On the Mathematics of Music: From Chords to Fourier Analysis

Mathematics is a far reaching discipline and its tools appear in many applications. In this paper we discuss its role in music and signal processing by revisiting the use of mathematics in algorithms that can extract chord information from recorded music. We begin with a light introduction to the theory of music and motivate the use of Fourier analysis in audio processing. We introduce the discrete and continuous Fourier transforms and investigate their use in extracting important information from audio data

Applications of Fourier Analysis to Audio Signal Processing: An Investigation of Chord Detection Algorithms

The discrete Fourier transform has become an essential tool in the analysis of digital signals. Applications have become widespread since the discovery of the Fast Fourier Transform and the rise of personal computers. The field of digital signal processing is an exciting intersection of mathematics, statistics, and electrical engineering. In this study we aim to gain understanding of the mathematics behind algorithms that can extract chord information from recorded music. We investigate basic music theory, introduce and derive the discrete Fourier transform, and apply Fourier analysis to audio files to extract spectral data

Integrating sheep grazing into wheat–fallow systems: Crop yield and soil properties

The two predominant systems for weed management in summer fallow are tillage with a field cultivator or multiple applications of broad spectrum herbicides with zero tillage. Both systems are based on substantial use of off farm resources. Our objective was to determine if strategic grazing of sheep may allow grain growers to more sustainably manage crop residues, volunteer crop, and other weeds during fallow periods. We conducted a study near Bozeman, Montana, USA, comparing three fallow weed management systems in two crop rotations from 2005 to 2008. Fallow weed management systems were conventional tillage, chemical-fallow (herbicide application), and sheep grazing. The crop rotations were summer fallow–spring wheat and summer fallow–winter wheat. In late fall, chemical-fallow treatment had greater residue cover and soil water content than did tilled- or grazed-fallow. At 0–15-cm depth, soil had lower bulk density in chemical- and tilled-fallow than in grazed fallow. Similarly, soil NO3-N, Ca, SO4-S concentrations and EC were lower following grazed-fallow than tilled-fallow, but Na concentration was higher following grazed-fallow than tilled- or chemical-fallow. Following spring and winter wheat, soil properties were not influenced by treatments. Grain yield was greater in winter wheat than in spring wheat but the trend reversed in protein concentration. Although soil properties varied among treatments, fallow management system had little influence on yield or quality of spring and winter wheat. Sheep grazing during fallow periods had limited impact on subsequent wheat yield and quality, and is a suitable practice for weed and residue management in wheat–fallow systems

MF918

Randall A. Higgins, Sue L. Blodgett and Andrew W. Lenssen, “Alfalfa weevil management in Kansas: II. Non-chemical controls,” Kansas State University, April 1989

Alternatives for Drought-damaged Soybeans—Bean Crop or Forage

As people reflect on the reasons for the irregular development and poor soybean production in Iowa this year, the next important questions relate to evaluation of crops in individual fields and planning when and how to harvest them to the greatest economic advantage. This evaluation involves reviewing normal crop growth and development, assessing the condition of the crops in individual fields relative to normal and to think through several harvest scenarios. Will this field have a harvestable soybean crop? Are there concerns about the crops? What use or management alternatives do I have

Dryland Soil Greenhouse Gas Emissions Affected by Cropping Sequence and Nitrogen Fertilization

Information is needed to mitigate dryland soil greenhouse gas (GHG) emissions by using novel management practices. We evaluated the effects of cropping sequence and N fertilization on dryland soil temperature and water content at the 0- to 15-cm depth and surface CO2, N2O, and CH4 fluxes in a Williams loam (fine-loamy, mixed, superactive, frigid, Typic Argiustolls) in eastern Montana. Treatments were no-tilled continuous malt barley (Hordeum vulgaris L.) (NTCB), no-tilled malt barley–pea (Pisum sativum L.) (NTB–P), and conventional-tilled malt barley–fallow (CTB–F) (control), each with 0 and 80 kg N ha−1. Gas fluxes were measured at 3 to 14 d intervals using static, vented chambers from March to November 2008 to 2011. Soil temperature varied but water content was greater in CTB–F than in other treatments. The GHG fluxes varied with date of sampling, peaking immediately after substantial precipitation (\u3e15 mm) and N fertilization during increased soil temperature. Total CO2 flux from March to November was greater in NTCB and NTB–P with 80 kg N ha−1 than in other treatments from 2008 to 2010. Total N2O flux was greater in NTCB with 0 kg N ha−1 and in NTB–P with 80 kg N ha−1 than in other treatments in 2008 and 2011. Total CH4 uptake was greater with 80 than with 0 kg N ha−1 in NTCB in 2009 and 2011. Because of intermediate level of CO2 equivalent of GHG emissions and known favorable effect on malt barley yield, NTB–P with 0 kg N ha−1 might mitigate GHG emissions and sustain crop yields compared to other treatments in eastern Montana. For accounting global warming potential of management practices, however, additional information on soil C dynamics and CO2 associated with production inputs and machinery use are needed

