The Physics of the Pump Organ

By Kristina Knupp

Overview

The reed organ, in various forms, has existed for hundreds of years. In China, the reed organ was in the form of a mouth instrument. The next advancement in the reed organ occured early in the nineteenth century, when pressure harmoniums were constructed in England and France. The reeds of these instruments sounded when air was blown over them. The first full reed organ that operated on the vacuum principle, however, is thought to be created by Alexandres of Paris around 1835. These instruments sounded when air was pulled across the reeds and a vacuum was formed. Vacuum operated organs were the principle type of organ constructed in the United States.

The reed organ used explicitly for this research was constructed by W.W. Putnam and Company of Staunton, Virginia in 1901. This project examines the physics of the pump organ by looking at several different aspects of the instrument. First, the mechanics of various actions of the organ were analyzed. These actions include the reeds, bellows, keys and stops.  Secondly, the frequency of each note was discovered using an oscilloscope and wave analyzer. Finally, the effect of each stop on a particular set of notes was studied.

The Reeds

The reed organ, commonly known as the pump organ, is a reed instrument. "The reed instrument consists of an air-actuated vibrating reed which interrupts the acting air stream at the vibration frequency of the reed." (Olson 138). In the case of the reed organ, the reed is made of brass and is clamped at one end, like a cantilever bar. It is a free reed which does not strike a surface; instead, it is coupled directly with the air (Rossing "The Science" 240).

A reed is divided into several sections. The front rounded portion is termed the toe, while the end of the reed attached to the frame is termed the heel, and the vibrating part is called the tongue. The reed is inserted into a reed cell which is a small opening in a block of wood which in turn is mounted on the reed pan. The reed pan, also called the reed chest or sound board, is the foundation for the reed cells. This structure is a shallow box which resembles an inverted pan.

The reed cells that support a certain group of reeds are sealed off with triangular pieces -- termed mutes. When a given stop is pushed in, the mute is shut, and the reed associated with that note does not play. Reeds are divided into two ranges, high notes or the treble clef and low notes or the bass clef. One mute will control all of the reeds in a specific register.

The openings under the reed pan are covered with a piece of wood termed the pallet or reed valve. The pallets, which cover two reed openings, are felt and leather covered. A spring action pushes the leather to seal the opening and prevent air from entering the reed cell. In order to raise the pitch of a particular note, the flat surface or tongue is filled in with brass near the toe or vibrating end. On the other hand, the pitch is lowered by filling in the tongue of the reed with brass near the heel or clamp end (Getz 154). On the contrary, the same effect can be reached if the vibrating end is filed, effectively raising the pitch, or the clamp end is filed, thus lowering the pitch. In this manner the reed organ can be tuned.

A stream of air, sent from the bellows, causes the reed to vibrate, thereby initiating a sound. The fundamental frequency of the free reed is controlled by two factors. First, the blowing pressure, or excess pressure in the wind box, and secondly, the elastic properties of the reed both affect the frequency with which the reed resonates. "In general, the vibratory motion of a reed is complex, except at very small amplitudes for which it is nearly sinusoidal" (Roederer 116). The frequency with which the forces acting on the reed occurs is very low, therefore the motion of the reed corresponds to the motion of the air, while the magnitude of the reed motion is primarily determined by the reed's springiness (Benade 38).

The reed dimensions can actually be calculated to give the resonant frequency of the reed. The brass reed, unlike the piano string, is not under tension. Therefore, the restoring force is due entirely to the springiness of the reed. "The fundamental frequency is given by f = (0.5596/l^2) (QK2/r)^½ where l is the length of the bar in centimeters, is the density in grams per cubic centimeter, Q is Young's modulus in dynes per square centimeter, (and) K is the radius of gyration. For a rectangular cross section, the radius of gyration is K = a/12 where a is the thickness of the bar in centimeters, in the direction of vibration" (Olson 76).

A bar clamped at one end, like the reed, involves various modes of vibration. For each mode, a different tone results and there are a unique number of nodes that occur along the reed. The frequency, as a multiple of the fundamental frequency, f1, also increases with an increase in the number of nodes (Olson 76).

