the jordan loudspeaker manual chapter 3

7/29/2019 The Jordan Loudspeaker Manual Chapter 3

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Chapter 3: MUSICAL INSTRUMENTS.

There can be no better way of illustrating the nature of sound than by lookingat the way sound is produced by traditional instruments of music. Mostinstruments, with the exception of some of the percussion family, areconstructed to enhance harmonically related, high Q resonances, whichdetermine the pitch of their notes and define their tonal character. The

development of orchestral instruments has taken place over many centuriesand the tonal quality of good instruments is beyond objective analysis. (Ionce visited a company that manufactured cathedral organs and had theopportunity to watch the fine-tuning of organ pipes. The tuners lacked myunderstanding of the physics and mathematics of what they were doing, butthey could do it. I could not).

Stringed instruments control pitch by the mass, tension and length of theirstrings. A stretched string will resonate when stimulated, for example, bystriking, plucking or bowing. The frequency of resonance is determined by itslength, tension and mass per unit length. In addition to its fundamentalfrequency the string will also simultaneously resonate at the complete seriesof harmonic frequencies.

Fig:3, shows a string vibrating at its fundamental frequency, and at itssecond and third harmonics. The whole series of harmonics will be presentand will add together, as was shown earlier, to produce the characteristicwaveform of that particular string. The nodes where ths string is stationaryare marked N. There will, of course, always be nodes at each end where thestring is clamped.

Fig 3

The Violin family has a dominant place in the traditional concertorchestraand includes the viola, violoncello and double bass. These have four strings,each tuned to a different pitch. The notes are produced by the fingersdepressing the strings against stops on the fingerboard, which effectivelychanges the length of the strings and, therefore, the pitch. The sound isnormally produced by bowing or plucking. The act of bowing imparts its own

composite waveform to the string. As the bow is drawn across the string, thestring adheres the bow hairs and is displaced in the direction of bowing untilthe increasing tension in the string overcomes its frictional adhesion to thebow and it springs back to a point past its original position of rest when theprocess is repeated.

This results in the saw-tooth waveform shown in Fig; 2a. The vibrationsfrom the strings are transmitted to the body of the instrument via the bridgewhere they are reinforced and the harmonic structure enhanced by its shapeand structure to provide unique qualities of the violin sound.

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The Classical Guitar has many practical similarities to the violin but has sixstrings, which are made of steel and played by plucking. The sound quality ismuch sharper and brighter than that of a plucked violin due to the lowerinternal friction and, therefore higher Q of the steel strings giving moreprominence to the upper harmonics.

The Harp, Together with the flute, has existed in various forms since pre-

history. Cycladic figurines circa 1500 BC depicting these instruments can befound in the Archaeological Museum of Athens and copies in every Greektourist shop. The shape, which is familiar to most people, may be roughlydescribed as a triangle standing on one corner with one side nearly vertical,which is known as the pillar. The strings are stretched, parallel to the pillarbetween the other two sides. The upper side is elegantly curved toaccommodate the required string length whilst the lower side is hollow andacts as a resonator to enhance the sound. The sound is produced by pluckingthe strings.

Fig: 4

The Piano can be regarded as both a stringed and a percussion instrument.It has separate strings for each note, the lowest of which is produced by astring vibrating at about 27.5 times per second. (27.5Hz) and the highest at4224 Hz. Middle C is 264 Hz. At rest the strings are in contact with

dampers. When a key is depressed the damper lifts and the hammer strikesthe strings. When the key is released the damper falls back to the stringssubduing the note, in other words reducing the Q of the string after thestrike. The piano also has two pedals, soft, (piano) and loud, (forte). Thefirst, when depressed, keeps the dampers in continued contact with the

string, the second keep the dampers away from the string. From this, theinstrument gets its name: pianoforte, usually contracted to piano.



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Wind instruments. Produce notes by resonating columns of air in pipes.Any pipe, even a drainpipe will produce a note if stimulated by tapping oneend. This is explained by reference to Fig: 5, If a momentary air pressure iscreated at one end of an open pipe this will travel at a little less than the

speed of sound to the far end of the pipe where it will be expelled. Theresulting vacuum will suck a corresponding air pulse back into the pipe,which will then travel back to the beginning where, assuming no frictionallosses, the process would repeat resulting in a tone of a specific pitch. Thetime taken for the pressure pulse to travel the length of the pipe and backwould depend upon the length of the pipe. If the far end of the pipe wereclosed the incident pressure would not be expelled but reflected back. Thetime between two successive pressure pulses would be half that of an openpipe This is illustrated where points of zero pressure and maximum pressureare called nodes and antinodes respectively.

