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The Physics of the Pump Organ
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 reedvalve. 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).
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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 footpedal 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).
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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.
Guidepins are implemented into the manual action of the key. Two guidepins 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.
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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.
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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 wavelengh, 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.
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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.
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 |
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
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 |
Bibliography