"The player (by pumping the bellows) supplies a steady flow of air to his instrument, which is converted into a regular sequence of puffs by the back and forth motion of the reed" (Rossing "Musical Acoustics" 99). In contrast to a piano, whose note dissipates when the struck string stops vibrating, the pump organ is a self sustaining oscillator. This means that sound will occur as long as air is supplied and allowed to flow through the reed. The reed of the Pump organ works on a vacuum. The air is drawn "from the outside, through the reed and into the main bellow" (Presley 297). The reed undergoes a specific type of action. First, air is forced through the reed while it is in its normal position. After the air initially rushes through, the opening through which the air has moved is suddenly reduced because the pressure on the flow side is reduced, according to Bernoulli's theorem (Berg 257). The Bernoulli effect occurs when "the pressure in a fluid is decreased when - the flow velocity is increased" (Fletcher 235). When the opening is thus reduced, the airflow is also reduced. Therefore, the pressure on the flow side of the reed is increased, and the reed resumes its original position. With the energy the reed gained from its movement, it exceeds its original position. This larger opening that is created reduces the pressure on the flow side of the reed as the air rushes through, and the reed resumes its normal position (Olson 139).

The Bellows

The bellows, operated by a hand lever or by two foot pedals, supply the vacuum which draws the air over the reeds. The sides of the bellows are fluted and collapsible. When the bellows are expanded, the vacuum occurs and the bellows are filled with air. Contrarily, when the bellows are collapsed, excess air is discharged from the system.

"The bellows consists of two main parts: the main vacuum reservoir and the exhauster bellows that are activated by the foot pedals. As the foot pedal is depressed, the exhauster is drawn out, causing the exhauster valve to close and the inside valve to open. This action allows air to be drawn out of the reservoir" (Presley 51). Then the foot pedal resumes its original position, a spring pushes the exhauster to the reservoir. The valve on the reservoir closes so the vacuum is maintained, and the valve on the exhauster opens "allowing the air it has drawn out of the main reservoir to escape" (Presley 51).

The exhauster is attached directly to the foot pedals. The exhauster pulls air from the main bellows, creating a partial vacuum. Each bellow has a one-way intake valve. This device allows air to enter but prevents air from escaping. A similar valve is located in the wind chest, which is positioned between the bellows and the action (Anderson 99).

A safety valve is also used on the bellows. When the fluid sides reach a certain height, a string is pulled which opens the valve. In sane cases, the valve is more primitive. A hole is cut directly in the bellows chest and is covered by a block of wood suspended by a leather hinge. In this case, when the bellows reach their maximum capacity, air is forced through this hole and the wooden block is lifted. Therefore, extra air can escape and the bellows will not burst because of excessive air pressure.

In order for a quality note to be issued by the reeds, it is highly important that the pressure of the air from the bellows remains relatively constant. In order for this to occur, the folds in the bellows work in opposite directions. Therefore, if the bellows are nearly empty or almost full, the pressure is basically equal. "If the folds were both inside or both outside folds, the pressure would be constantly varying" (Wicks 105).

The wind pressure of the bellows can be determined through the the implementation of a mercury manometer, a U-shaped glass tube half filled with mercury. One end of the tube is connected to the wind chest or bellows. When air enters or leaves the tube from the bellows, the mercury in the two prongs of the manometer equilibrates at different heights. This difference represents the amount of pressure in the wind chest.

The wind pressure can be determined by the equation P = Pa + rgh. Pa represents the pressure of the atmosphere, r equals the density of the mercury, g equals the force of gravity and h is the height the mercury gained or lost. If h is positive, the pressure of the system is greater than atmospheric pressure. If h is negative, the pressure of the system is less than atmospheric pressure, and a partial vacuum is created (Serway 399).

Different wind pressures are characteristic of organs with specific uses. A typical parlor organ may have a pressure between 40 and 130 nm, while a theater organ which requires more volume ranges from 300 to 450 nm (Anderson 100).

The Keys

"The key is the end of a lever system, actuated by the fingers, in conjunction with a valve for controlling the air flow which actuates a reed" (Olson 196). The keyslip is the panel directly under the keyboard which covers the reed. Guide pins are implemented into the manual action of the key. Two guide pins are used for each key. One extends through the rear end of the key and allows the key to pivot up and down. The pin at the front of the key fits into a felt-lined cavity. This prevents a side-to-side motion at the front of the key.

A pitman is a devise that connects the organ key and the pallet. A depressed key pushes this rod down which opens the pallet and permits air to be drawn through the reed. A pitman is also employed when an octave coupler is used. In this case, another rod, the coupler collar, is glued to the dowel about one-third of the way from the top. This device allows the musician to depress one key but sound two notes of the same octave. The keys are prevented from rebounding by the use of a thumper. A heavy piece of wood, lined with felt, rests on the keys in a vertical groove in the keys. When a key is firmly or repetitiously pressed, the key will not continue to oscillate after the initial movement is discontinued.

The Stops

The stop is a mechanical device that serves to open mutes that allow air to flow through the reeds. A stop can also combine various ranks of reeds or can alter the amount of air that flows out of the reeds. Two types of stops, speaking and mechanical, exist in the pump organ. Speaking stops control the amount of air that reaches the reeds, and mechanical stops act as secondary controls for such apparatus as the vox humana and the octave coupler (Presley 45).

The stops control the mutes to different degrees. If a mute is opened only slightly, the sound will be soft. If the reed is opened fully, the resulting tone will be louder. The stop action also controls the swell. The swell is "a hinged flat panel that covers the entire front or back set of reeds" (Presley 29). When the swell stop is fully extended, this hinged flap is opened and the sound is louder. In essence, the swell stop is a form of volume control.

The mechanics of the stop action are quite complex. The stop knob, on the outside of the case, is attached to a rod that extends to the inside. The rod is attached to another dowel at a right angle with a pin. The other end of the dowel supports a trundle or upright roller.

Another wooden piece extends from the adjacent side of the trundle. A second pin connects this piece to another dowel which leads to a lever which pulls the mutes open and closed. When the stop is fully extended, the dowel moves backward, rotating the trundle and finally pulling the lever backward.

Sound Waves

Sound is produced by alternating pressures, displacing a particle or oscillating a particle in a particular medium with a certain frequency. In the pump organ, sound is produced when the medium is set into motion. The sound is generated when the vibrating reed converts an otherwise steady stream of air into a pulsating one.

Sound waves exhibit such characteristics as constant velocity, frequency, and wavelength. First, waves are propagated with a velocity of c = (gPo/r)^½ (Equation 1) where g is the ratio of specific heat for air, Po is the static pressure of the air, and r is the density of the air. Specific heat is the amount of heat (measured in calories) required to raise the temperature of one gram of a substance one degree centigrade. When an increase in pressure occurs, there is a proportional increase in density. Therefore, if the temperature remains constant so the density is steady, the velocity must remain constant. Finally, the speed of sound in air as a function of temperature is c = 33,100 (1 0.00366t)^½ (Equation 2) where t is measured in centigrade.

Secondly, sound waves cause a change in pressure from the static pressure or the atmospheric pressure when there is no sound. The instantaneous sound pressure, which occurs when sound is heard, is the difference between the static pressure and the total instantaneous pressure.

Thirdly, there is a direct correlation between the frequency and wavelength of sound waves. The frequency, measured in Hertz, is the number of waves, or cycles, which pass an observation point per second. The wavelength is the distance a wave travels in one cycle and can be calculated from the frequency measurement. If c is the velocity of propagation, l is the wave lenth, and f is the frequency, then the three variables are related by c =lf (Equation 3). When the sound waves occur, energy is transmitted. This transmission of energy per unit area per unit time is called intensity. The intensity, I, is given by I = p^2/2rc (Equation 4) where p is the bellows pressure, r is the density of the air and c is the velocity of the sound wave. The intensity is also equal to the square of the amplitude.

"Pitch is primarily dependent upon the frequency, of the sound stimulus" (Olson 25). The difference in pitch for similar notes is called an octave. The ratio of basic frequencies of these particular notes is equal to two. On the equally tempered scale in the key of C, the frequencies cover a range of 16 to 16,000 Hertz.

