1. 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 then seven octaves: 88 notes, A0 - C8)
Action
Strings (more then 200)
Bridge
Soundboard
Frame
Review question: Find frequencies of A0 and C4 if frequency of A4 is 440 Hz.
A3 = 220 Hz; A2 = 110 Hz; A1 = 55 Hz; A0 = A4/24 = 27.5 Hz; C4 = A2 /23/12 = A2 /23/12 = HZ

2. 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. 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. 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. 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

6. 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

7. (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 begin to decay the longer the keys are held.