The Loosening Role of Polyphony: Texture and Formal Functions in Mozart’s “Haydn” Quartets

This essay demonstrates that texture can act as a form-defining factor by focusing on one specific textural type: imitative polyphony. Mozart’s six quartets dedicated to Haydn illustrate this claim. Building on William Caplin’s form-functional theory and his distinction between tight-knit and loose organization, imitative texture is shown to serve two purposes: as a loosening device, and as a means of textural and phrase-structural contrast. To deepen our understanding of polyphony’s formal and expressive roles, two new concepts are proposed: contrast pair and imitative presentation. The contrast-pair principle is then explored in select Viennese quartets by Mozart’s contemporaries.

Simulating the vertical transition of soil textural layers in north-western China with a Markov chain model

The heterogeneity of textures in soil profiles is important for quantifying the movement of water and solutes through soil. Soil-profile textures to a depth of 300 cm were investigated at 100 sites in a 100-km2 area in the central region of the Heihe River system, where oases coexist with widespread deserts and wetland. The probability distribution of textural-layer thickness was quantified. The vertical transition of the soil textural layers was characterised by a Markov chain–log-normal distribution (MC-LN) model based on the probability of one textural type transitioning to another. Nine types of textural layers were observed: sand, loamy sand, sandy loam, silt loam, loam, clay loam, silty clay loam, silty clay, and clay. Sand was the most frequent in the profiles, whereas silt loam and clay were rare. The layers of sand and silty clay were relatively thick, and the layers of loam and clay were relatively thin. The coefficients of variation ranged from 36–87%, indicating moderate variation in the layer thickness of each textural type. The soil profile was characterised as a log-normal distribution. A χ2 test verified the Markov characteristic and the stability of the vertical change of soil textural layers. Realisations of the soil textural profiles were generated by the MC-LN model. A Monte Carlo simulation indicated that the simulated mean layer thickness of each textural type agreed well with the corresponding field observations. Element values of the transition probability matrix of the textural layers simulated by the MC-LN model deviated <12.6% from the measured values, excluding the data from the layers of clay and silt loam. The main combinations of upper to lower textural layers in the study area were loamy sand and sand (or sandy loam), sandy loam and sand (or loamy sand and loam), loam and clay loam, clay loam (or silty clay) and silty clay loam, and silty clay loam and silty clay. The MC-LN model was able to accurately quantify the vertical changes of textures in the soil profiles. This study will aid in quantification of water and solute transport in soils with vertical heterogeneity of soil textural layers.