October 10 Bowed Strings the Violin and the Cello

The Physics of Musical Instruments

Class Notes – October 10

Bowed Strings The Violin and the Cello

The Physics of Musical Instruments – Fall 2017 – October 10 – 1 Topics

• Review of plucked and hammered strings • Bowed strings – what’s different • Structure of the violin – Bridge – Body – f- holes • Violin frequency analysis • Cello demonstration – with thanks to Sigi Tishler

The Physics of Musical Instruments – Fall 2017 – October 10 – 2 Open Strings

• Open strings – Harp – Harpsichord – Piano

The Physics of Musical Instruments – Fall 2017 – October 10 – 3 Plucked or Hammered

• Harp – Plucked with finger or hand-held plectrum – Can control intensity with the pluck – Can control duration by damping with hand • Harpsichord – Plucked by fixed plectrum – Cannot control intensity – Forte pedal can lift dampers to lengthen sound • Piano – Hammered – Can control intensity by speed of the key – Can control duration with forte pedal

The Physics of Musical Instruments – Fall 2017 – October 10 – 4 Fretted Strings

• Fretted strings – Guitar family – Lute – Theorbo – Koto

The Physics of Musical Instruments – Fall 2017 – October 10 – 5 What the Fret Does

• Sets standard lengths for individual notes

• Creates a hard support edge for the finger- shortened string – Finger is soft – Without the fret, the damping of the plucked string would be very severe – With the fret, the vibration can sound longer

The Physics of Musical Instruments – Fall 2017 – October 10 – 6 Transition to Using Bows

• The Viol Family - fretted – Played in “da gamba” position – Violone still used

• Medieval fiddle – Played in “da braccio” position

• Bowing provides continuous energy – Don’t need frets for sustained notes

The Physics of Musical Instruments – Fall 2017 – October 10 – 7 Topics

The Physics of Musical Instruments – Fall 2017 – October 10 – 8 Stick-Slip

• Bow pulls string • Disturbance travels to the end • Is reflected back • Arrives back and creates a slip

The Physics of Musical Instruments – Fall 2017 – October 10 – 9 Another View

• Displacement of the string versus time

• The repeated crests have a period, but the recipe must be rich in harmonics • Before examining the recipe, we look at the structure of a modern violin

The Physics of Musical Instruments – Fall 2017 – October 10 – 10 Topics

The Physics of Musical Instruments – Fall 2017 – October 10 – 11 Violin

Belly is a softer wood (why?)

The rest is harder wood

The Physics of Musical Instruments – Fall 2017 – October 10 – 12 Cross-Section

• Sound post connects the belly with the back • Bass bar maintains arched shape of plates

The Physics of Musical Instruments – Fall 2017 – October 10 – 13 How It Works

• Bow sets the string into a complex vibration • The varying motion of the string wiggles the bridge • The softer wood of the belly transfers the wiggle of the bridge into a vibration • The sound post transfers the vibration to the back and the rest of the sound box • The f-holes modify the sound box resonances and help couple the sound to the surrounding air

The Physics of Musical Instruments – Fall 2017 – October 10 – 14 Topics

The Physics of Musical Instruments – Fall 2017 – October 10 – 15 String Motion at the Bridge

• It is the string motion right at the bridge that transfers motion to the belly and sound post • It has a very sharp stick-slip form

The Physics of Musical Instruments – Fall 2017 – October 10 – 16 Harmonic Analysis

• The motion at the bridge is rich in high harmonics of the string’s fundamental mode

The Physics of Musical Instruments – Fall 2017 – October 10 – 17 Demonstration

• Frequency analysis of the violin using the online spectrum analyzer

The Physics of Musical Instruments – Fall 2017 – October 10 – 18 Topics

The Physics of Musical Instruments – Fall 2017 – October 10 – 19 Cello Demonstration

• Free-form discussion – Life with a cello – Playing some notes – Doing a frequency analysis – Playing with effects Pizzacatto Spicatto Mute – Whatever else we can think of

The Physics of Musical Instruments – Fall 2017 – October 10 – 20