In musical terms, two different scales exist to which instruments are tuned. These two scales are the just intonation scale and the scale of temperment. "A scale of just intonation is a musical scale employing the frequencies intervals represented by the ratios of the smaller integers of the harmonic series" (Olson 39). For example, the ratio of an ocatave is 2:1 while the ratio of a semitone is 16:15, the ratio of a major tone is 9:8 and the ratio of a minor tone is 10:9.

"Temperment is the process of reducing the number of tones per octave by alternating the frequency of the tones from the exact frequencies of just intonation. In the equally tempered scale, the octave is divided into 12 intervals in which the frequency ratios are as follows: 1, f, f^2, f^3, f^4, f^5, f^6, f^7, f^8, f^9, f^10, f^11, f^12 where f^12 = 2 or f = 2^1/12 (Olson 47). The Putnam organ, along with the piano, is tuned to the scale of equal temperment. This scale is used where the scale of just intonation would be impossible to use. In the reed organ, the tuning is fairly permanent and fixed. The tone of the reeds are not readily or easily changed. Therefore, "the just scale would not be practical because the number of fixed resonating systems would be too great" (Olson 54).

The reed organ produces both fundamental and over tone frequencies. "The fundamental frequency is the lowest frequency conponent in a complex sound wave" (Olson 202). The frequency ranges of the overtones exceed the fundamental frequency by one to two octaves.

Both overtones and the fundamental frequencies combine in the correctional phase and with corresponding amplitudes to produce a complex wave. For example, the frequency of the second harmonic is two times that of the fundamental frequency. Therefore, the amplitude of the second harmonic will equal half of the ampliltude of the fundamental. Likewise, the frequency of the third harmonic is three times the fundamental and the amplitude is equal to one third the amplitude of the fundamental.

Mathematically, the complex wave is explained by Pr = P1 + P2 + P3, where P represents the frequencies of each harmonic. Each different harmonic can be described by Pr = 1/n sin(nwt), where n = 1 represents the fundamental frequency, n = 2 stands for the second harmonic and so forth; w equals 2pf, f represents the frequency and t stands for the time.

The Experiment

The experimental frequencies were discovered by using several different instruments. Each tone of the organ was recorded with a tape recorder when all of the sounding stops were opened. These tones were then fed into an amplifier set on the band pass mode. This mode blocked out all over-ones and left the fundamental frequency. The amplifier was then connected to a speaker and an oscilloscope.

An oscilloscope displays a time varying voltage in visible form on a screen. The cathode-ray tube, the main component of the oscilloscope, emits a continuous beam of electrons. "The electron stream is fired at a screen which has been treated with a special material that phosphoresces and gives off light when struck by the electrons" (Plintik 46). A waveform is produced on a screen when a fluctuating voltage, from the organ tone, moves up and down and is swept horizontally. The horizontal axis stands for time, while the vertical axis represents the amplitude.

In order to determine the frequency of each note on the organ, a function generator was also connected to the oscilloscope. The function generator allowed one to vary the frequency of the vertical axis. Since the frequency of the function generator matched the frequency of the organ, a circular Lissajou figure resulted on the oscilloscope screen.

The different stops on the organ cause specific portions of the keyboard to be muted. In order to discover how the volume changed with the opening and closing of different stops, four notes each in the treble and bass clefs were played with different stops opened. The amplitude resulting on the oscilloscope is directly related to the volume emitted by the organ. The intensity of the sound is the square of the amplitude. These intensities can then be converted into decibels using the formula b = 10 [log (I/Io)] where b is the sound intensity level in dB, I is the sound intensity, and Io is the threshold of hearing intensity of 10^-12 W/m^2.

In this particular experiment the amplitude was gained by reading the amplitude of the wave off of the oscilloscope screen. In this case, a recorder, in which the internal amplifier could be turned off, was used to tape the tones produced by the organ. As each stop was pulled and the same four notes were played, the rate at which the bellows were pumped was kept relatively constant. The taped tones were fed into the oscilloscope and the wave amplitudes were read. Therefore, the amplitude readings are relevant to each other.

Table 2: Amplitude of Specific Notes Using Individual Stops of the Treble Clef

Note

Middle C

E

G

C

Stop #1 - Celeste Amplitude

8.0

3.0

1.5

7.0

Stop #2 - Melodia Amplitude

10.0

3.0

1.0

6.0

Stop #3 - Aoline Amplitude

9.0

3.0

2.0

3.0

Stop #4 - Forte Amplitude

2.5

1.5

3.0

6.0

Table 3: Amplitude of Specific Notes Using Individual Stops of the Bass Clef

Note

E

G

C

G

Stop #1 - Dolce Amplitude

1.0

4.0

3.0

1.5

Stop #2 - Diapson Amplitude

1.0

7.0

6.0

2.0

Stop #3 - Viola Amplitude

4.5

5.5

5.0

2.0

Stop #4 - Dulciana Amplitude

4.0

5.0

4.5

3.0

According to Table 2, the amplitude, and thus the volume, changes for each individual note for the separate stops. Middle C changes from an amplitude of 8.0 to 10.0 to 9.0 to 2.5. The note E stays constant at 3.0 for three of the stops and drops to 1.5 for Stop #4, or Forte. The G ranges from 1.0 to 3.0 while C remains constant for two stops, then increases by 1.0 or decreases by 3.0. Overall, the volume of the organ as a result of opening the stops increases in the following order: Forte, Aoline, Celeste, and Melodia.

According to Table 3, E remains at 1.0 for two stops and jumps to 4.0 and 4.5 for the remaining two stops. G ranges from 4.0 to 7.0. C, which is one octave below middle C, differs by approximately one integer from 3.0 to 6.0, while G ranges from 1.5 to 3.0, with two identical readings. Overall, the volume of the bass clef as a result of openinq the stops increases in the following order: Dolce, Diapson, Dulciana and Viola.

Calculation of the air pressure in the bellows when the manometer reading is 0.2 cm.

P = Pa + ggh
P = (1.01 x 10^5 Pa) +(13.6 x 10^3 kg/m^3)(9.80 m/s^2)(.002m)
P = 1.01 x 10^5 Pa

The difference in pressure from atmospheric pressure and the pressure in the bellows is

DP = (1.01 x 10^5 Pa) - (1360.802 Pa)
DP = 9.99 x 10^4 Pa
Therefore, the pressure in the bellows is greatly below atmospheric pressure. The speed of sound in air can be calculated using Equation 2

c = 33,100 ( 1 + 0.00366t)^½
If room temperature is 22.2 degrees centigrade, then
c = 3.31 x 10^4 cm/s

According to Equation 3, the wavelength of each note can be determined. l = c/f where c is the velocity and f is the frequency. Therefore, the wavelength of each C on the keyboard is: l = (3.31 x 10^4 cm/s)(65.2 Hz) l = 508 cm

l = (3.31 x 10^4 cm/s)(130.8 Hz) l = 253 cm

l = (3.31 x 10^4 cm/s)(261.2 Hz) l = 127 cm

l = (3.31 x 10^4 cm/s)(522.4 Hz)
l = 63.4 cm
l = (3.31 x 10^4 cm/s) (1047.8 Hz)
l = 31.6 cm

Table 1: Intervals, Experimental and Given Frequencies, Periods and Angular Frequencies of each note

Note

Interval on Scale of Equal Temperment

Experimental Frequency (Hz)

Given Frequency (Hz)

Angular Period (s)

Frequency (rad/s)

