; the [affective] characteristics of different keys; the characteristics of individual themes; … how the voices engage in dialogue or games of chase...” — Lee Ridgway, harpsichordist, BEMF 2011 Fringe Recital.
T he impetus for composing in specific musical forms may be partly extra-musical, connected with the function of the music in question. The fact that humans have two legs greatly influences the structure of dance, which in turn is responsible for the symmetrical forms of most dance music. The dialogue between priest and congregation in religious services is the functional background for the responsorial forms in Gregorian chant. [And by analogy, the random, desultory, and deleterious functional patterns of illness may have motivated the forms developed by Michael Gardiner in ‘Course of the Symptom’. DSM.]” — Finn Egeland Hansen, p. 312.
P revious generations of musical scholars attributed [phrase structure schemata and evolution] to a spiritual life-cycle. They held that artistic forms shared periods of birth, growth, flowering, aging, sickness, and death because all living things share these periods.” — Robert Gjerdingen, Northwestern Univ, 'Formation and Deformation of Classic/Romantic Phrase Schemata', Music Theory Spectrum x.
F inally, a deep, scholarly accounting of the aesthetics of failure. Props to Caleb Kelly for laying bare the various histories of ‘malfunction’ as a compositional device. This book should be required reading for anyone working in electronic music today.” — Kim Cascone, composer and writer, jacket blurb for Caleb Kelly’s book, ‘Cracked Media: The Sound of Malfunction’.
I am deeply touched by the new Michael Gardiner composition, a 9-movement piece entitled ‘Course of the Symptom’ (link to CD and MP3s below). Maybe the reason why this music hits me so hard has something to do with my training as a doctor, and with the experiences of trying to help people who are very sick or dying during the years when I was working in hospice.
T hen I think, no, the music’s effect does not depend on having been conditioned by those experiences or that training. Anybody who is ‘primed’ by reading the title and the liner notes and by even one first-hand experience of life-threatening illness involving a friend or family member can hardly help but be affected.
B ut in just such a case as this, I am grateful for the ‘set-up’—grateful for the composer’s cues as to the context and imagery that motivated the process of composing and performing (and recording and engineering/post-processing). The hints do not diminish or constrain the subsequent hearing; instead, the hints enrich it.
T he thing that Michael Gardiner’s new composition most reminds me of is the poetry of Donald Hall’s memoir of the illness and death of his wife, Jane Kenyon—the tedium of prolonged periods of sickness and dying; the upwellings of hope, sometimes triggered by the flimsiest of new evidence; the fulminations and the “witless” love that refuses to acknowledge imminent loss—all of these seared in the pages of ‘Without’, unbidden layers upon layers, through which Hall’s voice persists and copes; the metrical irregularities of it and the malady (cancer) that was her adversary. Pain in general, and cancer pain in particular, brings a special emphasis on time and meter.
S usan Sontag’s writing does not have the rhythmic or poetical musicality of Hall’s, but some of the ideas are the same.
G ardiner’s composition is direct, honest. It leverages algorithmic procedures—including stochastic, aleatoric procedures—to override determinations made by human voluntary structures and by algorithmic serial structures, such as Gardiner’s deterministic intervals. The declamatory narrative of the casual human is overtaken or overridden by ‘the symptom’—a virtual organism that possesses an independence or autonomy that is distinct from its host’s body, like an infection or a cancer or an inherited disease that emerges in adulthood—overriding even one’s ability or will to reason, subsequently falling prey to self-delusions and scamsters who address the symptom with potions or ‘fields’.
S ystemic overrides in ‘Course of the Symptom’ are manifested in duration material. If you notate rhythmic durations as fractional values, denominators represent the number of units that divide a quarter note, i.e., beat-divisions. An eighth-note dividing a quarter-note into halves has a denominator of 2; an eighth-note triplet has a denominator of 3; and so forth. Numerators are factors given by serial and stochastic systems, which beat-divisions then distort. For example, a duration factor 12 strongly bears the influence of the beat-division applied to it. With a beat-division of 3, the duration (12/3) has a duration equivalent to four quarter-notes. With a more finely-granular beat-division such as 4, the duration (12/4) gives a shorter length, equivalent to three quarter-notes only.
