![]() ![]() Although attaching short sugar oligomers as branch-points to linear polysaccharides does increase their rigidity as the molecules are extended, this increases the molecular weight a lot. Starches and other biopolymers are like this. ![]() At low concentrations where there is minimal interaction between molecules, the viscosity may be about the same as water. In dilute solutions this relationship depends on the microscopic volume ‘swept out’ by the molecules as they tumble in the solution (their ‘hydrodynamic volume’). Linear and nearly-linear polymer liquids are predictable in the relationship of their viscosity to their structure and the polymer molecules’ conformation. Liquefaction upon commencing the next movement amounts to a kind of psychic relief-resolution of a dramatic tension. The shaking stops at the fermatas between the movements in BWV 1052. The analogous thing happens in musicat least in tonal music of the 20th Century and earlier. They may liquefy on being shaken and then solidify when the shaking has stopped. Thixotropic liquids exhibit a time-dependent response to the shear strain rate over a longer period than that associated with the actual changes that occur in the shear strain rate. Rothstein said something that amounted to this, in one of his papers some years ago.Īnd our psychological response to ritardandos and fermatas-the rubato of the harpsichord in BWV 1052, for example, juxtaposed as it is with the rhythmic consistency of the other parts-is empirically an apprehension of vortices and rhythmic slippage. For example, the idea of accelerating through an anacrustic motive is a prevalent interpretation of much baroque and nineteenth-century music, if and only if the motive itself is frictionless. But it seems empirically to be valid within some bounds. Sometimes music is like whipped cream-its viscosity is high enough to hold a “peak”? Maybe I am generalizing this idea of musical rheology further than I ought to do. The ‘relaxation time’ for viscoelastic effects in musical fluids can be similar to a nice latex paint. Sometimes music is less like blood and more like paint-with lots of reverb (or, equally well, with lots of minimalist composers’ written short-timescale recapitulations of motifs), it flows and creeps after the performer (the ‘paint brush’) has passed that motif, onward to the next measure. ![]() (I suppose the converse, shear-thickening, is also possible in music-although it must be rare, just as rheopexy is rare in physical liquids.) There is shear-thinning or thixotropy in BWV 1052. Why are there musician-mathematicians and musician-EEs but no musician-ChemEs? But I think that no physicist or chemical engineer who specializes in rheology of complex liquids has ever done so-or, at least, has never done so and written about it. I realize that others have thought some of these thoughts before: William Rothstein comes to mind. (The pulsatility of attractive compositions and performers’ interpretations is also subconsciously informed by the pulsatility of our hearts, our circulation?) A fancy word for the study of this sort of flow is ‘non-Newtonian rheology’. Yes, music is a liquid-it flows like blood. Layers in that sonic emulsion have different viscosities and velocities and shear rates, and the layers “slip” against each other, just as disparate layers in a physical liquid would slip. Individual musical parts embody shear contours and rhythmic isopleths in the compositionin the larger shear field that is comprised of the union of all of the parts. It varies with tempo, with rhythmic velocity in individual parts, and with the biophysical possibilities and limitations of the interactions between the human flesh and the real-world instrument/voice. And that friction or viscosity is not constant. As a ‘liquid’, music has internal friction. It has viscosity: the rhythmic rate at which the parts unfold and the rate at which rhythmic change can occur are not infinite. And its physics closely resembles the physics of complex fluids in general. It is an ‘emulsion’ of the parts or voices that comprise it. Basically, polyphonic music is an emulsion. And since any physical medium contains some friction, the rate of acceleration will not be constant, either it will increase until the effect of friction is largely overcome.” Downward slides are not constant in speed they accelerate. Since human beings experience gravity as a downward pull, is readily felt as a downward fall or slide to the bottom of something. W here a rhythm is heard as anacrustic, moving from upbeat to downbeat, the downbeat exerts a kind of gravitational force, attracting notes of the upbeat to it. ![]()
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