Fourier phase and pitch-class sum

Music theorists have proposed two very different geometric models of musical objects, one based on voice leading and the other based on the Fourier transform. On the surface these models are completely different, but they converge in special cases, including many geometries that are of particular analytical interest.Accepted manuscrip

Tonal prisms: iterated quantization in chromatic tonality and Ravel's 'Ondine'

The mathematics of second-order maximal evenness has far-reaching potential for application in music analysis. One of its assets is its foundation in an inherently continuous conception of pitch, a feature it shares with voice-leading geometries. This paper reformulates second-order maximal evenness as iterated quantization in voice-leading spaces, discusses the implications of viewing diatonic triads as second-order maximally even sets for the understanding of nineteenth-century modulatory schemes, and applies a second-order maximally even derivation of acoustic collections in an in-depth analysis of Ravel's ‘Ondine’. In the interaction between these two very different applications, the paper generalizes the concepts and analytical methods associated with iterated quantization and also pursues a broader argument about the mutual dependence of mathematical music theory and music analysis.Accepted manuscrip

Decontextualizing contextual inversion

Contextual inversion, introduced as an analytical tool by David Lewin, is a concept of wide reach and value in music theory and analysis, at the root of neo-Riemannian theory as well as serial theory, and useful for a range of analytical applications. A shortcoming of contextual inversion as it is currently understood, however, is, as implied by the name, that the transformation has to be defined anew for each application. This is potentially a virtue, requiring the analyst to invest the transformational system with meaning in order to construct it in the first place. However, there are certainly instances where new transformational systems are continually redefined for essentially the same purposes. This paper explores some of the most common theoretical bases for contextual inversion groups and considers possible definitions of inversion operators that can apply across set class types, effectively decontextualizing contextual inversions.Accepted manuscrip

Foliar Application of N and Fe to Kentucky Bluegrass

The goal of the professional lawn care industry is to provide the homeowner with a dark green weed-free lawn. Members of this industry are interested in techniques to enhance the color of a turfgrass stand in lieu of excessive N fertilization. The purpose of this research was to evaluate the use of foliar applications of Fe alone or in combination with N on the color response of Kentucky bluegrass (Poa pratensis L.). Iron sulfate or an iron chelate was applied at the rate of 1.1, 2.2, or 4.5 kg Fe ha–1 in combination with either 0, 25, or 49 kg N ha–1 to a mixed ‘Columbia’/‘Touchdown’ Kentucky bluegrass turf growing on a Catlin silt loam (fine-silty, mixed, mesic Typic Argiudoll). Color ratings and clipping weights were determined on a weekly basis until treatment effects were no longer significant. In a separate experiment, both sources of Fe were applied at rates of 1.1 to 72.4 kg Fe ha–1 to Kentucky bluegrass to evaluate phytotoxicity. The color enhancement due to Fe applications without N lasted from several weeks to several months depending on the weather following application. Use of Fe during cool wet periods enhanced turf color for only 2 to 3 weeks and therefore, was considered of limited value. Iron applications during cool dry periods enhanced turf color for several months. The treatment of 2.2 kg ha–1 of Fe from iron chelate was judged to be the most effective Fe treatment because the color enhancement was usually equal to that provided by a 4.5 kg rate of either source but it did not result in any discoloration as was found with the 4.5 kg rate. Combining Fe with the 25 kg ha–1 rate of N resulted in color enhancement equal to that caused by applying 49 kg ha–1 of N alone. The results of the study indicate that combining Fe with N can result in acceptable turfgrass color with lower rates of N. No permanent damage was caused to turfs receiving Fe at rates up to 72.2 kg ha–1 although foliar phytotoxicity was observed

Mejora de la extracción proteica de la harina de girasol mediante hidrólisis con alcalasa

Extraction of proteins from defatted sunflower meal has been improved by addition of the protease alcalase during alkaline extraction. This method offers several additional advantages as compared to the traditional alkaline extraction without alcalase, which is usually carried out after a sedimentation/flotation step to remove the lignocellulosic fraction. As compared to extraction without alcalase, addition of 0.1% (v/v) alcalase improved the yield of protein extraction from 57.5% to 87.4%, providing an extract that is 22% hydrolyzed. In addition, an increment of up to 4.5 times in protein solubility at low pH values is achieved, which correlates with the degree of hydrolysis. The extracts that were obtained in the presence of alcalase had a higher proline and glycine content, suggesting that the protease improves extraction of proline-rich and glycine-rich cell wall proteins that are part of the lignocellulosic fraction. These protein extracts can be directly dried without generation of wastewater, and the resulting fiber-rich material could be used for animal feeding.Se ha mejorado la extracción proteica de la harina desengrasa de girasol mediante la adición de la proteasa alcalasa durante la extracción alcalina. Este método ofrece varias ventajas adicionales en comparación con la extracción alcalina tradicional sin alcalasa, que se desarrolla normalmente mediante un proceso de flotación/sedimentación para retirar la fracción lignocelulósica. En comparación a la extracción sin alcalasa, la adicción de 0.1% (v/v) de alcalasa mejora los rendimientos de extracción proteica desde un 57.5% a un 87.4%, dando un extracto con un 22% de grado de hidrólisis. Además se obtiene un incremento de hasta 4.5 veces de la solubilidad proteica a bajos pHs, que se correlaciona con el grado de hidrólisis. Los extractos obtenidos con alcalasa tenían un mayor contenido de prolina y glicina, sugiriendo que la proteasa mejora la extracción de las proteínas ricas en prolina y glicina de la pared celular que forma parte de la fracción lignocelulósica. Este extracto proteico puede ser secado directamente sin generación de aguas residuales, y el material resultante rico en fibra podría ser usado para alimentación animal