MUSIC 318 MINICOURSE ON PLUCKED STRING INSTRUMENTS
BANJOS
“How a Banjo Works” J. Rae and T. Rossing, Proc. ISMA 2004.
“Banjos” J. Rae (in Science of String Instruments ed. T. Rossing, Springer 2010)
“The structural dynamics of the American five-string banjo” J. Dickey, JASA 114, 2958
(2003)
“Experimental investigation of an American five-string banjo” L.Stephey and T. Moore,
American Journal of Physics 124, 3276 (2008)
BANJOS
BANJOS ARE MAINLY OF THREE TYPES:
4-STRING BANJO WITH RESONATOR: POPULAR IN RAGTIME AND DIXIELAND JAZZ;
USUALLY PLAYED IN STRUMMING OR FLAT PICKING STYLE
5-STRING BANJO WITH RESONATOR: POPULAR IN BLUEGRASS MUSIC; USUALLY PLAYED
WITH PICKS
5-STRING BANJO WITHOUT RESONATOR: USED IN OLD-TIME MUSIC; OFTEN PLAYED IN
“CLAW HAMMER” STYLE (STRINGS ARE PICKED AND BRUSHED WITH THE FINGERS)
THE BRIDGE RESTS ON A MYLAR MEMBRANE WHOSE TENSION CAN BE ADJUSTED WITH
A HOOP AND BOLTS
WITH THE RESONATOR IN PLACE, THE INSTRUMENT HAS AN ENCLOSED AIR CAVITY, AS
FOUND IN GUITARS, VIOLINS, MANDOLINS, AND OTHER INSTRUMENTS. TUNING OF
THE CAVITY IS POSSIBLE BY USE OF ADJUSTABLE SPACERS CALLED “RAEJUSTERS” WHICH
CHANGE THE SPACING BETWEEN THE RESONATOR AND THE REST OF THE BANJO POT
BANJO
BANJO WITH RESONATOR
OFF AND ATTACHED
BANJO SOUND
A 5-STRING BANJO IS USUALLY TUNED TO D,B,G,D,G (294, 248, 196, 147, AND 393 Hz,
RESPECTIVELY). THE BRIGHT SOUND HAS MANY HARMONICS.
SPECTRUM OF BANJO SOUND FOLLOWING A PLUCK OF THE OPEN 1ST STRING
BANJO SOUND
FRACTION OF TOTAL SOUND UP TO AND INCLUDING HARMONICS Hn
MODES OF VIBRATION
THE COMPLEX VIBRATION OF A SYSTEM CAN BE CONVENIENTLY DESCRIBED IN TERMS OF
NORMAL MODES OF VIBRATION. A NORMAL MODE IS CHARACTERISTIC OF THE
VIBRATING OBJECT ITSELF AND IS NOT DEPENDENT ON HOW THE OBJECT IS EXCITED OR
OBSERVED. FOR A MANDOLIN, A NORMAL MODE IS DETERMINED BY THE COUPLED
MOTION OF ITS STRINGS, BRIDGE, HEAD, ENCLOSED AIR CAVITY, AND THE
NECK/HEADSTOCK/FINGERBOARD ASSEMBLY.
THE DEFLECTION OF AN OBJECT AT A PARTICULAR FREQUENCY IS CALLED AN OPERATING
DEFLECTION SHAPE (ODS). AN ODS MAY RESULT FROM THE EXCITATION OF MORE THAN
ONE NORMAL MODE. A CURVE FITTING PROGRAM MAY BE USED TO DETERMINE THE
INDIVIDUAL NORMAL MODES FROM THE ODS.
HOLOGRAPHIC INTERFEROMETRY
EXPERIMENTAL MODAL ANALYSIS MY BE ACCOMPLISHED USING ANY TRANSDUCER
CAPABLE OF DETECTING MOTION, BUT HOLOGRAPHIC INTERFEROMETRY OFFERS THE
BEST SPATIAL RESOLUTION.
ELECTRONIC TV HOLOGRAPHY IS A FAST AND CONVENIENT WAY TO RECORD ODSs FROM
WHICH NORMAL MODES CAN BE DETERMINED.
SYSTEM USED FOR TV
HOLOGRAPHY
VIBRATIONAL MODES OF THE HEAD
HOLOGRAPHIC INTERFEROGRAMS OF SEVERAL VIBRATIONAL MODES OF THE HEAD OF A
HUBER LEXINGTON BANJO.
VIBRATIONAL MODES
OF THE HEAD
HEAD MODES
SPECTRUM FROM TAPPING HEAD SHOWING LOW-FREQUENCY HEAD MODES
RESONATOR
THE RESONATOR VIBRATES VERY LITTLE. ITS MAIN ROLE IS TO DEFINE AN AIR CAVITY
WHICH HAS QUITE A LARGE EFFECT ON THE HEAD VIBRATION AT LOW FREQUENCY.
INCREASING THE SIZE OF THE RESONATOR-RIM GAP BY MEANS OF A RAEJUSTER
INCREASES THE RESONANCE FREQUENCY OF THE ENCLOSED AIR CAVITY
EFFECT OF RESONATOR ON SOUND
FRACTION OF TOTAL SOUND vs FREQUENCY WITH AND WITHOUT THE RESONATOR
BRIDGES
BRIDGES ARE MADE OF DENSE HARDWOOD WITH A CAP OF EVEN DENSER WOOD. MOST
BRIDGES HAVE 3 LEGS, ONE AT EACH END AND ONE AT THE CENTER. A USEFUL TRICK IS TO
DRILL VERTICAL HOLES THROUGH THE OUTER LEGS WITH ALUMINUM RODS TO STIFFEN
THE BRIDGE.
FRACTION OF SOUND vs FREQUENCY FOR TWO BRIDGES. BRIDGE 1 IS MADE OF A STIFFER
TRANSFER OF VIBRATION ENERGY WITHIN THE BANJO
ACCELERATION AMPLITUDES OF VARIOUS PARTS OF THE BANJO WHEN THE BRIDGE IS
VIBRATED. BY FAR THE MOST ENERGY IS TRANSFERRED TO THE HEAD , ESPECIALLY AT
LOW FREQUENCY (Rae, 2009)
SOUND DECAY
SOUND SPECTRA FROM 1st STRING EXCITED 1 INCH FROM THE BRIDGE RECORDED 0-2 s
AFTER PLUCKING