Monday, January 30, 2006
The Physics of Music
I've been reading up on the physics of the violin family and of bowed strings. Back in the 16th century, stringed instruments were evolving from lutes and lyres in two somewhat parallel but independent paths in Italy: the viol family and the violin family.
The viols, which included the viol da gamba, the viol da bastarda, and the viol da braccio were developed first. While these instruments are somewhat similar in appearance to today's modern violins on first glance, they are quite different in detail and in sound. Viols have a flat back, have five or six strings that are more loosely strung, and many have gut wrapped around the fingerboard to serve as frets. Most of the viols have a pair of C-shaped cutouts in the top plate.
The violin family is believed to have originated by Andrea Amati in Cremona, Italy in the mid to late 1500s – many decades after the emergence of the viols. It’s likely he adapted the design of the viol da braccio, incorporating his own ideas into his new design. For a long time the viols and the violins vigorously competed with one another in the salons and music halls across Europe, with different composers and music patrons preferring one over the other. With their richer and more powerful sound, the violins eventually displaced the viols completely. Only the largest bass viol da gamba, known today as the double bass, is still in common use.
What made the violin, viola, and later the cello win out over the viols is probably their prominently arched backs, which were usually carved from solid maple. The size and shape of the chambers inside the violins, along with their F-shaped cutouts have everything to do with their quality and sound.
The shape of the instruments in the violin family is thought to have been derived from Renaissance ideals about beauty and perfection, which they expressed mathematically with formulae based in part on ratios of radii of circles. These shapes have remained largely unchanged ever since.
Other factors that are thought to be important to the quality of the sounds include the age, grain and drying of the wood. Even whether or not the spruce trees used for the top plates grew at higher altitudes, where they were subjected to greater stresses – which are thought to impart a higher quality resonance to the wood. It is widely believed that the violins improve over time with playing – with the repeated stresses and resonances essentially “training” the wood.
Another issue long believed important is the filling and finish of the wood. Some believe that the key to the remarkable quality of the Stradivarius instruments is in the varnishes he developed. These varnishes are prepared using various insects and natural solvents.
While the basic design and manufacture of the violin remains largely unchanged in the last 300 years, the secrets of the varnish are lost.
Then there are the strings. The physics of vibrating strings is the base for all of these instruments. The violins amplify these vibrations by transferring it through the bridge to the top plate and through the soundpost to the back plate. These vibrations transfer into the air inside the chambers and are affected by the F-holes on the top plate. The materials used in the strings also affect the quality and tone. Some types of strings use pig gut that is wrapped with fine steel wires. Others have a wire core similarly wrapped.
Finally, there is the bow. All bows use horsehair. Most bows are made of rosewood or pernambuco; some are round and some are octagonal. The natural shape of the bow keeps the horsehair tight.
After all this, even the best violin and bow require skill and practice on the part of the player. A skilled player can get a fair sound even from a poor quality instrument, while a poor player can never get a good sound from the best violin.
Today’s workout focused on: 1) keeping the right hand/wrist/arm in line with the proper hold on the bow (this was not easy, I had to keep repositioning my thumb); 2) drawing the bow perpendicular to the strings, using the right elbow at the upper end of the bow; 3) keeping the left arm out, relaxed; 4) keeping the left thumb relaxed and the fingers light on the strings. It was a challenge to try to do all this at once. But, every once in a while, I got it all together for a minute or two. Clearly this is going to take time. I’m know my teacher earned her $50 for that first lesson.
I worked through the Suzuki pieces for about an hour and a half, and then went back to my exercise book for a while. My teacher hadn’t seen this particular Mel Bay exercise book before, but she thought it would be OK for me to use it – especially for finger exercising and music reading.