| Read Chapter 12.
Issues in Strings
Tone formation—the string
- Harmonic modes of stretched string
- Vibration recipes—spectra
- Tone projection—the body
- Low Q resonator
- Large area/volume needed for low pitches
- Coupling the body to the string
Plucked Strings
- Normal modes of a string form an Harmonic Series.
- String of length L has normal modes of wavelength λn = 2L/n
where n is an integer
and frequencies where T is the string
tension, L is the length of the string, and μ is the mass/length
- When
a string is plucked a pair of kinks travel along the string
backwards and forwards at the wave speed.
- The sharpness of the
kinks depends on the size and hardness of the plucking material
- Sharper kinks involve the highest frequency modes
- Softer kinks will lack those highest modes and so have
a less bright sound.
Plucking Strings
- The plucking point affects the tone color of the sound.
- The Modes with anti-nodes near the plucking point are emphasized.
- The nearer the plucking point is to the anti-node the more the
mode is emphasized.
- Modes with nodes at the plucking point are missing from the spectrum.
- Plucking at the mid-point gives a hollow, lute-like sound that
is missing the even harmonics.
- Plucking closer and closer to
the bridge gives brighter and harsher sounds
- We can suppress
lower modes by damping the string to produce “harmonics”.
The Harpsichord
- Wire strings on a wood frame plucked by tiny, sharp
quills called Jacks.
- Scaled at /octave and wire diameters increase
from .008” to 0.024”.
- No overwound strings.
- Sound is rich in
harmonics and upper partials are strong, especially in the lower
notes.
- See overall -6B/octave of plucked string
- See envelope of spectrum set by plucking point.
- Spectrum continues up through
complete audio range, no sudden cut-off.
The Piano
- Strings are hammered instead of plucked.
- Hammer stays in contact with
the strings until the string vibration throws it off. This results
in a much steeper fall-off of the higher partials.
- The highest notes show the steepest fall off because the hammer stays on
the string longer in proportion to the period of the note.
- In addition to the generally steeper fall in frequency caused by
hammering, the spectra show a clear cut-off at the high frequency
end due to the damping action of the hammer.
- Especially in the
lower notes see strong modulation of spectrum from strike point.
Modes with nodes near the strike point are strongly suppressed.
- See non-uniform decay due to triple stringing
- See beating between
the individual strings.
- See anharmonicity in the highest strings
where stiffness plays the greatest role.
Bowed String Spectrum
- Same basic structure as plucked, higher partials fall off at
constant rate up to some limit.
- Key difference: no missing modes
due to pluck point—stick-slip gives smooth spectrum.
- Violin body resonates, couples to air, modifies tone.
- Low frequency modes including breathing mode important for warmth of tone
- High frequency modes mostly of front plate important for brilliance.
- Smooth distribution of modes important for even-ness of tone.
Violin and Guitar Bridges
- Bridge serves to couple vibrations of spring to body.
- High violin bridge with angled strings has large down-bearing.
Transfers energy from string to body with high efficiency
and so instrument is loud but plucked sound is short duration.
- Cut-outs in violin bridge convert side-to-side vibrations
of the string into up-and-down vibrations of the body.
- Flat guitar bridge couples energy to body less efficiently.
Guitar is quieter for its size (compare cello) but plucked
notes last much longer.
- Note that violin is bowed so it makes sense to trade duration
for volumer. Guitar is plucked and so sound must last longer.
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