Keyboard Instruments A. Piano Types of keyboard instruments: Piano (strings are set into vibration by striking hammers) Harpsichord (strings are plucked) Organ (sound is produced by air blowing into pipes) A. Piano Invented in 1709 by Bartolomeo Cristofori in Florence The upright piano has been developed in the middle of 19th century Construction of piano Keyboard (more than seven octaves: 88 notes, A0 - C8) Action Strings (more than 200) Bridge Soundboard Frame Review question: Find frequencies of A0 and C8 if frequency of A4 is 440 Hz. A3 = 220 Hz; A2 = 110 Hz; A1 = 55 Hz; A0 = A4/24 = 27.5 Hz; A7 = A3 (23) ; C8 = A7(23/12 ) = A3 (23) (23/12 ) Hz; C8 = 4186.0 Hz

2. Piano strings (general information) Typical concert grand piano has 243 strings: 8 single strings wrapped with one or two layers of wire 5 pares wrapped (5x2=10) 7 sets of three wrapped (7X3=21) 68 sets of three unwrapped (68x3=204) Small grand piano has less strings String length from ~2m to ~5cm String extend from the pin block across the bridge to the hitch-pin rail Vibration of the strings is transmitted to the sound board by the bridge Bass strings overlap the middle strings, to act nearer to the center of the sound board

3. Tension in piano strings To obtain high level of loudness tension should be as high as possible To minimize the inharmonicity the diameter of the string (core diameter in a wrapped string) should be as small as possible Stings are made of high-strength steel wire Tension of a string may exceed 1000 N (100 kg, or 220 lb). This leads to a tensile stress that is about half of the yield strength of steel, and an elongation of about 2% Fortunately, if string brakes it is usually happened near the keyboard end, so that it recoils away from the pianist Total force of all strings in a concert piano > 20 tons! To withstand this tension grand pianos have frames made from cast iron

4. Real strings (inharmonicity) An ideal string vibrates in a series of harmonic modes A real string has some inharmonicity (modes are spread apart in frequency) The inharmonicity is due to additional restoring (force created by the displacement of the string) Restoring force is higher for higher modes because the string is more bended and more elongated r –radius of the string L - length of the string T – tension E – Young’s modulus The inharmonicity sharply increase with radius Because of that bass strings are wrapped Small inharmonicity is desirable (making sound more natural in contrast with synthesized harmonic sound)

5. Tuning Because of inharmonicity piano are “stretch–tuned” to avoid beats (to compensate mismatch) between partials of a note with the notes upper octaves. Upper octaves are stretched up and lower are stretched down Long bass strings of large grand pianos need to be stretched less then bass strings of small pianos Deviations from the average curve can be attributed to two factors: soundboard resonances personal preferences Most piano notes have three strings tuned one or two cents different from each other. This increase decay time and makes sound better 6. The soundboard The main source of sound Opposes the vertical force component of the strings Made of spruce ~1cm thick Ribs on underside of the soundboard stiffen it Not flat and often thicker near the center

“SQUARE GRAND PIANO" OR "BOX PIANO" This STEINWAY piano has serial number 47002, it was produced in 1883. Steinway & Sons was founded in1853 by German immigrant Henry Engelhard Steinway  http://www.steinway.com/pianos/steinway/grand/

B. Harpsichord Strings are plucked Strings have much lower tension than the piano strings Strings have much stronger inharmonicity than the piano strings It has much lighter soundboard than piano To vary loudness and timbre harpsichords have additional sets of strings Virginal or spinet – small instrument similar to harpsichord

(King of musical instruments) C. Organ (King of musical instruments) Sound is produced by driving pressurized air (called wind) through pipes Each organ pipe produces a single pitch Pipes are provided in sets called ranks Each rank has a common timbre Most organs have multiple ranks of pipes of differing timbre, pitch and loudness that the player can employ singly or in combination through the use of controls called stops An organ stop admits pressurized air (wind) to a set of pipes A pipe organ may have one or several keyboards (called manuals) played by the hands, and a pedalboard played by the feet, each of which has its own group of stops The organ's continuous supply of wind allows it to sustain notes for as long as the corresponding keys are depressed, unlike the piano and harpsichord, the sounds of which decay even if keys are held.