World of Sound

“A World of Sound”
An Organ Concert with Physics Interludes
Presented by Dr Laurence Rogers
Emeritus Senior Lecturer in Education, University of Leicester, UK
Given to Celebrate the 50th Anniversary of GIREP at the 2016 Seminar, Krakow
on 31st August 2016 at the Church of St. Stanisław Kostka, Dębniki
Introduction
The use of pipes to make musical sounds goes back to antiquity. Certainly pipe organs have been built since
Roman times and through generations of innovation ranks of pipes became organised with keyboards to play music.
By the 16th Century the organ as we know it, with multiple pipes, bellows, manuals, stops and pedals, had evolved.
Builders had discovered how to create new sounds by combining the sounds of several pipes at different pitches
simultaneously. Borrowing ideas from harmony, a system of creating musical intervals of octaves (8 notes apart),
fifths and thirds evolved, a system which forms the basis of organ design to the present-day.
In the 19th Century builders invented many new sounds imitating musical instruments of the orchestra, including
strings, enabling the organ to function as a whole orchestra. In the latter half of the 19th Century organ concerts
featuring transcriptions of orchestral music were popular and could be heard in town halls and concert halls
throughout England. In the early part of the 20th Century organs provided popular musical entertainment in cinemas,
frequently including percussion departments. In our own lifetime the sounds from pipes have been recorded, digitised
and stored in computers such that you can now play the sounds of numerous historic organs of your choice from a
keyboard connected to a personal computer. The pipe organs we inherit today truly offer a ‘world of sound’.
There is much that the tonal structure of a pipe organ can teach us about physics; the characteristics of sound as
understood by physicists and mathematicians are beautifully demonstrated on the organ. At the simplest level, the
instrument is a sound synthesizer, capable of creating an enormous palette of different sounds. Of particular interest
to physicists, the organ facilitates the study of sound waves, tonal quality, beats, harmonics, Fourier analysis,
intonation and temperament. The properties of interference, diffraction, resonance, reverberation are ever-present in
the physics story that the organ can tell. This concert, whilst offering a programme of music as entertainment,
includes demonstrations and commentary exploring the synergy between physics and organs.
The guiding principles for the choice of pieces have been to illustrate the variety of tones and textures of the
instrument and the many different moods of organ music in both sacred and secular contexts.
Programme
Sinfonia from Cantata No.29
Prelude on the Welsh Hymn Tune ‘Rhosymedre’
Voluntary in A minor
Offertoire sur les Grands Jeux
J.S.Bach (1685-1750)
R.Vaughan Williams (1872-1958)
John Robinson (1682-1762)
François Couperin (1668-1733)
Physics interlude – Sound production, Resonance, Harmonics
Fanfare for the Common Man
The Prince of Denmark’s March
Prière à Notre Dame & Toccata
Aaron Copland (1900-1990)
Jeremiah Clarke (1674-1707)
Léon Boëllmann (1862-1897)
Physics interlude – Fourier Analysis, Diffraction, Acoustics
Cannonade
Sortie in E flat
Scherzo for the White Rabbit
Toccata & Fugue in D minor BWV 565
Claude Balbastre (1727-1799)
A.L.J.Lefébure Wély (1817-1870)
Nigel Ogden (b.1954)
J.S.Bach (1685-1750)
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The organ as an instrument
By definition, a pipe organ uses pipes to make music! The number of pipes needed often surprises lay observers,
because, apart from those on display in the case facade, the vast majority of pipes are not visible, being hidden within
the instrument. The organ at the Church of St Stanislav Kosta, Dębniki, Kraków, has approximately 2,700 pipes. As
with all pipe organs, every single pipe is hand-made and individually 'voiced' for the building in which the instrument
is situated. As will be explained later, the acoustic properties of the building have a vital effect on the ultimate quality
of sound and hand finishing and fine tuning of the pipes to match the acoustic demands a high degree of skill. Pipes
are made from either wood or metal. The latter is usually an alloy of lead and tin, but zinc is sometimes used for very
large pipes.
