Showing posts with label orality. Show all posts
Showing posts with label orality. Show all posts

Monday, May 26, 2008

Tempi and Saliency: Psychophysiology, or Why Deceptive Cadences Are Not Always Deceptive

Sloboda book
W  e do not doubt that attention, recurrent computations, and complexity are important aspects to understand consciousness. However, we propose that these aspects are often trivially necessary rather than sufficient. For example, often it is assumed that consciousness emerges not before several hundreds milliseconds after stimulus onset. Hence, given the short time constants of membranes of neurons, recurrent connections are obviously necessary to store and process the stimulus before consciousness is reached. Complexity is for sure of primary importance for consciousness because networks with the same number of neurons can create trivial as well as complex behavior depending on their connectivity. Therefore, the important question is which kind of connectivity or which exact degree of complexity, determined with which mathematical norm, is sufficient for consciousness ...”
  —  Michael Herzog (Laboratory of Psychophysics, Lausanne), Michael Esfeld (Dept of Philosophy, Univ Lausanne), and Wulfram Gerstner (Computer Sciences and Brain-Mind Institut, Ecole Polytechnique Federale de Lausanne), Neural Networks 2007.
This is a quick post-script on the topic of the previous CMT post, about psychophysiology of modality and tempi.

It turns out that Tibor Bosse and collaborators at the Vrije University in Amsterdam have recently been developing mathematical models of attention, mostly for military applications. Some of these models (and the differential equations underlying them) resemble hydrodynamic models used in cardiovascular physiology (‘windkessel’ models; in German, windkessel means elastic reservoir) and in functional magnetic resonance imaging (fMRI).

3-element windkessel electrical model
The effect of stimulus rate and its interaction with stimulus type on brain activity during the visual or acoustic stimulus has been investigated using fMRI. Different brain regions show differential responses as a function of time and as a function of the ‘tempo’ or stimulus rate. These results differentiate functionally specific responses in rate-dependent and rate-independent areas.

4-element windkessel electrical model, with inductance-inertance element
The best approach to the dynamics, though, is probably not a ‘lumped-parameter’ analytical one, like simple windkessel models. Instead, nonlinear wave-front propagation models (Stefan moving-boundary differential-equations) or stochastic network representations may be more realistic as mathematical formalisms. An intermediate approach, such as mathematical approaches used to solve equations for liquid flow through porous media (like aquifers), may be useful, to represent the mesh-like connections and multi-path propagation of signals related to our brains’ perception of musical suspense and resolution (cadences). Have a look at Herzog’s and colleagues’ paper in the recent special issue of the journal Neural Networks and at Tibor Bosse’s papers for a glimpse of how feasible such a quantitative cognitive modeling project is these days.

The results of fMRI (and, presumably, of mathematical modeling of the rate-dependent effects) may enable us to better understand the inter-relationships between tempi and our apprehending meaning in music. For example, so-called ‘deceptive cadences’ to vi (or VI in the minor key) and similar progressions are normally treated in a time-independent way, as a prolongation of the dominant. But in some instances it is better understood as prolonging the tonic, through I-vi. Understanding it in that way, though, depends not only on the context but also on the tempo. In general, the second alternative only if the vi is a middleground harmony or key region and the tempo is relatively slow. Otherwise, we choose the first way as more compelling. The underlying idea of the expansion of the V is that tension in the dominant is not resolved by the deceptive move to vi, but actually heightened; it is only when the true tonic arrives that the tension is removed. But if the tempo is sufficiently slow, the mind anticipates everything. The mind calculates and re-calculates and gauges and re-gauges all the possibilities. The deceptive cadence becomes instead a meta-commentary on irony itself.

Haydn Sonata Deceptive Cadence Example
In Five Graphic Music Analyses, Schenker showed that the Haydn Sonata analysis includes an extended prolongation of vi within the V that is the underlying harmony of the entire development (see the bass of the top system for the V; see mm. 81-111 of the other levels for the vi, which changes to VI (as V/ii) near the end of the passage).

By definition, a deceptive cadence is any phrase the ends in a way that is different from the anticipated outcome. Deceptive cadences can be disruptive, creating ‘Wow !’ moments in music. Usually, deceptive cadences require a melodic line and an accompaniment. A cadence is deceptive only if the melody ends up on the proper note to end the phrase, but the accompaniment contains unexpected harmony underneath. For example, if your song is in C-Major, you might expect the phrase to end up on a C Major chord, with the melody playing a ‘C’. If, though, the melody ends up on a ‘C’, but the harmony is an A-Minor chord, then this is an unexpected harmony and therefore a deceptive cadence.

