II Acoustic Reality II.4.1 (M Sept 17) The Piano

Some History In 1709 harpsichord (cembalo) constructor Bartolomeo Cristofori in Florence invented the instrument, he called gravicembalo col piano e forte. Here an instrument built in 1720 at Metropolitan Museum of Art (sound_example_1)

hammer (leather on wood) Some History string hammer (leather on wood) The historical instrument’s action looks like this harpsichord action: key

An exploded grand piano cast iron plate sound board, spruce rim, maple

Modern piano‘s anatomy

The action of a modern piano Have also Erard‘s repetition action on grand pianos!

The agraffe and the bridge terminate the free strings tuning pins

The pull forces for Cristofori‘s and for modern pianos versus 830 N per string total: 7,500 N versus 210,000 N ~ 30 x more! Since 1855 (Steinway) need no more wooden, but cast-iron string plate, 160-180 kg

The durometer to measure hammer hardness

Where to hit the strings L d hammer

The soundboard (spruce), 6.5-9.5 mm, 4 modes (with Chladni figures) 49Hz 67Hz 89Hz 184Hz

mobility = velocity/force Modes mobility = velocity/force without strings and plate fully equipped

The piano case/rim 80-90 mm 150-200 kg maple or beech wood, important for massive termination of vibration of the soundboard

string(s) bridge/soundboard The interaction of strings and soundboard exchange of energy bridge/soundboard strong coupling —> high energy transfer —> loud, fast decay weak coupling —> low energy transfer —> quiet, slow decay need „trade-off“!

vertical horizontal longitudinal Three directions of string and bridge vibrations vertical horizontal longitudinal

E1 = 41 Hz Sound Level Frequency sound_example_4, 5, 6, 7 Longitudinal vibrations E1 = 41 Hz Sound Level Frequency sound_example_4, 5, 6, 7

Vertical and horizontal vibration for decay function

Horizontal and vertical vibration for decay function strong coupling caused by vertical vibration, loud, energy transfer to bridge —> fast decay weak coupling —> low energy transfer —> quiet, slow decay the second is caused by horizontal vibration and coupling with second string

coupling with second string and mistuning uncouple second string strong energy exchange via bridge/soundboard