At Dębniki, the organ, being elevated in the western gallery, is in an ideal position for the egress and blending of
sound. The design of the case makes the four divisions within the organ quite explicit:
· Great organ · Swell organ · Positive organ · Pedal organ
Each division is playable from a separate keyboard; three manuals and pedals. These are situated in the console
immediately below the main facade, partially hidden from view in the body of the church. Within each division
there are several ranks of pipes, each specialising in a different tone colour. The player selects one or more ranks
at a time by pulling out the appropriate stops. There are 37 stops at Dębniki, the names of which, in Polish, may be
slightly bewildering, but an organist can recognise a structure common to most organs; pipes are organised in
distinct families according to their tone:
· █ Flutes - sweet mellow tones
· █ Diapasons (or 'principals') - bold bright tones
· █ Reeds - sharp clear tones,
· █ Strings - softer 'thin' tones
· █ Mixtures - brilliant high-pitched tones
(Colours identify the tone families in the specification below.)
The coupling between the stops and keys to the wind mechanisms is entirely mechanical, consisting of multiple
connecting rods and levers, most of which are made of wood. These days, large organs often employ electrical
connection between the keys and electromagnets to control the wind action. This is not the case at Dębniki.
Artistically, mechanical action to the manuals is considered superior to electric action, as it affords expressive
control over the attack and release of notes, so important for phrasing of the music and the articulation of
ornaments such as trills. The challenge to the organ builder is to make such action light enough; if the traction is
too heavy, the organist would have to thump the keys, completely negating the advantages for artistic expression.
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Manuał I Główny
(Great) 10 stops
Manuał II Górny
(Swell) 10 stops
(enclosed with expression)
Manuał III Pozytyw
(Positive) 9 stops
Pedal division
8 stops
█ Bourdon 16′
█ Pryncypał 8′
█ Flet rurkowy 8′
█ Oktawa 4′
█ Gemshorn 4′
█ Flet otwarty 2′
█ Cornett 3-4x
█ Mixtura 6x
█ Fagot 16′
█ Trąbka (Trumpet) 8′
█ Flet drewniany 8′
█ Salicjonał 8′
█ Pryncypał 4′
█ Flet rurkowy 4′
█ Sesquialtera 2x
█ Flet leśny 2′
█ Larigot 1 1/3′
█ Mixtura 4x
█ Dulcjan 16′
█ Szałamaja 8′
█ Flet kryty 8′
█ Quintadena 8′
█ Flet prosty 4′
█ Nasard 2 2/3′
█ Pryncypał 2′
█ Tercja 1 3/5′
█ Oktawa 1′
█ Cymbel 3x
█ Regał 8′
█ Pryncypał drew. 16′
█ Subbas 16′
█ Oktawa 8′
█ Flet basowy 8′
█ Oktawa tenorowa 4′
█ Mixtura 4x
█ Puzon 16′
█ Clairon 4′
Specification of the organ at St. Stanisław Kostka, Dębniki, Kraków, built in 1983 to the design of the Department of Organ W.
Truszczyński, Warsaw.
How does a pipe make a sound?
The basis of all sound is that it emanates from a mechanical vibration. A simple plastic tube can be made to
produce a musical sound of distinct pitch merely by tapping one end. This is hardly practical for a musical instrument
since the percussive method of creating a vibration produces a note which decays very rapidly. A more sustained
sound may be obtained by blowing across the end of the tube. The Peruvian 'pan' pipes use this principle, and they
illustrate the basic relationship between the length of a tube and the pitch of the note produced; the shorter the tube,
the higher the pitch. When we look closely at a typical organ pipe to see how the vibration is produced, we observe
near its base a 'mouth' where a ribbon-shaped jet of air emerges from a narrow slot and directed towards a sharp
horizontal edge.
The physics of this arrangement indicates the
creation of vortices as the jet cuts the sharp edge. A
computer simulation of the air flow reveals how the
jet vibrates from side to side in the wake of the
edge. However, this air vibration alone is
insufficient to explain the sound made by the pipe at
a particular pitch. The column of air in the pipe
above the mouth resonates at a frequency dependent
on this 'speaking length' of the pipe. Wave theory
predicts the formation of a standing wave as the
wave initiated by vibration at the mouth travels up
the pipe and becomes reflected at the upper end. For
an 'open' pipe, an antinode is formed at each end of
the speaking length. Since the distance between
successive antinodes is a half wavelength, the
wavelength of the resonant standing wave is twice
the speaking length of the pipe. A simple
calculation gives the corresponding frequency and
the pitch of the note.
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It may be noted that since the frequency depends upon the velocity of sound, as this varies with climatic conditions,
the general pitch of an organ will also slightly vary. The result is that during the winter the organ sounds at a slightly
lower pitch than during the summer.
It may also be noted that, despite global metrication in many fields, organ builders retain the use of feet to denote the
length of pipes. (1 foot = 30.5 cm)
The role of resonance
It is a common misconception that the air
entering a pipe flows up towards the open
end. In a simple experiment to test this we
can attempt to extinguish a lighted candle by
blowing into a pipe whilst pointing its open
end towards the flame. The flame turns out to
be quite resilient to such an attempt,
suggesting that very little air emerges from
the open end of the pipe. In contrast, if the
mouth is positioned near the flame, the latter
is rapidly extinguished. The role of the
speaking length of the pipe as a resonator is
clearly demonstrated.
To help visualise the formation of nodes and
antinodes, longitudinal vibrations may be
induced in a long spring. In a classic
demonstration, such a spring is suspended
from a clamp and vertical vibrations are
initiated at the lower end by attachment to an
electromechanical vibrator. The vibrator is
energised by connection to a signal generator
offering a variable voltage in amplitude and
frequency. As the frequency is adjusted,
nodes (indicated by completely stationary
coils) and antinodes (at positions of maximum
vibration) are observed at certain discrete
frequencies. This selectiveness of frequencies
to produce a longitudinal standing wave
indicates resonance which is similar to the
behaviour of the air in the organ pipe.
A more dramatic visualisation of the
formation of standing waves may be
demonstrated in a horizontal length of string
held at constant tension and with one end
attached to the vertical vibrator (Melde’s
Experiment). In this case the vibration is
transverse to the propagation of waves along
the string, and although this mode differs from
the longitudinal vibrations of the spring in the
previous demonstration and the air molecules
in the organ pipe, the visibility of the nodes
and graduations of the amplitude of vibration
are more explicit; distinct segments of
vibration appear between stationary nodes.
The results show that resonance occurs and standing waves are produced not at a single frequency, but at a
series of discrete frequencies related to each other as integer multiples of a ‘fundamental’ frequency f. These
frequencies form a harmonic series, as illustrated here.
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A: Antinode
N: Node
f: Fundamental frequency
The contribution of harmonics
Returning to the simple plastic tube, if one blows harder across one end of the tube, two or three harmonics may be
heard at different pitches corresponding to higher frequencies compared with the fundamental. (The effect is most
efficient when the opposite end of the tube is blocked to form a strong reflection. The proportion of the diameter to
the length of the tube is also critical in determining how many harmonics may be produced by a given blowing effort.)
This simple demonstration illustrates well the behaviour of an organ pipe. The fundamental (lowest resonant
frequency f) determines the pitch of the sound, but a selection of harmonic frequencies are simultaneously present at
reduced amplitudes. In an ‘open’ pipe a complete series of harmonics may be present. In a ‘stopped’ organ pipe,
closed at its upper end, a node is always formed at the closed end which limits the harmonic series to consist of odd
frequencies only.
Stopped organ pipes are useful for producing lower pitched notes compared with open pipes of the same length (this
saves material and space), but the tone of the sound is characteristically different as a result of the different harmonic
series. The fact that all the harmonics are simultaneously present in a pipe is the essence of its tone quality.
Generations of organ builders have specialised in designing pipes that produce certain ‘cocktails’ of harmonics. The
properties of the material of the pipes, thickness, stiffness, their shape, dimensions and proportions, the wind pressure
and velocity all contribute as variables that influence the resulting sound. The characteristic tone of a rank of pipes
can be shown to depend upon the profile of amplitudes of the harmonics present in a pipe when it speaks.
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To achieve a variety of sound
tones, pipes come in many
different shapes, sizes and
materials
1. Gedact (flute)
2. Clear flute
3. Viola
4. Rohr flute
5. Principal (50% tin)
6. Principal (30% tin)
7. Doppel flute
8. Vox humana (reed)
9. Trumpet (reed)
10. Oboe (reed)
11. Gemshorn
Reed pipes
A particular type of pipe is noted for a rich selection of harmonics, giving a characteristic clear tone which may be
strident and loud, or subtle and more muted. This is the type known as the ‘reeds’, so named because the method of
producing the initial vibration is not a fluttering jet of air, as previously described for ‘flue’ pipes, but a vibrating
tongue of metal situated in the ‘boot’ of the pipe. The physical process is not disimilar to that used by the reeds of a
mouth organ or that of the clarinet in the wind section of an orchestra. The metal vibrator sits beneath the upper
resonating part of the tube. When tuning a reed pipe, both the length of the vibrator and the length of the tube need
adjustment. The former is achieved by tapping a wire restrainer protruding from the boot; the latter is achieved by
adjusting a small slot near the top of the pipe. Reed pipes have the reputation of being rather temperamental,
demanding more attention to tuning than most of the flue pipework. They give the impression of being more sensitive
to climatic change, which is a bit unfair when one considers that the metal reeds are less affected by temperature
change than the frequency shift of the whole organ as the velocity of sound varies. In this respect the frequencies of
reeds are more stable than those of flues, but their mechanical vibrations do expose them to tuning variance.
