Supplements for Chapter 20
Hybrid Musical Instruments
National Music Museum, University of South Dakota, Vermillion, S.D.
The wide world of experimental and hybrid instruments
Certainly millions of variations of standard musical instruments, and hundreds of thousands of radical variations, have been tried in the last millennium. Some of these produce gratifying or even mysterious sounds, and many are ingenious. The web is a wonderful resource for this subject, apart from the preponderance of commercial or otherwise over the top sites that must be waded through. Here are a few worthwhile sites:
The Tromba Marina
Here is the sound of a Tromba Marina. It comes from the website "Unprofitable Instruments", makers of a modern Tromba Marina. This is the best available recording by far of the sound and capabilities of this instrument.
The tromba marina uses a clever rattling bridge to add harmonics to the bowed string tone, making the overall timbre close to a natural trumpet. (Only one of the two feet of the bridge is anchored; the other floats just above the body so as to rattle as the string vibrates, in synchrony with the string of course, adding harmonics of the fundamental). One doesn't hear the rattling per se, a feature of our synthetic hearing: the "rattle" harmonics, that tend to fall in the higher ranges, are added to the lower string partials to synthesize a natural, trumpet like sound. The bow and finger position is set very high, with the bow above the finger. This allows a sequence of higher harmonics of the string to be played, by placing the finger at the nodes of these harmonic modes. It is to be noted that the whole string vibrates with the finger at a node; the bridge is at the bottom of the instrument.
As we learn in chapter 26, the higher harmonics of a given fundamental are not placed at the frequencies of the notes of any particular scale, with some harmonics out of tune with the musical notes on the scale by more than others (see figure yyy in Why You Hear What You Hear, and below, where the harmonics of a given fundamental are placed on a musical scale).
The seeming perfection of a series of string harmonics, equally spaced in frequency, is actually horribly imperfect because the equal spacing is linear rather than logarithmic in frequency. The errors in these nominal notes compared to an equal tempered scale is shown in cents. There are 1200 cents to an octave. Nonetheless a series of (slightly sour) notes is available by playing the harmonics one by one on a single string, without changing tension.
The natural trumpet also has a set of (roughly) equally spaced playable harmonics on one long tube with no valves. A skilled natural trumpet player can however "lip" some of these nearer to desired pitches.
StroViol, Stroh Cello
This is what happens when you combine a stringed instrument with a reproducer/horn, using the principle of the gramophone. The vibrations of the bowed string, rather than the vibrations of a needle in a groove, are the energy source. The reproducer and horn are key to making the instrument louder than a wooden violin, with the sound also somewhat directed by the bell. Aimed at an early wax cylinder recording device, the violin was finally loud enough to be recorded!
The horn seems to be continuously increasing in diameter, that makes it at least approximate a horn designed to reduce resonances caused by impedance mismatches. However the bell flair is rather too abrupt. This would cause resonances and add a brassy timbre to the violin sawtooth power spectrum pattern, that indeed the Stroh Violin possesses.
The Aeolian Harp
An aeolian harp, in one of its original and most useful settings: a window-box, providing "music" to a room, through a window that probably has more reliable and variable air movement than outside.
It is important to note that the strings are not tuned to various fundamental frequencies; in fact they can be all tuned to the same "plucking" frequency. Their lowest few modes are not excited by wind, because these modes are too sluggish to respond resonantly to vortex shedding off the string. Higher modes are excitable by wind, but if they are all the same fundamental frequency, where are the different notes on different strings to come from?
Here's the secret: The strings are made of different different diameter wires, so they shed vortices at different frequencies (see chapter 20, sec. yyy). The modes of different diameter strings are driven at different frequencies even at the same wind velocity. Each string may resonate at several different frequencies, (i.e. the natural harmonics of a stretched string) when the vortex shedding becomes resonant with the harmonics at different wind velocities. As discussed in Why You Hear What You Hear and also above, the higher modes of the strings approximate (but only crudely) the notes on a musical scale. Try to imagine the possibilities as the wind velocity varies randomly and perhaps a dozen or more strings go in and out of resonance with one of their upper harmonics. The result is an eerie, pleasant sound. It is a shame that more Aeolian harps are not found today.
The world's smallest guitar and smaller than many bacteria, this instrument was etched out of a substrate. The strings are indeed free to vibrate, but their frequency is thousands of times too high for our hearing. The strings are about 50 nanometers, or 100 atoms wide. Other instruments on this site, "Odd Music", are worth contemplating.
Google "Earth Harp" and you will find several installations that call themselves by that name. This earth harp has "strings" 400' long, attached to something solid at the top, and anchored soundly near the playing area in concrete footings. The "strings" are heavy gauge metal wire. Even at several thousand pounds of tension, the 400' length and weight mean the wires can't possibly be vibrating at audio frequencies, in the transverse way that an ordinary harp or violin string does. Still, the harps do sound, and are connected to a chamber or sounding board.
The trick is to excite the longitudinal vibrational modes of the rods, by stroking them with a gloved hand coated with rosin. These modes do not involve and bending of the rod, only compression along its length. The compression/rarefaction waves travel at about 6 kilometers per second along the length of the rod. The situation is very analogous to the longitudinal air vibrations in a pipe, as first discussed in chapter 1, only the speed of the waves is about 20 times faster. Even at 400' long, a standing wave resonance is set up. It takes only about 0.04 seconds for a longitudinal pulse initiated by stroking with a gloved and rosined hand to return, or about 25 Hz. However it is possible to excite higher modes: if the gloved hand initially sends out 110 Hz pulses in its stick-slip motion, they might return in phase with the glove motion only at 125 Hz, coaxing the gloved stick-slip stroking of the wire to change to 125 Hz. A cooperative resonance is at work, and a 125 Hz tone is set up.
The frequency of the notes obtained is not tunable by tension of the wire, since the speed of longitudinal sound propagation in the wire is independent of that tension.
A version of this idea with 30' to 100' wires is seen in the video, by MASS Ensemble: