1 II Acoustic Reality II.4.1 (M Sept 18) The Piano

2 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)

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

4 An exploded grand pianocast iron plate sound board, spruce rim, maple

5 Modern piano‘s anatomy

6 The action of a modern pianoHave also Erard‘s repetition action on grand pianos!

7 The agraffe and the bridge terminate the free stringstuning pins

8 The pull forces for Cristofori‘s and for modern pianosversus 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, kg

9 The durometer to measure hammer hardness

10 Where to hit the stringsL d hammer

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

12 mobility = velocity/forceModes mobility = velocity/force without strings and plate fully equipped

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

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

15 vertical horizontal longitudinalThree directions of string and bridge vibrations vertical horizontal longitudinal

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

17 Vertical and horizontal vibration for decay function

18 Horizontal and vertical vibration for decay functionstrong 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

19 coupling with second string and mistuninguncouple second string strong energy exchange via bridge/soundboard