However, as well as providing meaty choruses, reed stops, like opera divas, are star soloists and often define the
brilliance of an organ. An outstanding and highly prized example of reed pipes is to be found in the ‘Trumpet’ stop.
The Dębniki organ has a fine specimen and the concert programme features this in Aaron Copland’s Fanfare for the
Common Man. Although the piece was written for an orchestral trumpet and timpani, it affords a fine demonstration
of the solo properties of the organ Trumpet.
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In complete contrast, for school demonstration purposes, reed action may be improvised with a simple plastic straw.
A double reed may be formed by flattening and cutting the sides of the straw at one end. Blowing through the straw
and applying some pressure with the lips in the manner of an oboeist, a note of discernable pitch may be produced but
without beauty of tone! Successive trimming of the open end with sharp scissors can produce an ascending scale of
notes, much to the delight of a class.
With the reeds, flutes, strings and diapasons pipe families, the organ possesses tonal resources as diverse as a
symphony orchestra. Two pieces by Léon Boëllmann give a taste of this diversity; Prière à Notre Dame uses soft
flute and string stops with crescendos and diminuendos assisted by controlling the louvres of the Swell box, visible on
the front of the organ; Toccata employs a huge dynamic range from soft beginnings accompanying a pedal theme and
gradually building up to a full organ exposition including the reeds.
Harmonics – the key to tone quality
Using a microphone and oscilloscope or data-logging software, we can observe the waveforms produced by
different types of pipe. The shapes of waveforms are characteristic of the tone of a pipe.
The mellow tones of flute pipes deviate
only a little from pure sine waves.
Diapasons have more jagged waveforms
and reeds produce even more complex
shapes. If we look at the frequency
spectrum of these waveforms, the presence
of harmonics is readily confirmed. Flute
tone is dominated by the fundamental
harmonic with an almost total absence of
upper harmonics; Diapason tone contains
a strong second harmonic with a
sprinkling of weaker upper harmonics;
Trumpet tone contains a shower of upper
harmonics, the strongest of which is the
third harmonic rather than the
fundamental.
Fourier analysis teaches us that any
complex waveform may be analysed into
an infinite series of sine waves at
harmonic frequencies. The case of the
tone of organ pipes beautifully bears this
out. Conversely, if we combine two or
more pure harmonics, we can synthesise
new tones. This may be demonstrated
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using a simple piece of software for mixing harmonics. Here we see and hear the pure sine wave of the fundamental
and its relationship to the keyboard; to play a note followed by another an octave higher doubles the frequency, for a
note twelve notes higher, the frequency is trebled. Thus the second and third harmonics are an octave and twelve
notes above the fundamental. The program allows us to experiment with mixing up to seven harmonics at different
amplitudes; the resulting tone may be heard in a loudspeaker and the waveform seen directly on the screen.
Harmonics – the key to organ structure
Examining the relationship between harmonics and keyboard closer, we can attempt to replicate the harmonic series
on the organ itself. The first eight harmonics appear thus:
Playing these notes on the organ in turn, we hear the intervals between the notes becoming smaller as we progress
through the series. If instead of releasing each note we sustain each, the chord of C major emerges in convincing
harmony! It is therefore extremely appropriate that scientists use the term ‘harmonics’ to describe the series of
frequencies which, to a musician, produce perfect harmony.
The importance of the harmonic series was discovered empirically several centuries ago by organ builders, long
before the theories of Fourier and Helmholtz had been established in the 19th Century. Within the specification of the
stops available on an organ, there are many stops whose longest pipes start at a variety of pitches above normal. For a
keyboard of 56 notes, clearly a rank of 56 pipes is needed. For normal pitch, the longest open pipe is 8 feet long and
produces the note of bottom C. Most organs contain a variety of stops at this pitch of varying tone and loudness.