Dryland soil chemical properties and crop yields affected by long-term tillage and cropping sequence

Information on the effect of long-term management on soil nutrients and chemical properties is scanty. We examined the 30-year effect of tillage frequency and cropping sequence combination on dryland soil Olsen-P, K, Ca, Mg, Na, SO 4 –S, and Zn concentrations, pH, electrical conductivity (EC), and cation exchange capacity (CEC) at the 0–120 cm depth and annualized crop yield in the northern Great Plains, USA. Treatments were no-till continuous spring wheat (Triticum aestivum L.) (NTCW), spring till continuous spring wheat (STCW), fall and spring till continuous spring wheat (FSTCW), fall and spring till spring wheat–barley (Hordeum vulgare L., 1984–1999) followed by spring wheat–pea (Pisum sativum L., 2000–2013) (FSTW-B/P), and spring till spring wheat-fallow (STW-F, traditional system). At 0–7.5 cm, P, K, Zn, Na, and CEC were 23–60% were greater, but pH, buffer pH, and Ca were 6–31% lower in NTCW, STCW, and FSTW–B/P than STW-F. At 7.5–15 cm, K was 23–52% greater, but pH, buffer pH, and Mg were 3–21% lower in NTCW, STCW, FSTCW, FSTW–B/P than STW-F. At 60–120 cm, soil chemical properties varied with treatments. Annualized crop yield was 23–30% lower in STW-F than the other treatments. Continuous N fertilization probably reduced soil pH, Ca, and Mg, but greater crop residue returned to the soil increased P, K, Na, Zn, and CEC in NTCW and STCW compared to STW-F. Reduced tillage with continuous cropping may be adopted for maintaining long-term soil fertility and crop yields compared with the traditional system

Satisfying Their Need: Graduate Students' Perceptions of the Adequacy of Their Health Insurance

First Student Poster Presentation. Presenter: Elisa Lenssen - "Satisfying Their Need: Graduate Students' Perceptions of the Adequacy of Their Health Insurance".The Ohio State University College of Social Wor

Net Greenhouse Gas Emissions Affected by Sheep Grazing in Dryland Cropping Systems

Sheep (Ovis aries L.) grazing is an inexpensive method of weed control in dryland cropping systems, but little is known about its effect on net greenhouse gas (GHG) emissions. We evaluated the effect of sheep grazing compared with herbicide application for weed control on GHG (CO2, N2O, and CH4) emissions from May to October 2010 and 2011, net global warming potential (GWP), and greenhouse gas intensity (GHGI) in a silt loam under dryland cropping systems in western Montana. Treatments were two fallow management practices (sheep grazing [GRAZ] and herbicide application [CHEM]) and three cropping sequences (continuous alfalfa [Medicago sativa L.] [CA], continuous spring wheat [Triticum aestivum L.] [CSW], and spring wheat–pea [Pisum sativum L.]/barley [Hordeum vulgaris L.] hay–fallow [W-P/B-F]). Gas fluxes were measured at 3- to 14-d intervals with a vented, static chamber. Regardless of treatments, GHG fluxes peaked immediately following substantial precipitation (\u3e12 mm) and N fertilization mostly from May to August. Total CO2 flux from May to October was greater under GRAZ with CA, but total N2O flux was greater under CHEM and GRAZ with CSW than other treatments. Total CH4 flux was greater with CA than W-P/B-F. Net GWP and GHGI were greater under GRAZ with W-P/B-F than most other treatments. Greater CH4 flux due to increased enteric fermentation as a result of longer duration of grazing during fallow, followed by reduced crop residue returned to the soil and/or C sequestration rate probably increased net GHG flux under GRAZ with W-P/B-F. Sheep grazing on a cropping sequence containing fallow may not reduce net GHG emissions compared with herbicide application for weed control on continuous crops