Deceptive cadences are an example of how composers blur one phrase into the next. In a deceptive cadence, the melody is finishing off the phrase, while the harmony/accompaniment has already moved ahead, to the beginning of the next phrase. But if the tempo is slow enough, the synapses have had time to caucus with each other and anticipate everything. The ‘Wow!’ is of a totally different type. And the blurrings are no longer blurrings at all: they become meta-commentaries on what transitions are about, and why.

Cadwallader-Gagne book; Mozart (K. 457) I, mm. 46-52
In Mozart’s piano sonata (K. 457, I), there is the tonic of mm. 36-41 leading to II6 in m. 46, suggesting the imminent arrival of an authentic cadence. But instead we get a deceptive cadence in mm. 47-48 that delays resolution to the mediant key. The delaying effect resets our expectations and inhibits our reaching conclusions so quickly or relying on them so much once we’ve reached them. Cadwallader and Gagne’s book is excellent in its extensive coverage of effects like these. They don’t talk about Glenn Gould’s peculiar treatments of Mozart, though.

In Glenn Gould’s 1981 recording of Bach’s Goldberg Variations he takes a much slower tempo for the aria/sarabande that bookends the variations, or Variation 7, for example. In the recordings of Haydn’s six late piano sonatas (Hob. XVI: 42, 48-52) he plays the slow
movements very slowly, and with more interpretive inflection. His interpretive eccentricities came not from perversity but from a deep fascination: a love that demands a lingering largo; an experimenter's desire to find out nature’s secrets by way of stop-motion photography; an introspection that was selfless, timeless, otherworldly. To Gould, the slow, measured tempi were tools to reveal hidden profundities—in much the same way as they are to Simone Dinnerstein, for example.

In summary, my idea of ‘funnels’ or hydrodynamic windkessel mathematical models for representing the psychophysiology of generation of musical meaning is, evidently, not so rash or novel after all. True, nobody has yet applied these techniques with fMRI and musical stimuli, in the way that Bosse and others have done with visual stimuli for naval and aviation psychophysiology. But the maths and experimental methods are today up to such a task. Cheers!

Dayan-Abbott book

Parasuraman book


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Friday, May 23, 2008

Josquin’s Modality, ‘Meaning’ Funnels, Modal ‘Budgets’

Josquin portrait, © Naxos
A  lthough Josquin’s decision to repeat the opening words of the psalm after each verse owes a debt to Savaronola, the idea of making one of the tenor voices sing a motto melody during each of those repeats is entirely his own. No inflexible grid of durations is called for here. Instead, the tenor bides his time until the remaining four voices reach the end of a verse, then joins them in singing the refrain... The spareness of texture that results, together with the sober parlando of the word-setting, the dark minor modality, and the sheer length of the piece all contribute to the monumental gravity of the work.”
  —  Richard Sherr, Josquin Companion, p. 295.
R  ather than ‘proximity’ of modal theory and practice, I believe we should speak of ‘coincidence’ of two kinds of discourse (textual and musical) about the modes, acknowledging their closely-related, but not identical, manifestations... [The history of polyphonic modality] is a double discourse on the modes, because of teh two (principal) media involved, music and language. The term ‘discourse’, used here in a loosely Foucauldian manner, emphasizes the interaction between thought and language, and especially the role of language in the formation of thought. Further, this expression draws attention to the dynamics and the relative instability which polyphonic modality demonstrated during its history, while at the same time suggesting a way of ordering the variety of views.”
  —  Frans Wiering, Language of the Modes, p. 21.
T  he emergence of Renaissance polyphony from medieval modality appears to be one example of a culminating moment in which musical forms and textures responded ideally to their tonal basis. The simple grandeur of major and minor modes delicately inflected with musica ficta perfectly suits the project of floating and coordinating independent lines into a transparent and wholly absorbing unity. Surely the brains of Josquin’s listeners were inwardly delighted—if we permit ourselves to imagine that human brains have some separate, inner consciousness unavailable to the ebb and flow of surface awareness.”
  —  Alan Fletcher, Gramophone, Music and Neuroscience blog.
Sometimes, don’t you wish more composers were music theorists and vice versa? It just seems that too often music theory constructs analyses that neglect the improvisatory nature of much of composing and presumes that the as-delivered scores (or intermediate sketches and other documents) accurately reveal original composerly intentions, convictions, certainties. In reality, there is far more ambiguity and ad hoc innovation than most would care to admit, much less analyze. The notion is maybe a not uncommon one, but I was reminded of it again recently when listening to the new Tallis Scholars recording of some Josquin des Prez pieces.

Yes, we have fugal imitation at the octave, fifth, and fourth. Yes, each phrase of text is assigned a musical subject that is then taken up in turn by each of the voices. Yes, after finishing the subject each voice either drops out or continues in free counterpoint. Josquin avoids cadences while keeping the words clear. There are characteristic patterns that suggest ‘certainties’ and a ‘method’ to his modality.