A large factor can be applied to a small beat-division (12/6, equivalent to two quarter notes) and cause a shorter duration than a small factor applied to a large beat-division (5/2, equivalent to two-and-a-half quarter notes). Beat-division distortions impart rhythmic diversity, which Gardiner utilizes to lend extra dramatic tension within whatever base-duration series prevails in the piece.
C ourse of the Symptom’ explores schemata of music on different temporal/gestural scales—large-scale idioms analogous to sonata form, rondo form, etc.; small-scale idioms like voice-leading rhythmic motives, cadences, rules of counterpoint, etc.; intermediate-scale schemata—hypermeter; sequences; phrasing and compound phrases or segments—these are more indeterminate or unpredictable. Download the MP3s or listen to the CD in WindowsMediaPlayer with the ‘BarsAndWaves’ visualization display plug-in ‘on’. In the low-frequency range, you will see cues that are associated with rumble and other hypermeter structures that are not obvious when listening unless the volume is cranked way up. There are rhythmic and phrase-frequency ambiti in here, as well as melodic ambitus.
T he composition of music has evolved into an interactive process of directly sculpting sound morphologies on multiple time scales... [Vaggione’s] durations were, in general, very short. Silences of different lengths were placed between events. The density (or speed of succession) was very high: more than 20 events per second. This rate exceeds the limit of applicability of the Poisson law, which is valid to control sound distributions whose density are lower than 10–20 events per second. Beyond 20 events per second, one is no longer dealing with sounds as individual entities. However, the goal in building this structure by combining high density of sounds with highly contrasted parametric values was to create a texture showing a kind of kaleidoscopic ‘internal’ behavior.” — Curtis Roads, 2005.
T his ‘Course of the Symptom’ would make excellent film soundtrack, evoking concepts of time, memory, tradition, and expectation in music listeners/viewers. The musical rhetoric is aggressive, riveting—very realistically embodying features of serious chronic illness... phrase structure; illocutionary acts.
T he distorted, noisy digital synth sound intrudes upon and overrides analog atonal piano sound ... each of these are gestural ‘signs’ that stand for other concepts, such as pain and the processes of illness and the body’s responses to it. Gardiner’s post-processing involves extensive timbre/palette filtering with EQ. The piano gets infected by the electronics; the disease progresses through multiple tissues and organ-systems... contagion; metastasis.
I nitially, the abnormalities are intermittent, and intense anticipation through the silences and pianississimos predominates in the epoch surrounding the onset of the symptom... the patient (and family) hold doubts as to whether the abnormality is real, whether it will persist, etc. Everyone hopes that it will subside and go away. But it does not. The disease and its large-scale generators of noise and music persist. Gardiner’s digital audio workstation editing reveals itself as fundamental to composition and to performance...
I n ‘Location of the Symptom’, small-scale linear progressions draw attention to position and sequence. More locally, descending motions might be contra-structural to a deeper level ascending line. This would usually exclude melodic activity “in service of the fundamental line”, such as initial ascent or motion out of an inner voice; Schenkerians would have a field-day with this... A contra-structural directionality deflects Gardiner’s Urlinie away from the obligatory register (usually upwards in the electronics tracks). But ascending impulses turn out to be frequently misleading, adding dramatic tension as to what the next phase or the ultimate outcome of this insidious illness might be.
O r if you prefer, Leonard Meyer’s notions of implication/deflection could be applied to Gardiner’s complex noise/atonal/tonally-inflected musical language—the forms built up by the accretion of fragmentary utterances by the synth and by the piano, the personae of the movements’ two ‘characters’—the patient and the symptom-producing disease.
