Twelve-tone Serialism: Exploring the Works of Anton Webern

Mathematics and Music are related and intertwined, and the invention of serialism in the 20th century highlights this fact. Serialism is a technique of music composition that uses mathematics to structure different elements of music, such as pitch and rhythm. For hundreds of years, music all over the Western world was tonal, which means there is a hierarchy of some pitches being more important than others. Serialism is a form of atonality, which is the composition of music that attempts to use all twelve pitch-classes equally. I examine twelve-tone serialism, which was created by Arnold Schoenberg and developed by his students Alban Berg and Anton Webern. This form utilizes a row, which is an ordering of the twelve pitch classes that can be transformed in various ways and serves as the thematic material for the entire piece. In particular, I analyzed Webern’s Variations, Op. 27 to examine how he utilized twelve-tone serialism

Emergency Conservation on Indian Lands

The commercial forests on Indian reservations within the United States cover approximately 6,500,000 acres. Over 5,000,000 acres may be classed as woodland because of a growth thereon of pinion, juniper and other non-commercial species. Nearly 40,000,000 acres are classed as being primarily grazing lands. While the amount of forest and grazing areas comprises but a small percentage of the lands of such classification in the nation, such land is o£ great economic importance and forms a substantial portion of the total area within such States as Arizona, New Mexico, Oklahoma and South Dakota

Indiana’s Malpractice System: No-Fault by Accident?

Indiana\u27s medical malpractice tort and insurance reforms were studied. The analysis showed that relatively subtle administrative arrangements for the management of claims at the state level may influence whether claimants are treated fairly by a system that is tightly structured to control claim severity and thus the price and availability of malpractice insurance for providers

Slow roll in simple non-canonical inflation

We consider inflation using a class of non-canonical Lagrangians for which the modification to the kinetic term depends on the field, but not its derivatives. We generalize the standard Hubble slow roll expansion to the non-canonical case and derive expressions for observables in terms of the generalized slow roll parameters. We apply the general results to the illustrative case of ``Slinky'' inflation, which has a simple, exactly solvable, non-canonical representation. However, when transformed into a canonical basis, Slinky inflation consists of a field oscillating on a multi-valued potential. We calculate the power spectrum of curvature perturbations for Slinky inflation directly in the non-canonical basis, and show that the spectrum is approximately a power law on large scales, with a ``blue'' power spectrum. On small scales, the power spectrum exhibits strong oscillatory behavior. This is an example of a model in which the widely used solution of Garriga and Mukhanov gives the wrong answer for the power spectrum.Comment: 9 pages, LaTeX, four figures. (V2: minor changes to text. Version submitted to JCAP.

Damping of Electron Density Structures and Implications for Interstellar Scintillation

The forms of electron density structures in kinetic Alfven wave turbulence are studied in connection with scintillation. The focus is on small scales $L \sim 10^8-10^{10}$ cm where the Kinetic Alfv\'en wave (KAW) regime is active in the interstellar medium. MHD turbulence converts to a KAW cascade, starting at 10 times the ion gyroradius and continuing to smaller scales. These scales are inferred to dominate scintillation in the theory of Boldyrev et al. From numerical solutions of a decaying kinetic Alfv\'en wave turbulence model, structure morphology reveals two types of localized structures, filaments and sheets, and shows that they arise in different regimes of resistive and diffusive damping. Minimal resistive damping yields localized current filaments that form out of Gaussian-distributed initial conditions. When resistive damping is large relative to diffusive damping, sheet-like structures form. In the filamentary regime, each filament is associated with a non-localized magnetic and density structure, circularly symmetric in cross section. Density and magnetic fields have Gaussian statistics (as inferred from Gaussian-valued kurtosis) while density gradients are strongly non-Gaussian, more so than current. This enhancement of non-Gaussian statistics in a derivative field is expected since gradient operations enhance small-scale fluctuations. The enhancement of density gradient kurtosis over current kurtosis is not obvious, yet it suggests that modest fluctuation levels in electron density may yield large scintillation events during pulsar signal propagation in the interstellar medium. In the sheet regime the same statistical observations hold, despite the absence of localized filamentary structures. Probability density functions are constructed from statistical ensembles in both regimes, showing clear formation of long, highly non-Gaussian tails