But there are also passages whose modality is unclear or unstable—these are not in any way ‘defects’ in the writing but are instead apparently deliberate, composerly locutions meant to express semantic tension or uncertainty by means of modal instability. Later the same night that I listened to the Tallis Scholars CD, I dreamt about the pieces again and imagined each piece as a bottle that could contain a finite amount of liquid ‘meaning’ that was poured into the bottle through a funnel, liquid flowing into the bottle at varying rates from the beginning of the piece to its tidy end. The capacity of the funnel is finite, the maximum flow-rate through it is finite, and an aesthetically commendable, coherent composition ought not to overflow the funnel or over- or under-fill the bottle. While the flow is proceeding (while the music is being performed), we perceive the current state of the liquid in each compartment and understand/gauge the history of the flows (into the funnel; into the bottle) that have already occurred, and we intuitively anticipate the contingent future statuses that the present flow rates suggest are plausible.

Liquid analogy for ‘modal budget’ dynamics in musical compositions
There are ‘budgets’ for the volumes and flow-rates in the physical liquid situation. And, as I want to suggest to you now, there are composerly ‘budgets’ for linguistic modality, too. If you construct your polyphonic piece in such a way that the semantic and cognitive ‘budgets’ are exceeded or mis-spent—either in terms of absolute amounts or dynamic rates of change in modality—you will get an aesthetically bad result. True for Renaissance music and everything subsequently. To my knowledge, there is no physics ‘hydrodynamics’ theory of modality in music. Maybe there should be such a thing!

Incidentally, Cristal Judd was concerned (about 25 years ago) with biased perspectives that arise when tonal analytical methods are applied to pre-Baroque compositions. She proposed a new approach that alternately considers text and mode and synthesizes the findings from both perspectives. Before Christal, most analysts believed that the text should determine every dimension of the musical form. Such a view is reinforced by centuries of tradition, of people insisting that printers put the text syllables precisely under the corresponding notes, never allowing a rest to interrupt a word or meme, allowing full cadences only at significant textual breaks, and so on. Text was king.

But in Josquin we hear what seem to be ‘evaded cadences’: voices give the impression they are about to cadence (usually with a suspension), but turn instead in a different direction. We have multiple ambiguous, tension-creating suspensions, and strategically placed dissonances.

Theoretical linguists would call this sort of thing ‘grammaticalization of evidentiality’, a fancy but evocative term. Makes me think that music theory people ought to read more of the theoretical linguistics journals and try applying to music some of the methods that have been producing results in linguistics. Interdisciplinary cross-pollination!

So, when a predominantly Lydian piece shows tendencies in a prevailing Phrygian mode, and a predominantly Phrygian piece from a ‘neighboring region’ shows tendencies toward Lydian melodies, those differences are maybe evidence of ‘autochthonous originality’, as Schoenberg put it (in ‘Symphonien aus Voksliedern’ in Stil und Gedanke: Aufsatze zur Musik, ed. I. Vojtech, 1976, p. 134). [See! Fancy but evocative! Linguists rampant! Or Schoenberg as interdisciplinary wolf in sheep’s clothing.]

Modes
A u·toch·tho·ny: Pathology- found in the part of the body in which it originates, as a cancerous lesion; found in a locality in which it originates, as an infectious disease.
Psychology- of or pertaining to ideas that arise independently of the individual’s own train of thought and seem instead to have some alien or external agency as their source.
Sociology- aboriginal, indigenous.”
Apropos of these topics, Otsuka and co-workers at the Center for Evolutionary Cognitive Sciences at the University of Tokyo published an interesting neurophysiology paper this winter on cognition of tonal and modal structure in Western music. They found that tonic chords were judged to be ‘stable’, whereas the submediant chords were judged to be ‘unstable’. EEG dipole moments of N1m responses originating in the auditory cortex in the brain were larger in the left hemisphere for submediant chords than for tonic chords preceded by major-key tonal passages but not when tonic chords were preceded by minor-mode material. No difference in the N1m or P2m moment was found for chords presented without preceding (‘meaning’ funnel-filling; ‘meaning’ bottle-filling—) scales.

These results suggest ‘priming’ effects of tonal schemata interacting with contextual modality, on neural activity of the auditory cortex as well as on perceptual stability of the chords’ semantics. Otsuka and colleagues inferred that modulating the auditory cortical activity is associated with listeners’ attention actions that are induced by the tonal instability and modality shifts, and these are especially characteristic of submediant chords. The instability is temporally local within a piece, and is not necessarily idiomatic or ‘local’ to a composer or to the composer’s previous or characteristic solutions to compositional problems. The composer continues to discover and improvise and compromise until the day she/he stops composing. The composer continues to speculate or engage in conjectural musical statements, as part of the compositions’ gestural and locutionary plans, throughout the composer’s active composing life.

