THE PIANO KEYBOARD INSTRUMENTS 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).