Architectural Engineering


Date of this Version



Davidson, M. A. (2016). "Quantification of time varying directivity of musical instruments". Master's thesis, Durham School of Architectural Engineering & Construction, University of Nebraska - Lincoln.


A THESIS Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirements For the Degree of Master of Science, Major: Architectural Engineering, Under the Supervision of Professor Lily M. Wang. Lincoln, Nebraska: April, 2016

Copyright © 2016 Madeline A. Davidson


Static directivity patterns of musical instruments have been mapped somewhat extensively, but little research has been done in analyzing the directivity patterns of musical instruments over time as they play. Directivity patterns can be affected by variables such as instrument, frequency, dynamics, and style. This thesis proposes a set of quantification methods of time varying directivity, all derived from the maximum Directivity Index analyzed at consecutive short-duration time windows comprising the musical excerpt. The instrumental recordings used in this paper are taken in an anechoic chamber using either a 5, 13, or 32 multichannel setup. From the values of maximum Directivity Index evaluated using the windowing technique, quantifiers including Average Maximum Directivity Index, Average Change in Maximum Directivity Index, Location Change Ratio, Dominance Ratio, and Dominating Location are calculated. In addition to establishing time varying directivity metrics, this thesis looks at how factors such as instrument family, orchestral excerpt, and number of microphone channels used in data acquisition affect the values of the proposed metrics. The importance of understanding time varying directivity patterns of musical instruments as well as architectural acoustic applications connected to this research are also discussed.

Advisor: Lily M. Wang