A tapping bridge adds trumpet-like harmonics to a bowed monochord

Evidence

Can something be inserted between string and violin body to lessen the impedance mismatch, thus allowing the energy to take two smaller steps, instead of one large one? While we are at it, can we sweeten the sound by modulating the impedance (and ultimately the loudness of the instrument) according to frequency? The answer is yes: this is the job of the bridge, as we discuss in chapter 18. The bridge is the “intermediate coin” that mediates the transfer of energy from string to body. Its impedance is cleverly tuned by choice of shape, size, and material to depend in a certain way on the frequency of vibration. — Eric J. Heller, Why You Hear What You Hear- An…, 79 (#expands, via linked claim)

In order that notes can be played which have a clearly perceived pitch on percussion instruments such as the xylophone, marimba and vibraphone—with playing ranges from C5 (523 Hz) to C8 (4186 Hz), A2 (110 Hz) to C7 (2093 Hz) and F3 (175 Hz) to F6 (1397 Hz), respectively—the bars are shaped with an arch on their undersides to tune the modes to be close to harmonics of the first mode. In the marimba and vibraphone, the second mode is tuned to two octaves above the first mode, and in the xylophone, it is tuned to a twelfth above the first mode. These instruments have resonators, which consist of a tube closed at one end, mounted under each bar. The first mode of these resonators is tuned to the f0 of the bar to enhance its loudness, and therefore the length of the resonator is a quarter of the wavelength of f0 (see Equation 1.36). — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1287 (#expands, via linked claim)

Categorization

• XREF: connects to: Flute playing frequencies are impedance minima; trumpet’s are maxima; The violin bridge acts as a frequency-tuned impedance-matching intermediary — Eric J. Heller, Why You Hear What You Hear- An…, 79; Percussion bars are shaped to tune their modes toward harmonic ratios — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1287 (+2 more)

Broader Connections

• The violin bridge acts as a frequency-tuned impedance-matching intermediary #expands (0.80) — Eric J. Heller, Why You Hear What You Hear- An…, 79
• Percussion bars are shaped to tune their modes toward harmonic ratios #expands (0.75) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1287
• Pipe organ stops can reinforce non-octave harmonics to reshape timbre #expands (0.72)