Resonant Air Column in Wind Instruments

Abstract

Wind musical instruments are aerophone, producing sound through the vibration of an air column. A simplified model of a wind instrument includes the source of air, the sound generator, the resonating air column and the radiation of sound. If we make reference to how air column is excited by means of vibrating reed, the following classification of wind instruments can be proposed: mechanical reed instruments, lip valve instruments and air jet instruments. For clarinet, oboe, bassoon, saxophone—the playing pitch is based on the first two modes of the resonating air column. The length of the air column of these instruments is adjusted by tone-holes that are opened or closed in various combinations to play a required musical note. The geometry of lip driven instruments (horn, trombone, trumpet, etc.) is rather simpler than that of air jet or mechanical reed instruments (clarinets, oboes, etc.). At the same time lip driven instruments are more difficult to manufacture. The resonance peaks observed on an impedance graph are located at the harmonics of the vibrating air column of a specific length. The alignment of input impedance peaks is a very important property of a brass instrument for its acoustic response and for accurately playing different notes in tune. Acoustical behaviour of wind instruments can be studied through their acoustic impedance spectrum, measured at embouchure or “input” to the instrument. The acoustic impedance is defined as the ratio of acoustic pressure to acoustic volume flow. Commonly the input impedance variation is represented versus frequency, illustrating the linear acoustic response to a sinusoidal input signal.

Appendix

Qualitative appreciation of the effects of geometric parameters of the mouthpiece on brass instruments’ playability (data from www.dannychestnut.com, 30 April 2015)

Inner diameter	Smaller	High register easier to reach, better fit for smaller embouchure	Tendency to play sharp, thinner, with a more brittle tone , and lack of endurance
	Larger	Low register easier to reach, better fit for larger embouchure	Tendency to play flat, darker, with a fuzzy tone , and lack of endurance
Rim thickness	Thicker	More endurance, better for thin lips	Less response and flexibility
	Thinner	Better response, more definite placement, better for thick lips	Less endurance
Rim contour	Flatter	More endurance, more stability	Less response and flexibility
	Rounder	Better response, more definite placement	Less endurance
Crown	Higher	Better response, more definite placement	Less endurance
	Lower	More endurance	Less response
Rim bite	Sharper	Better response	Less endurance
	Rounder	More endurance	Less response
Cup	Shallower	High register easier to reach, better fit for smaller embouchures	Thinner, brighter tone
	Deeper	Low register easier to reach, better fit for larger embouchures, bigger, darker sound	Darker, fuzzy tone
	“C”	Bigger, darker sound with more warmth	More resistance, larger volume of air to control
	“V”	Brighter sound, more projection	Less resistance, thinner sound
Throat	Larger	Less resistance, darker sound	High register harder to attain, fuzzy sound
	Smaller	Brighter sound, more projection	More resistance, thinner sound
Bore	Larger	Less resistance, darker sound	High register harder to attain, fuzzy sound
	Smaller	More resistance, brighter sound	Stuffy, thinner sound
Backbore	Larger	Less resistance, darker sound	High register harder to attain, fuzzy sound
	Smaller	More resistance, brighter sound	Stuffy, thinner sound
Mass	Less	Increased projection, response, comfort	Thinner sound
	More	Intensify, darken, and stabilize tone	Decrease projection and response