Acoustics of pianos: An update of recent results

Transcription

1 Acoustics of pianos: An update of recent results Antoine Chaigne Department of Music Acoustics (IWK) University of Music and Performing Arts Vienna (MDW) Projekt Nr P29386-N30 1

2 Summary An overview of recent results on piano acoustics Piano action Strings and stringing Soundboard Radiation Simulations and perceptual studies Simulation of complete instruments Perception of piano tones Conclusion and open questions 2

3 Piano action: vibrations of hammer shank (Chabassier et al., JSV, 2014) Piano touch: influence of the hammer shank flexibility on the sound Hammer/shank interaction studied with time-domain numerical simulations Input: staccato vs. legato jack force (extracted from measurements by Askenfelt and Jansson, Jasa 1991) Differences in tone spectra (see Fig.) 3

4 Piano action: Multibody dynamics (1) (Thorin et al., Meccanica, 2017) Non-smooth dynamics dry (Coulomb) friction stick/slip transitions Discontinuous velocities and/or accelerations Input = displacement. Predictions in terms of forces 4

5 Thorin et al. (2) Position-driven simulations Comparison between measured and simulated reaction force at the end of the key (player's side). Maths: use of specific methods (here: Measured Differential Inclusion) 5

6 Piano action: reconstruction of hammer force (Chaigne, Jasa, 2016) Main principles of the hammer force reconstruction procedure: Measure the string velocity at appropriate locations Calculate the transfer function between string velocity and hammer force Apply inverse filtering to the measured velocity to recover the force Validation through resynthesis of the string velocity 6

7 Strings and stringing: piano registers (1) (Chaigne et al., ) Parallel (straight) stringing cross-stringing 7

8 Piano registers: example of Brahms's piano (J.B. Streicher 1868) z B M T B M T 8

9 Piano registers: modal cloud (3) PARALLEL STRINGING Played note Played note TREBLE TREBLE MEDIUM MEDIUM BASS BASS Soundboard Modes (Hz) CROSSED STRINGS Soundboard Modes (Hz) 9

10 Stringing: musical consequences Example: Brahms's piano (J.B. Streicher 1868) Piece: Rhapsody op. 119, Nr 4 (final part) 10

11 Soundboard: vibroacoustical studies (1) (Corradi et al., Applied Ac., 2017) 11

12 Soundboard: vibroacoustics (2) (Trevisan et al., Jasa, 2017) Purpose of the paper Influence of the string coupling position Effects of soundboard design on timbre Relevance of structural discontinuities Method Modal decomposition Springs for modeling the clamped ends. Radiation impedance for the calculation of the radiated field Distribution of springs 12

13 Soundboard: vibroacoustics - results (3) (Trévisan et al., Jasa 2017) Mobility level LM Sound power LW Successive excitations at the string-bridge coupling positions (x-axis: key frequency) Inhomogeneties of LM and LW at the bridge discontinuities, and at the bridge end. Here: upright piano Pleyel P

14 Radiation: contributions of the different piano components (Tan et al., ICA, 2016) QUESTION: Is the soundboard the only radiating element? What is the respective contribution of each piano element? Attempt to respond through an investigation with a Boesendorfer CEUS (MDW, 2016): Repetitive and controlled excitation Method of analysis: correlations between accelerations and sound pressure (Operational Transfer Path Analysis) Hz 14

15 Time-domain piano simulations: principles of the used model (Chabassier et al., ) Hammer Strings Soundboard Air (acoustic field) (A. Askenfelt, Five lectures on the acoustics of the piano, 1990) 15

16 Simulations: generalisation to historic instruments (Chaigne, ) Important evolution of strings, soundboard and design during the period A. Walter 1851 JB Streicher 1980 Steinway 16

17 Simulations: results (1) Influence of string tension on timbre Variation of string tension Same pitch and loudness Reference - Low tension - High tension Ex: Steinway D - note C#5 17

18 Simulations: results (2) String-bridge coupling parameters Effect of attachment point Piano: JB Streicher 1868 Note C4 C2 normal position (medium range) bass range (C2 position) treble range (C6 position) Demo repeated twice C4 C6 18

19 Simulations: results (3) Soundboard parameters Geometry and material Same pitch and loudness Reference - thin plate - rigid plate Ex: Steinway note C#5 19

20 Simulations: results (4) Effect of string amplitude on timbre NL motion of strings Phantom partials Lin - NL - Lin -NL Piano Nanette Streicher 1819 String C2 20

21 Spectra of NL string demo LIN NL 21

22 Simulations: results (5) A few comparisons between measurements and simulations State of the art (current work) Some features are missing in the model (Ex: room reverberation) Tuning conditions (Museum) Note D#3 ; Piano J.B. Streicher 1868 Note A3 ; Piano J. B. Streicher 1836 Note C4 ; Piano J.B. Streicher 1868 Note C6 ; Piano N. Streicher 1819 Sim - Meas - Sim - Meas 22

23 Similarity of piano tones: Two perceptual studies (joint work TUe-MDW) Ultimate goal: correlate the perceptual judgment of similarity of the tones to the physical properties of the pianos. Same database of recorded sounds. Study #1 (A. Osses, TUe) Same note (C#5) played on 7 different pianos (built between 1805 and 1873) Triadic comparisons (A-B-C: which pair is the most similar, resp. dissimilar ) Instrument-in-noise test Study #2 (A. Chaigne, MDW) 6 notes played on 6 different pianos 3-AFC (3 Alternative Forced Choice) 3 sounds A-B-C. One is different. Question: which one? 23

24 Similarity of piano tones: 3-AFC raw data (chaigne et al., ) TREBLE Exp 1: Notes C2, F3 and C4 Exp 2: Notes A4, C#5 and G6 BASS The listeners have more dificulties to discriminate the piano sounds in the treble range compared to the bass range. Possible reasons (current study): - more cues are present in the bass tones (ex: longitudinal frequency) - the bass range show more differences between early and late historic pianos than the treble range. 24

25 Similarity of piano tones Preliminary interpretation of the results (analysis) JBS (EA) JBS (VA) Very similar spectral content. Some differences in the initial transient. Some differences in the temporal envelope. Two (A4) sounds judged as "rather similar" in the listening test. 25

26 Similarity of piano tones: Analysis (2) Significant differences in the spectral envelope. Comparable temporal envelopes. Judged as "clearly different" by the listeners. 26

27 And, before the conclusion a short (an informal) listening test with you! 1 Same piece played on two different pianos Guess which is the older piano? 2 27

28 Conclusion and open questions Recent results on piano acoustics and dynamics were presented Piano action Strings and stringing Soundboard and radiation The use of simulations for the exploration of parameters was highlighted Strings (tension, amplitude, attachment position,...) Soundboard (thickness, rigidity,...) Complementary studies on piano perception have started Similarity of piano tones And there are still open questions and work in progress (are you surprised?) Determination of audibility thresholds for the main parameters (listening tests with simulated tones) 28

29 Acknowledgements Austria Caroline Haas (Technisches Museum Wien) Gert Hecher (Das KlavierAtelier) France Juliette Chabassier Marc Duruflé (Inria Bordeaux) Jin Jack Tan (ENSTA ParisTech) 29

30 Questions? Books? 30