I would get away from defining the radiating pattern as stereo and maybe more like this which might help out a bit more on the subject.
The four main instruments of the string section — the violin, viola, cello, and double bass — emerged in their current form around the start of the 17th century, so they are very 'mature' instruments. Like all acoustic stringed instruments, the string vibrations are much too weak on their own to move enough air to be audible at any distance, so a 'mechanical amplifier', namely the body of the instrument, is used to boost the sound intensity. The string vibrations are coupled to the body of the instrument through the bridge, and that body is essentially a resonant box (albeit of a complex shape and construction) designed to amplify the appropriate range of frequencies generated by the vibrating strings.
Given the complex panel shapes and sizes, different parts of the instrument's body resonate at different frequencies, and thus both the tonal character and radiation pattern of the instrument vary considerably with frequency. The diagrams in this box give some idea of the average polar responses of the violin and cello at a range of different frequencies, and illustrate how the bulk of the instruments' sound comes from the top or front panel. However, the width of sound dispersion and the dominant axis vary considerably with frequency — sometimes in most unexpected ways!
The nature of stringed instruments is that they are all slightly different in their construction, and so the actual radiation pattern of a specific instrument may well be slightly different to the typical plots here. Consequently, it is important to listen to the actual instruments and position the microphones accordingly. Moving a mic a few inches can make all the difference between a bright, detailed sound or a rich dark tone.
Typical dispersion characteristics of string instruments at different frequencies.
Typical dispersion characteristics of string instruments at different frequencies.
It is interesting that the body resonances play a big part in determining the harmonic structure of the instrument. When playing high notes on a violin, for example, the fundamental is the strongest component (the highest being around 2.6kHz). However, in the lower registers the fundamental can be as much as 25dB below the strongest second or third harmonic, simply because the body is not large enough to resonate efficiently at the true fundamental frequency — the lowest open string on a violin, for example, vibrates at 196Hz, which has a wavelength of around 0.6 metres. The audible effect of the weakened fundamental is that the upper strings tend to have a slightly more mellow sound than the lower ones.
The distinctly nasal tone of the viola is due to the same effect. The viola is tuned a fifth lower than a violin (the lowest fundamental is 130Hz), and thus the wavelengths are 1.5 times longer. If the viola body were also 1.5 times larger than a violin it would have a similar tonal character, but in fact the body is only about 1.2 times larger. This means that the fundamentals are even weaker across the lower registers and the harmonics are an even more dominant part of the sound.
The cello is tuned an octave below the viola, with the bottom open 'C' string producing a fundamental at 65Hz. However, the body of the instrument is again undersized and poor at amplifying such low fundamentals. In fact, the enclosed volume of air in the body resonates at around 110Hz, which amplifies the first overtone extremely well.
The double bass produces fundamentals as low as 31Hz, but the lowest resonance peak in the body (air resonance again) is an octave above this. Hence the fundamental is a relatively weak component of the sound of the lowest strings, and the majority of the sound energy is contained in the band between 70Hz and 250Hz.
At the top end of the spectrum, the violin can generate strong harmonics that extend up to 10kHz or so — although the level of these is very dependent on the playing technique. The type of strings and the dimensions of the panels in a double bass work to restrict it's harmonic structure to about 2.5kHz, while the cello goes a little higher, as you would expect, to about 3kHz.
Open strings produce a full harmonic structure because the ends of the string are defined precisely by the bridge and nut. However, stopped strings (in other words, those shortened by pressing a finger on the fingerboard) produce a smoother sound with fewer harmonics, purely because of the less well-defined string end under a relatively soft finger! Pressing harder against the finger board can boost the harmonics quite significantly.
The more critical element of harmonic balance is the position of the bow. Drawing it over the strings close to the bridge produces a harmonically rich sound, whereas a position over the fingerboard gives a softer quality.
Topic: Cello mic recommendations (Read 14719 times)