F

1.334

43.5

43.7

0.023

273

F#

1.411

46.0

0.022

289

G

1.491

48.6

49.0

0.021

305

G#

1.586

51.7

0.019

325

A

1.672

54.5

55.0

0.018

342

A#

1.773

57.8

0.017

363

B

1.871

61.0

61.7

0.016

383

C

2.000

65.2

65.4

0.015

410

C#

1.054

68.7

0.015

432

D

1.117

72.8

73.4

0.014

457

D#

1.186

77.3

0.013

486

E

1.261

82.2

82.4

0.012

516

F

1.337

87.2

87.3

0.011

548

F#

1.414

92.2

0.011

579

G

1.498

97.7

98.0

0.010

614

G#

1.600

104.3

0.001

655

A

1.683

109.7

110.0

0.009

689

A#

1.770

115.4

0.009

725

B

1.887

123.0

123.5

0.008

773

C

2.006

130.8

130.8

0.008

822

C#

1.059

138.5

0.007

870

D

1.119

146.4

146.8

0.007

920

D#

1.185

155.0

0.006

974

E

1.252

163.8

164.8

0.006

1029

F

1.339

175.1

0.006

1100

F#

1.419

185.6

0.005

1166

G

1.494

195.2

196.0

0.005

1226

G#

1.594

208.5

0.005

1310

A

1.675

219.1

220.0

0.005

1377

A#

1.778

232.6

0.004

1461

B

1.877

245.5

246.9

0.004

1542

mid C

1.997

261.2

261.6

0.004

1641

C#

1.052

274.8

0.004

1727

D

1.128

294.7

293.7

0.003

1852

D#

1.193

311.5

0.003

1957

E

1.259

328.8

329.6

0.003

2066

F

1.336

348.9

349.2

0.003

2192

F#

1.415

369.6

0.003

2322

G

1.493

390.1

392.0

0.003

2451

G#

1.585

414.1

0.002

2602

A

1.671

437.4

440.0

0.002

2748

A#

1.775

463.5

0.002

2912

B

1.892

494.2

493.9

0.002

3105

C

2.000

522.4

523.3

0.002

3282

C#

1.059

553.1

0.002

3475

D

1.121

585.6

587.3

0.002

3679

D#

1.193

623.0

0.002

3914

E

1.257

656.6

659.3

0.002

4126

F

1.337

698.4

698.5

0.001

4388

F#

1.421

742.5

0.001

4665

G

1.501

784.0

784.0

0.001

4926

G#

1.586

828.5

0.001

5206

A

1.680

877.4

880.0

0.001

5513

A#

1.775

927.1

0.001

5825

B

1.884

984.3

988.0

0.001

6185

C

2.006

1047.8

1046.5

0.001

6584

C#

1.064

1114.4

0.001

7002

D

1.124

1177.4

1174.7

0.001

7398

D#

1.189

1245.6

0.001

7826

E

1.260

1320.6

1318.5

0.001

8298

F

1.335

1399.0

1396.9

0.001

8790

According to Table 2, the interval on the scale of equal temperment calculated from the experimental data is given. This data has an uncertainty ± 0.002. These experimental calculations can be compared to the standard values given in Appendix A. The experimental frequency is also given. This data has an uncertainty of ± 0.1. The readings from the wave analyzer, in the experimental columnm, can be directly compared to the given frequencies of the whole notes. The period, given in column four is one over the experimental frequency. Finally, the angular frequency of the last column is calculated by dividing 2 by the period.

Conclusion

The main objective of this project was to identify several physical principles that lie behind the operation of the pump organ. In order to accomplish this goal, the frequencies of each note were determined. These frequencies were extremely close to given frequencies. This discovery was quite surprising considering all of the reed tuning was done by ear when the organ was constructed. Secondly, the role of the stops in the changing of the volume of the organ was analyzed. Finally, the physical mechanics of the inner workings of the organ were studied.

Overall, the tone of each note on the organ maintains surprisng accuracy even after years of use, which points to quality construction and ingenious design.

Interval

Frequency Ratio from starting point

Corresponding Note

Unison

1:1

C

Semitone/
Minor Tone

1.059:1

C#

Whole Tone/
Major Tone

1.122:1

D

Minor Third

1.189:1

D#

Major Third

1.260:1

E

Perfect Fourth

1.335:1

F

Diminished Fifth/
Augmented Fourth

1.414:1

F#

Perfect Fifth

1.498:1

G

Minor Sixth

1.587:1

G#

Major Sixth

1.682:1

A

Minor Seventh

1.782:1

A#

Major Seventh

1.888:1

B

Octave

2:1

C

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