Modal-acoustic radiation measurements on 17 "bad-to-excellent" quality-rated violins--including three-dimensional modal analyses of Titian and Willemotte Stradivari and Plowden Guarneri del Gesu violins to investigate extensional as well as flexural motions-were examined for quality-related trends, generally by contrasting the properties of "excellent" and "bad" violins. All violins tested showed the same five "signature" modes below 600 Hz, with no obvious quality trends for mode frequencies or total damping. Bad-excellent comparisons of band-/modal-averaged damping (total, radiation and internal), mobility, radiativity, directivity, fraction-of-vibrational-energy radiated, effective critical frequency, and radiativity profiles up to 4 kHz generally showed no significant difference; the only "robust" quality differentiator was the approximately 280 Hz, Helmholtz-type A0 cavity mode radiativity where excellent violins were significantly higher. Radiation and total damping of two old Italian violins appeared slightly higher than those for bad violins below 2 kHz, partly due to lower effective critical frequency and partly because of slightly lower mass. Stradivari violins showed the highest and lowest directivity of all instruments tested. The Titian and Plowden top plate flexural/extensional mobility ratios appeared correlated with their directivity. Extensional motion in the "bridge island" between f holes peaked near 2.4 kHz, coinciding with the BH peak and a bridge/bridge-island impedance ratio minimum.

The violin bridge filter role was investigated using modal and acoustic measurements on 12 quality-rated violins combined with systematic bridge rocking frequency f(rock) and wing mass decrements deltam on four bridges for two other violins. No isolated bridge resonances were observed; bridge motions were complex (including a "squat" mode near 0.8 kHz) except for low frequency rigid body pivot motions, all more or less resembling rocking motion at higher frequencies. A conspicuous broad peak near 2.3 kHz in bridge driving point mobility (labeled BH) was seen for good and bad violins. Similar structure was seen in averaged bridge, bridge feet, corpus mobilities and averaged radiativity. No correlation between violin quality and BH driving point, averaged corpus mobility magnitude, or radiativity was found. Increasing averaged-over-f(rock) deltam(g) from 0 to 0.12 generally increased radiativity across the spectrum. Decreasing averaged-over-deltam f(rock) from 3.6 to 2.6 kHz produced consistent decreases in radiativity between 3 and 4.2 kHz, but only few-percent decreases in BH frequency. The lowest f(rock) values were accompanied by significantly reduced radiation from the Helmholtz A0 mode near 280 Hz; this, combined with reduced high frequency output, created overall radiativity profiles quite similar to "bad" violins among the quality-rated violins.

Mechanical and acoustical consequences of removal of the soundpost in the violin were examined using (a) experimental modal analysis on a violin with (SP) and without soundpost (no-SP) to examine the approximately 50 modes observed over a 0- to 2-kHz range and (b) boundary element radiation calculations of radiation efficiency and directivity for each normal mode. A majority of modes were tracked between SP and no-SP states by correlating frequency, damping, mode shape, and interviolin MAC values. On removal of the soundpost, (a) mode frequencies below 1 kHz usually dropped a few percent, while those above increased similarly, (b) average mechanical response at the bridge increased 14%, (c) average radiation efficiency dropped 17%, most noticeably from 500 to 800 Hz, especially for a very strong corpus SP mechanical mode at ∼550 Hz whose radiation efficiency dropped from 0.105 to 0.022, and (d) radiation patterns altered substantially. A vibration-radiation model to simulate response curves agreed well with general features of previous SP violin response and radiativity measurements, and with Fourier analysis of recorded SP and no-SP slide tones. Calculated SP radiation patterns were also compared to previous violin directivity measurements.

Experimental modal analysis of a complete Hutchins-Schelleng violin octet, combined with cavity mode analysis and room-averaged acoustic analysis, gives a highly detailed characterization of the dynamics for this historic group of instruments. All the "signature" modes in the open string pitch region--cavity modes A0 ("main air") and A1 (lowest longitudinal), C-bout "rhomboid," the first corpus bending modes B1- and B1+ (comprising the "main wood")--were observed across the octet. A0 was always the lowest dominant radiator, below all corpus modes. A1 contributed significant acoustic output only for larger instruments, but was the dominant contributor for the large bass in the "main wood" region. Acoustic results indicate either B1- or B1+ can be the major radiator. Damping results indicate that B1 modes overall radiate approximately 28% of their vibrational energy. "Doublet" B1 modes from substructure couplings were observed for three instruments. "A0-B0" coupling was not significant for the largest instruments. The original flat-plate-based scaling of the "main wood" resonance was generally successful across the octet, although that for the "main air" was not.

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