Application of High T/High P Rock Mechanics to the Problem of Extraction of Granitic Magma from its Protolith

The mechanical deformation behaviour of a partially molten granitic protolith is investigated, implications towards a mechanism for extraction of low melt percentages («30 %) are mathematically explored. For this purpose a series of experiments on Westerly granite (with no added water) are presented in which samples were heated to temperatures between 800 and 1200 °C, at a confining pressure of 250 MPa. Samples were uniaxially deformed to study the effects of constant strain-rate (4 * 10-4 to 2 * 10-7 s-1), creep and stress relaxation tests on the mechanical behaviour. The volumetric percentage of melt (Φ) in samples ranged from 3 % at 800 °C to 77 % a t 1200 °C at heating times between 2.5 and 170 hours. However, none of the samples attained chemical equilibrium, due to the short duration of tests. An equilibrium melt percentage was also not reached. Over this temperature interval the supported strength decreased from 500 MPa to less than 1 MPa (at a constant strain rate of 8 * 10-5 s-1) monotonically. No step-like drop in strength, corresponding to a rheological critical melt percentage (van der Molen & Paterson 1979) was observed. A preliminary flow law for the partially molten rock was obtained to allow extrapolation to lower strain-rates. The viscosity of the melt was estimated at 950 and 1000 °C from distances it could be made to permeate into porous sand under a known pressure gradient. Melt distribution in static tests indicated a very low wetting angle (< 5°) which results in high melt contiguity even at low melt percentages along grain boundaries. Under all conditions, the solid phases deformed by brittle fracture only. Samples with 3 shear enhanced compaction of melt filled voids by analogy with uniaxial compaction of porous sands. In samples with Φ > 45 % grains were carried about passively in the flowing liquid. A simple mathematical model is erected to describe a two stage process of extracting low volume percentage, granitic melt from its partially molten protolith with the aid of non-hydrostatic stress. Shear-enhanced compaction drives melt from the protolith into a series of interconnected melt-filled veins, whereupon porous flow through the high-permeability vein network allows rapid drainage of melt to higher crustal levels. Modeling suggests that melt extraction, with Φ11 Pas, is possible within geologically realistic time periods (10 Ma)

Hearing the Tonality in Microtonality

In the late 1970s and 1980s, composer-pianist Easley Blackwood wrote a series of microtonal compositions exploring the tonal and modal behavior of a dozen non–twelve-tone equal temperaments, ranging from 13 to 24 tones per octave. This dissertation investigates a central paradox of Blackwood’s microtonal music: that despite being full of intervals most Western listeners have never heard before, it still seems to “make sense” in nontrivial ways. Much of this has to do with the music’s idiosyncratic approach to tonality, which I define as a regime of culturally conditioned expectations that guides one’s attentional processing of music’s gravitational qualities over time. More specifically, Blackwood configures each tuning’s unfamiliar elements in ways that correspond to certain schematic expectations Western listeners tend to have about how tonal music “works.” This is why it is still possible to hear the forest of tonality in this music, so to speak, despite the odd-sounding trees that comprise it. Because of its paradoxical blend of expectational conformance and expectational noncompliance, Blackwood’s microtonal music makes for a useful tool to snap most Western-enculturated listeners out of their ingrained modes of musical processing and reveal certain things about tonality that are often taken for granted. Accordingly, just as Blackwood writes conventional-sounding music in unconventional tunings, this dissertation rethinks several familiar music-theoretic terms and concepts through the defamiliarizing lens of microtonality. I use Blackwood’s microtonal music as a prism to shine a light on traditional theories of tonality, scale degrees, consonance and dissonance, and harmonic function, arguing that many of these theories rely on assumptions that are tacitly tied to twelve-tone equal temperament and common-practice major/minor music. By unhooking these terms and concepts from any one specific tuning or historical period, I build up a set of analytical tools that can allow one to engage more productively with the many modalities of tonality typically heard on a daily basis today. This dissertation proceeds in six chapters. The four interior chapters each center on one of the terms and concepts mentioned above: scale degrees (Chapter 2), consonance and dissonance (Chapter 3), harmonic function (Chapter 4), and tonality (Chapter 5). In Chapter 2, I propose a system for labeling scale degrees that can provide more nuance and flexibility when reckoning with music in any diatonic mode (and in any tuning). In Chapter 3, I advance an account of consonance and dissonance as expectational phenomena (rather than purely psychoacoustic ones), and I consider the ways that non-pitched elements such as meter and notation can act as “consonating” and/or “dissonating” forces. In Chapter 4, I characterize harmonic function as arising from the interaction of generic scalar position and metrical position, and I devise a system for labeling harmonic functions that is better attuned to affective differences across the diatonic modes. In Chapter 5, I synthesize these building blocks into a conception of fuzzy heptatonic diatonic tonality that links together not only all of Blackwood’s microtonal compositions but also more familiar musics that use a twelve-tone octave, from Euroclassical to popular styles. The outer chapters are less explicitly music-analytical in focus. Chapter 1 introduces readers to Blackwood’s compositional approach and notational system, considers the question of his intended audience, and discusses the ways that enculturation mediates the cognition of microtonality (and of unfamiliar music more generally). Chapter 6 draws upon archival documents to paint a more detailed picture of who Blackwood was as a person and how his idiosyncratic worldview colors his approach to composition, scholarship, and interpersonal interaction. While my nominal focus in these six chapters is Blackwood’s microtonal music, the repertorial purview of my project is far broader. One of my guiding claims throughout is that attending more closely to the paradoxes and contradictions of Blackwood’s microtonality can help one better understand the musics they are accustomed to hearing. For this reason, I frequently compare moments in Blackwood’s microtonal music to ones in more familiar styles to highlight unexpected analogies and point up common concerns. Sharing space with Blackwood in the pages that follow are Anita Baker, Ornette Coleman, Claude Debussy, and Richard Rodgers, among others—not to mention music from Curb Your Enthusiasm, Fortnite, Sesame Street, and Star Wars. Ultimately, this project is a testament to the value of stepping outside of one’s musical comfort zone. For not only can this reveal certain things about that comfort zone that would not be apparent otherwise, but it can also help one think with greater nuance, precision, and (self-)awareness when “stepping back in” to reflect upon the music they know and love