KEYBOARD INSTRUMENTS
THE PIANO
The Science of Sound, Chapter 14
The Physics of Musical Instruments, Chapters 11, 12, 17
The Science of String Instruments, Chapters 8, 9, 19, 20
GRAND PIANO
PIANO
BARTOLOMEO CRISTOFORI (1709): “Gravicembolo col piano et forte”
GOTTFRIED SILBERMANN
JOHANNES ZUMPE
ANDREAS STEIN – Invented escape mechanism
PIERRE ERARD – Invented agraffe, double repetition action
JOHN HAWKINS, ROBERT WORNUM – Upright pianoforte
243 Strings (5cm to 2m in length) on typical concert grand
8 Single strings (wrapped)
5 Pairs of strings (wrapped)
7 sets of 3 strings (wrapped)
68 sets of 3 strings (unwrapped)
Strings tensions may exceed 1000 N (215 lb.)
(Total force: over 20 tons)
SIMPLIFIED DIAGRAM OF PIANO
When a key is depressed, the damper is raised and the
hammer is “thrown” against the string.
Vibrations of the string are transmitted to the
soundboard by the bridge.
GRAND PIANO ACTION
UPRIGHT PIANO ACTIONS
FULL SIZE
CONSOLE
SPINET
(a) SINGLY-WOUND STRING AND (b) DOUBLY-WOUND STRING
DEVIATION FROM EQUAL TEMPERAMENT
IN A SMALL PIANO
HAMMER
VOICING
SOUND SPECTRA FOR C4 ON GRAND PIANO
MODE SHAPES
GRAND PIANO
SOUNDBOARDS
Soundboard
acts as a large
“loudspeaker”
VIBRATIONAL
MODES OF AN
UPRIGHT PIANO
SOUNDBOARD
Vibrational frequencies
of piano soundboard
compared to plate with
supported and fixed
edges
DECAY TIMES FOR A SINGLE D4# STRING
COMPOUND DECAY IN A TRICORD
When a hammer strikes a tricord (3 unison strings), it sets all three
strings into vibration with the same phase. Because of small
differences in frequency, however, they soon get out of phase, and
the resultant force on the bridge is diminished
Initially the decay is rapid and the sound is loud;
Then the decay rate diminishes, and the softer sound continues for
an extended time.
In this way the piano plays both LOUD and SOFT (“forte-piano”)
DECAY TIMES FOR
DIFFERENT
PARTIALS IN FIVE
NOTES ON A
GRAND PIANO
(Meyer 1978)
RADIATION PATTERN
(VERTICAL PLANE)
HARPSICHORDS
AND
CLAVICHORDS
SCIENCE OF SOUND, Chapter 14
PHYSICS OF MUSICAL INSTRUMENTS, Chapter 11
“ANALYSIS OF THE DESIGN AND PERFORMANCE
OF HARPSICHORDS” (N.H.FLETCHER, ACUSTICA
37, 139 (1977).
Modern Flemish harpsichord
by Australian Carey Beebe,
based on classical instruments
by the 17th Century maker
Andreas Ruckers.
The keyboard compass has
been extended down to G3 in
the bass and up to D6 in the
treble.
The small protrusions on the
right side (cheek) enable the
player to engage either of the
two sets of jacks by sliding the
register on or off.
HARPSICHORD ACTION (SIMPLIFIED)
HARPSICHORD ACTION
ACTION OF A FLEMISH HARPSICHORD. IN THIS INSTRUMENT
THERE ARE TWO CHOIRS OF STRINGS, THE SHORTER 4-FT
CHOIR AND AN 8-FT CHOIR. THE LEATHER PADS OF THE
BUFF STOP ARE VISIBLE BEHIND THE 4-FT TUNING PINS
PHYSICAL MODEL OF HARPSICHORD
PLUCK
CCRMA graduate student Chao-Yu Jack Perng
observed the plucking action of a harpsichord string
using a high-speed camera and constructed a
physical model of the pluck.
He then used this to synthesize harpsichord sound
(Perng, Smith, and Rossing, 2011).
CLAVICHORD
T he clavichord, like the piano,
depends on struck strings for
its sound.
A clavichord is a portable
instrument with a soft delicate
sound.
Clavichord action:
A tangent strikes the string
(or pair of strings) and
causes the portion between
the tangent and the bridge to
vibrate.
CLAVICHORD SOUND
Unlike the harpsichord, the clavichord gives the player direct
dynamic control over the sound by varying the speed at which the
tangent strikes the string and the force while the sound is sustained.
The force on the bridge has a spectrum that falls smoothly at about
8 dB/octave.
Because the displacement of the string by the tangent increases its
tension by a small amount, the player can create a pitch vibrato by
varying the finger force on the key.
The fact that each note is produced by two strings produces an effect
similar to that found in pianos.
Immediately after striking, the strings vibrate in phase, and
vibrational energy is transferred rapidly to the bridge and
soundboard, leading to a rapid initial sound decay with an
“aftersound” after the two strings get out of phase. This leads to an
initial clarity of sound combined with a “mellowness.”
HARPS
CONCERT HARP
MODERN CONCERT HARP
The modern concert harp has 46 or 47 strings running
from C1 or D1 to G7.
The strings run from the center of the soundboard to the
left side of the neck. At the top they are wrapped around
a tuning peg, used for tuning, and a bridge pin.
Beneath the bridge pin are the tuning discs which raise
the pitch one or two semitones.
The strings are tuned a semitone flat: the first disc raises
the string to natural; the second to sharp. The sharping
mechanisms are controlled from 7 pedals.
The mechanism is quite complex and runs up the
forepillar or post into the neck.
PLAYING SHARPS AND FLATS
Depressing one of the tuning pedals
increases the tension on all the
strings with that note name by one (for
naturals) or two (for sharps) units.
PIPE ORGAN
The pipe organ has been called the
“king of musical instruments.” No
two pipe organs in the world are
exactly alike.
A large variety of pipes are arranged into divisions.
Each division is controlled by a separate keyboard or manual,
including the pedalboard played with the feet.
SWELL ORGAN: usually enclosed behind shutters
GREAT ORGAN: principal division with many stops
POSITIVE ORGAN: includes solo stops
PEDAL ORGAN: includes the lowest bass stops
ORGAN WINDCHESTS HAVE VALVES THAT CAN BE OPENED TO
ADMIT AIR INTO THE PIPES
THE OLDEST TYPE IS THE TRACKER OR MECHANICAL ACTION:
KEYBOARDS ARE CONNECTED DIRECTLYTO THE WINDCHESTS
DIRECT ELECTRIC: ELECTROMAGNETS OPEN VALVES
ELECTROPNEUMATIC: ELECTROMAGNETS EXHAUST AIR FROM
THE BELLOWS, WHICH OPEN THE VALVES INTO THE PIPES
FULL PNEUMATIC: (RARE THESE DAYS) KEY CONTROLS AIR VALVE
TRACKER
DIRECT ELECTRIC
ELECTROPNEUMATIC
FLUE PIPE: A jet of air strikes a sharp edge
and alternately flows into and out from the
pipe (as in a recorder) , driven by positive
feedback from the pipe.
Schlieren photographs showing airflow when a jet strikes
a sharp edge (A. Hirschberg)
Organ pipes are organized into ranks of similar pipes.
A rank will include one pipe for each note (except for mixture stops)
FLUE (LABIAL) pipes produce sound by means of a vibrating jet (like a
flute)
REED (LINGUAL) pipes have a vibrating reed (like a clarinet)
OPEN FLUE PIPE (metal)
STOPPED PIPE (wood) REED PIPE
IN AN ORGAN REED PIPE, a metal reed vibrates against a shallot,
much as a clarinet reed vibrates against the lay of the moutpience.
Pressure (positive) feedback locks the reed vibrations to a resonance
of the pipe.
The vibrating reed is tuned by
means of a tuning wire to a
frequency near that of one of the
pipe resonances.
Reed pipes, which have
cylindrical or conical resonators,
are given such names as
clarinet, krummhorn, trompette,
rankette, etc.
RESONANCE FREQUENCIES OF OPEN AND
CLOSED PIPES, CYLINDRICAL AND CONICAL
COUPLING OF REED TO RESONATOR
THE REED CAN COUPLE TO ANY OF THE PIPE RESONANCES
A G4 trompette pipe has
resonances at 243, 488,
729, AND 972 Hz, shown
by the horizontal lines.
By varying the vibrating
length of the reed, it can
be made to lock into any
of these resonances
(Miklόs, Angster, Pitsch,
and Rossing, 2006)
PIPE RESONATORS MAY BE OPEN OR CLOSED CYLINDERS, CONES.
Broad flute pipes emphasize the fundamental, while “string” stops have
narrow pipes with more harmonics. Diapason or principal stops are
somewhere between..
PIPE SCALING
The scale of a rank of pipes refers to the ratio of diameter to length for the pipe of
lowest pitch.
For an open cylindrical pipe, the end correction at the open end adds 0.6 times the
radius, whereas at the mouth of a flue pipe, one adds about 2.7 times the radius.
Thus, in a large-scale pipe, only the lowest harmonics are sounded.
Normally, the mouth width, lip cut-up, and width of the flue opening follow the
same scale as the pipe diameter.
SOUND RADIATION FROM FLUE PIPES
A stopped pipe radiates only from its mouth. The radiation of the
fundamental and low harmonics is nearly isotropic.
For higher harmonics, the radiation is more concentrated in front
of the mouth.
An open pipe has two coherent sources at the mouth and open
end, which are in phase for odd harmonics and out of phase for
even harmonics. Typical radiation patterns are:
The pipes of an organ can be laid out in a matrix.
Each row contains pipes of a single rank.
Each column contains all pipes for a single note.
Drawstops control admission of air to the pipes of a rank.
Keys control air to pipes of a note.
Pipes at all active intersections produce sound.
ORGANS IN STANFORD MEMORIAL CHURCH
MEMORIAL CHURCH HAS FOUR ORGANS:
●THE MURRAY HARRIS ORGAN WAS
BUILT IN 1901 AND ENLARGED IN 1915.
●THE FISK-NANNEY ORGAN, BUILT IN
1985, IS THE LARGEST, WITH 73 RANKS
AND ALMOST 4500 PIPES
●THE SIDE CHAPEL HOUSES THE
KATHERINE POTTER-BRINEGAR ORGAN,
A ONE-MANUAL RENAISSANCE-STYLE
ORGAN BUILT IN 1985
●THE CONTINUO ORGAN WITH THREE
STOPS, BUILT BY MARTIN PASI, WAS
ACQUIRED IN 2001
WANAMAKER ORGAN (PHILADELPHIA)
Built by the Los Angeles
Art Organ Company for the
1904 St. Louis World's
Fair, the Wanamaker
Organ was designed by
renowned organ architect
George Ashdown Audsley..
This heroic instrument had
more than 10,000 pipes,
and its construction was
on such a lavish scale that
costs soared to $105,000,
bankrupting the builder.
CONVENTION HALL (ATLANTIC CITY)
The world’s largest organ, with 30,000 pipes, is in the Atlantic
City Convention Hall.
TUNING ORGAN PIPES
REED PIPES ARE TUNED BY MOVING THE TUNING WIRE UP
AND DOWN.
FLUE PIPES ARE TUNED BY CHANGING THE EFFECTIVE
LENGTH . IN A CLOSED PIPE, THIS IS ACCOMPLISHED BY
MOVING THE STOPPER UP OR DOWN.
MANY OPEN PIPES HAVE A TUNING SLEEVE THAT SLIDES UP
AND DOWN; OTHERS HAVE AN ADJUSTABLE SLOT NEAR
THE OPEN END.
VOICING ORGAN PIPES
VOICING MEANS MAKING ADJUSTMENTS IN THE VARIOUS
PARTS OF THE PIPE SO THAT IT “SPEAKS” PROPERLY. SOME
OF THE MAIN PARAMETERS ADJUSTED DURING VOICING:
THE SIZE OF THE FOOT BORE
THE CONDITION OF THE BORE
NICKING
THE WIDTH OF THE FLUE
OBSTRUCTION NEAR THE MOUTH (“ROLLER BEARD”)
THE HEIGHT OF THE LANGUID
THE HEIGHT OF THE MOUTH (CUT-UP)
SETTING OF THE UPPER LIP
THE CONDITION OF THE UPPER LIP
Assignment for Wednesday:
Read Chapters 15 and 16;
Chapter 14 Exercises 1-7 (p.333).