I f you utter “Is it time for my Actiq yet?” in your sick bed, the illocutionary force is that you are having breakthrough pain and desire pain relief, as distinct from your explicit locutionary act (a question about the existence of opiates in the nursing station medicine cabinet) and the perlocutionary act (causing somebody to administer you the pain med). The suffering piano does this beautifully, and we fear for its life. Gardiner’s EQ post-processed synth samples are themselves capable of illocutionary acts. The human pianist continues on his/her way, programmatically, deterministically, while, by contrast, the symptom machine becomes the dominant character...
A bout 30 minutes length, combining text, ambient sound of various sorts, sampled quotations from composed electro-acoustic music and possibly Schoenberg’s 6 Kleine Klavierstücke Op. 19? The piece embodies a dialectical balance between a number of polarities: speech/music, gesture/texture (e.g., Denis Smalley), linear time/multiply-directed time (e.g, Jonathan Kramer), and sick/well and male/female representations, a rich interplay of polarities with regard to timbral content and instrumentation.
T his is one brutal illness—a malady that gives no quarter to tenderness or recovery. A complex ‘patchwork’ of collocated elements and repetitions, the ‘Course of the Symptom’ invites a variety of listener-imagined meanings. Very convincing and more than a little ‘too close to home’ for clinicians and caregivers who tend to the needs of those with life-threatening illness. But clinicians and caregivers are the very ones who may benefit most from hearing this work. So, too, the participants and faculty in courses in Medical Humanities (see links below), for whom this recording may become an iconic element of the syllabus in years to come.
W e are reassured that the composition is not autobiographical, and we sincerely hope that Gardiner’s family members are all okay. At least at times of future health problems, from this music they know they can count on Michael’s empathetic and effective support...
[30-sec clip, Michael Gardiner, Course of the Symptom, ‘Character of the Symptom’, track4, 1.1MB MP3]
[30-sec clip, Michael Gardiner, Course of the Symptom, ‘Radiation of the Symptom’, track7, 1.1MB MP3]
[30-sec clip, Michael Gardiner, Course of the Symptom, ‘Course of the Symptom’, track9, 1.1MB MP3]
N ono’s work with electronic media revolved around spatial considerations and their acoustical effects. For instance, a sound approaching a listener rises in dynamics and fades as it passes. Its pitch level also rises and falls. By imitating the acoustic effects produced when a sound moves in relation to the perceiver, electronic instruments could simulate spatial motion. Actual spatial motion could also be achieved by having a signal travel across several acoustic sources. More importantly, a single electronic source could project several simultaneous movements quite clearly; multidimensionality required a large number of performers in comparison and created motion in several simultaneous dimensions much less audibly. Nono would refer to the spatially rendered music yielded by his electronic experiments as ‘il suono mobile’.” — Jeannie Ma. Guerrero, MTO, 2006, commenting on Luigi Nono’s ‘Il canto sospeso’ and later works.
I look in the music theory literature and recent doctoral dissertations, and so far I am unable to find anybody who has pursued this sort of thing. If I am wrong, please email me or add a comment below.
T here is more or less constant variation in articulation and timing... successive notes are crafted with varying durations—this is especially true on harpsichord more than other keyboard instruments, but it would be true as well for winds, voice, any instrument. The plot above is a composite across 2-part variations—a quick exploratory ‘look’ only; not what we would do for a proper analysis.
A nd, naturally, the variability and rhythmic power-spectrum measures change throughout the course of each piece. The power spectrum has ‘shoulders’ on it, on both the left (slower, longer IBI) and right (faster, shorter IBI) side of the median interbeat interval or rhythmic frequency. In principle, we would watch and measure the time-evolution of the power-spectrum from the beginning of a piece to the end of a piece—look at these evolutions or trajectories for different performers whose interpretations and styles differ. Then we would be better able to account objectively and quantitatively for how they do what they do!
