College of Sciences and Mathematics
http://hdl.handle.net/11200/3986
Sun, 30 Apr 2017 19:02:59 GMT2017-04-30T19:02:59ZExplaining the Railsback stretch in terms of the inharmonicity of piano tones and sensory dissonance
http://hdl.handle.net/11200/48533
Explaining the Railsback stretch in terms of the inharmonicity of piano tones and sensory dissonance
The perceptual results of Plomp and Levelt for the sensory dissonance of a pair of
pure tones are used to estimate the dissonance of pairs of piano tones. By using the spectra of tones measured for a real piano, the effect of the inharmonicity of the tones is included. This leads to a prediction for how the tuning of this piano should deviate from an ideal equal tempered scale so as to give the smallest sensory dissonance and hence give the most pleasing tuning. The results agree with the well known "Railsback stretch," the average tuning curve produced by skilled piano technicians. This is the first quantitative explanation of the magnitude of the Railsback stretch in terms of the human perception of dissonance.
Mon, 26 Oct 2015 00:00:00 GMThttp://hdl.handle.net/11200/485332015-10-26T00:00:00ZSimulation studies of a recorder in three dimensions
http://hdl.handle.net/11200/48529
Simulation studies of a recorder in three dimensions
The aeroacoustics of a recorder are explored using a direct numerical simulation based on the Navierâ€“Stokes equations in three dimensions. The qualitative behavior is studied using spatial maps of the air pressure and velocity to give a detailed picture of jet dynamics and vortex shedding near the labium. In certain cases, subtle but perhaps important differences in the motion of the air jet near the edge of the channel as compared to the channel center are observed. These differences may be important when analyzing experimental visualizations of jet motion. The quantitative behavior is studied through analysis of the spectrum of the sound pressure outside the instrument. The effect of chamfers and of changes in the position of the labium relative to the channel on the tonal properties are explored and found to be especially important in the attack portion of the tone. Changes in the spectrum as a result of variations in the blowing speed are also investigated as well as the behavior of the spectrum when the dominant spectral component switches from the fundamental to the second harmonic mode of the resonator tube.
Mon, 12 Oct 2015 00:00:00 GMThttp://hdl.handle.net/11200/485292015-10-12T00:00:00ZBounded Complete Embedding Graphs, Extended Version
http://hdl.handle.net/11200/48522
Bounded Complete Embedding Graphs, Extended Version
This is the extended version of my dissertation, "Bounded Complete Embedding Graphs." This version is presented in three parts, each in a separate file.
[Part 1] Bounded Complete Embedding Graphs
[Part 2] Extension A: The Superspectra of the Cohorts of Even Cycles, Revisited
[Part 3] Extension B: Satisfactory Divisors for the Dovetail Construction, Revisited
In the dissertation, we define bounded complete embedding graphs and bounded embedding graphs; establish that all bounded embedding graphs are bounded complete embedding graphs, but not conversely; show that all bounded complete embedding graphs are bipartite; and identify several infinite families of bounded complete embedding graphs.
One family of graphs receives particular attention: the cohorts of even cycles. The p-cohort of the 2k-cycle is the graph consisting of p vertex-disjoint copies of the 2k-cycle. In Chapter 4, we prove several results about the nature of the superspectrum of the p-cohort of the 2k-cycle; using these results, we have computed the exact superspectrum of this graph for all pairs of values of p and k such that p and k are both between 2 and 128. A few examples are given in Appendix A, along with the Python code we implemented to complete the necessary computations; the complete list of these superspectra is presented in the tables in Extension A.
Also in Chapter 4, we develop the Dovetail Construction, which allows us to build certain designs that are needed in order to obtain our bounded complete embedding graph results. Each time we apply this construction, we must verify its hypotheses, which include the existence, for certain numbers, of a divisor satisfying certain properties. We employ a short computer program to accomplish the necessary computations for these verifications; the Python code for this program is given in Appendix B, along with a complete listing of verification data for a few selected pairs of values of p and k. We have completed the verification computations for all pairs of values of p and k such that p and k are both between 2 and 128; full details are given for all pairs in the tables in Extension B.
Wed, 08 Jul 2015 00:00:00 GMThttp://hdl.handle.net/11200/485222015-07-08T00:00:00Z