String Instrument Measurements and Modeling

Participants: Esteban Maestre, Hossein Mansour, Vincent Fréour and Gary Scavone

Period: 2011 - ongoing

Enhanced Bowed-String Simulations

Despite having existed in their present form (for the most part) for over 400 years, bowed-string instruments remain the subject of active research in the musical acoustics community. While their general behaviour is reasonably well understood, measurable properties that can be used to distinguish instruments of very different perceived qualities have remained illusive. The goal of this research is to build numerical models of increasing refinement, parameterized by measurements when possible, to explore and test which physical characteristics play a significant role in defining an instrument’s “playability” and sound.

In collaboration with Dr. James Woodhouse at Cambridge University, Ph.D. student Hossein Mansour developed a variety of new model features, including the frequency-dependent behavior of the strings, modal properties of an actual body as determined from measurements, dual-polarization of the strings, longitudinal vibrations of the bow-hair, bow-stick properties, and sympathetic vibrations of the freely vibrating strings. He also derived a more robust version of a famous predictive equation for violin playability. The model was then used as a quasi-experimental tool to systematically investigate the effect of each detail on the timbre and playability of the instrument. This research represents important contributions to our understanding of bowed-string instruments, with potential applications for luthiers, string manufacturers, players, and researchers working to synthesize the sound of bowed strings.

  • Mansour, H., Woodhouse, J. and Scavone, G. (2017) “On minimum bow force for bowed strings.”, Accepted for publication in Acta Acustica united with Acustica, Vol. 103.
  • Mansour, H., Woodhouse, J. and Scavone, G. (2016). "Accurate time-domain modeling of the bowed string (A)." 172nd Meeting of the Acoustical Society of America, Honolulu, Hawaii, 28 November - 2 December, Journal of the Acoustical Society of America, Vol. 140, p. 3036, invited presentation.

Efficient and Accurate Synthesis of Strings

Since 2012, we have engaged in a research collaboration with Dr. Esteban Maestre and Dr. Julius Smith (Stanford University) to investigate the design of violin and guitar body filters, parameterized from measurements, for sound synthesis models. This research has included: modal decomposition of measured driving-point admittances obtained by means of a novel frequency-domain algorithm for optimization of digital filters in parallel form; passive modeling of radiativity and admittance by projection of measurements over a common modal basis, and an efficient implementation of bridge reflectance and sound radiativity filters from a single bank of shared resonant filters. The results make it possible to synthesize in real time the sound of a specific violin or guitar, with many possible commercial applications. For example, this technology could be used to virtually audition, via an online interface, a set of instruments for sale in a shop.

A recent collaboration with several researchers at Stanford and the Politecnico di Milano is focusing on the virtual restoration and resynthesis of a historically important violin, the 1716 “Messiah” by Stradivarius, which sits in the Ashmolean Museum in Oxford, England and cannot be played because of its fragile condition.

  • Maestre, E., Scavone, G. P., Smith, J.O. “Digital modeling of string instrument bridge reflectance and body radiativity for sound synthesis by digital waveguides.” IEEE Workshop on Applications of Signal Processing to Audio and Acoustics, New Paltz, NY, 18-21 October 2015, pp. 1-5.


We began a six-month research project in 2013 with Godin Guitars, a Quebec company that manufactures approximately 50,000 acoustic and 20,000 electric guitars each year. The project, funded by an NSERC Engage grant, investigated the use of measurements to allow the manufacturer to better categorize subsets of instruments according to sounding characteristics. The study benefitted from the availability of a large set (over 30) of nominally identical steel-string guitars, a truly unique asset among studies of this kind. One goal of the work was to find features of guitar admittances that could be used to automatically distinguish them according to three classifications (bassy, mid-even and treble) suggested by the manufacturer. A second goal was to investigate whether experienced guitarists agree with those classifications.

Results of this work, which was conducted by a team of three Ph.D. candidates (Hossein Mansour, Vincent Fréour and Charalampos Saitis), showed very low agreement across guitarists with the manufacturer-provided classifications. However, analysis of the measurements indicated that the guitars categorized as bassy had a lower breathing mode frequency (which can be related to the stiffness-to-weight ratio of the bodies). We also found that averaged mobilities in the 600–2000 Hz range could distinguish the mid-even and treble instruments, though results with new instruments outside the original analysis pool did not confirm this finding. The results are significant because they represent one of the few examples in string instrument research of a clear correspondence between a physical property derived from a measured body response and a perceptual characteristic (bassy-ness) of the resulting sound.