On this point, it’s interesting to note that, among Western languages, Basque is uniquely rich in grammatical ‘hearsay evidentials’. Reported evidence is in Basque marked with the particle ‘omen’. Omen-ous expressions appear before the tensed verb, as a sort of ‘reserved’ position in Basque syntax. Following descriptive and phrase-structure grammar theory, linguists remark on Basque modal/aspectual particles that occur in the same space, such as ‘bide’ (‘apparently’) and ‘ote’ (‘dubiously’). When ‘hearsay evidentials’ are carried by the text or by the mode, the funnel is filling; we are anticipating further evidence that will either corroborate or discorroborate our impressions so far—that will diminish the head of pressure that is building in the filling funnel. The continued flow—the discharge, tidy or otherwise, of evidence and meaning into the container, into the composition, into the performance—will either resolve the tension, or leave a residual ambiguity/poignancy at the end. Susan McClary has shown how 16th-Century composers used modality to create dynamic representations of subjective states, such as pleasure and pain. To me, it seems implausible that earlier composers did not have notions of subjectivity or 'interiority'. McClary and Korsyn and others probably agree with this; the performance of subjectivity just happened to become a dominant or explicit aim, beginning with Josquin. Stephen Greenblatt considered these things in the realm of Renaissance English literature. The era when representation of interiority was a time that held 'inwardness' as inherently ambiguous or conflicted, not as something simple or coherent. Our modern conception of modes takes the chromatic scale as a premise, and tends to view the modes as 'subsets' of this background system (the degrees of which are not so readily differentiated by intervallic properties) and views the intervallic qualities as characteristics of each of the modes. This biases our understanding of modality; the premise prejudices the interpretation. And this is what I am hoping might change in the future.

E  very good story is of course both a picture and an idea—and the more they are interfused, the better the [narrative/discursive] problem is solved.”
  —  Henry James, Partial Portraits: Guy de Maupassant, 1888.
Wiering book
So what we have is this: Modality in linguistics is the expression of the speaker’s attitude regarding evaluation of a fact or an hypothesis or a real or ‘hearsay’ circumstance in positive-negative terms (evaluative attitude) or as evaluation of the probability of a fact or circumstance (validative attitude). To-date in music theory, modality has been variously but pretty narrowly conceived. But if we hold existing music theory definitions of ‘modality’ in abeyance, we allow that modality in music analysis could in the future come to have a number of correspondences with linguists’ conceptions, and might leverage some of the analytical methods that have been found useful in linquistic analysis of modal structures. The links below will be useful to those of you who are interested in this stuff.

Judd book

B  y resisting the reductive, predictive, and generalizing tendency of ‘immanentist’ music analysis, imaginative close listening can encourage a social consciousness not wholly absorbed by what Georg Lukacs calls the 'reification' of capitalist rationality. In other words, imagination can supplement the gap upon which social conventions are founded and thus contribute to the devolution of power. For instance, if an analysis of Beethoven’s Violin Concerto is startled by the radical peculiarity of the D#s that interrupt the respectable tonal behavior of the first movement in mm. 10 and 12 ... then Beethoven’s organic connection to Machaut, Josquin, Monteverdi, and Bach cannot be taken with too much confidence.”
  —  Martin Scherzinger, in Andrew Dell’Antonio’s ‘Beyond Structural Listening’, p. 274.
I  mages of pleasure/pain evoke a quality of timeless, sustained hovering, produced by devices such as ostinato patterns or modal ambiguity. Images of desire, on the other hand, derive from the longing for the cadence.”
  —  Kevin Korsyn, Decentering Music, p. 19.
R  eminiscent of medieval music, marked by relatively noncoercive modal techniques that delight in the present moment.”
  —  Susan McClary, Feminine Endings, p. 119.
I  nasmuch as these pieces highlight the unstable status of the Self, they produce images of ‘modal’—that is, always provisional—subjectivities, which is why they do not translate easily into the imperative sense of ‘centered’ subjectivity that grounds 18th-Century tonality.”
  —  Susan McClary, Modal Subjectivities, p. 16.
I  have thought formerly that a playing with sounds could not be called ‘music’ if it wasn't based on a system of some kind. I am less sure of that today. Yet I think we should not jump to conclusions on this complex question. Usually, music theories have names for units (which may not always be pitches). Modality can be understood as a [probably nonsystematic, nondeterministic, improvisatory— ] discourse on the organization and the hierarchies of discrete pitches [and human experiences and subjectivity].”
  —  Nicolas Meeus, Sorbonne, 2004.
McClary book


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