The Physics of Musical Instruments

Class Notes – November 7

Reed instruments; The woodwinds

The Physics of Musical Instruments – Fall 2017 – November 7– 1 Topics

• How reeds work • Woodwinds vs brasses • Finger holes – a reprise • Conical vs cylindrical bore • Changing registers • Role of the bell • Woodwind timbre • Clarinet demonstration

The Physics of Musical Instruments – Fall 2017 – November 7– 2 Return to the Water Trumpet

• The critical component is the pressure- sensitive valve – a reed works exactly this way

The Physics of Musical Instruments – Fall 2017 – November 7– 3 Reeds and Mouthpieces

• Single reed on a mouthpiece – Clarinet, saxophone, basset horn • Double reed mounted on a tube – Oboe, bassoon, English horn

The Physics of Musical Instruments – Fall 2017 – November 7– 4 Clarinet Mouthpiece

• We pass around a clarinet mouthpiece with a reed attached – See how easily the reed can be pressed to close the gap – BUT – When the air pressure inside the instrument is at its maximum, it can force the reed to open up a little and let in some air – an ideal example of the pressure-activated valve.

The Physics of Musical Instruments – Fall 2017 – November 7– 5 Topics

• How reeds work • Woodwinds vs brasses • Finger holes – a reprise • Conical vs cylindrical bore • Changing registers • Role of the bell • Woodwind timbre • Clarinet demonstration

The Physics of Musical Instruments – Fall 2017 – November 7– 6 Two kinds of “reeds”

• Lip reeds – Brass instruments – The lips have a huge influence on which tone is reinforced, and can even select the tone with ease • Wooden reeds – Woodwind instruments – The instrument cavity has the greatest influence on which tone is reinforced – more in this later – The reed is essential, but it is not tone-selective without a lot of work by the player (I will demonstrate later)

The Physics of Musical Instruments – Fall 2017 – November 7– 7 Topics

• How reeds work • Woodwinds vs brasses • Finger holes – a reprise • Conical vs cylindrical bore • Changing registers • Role of the bell • Woodwind timbre • Clarinet demonstration

The Physics of Musical Instruments – Fall 2017 – November 7– 8 Impedance Again

Tiny discontinuity Big discontinuity in impedance; in impedance; weak reflection strong reflection

Resonance Resonance determined by determined by pipe length hole position

The Physics of Musical Instruments – Fall 2017 – November 7– 9 Side Holes add Reflections

• The side holes add small cavities that makes the resonator no longer a simple ideal pipe

Added volume and mass, like Benade’s assembly of bottles

Impedance “bumps” even when the hole is closed

The Physics of Musical Instruments – Fall 2017 – November 7– 10 How Many Holes are Needed?

• Enough to span from the lowest note to the first important harmonic that can be made to sound

• And that depends on the BORE of the instrument

The Physics of Musical Instruments – Fall 2017 – November 7– 11 Topics

• How reeds work • Woodwinds vs brasses • Finger holes – a reprise • Conical vs cylindrical bore • Changing registers • Role of the bell • Woodwind timbre • Clarinet demonstration

The Physics of Musical Instruments – Fall 2017 – November 7– 12 The Clarinet has a Cylindrical Bore

• Behaves like a pipe closed at one end

High pressure at Low pressure at the mouthpiece the bell

The Physics of Musical Instruments – Fall 2017 – November 7– 13 Closed Cylindrical Bore

• A cylindrical bore woodwind (ie the clarinet) only supports the odd harmonics

• It cannot support even harmonics, as that would require a node at the mouthpiece and air is injected only at pressure maximum, not at a node.

The Physics of Musical Instruments – Fall 2017 – November 7– 14 The Interval is a Twelfth

• The third harmonic of a pitch is an octave plus a fifth above the fundamental pitch • The interval is called a twelfth • When you include the half-steps, it takes a lot of holes to cover the twelfth. • You need 18 separate “lengths” to get a complete chromatic scale that covers a twelfth. That’s a lot of holes…

The Physics of Musical Instruments – Fall 2017 – November 7– 15 Conical Bores are Different

• In a conical bore, a supported vibration can have a node very close to the end • As a result, a conical bore supports both even and odd harmonics of the fundamental • Only one octave worth of holes is needed, just like on the flute. • Oboe, saxophone, and bassoon have conical bores

The Physics of Musical Instruments – Fall 2017 – November 7– 16 Conical Bore Cross Sections

• Oboe, saxophone, and bassoon cross-sections, with the diameters greatly exaggerated

• Each of these instruments have the octave as the first harmonic that can sound

The Physics of Musical Instruments – Fall 2017 – November 7– 17 Making Scales

Clarinet

Oboe

Flute

The Physics of Musical Instruments – Fall 2017 – November 7– 18 Topics

• How reeds work • Woodwinds vs brasses • Finger holes – a reprise • Conical vs cylindrical bore • Changing registers • Role of the bell • Woodwind timbre • Clarinet demonstration

The Physics of Musical Instruments – Fall 2017 – November 7– 19 How to Change Registers

• Brass – dominated by the player’s lips – Tighten, and one can select a harmonic • Reed instruments – dominated by the cavity • The technique is to add one or more holes, called speaker holes (or “octave keys”) near the reed that tends to suppress the fundamental, and allows the next register to sound. • The clarinet has one such key; the oboe has three

The Physics of Musical Instruments – Fall 2017 – November 7– 20 Topics

• How reeds work • Woodwinds vs brasses • Finger holes – a reprise • Conical vs cylindrical bore • Changing registers • Role of the bell • Woodwind timbre • Clarinet demonstration

The Physics of Musical Instruments – Fall 2017 – November 7– 21 Bell Affects Lowest Notes

• We will examine this when we do the demonstration, but when enough holes are open, the bell has little impact on the sound • The sound emanates from the open holes except when most of the holes are closed • We will compare the clarinet played with and without a bell, but first, we examine the recipe differences of the reed woodwinds

The Physics of Musical Instruments – Fall 2017 – November 7– 22 Topics

• How reeds work • Woodwinds vs brasses • Finger holes – a reprise • Conical vs cylindrical bore • Changing registers • Role of the bell • Woodwind timbre • Clarinet demonstration

The Physics of Musical Instruments – Fall 2017 – November 7– 23 Recipes

Low Register Middle Register

Saxophone Oboe

Clarinet Saxophone

Clarinet

The Physics of Musical Instruments – Fall 2017 – November 7– 24 Topics

• How reeds work • Woodwinds vs brasses • Finger holes – a reprise • Conical vs cylindrical bore • Changing registers • Role of the bell • Woodwind timbre • Clarinet demonstration

The Physics of Musical Instruments – Fall 2017 – November 7– 25