Fig 5

The waveform shows the nodes and antinodes over a complete waveformcycle. Nodes can only occur at the open ends of a pipe where the air is freeto move and the pressure is zero. Therefore, the fundamental resonance of aclosed pipe corresponds to the frequency where the length of the pipe isequal to a quarter wavelength. That of the open pipe corresponds to thefrequency where its length is equal to a half wavelength which is an octavehigher that that of the closed pipe. Following the same argument it can beshown that the closed pipe will resonate at every odd harmonic of thefundamental frequency whereas the open pipe will resonate at the full seriesof harmonics. Wind instruments use open pipes.

The Flute originates from the reed pipes of pre-history. Notes are produced

by the players breath impinging upon a sharp lip in the mouthpiece creatingvibrating eddy currents. Early instruments comprised a wooden pipe withholed drilled along its wall. Opening and closing the holes with the fingersproduced notes by altering the effective length of the pipe. The tonal rangewas limited by the number and position of the holes that could be reached bythe fingers. The modern flute is frequently made of silver, has 13 holesreached by a system of levers and pads and covers a range of 3 octavesstating at middle C.



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The Oboe, Clarinet and Bassoon are reed instruments where the playersbreath agitates a reed in the mouthpiece which produces a sharper quality ofsound. All work on the resonant pipe principle but each has its own verydistinctive harmonic signature.

The Saxophone, although made of brass is classified as a woodwindbecause its similarity in note production and the fingering is exactly like thatof the clarinet.

Brass instruments. These includethe Bugle, Trumpet, Horn, Tuba andTrombone Again the sounds are produce by pipe resonances but, in additionto their being made of brass, there are other essential differences from thewoodwinds inasmuch as the resonances are stimulated by the player forcingbreath through lightly closed lips The notes available to the bugle player arelimited to the harmonic series determined by its length, which is fixed, butspecific harmonics can be selected by varying the strength of the breath andlip muscle tension, the player. Notes from the trumpet, horn and tuba areproduced by changing the actual length of the pipe by means of finger-controlled valves. The trombone achieves this by a telescopic slid allowing acontinuous change of pitch.

Percussion instruments. These embrace a very wide range of instrumentsthat are played by being struck. Familiar examples in the concert orchestrainclude the piano, tubular bells, xylophone and triangle all of which producenotes of a specific pitch with harmonically related resonances, and thetimpani, bass drum, snare drum and cymbals which do not. Drums utilize atightly stretched skin over a circular frame. The tympani, (sometimes knownas kettledrums), of which there are never less than two but usually three orfour, are shaped like large copper caldrons with the skin and frame are fittedover the open top. They are tunable by varying the tension of the skin via aframe mechanism connected by a lever to a pedal. Unlike other tuned

instruments, the overtones are not harmonically related to the fundamental.This is also true for the bass and snare drums, which are not tuneable. Thesound of the cymbal is an excellent example of a very wide range of high Qnon-related overtones.

This has not been an exhaustive tour of the concert orchestra by any meansbut it does serve to show the efforts that have been made over the centuriesto secure the uniquely remarkable sonic qualities of each and everyinstrument described.

Now take 32 violins, 12 violas, 12 violoncellos, 8 double basses, 1piccolo, 3 flutes, 3 oboes, 3 clarinets, 1 bass clarinet, 3 bassoons, 1

double bassoon, 8 horns, 5 trumpets, 3 trombones, 2 tubas, 4tympani, 1 bass drum 1 snare drum, 1 triangle and 1 cymbal. Now

garnish with a full chorus and organ. Imagine now the conductorbringing his baton down on that last thunderous chord with everyone of these running at full throttle. Reproduce that in full detail and

spatiality and we are talking he Golden Age of Hi-Fi.

.and all from a 4 inch metal foil cone.


the jordan loudspeaker manual chapter 3

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