There are nearly always several stops whose longest pipe is 4 feet, an octave higher, and in terms of our analysis
correspond to the second harmonic. Then there are stops starting from 2 2/3 feet and 2 feet corresponding to the third
and fourth harmonics respectively.
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A type of stop which deserves special mention is the ‘Mixture’. As the name implies, this stop consists of several
ranks of pipes such that each note has two, three or four pipes sounding simultaneously. When we examine the tuning
of these ranks, we see once again that they all belong to higher order harmonics. At Dębniki, there is fine example of
a particular version of this type of stop, called a ‘Cornet’; consisting of four ranks, and with bold voicing, the resulting
sound comes very close to the rich tone of a reed pipe. The Voluntary in A minor by John Robinson gives great
prominence to this impressive stop.
Finally, in this discussion of harmonics, we must mention the 16 feet stops which produce notes an octave lower
than normal pitch. These deep tones add profundity to the sound and are largely concentrated in the Pedal division,
appropriately played using the feet and providing a foundation bass to music.
We can now justify the conclusion that the specification of organ stops follows the natural harmonic series, so a
scientist might describe the instrument as a ‘harmonic synthesiser’. An organist can select stops for their individual
tonal quality or he may also select combinations of stops to synthesise new sounds. Whether you regard the organ as
a sound synthesiser or a one-man orchestra, it is clear that a ‘world of sound’ is on offer.
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Acoustics
The ultimate and crucial influence on the sound of an organ is the location building itself. The acoustic properties
of the building depend upon its size, shape and the materials of the internal surfaces. From a scientific point of view
the key phenomena to be considered are diffraction, absorption, reflection, reverberation and echo. (The latter two are
often confused, reverberation describing the decay of sound energy, echo describing the sound images produced by
plane reflecting surfaces.)
Diffraction, the property of a wave to spread out and propagate around corners, is less efficient at higher
frequencies compared with bass frequencies. To demonstrate this effect on organ sound we only have to place a
microphone inside the organ chamber to discover a general ‘chiffiness’ of the sound which hardly reaches the body of
the church. In contrast, if the organ is playing when one enters the lobby of the church, the first sounds you hear are
those of the bass notes and those 16 feet tones. The gallery position of the organ is the best for minimising high
frequency loss due to diffraction. In English churches the organ is too often hidden away in a corner, with an
inevitable muffling effect.
High frequency waves experience less
diffraction than lower frequencies.
Absorption occurs in any surface exposed to the sound. Carpets and curtains are ‘death’ for organ acoustics
because they absorb so much of the sound energy, making the sound ‘stunted’ and coarse rather than blended. When
first built in 1951, the Royal Festival Hall in London had notoriously ‘dry’ acoustics due the the absorptive properties
of the carpets, seats and soft wooden surfaces of the ceiling and walls. For many years this was unflattering for the
wonderful organ in the hall, but recent renovations using hard woods and less carpet have greatly improved the
situation. To minimise absorption, hard smooth materials like plaster, marble or concrete are generally best for
surfaces. However one must be careful to avoid large plane or concave surfaces which can behave like mirrors and
cause sound images by reflection (echoes). Another London concert hall has suffered from this defect; the Royal
Albert Hall, built in 1871 has a domed ceiling which used to cause two distinct echoes before a forest of mushroom
shaped fibreglass reflectors, suspended from the ceiling, was installed in 1969. Many large churches and cathedrals
possess ideal organ acoustics; stone or marble surfaces are hard and reflective, but multiple reflections from
ornamentation help to suppress the hazard of echoes. The reverberation time of about 3 seconds at Dębniki is ideal for
organ sound.
Royal Festival Hall, London
- formerly noted for ‘dry’ acoustics
Royal Albert Hall, London
- formerly suffered from echoes
St Stanislav Kosta Church, Dębniki
- superb organ acoustics
This concludes the present tour of the ‘World of Sound’. There are more stories to tell, both of the organ and of
physics. Readers can find more information at www.insightresources.co.uk/CATO/. (This is an educational site
supporting teachers and pupils who attend workshops presented by Laurence Rogers and colleagues in the Derby &
District Organists’ Association.) Laurence Rogers may be contacted at laurencerogers46@gmail.com.
Laurence wishes to record sincere thanks to the Organist, Prof. Mieczysław Tuleja and the Assistant Organist,
Artur, for their tremendous support in the preparation and during the performance of the concert.
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