These are sample files to demonstrate the beating model proposed by Rauhala, Lehtonen, and Välimäki [1]. All samples are in PCM WAV 44.1 kHz 16-bit format. The piano model includes the dispersion filter [2], a multi-ripple loss filter [3], a tuning filter, and an excitation model [4] The piano model is calibrated using recorded piano samples [5].

CASE I: Single beating partial with varying indices

In this case, each piano tone have a single partial with a beating effect. The partial index varies from 0 (no beating) to 10 in an increasing manner.

Beating partial index 0-5 (2.63 MB)
Beating partial index 6-10 (2.19 MB)
> Tone details...

CASE II: Varying number of beating partials

The second case shows how the tone changes when the number of beating partials is increased from 0 to 9.

Number of beating partials 0-9 (4.39 MB)
> Tone details...

CASE III: Comparison between with and without beating

The last demonstration case is similar to the previous one, this time there are two 15s samples without and with beating. The latter sample has 9 beating partials.

Without and with beating (2.56 MB)
> Tone details...



[1] J. Rauhala, H.-M. Lehtonen, and V. Välimäki, "Towards next generation digital keyboard instruments," submitted to IEEE Signal Processing Magazine, 2006.
[2] J. Rauhala and V. Välimäki, "Tunable Dispersion Filter for Piano Synthesis," IEEE Signal Processing Letters, vol. 13, no. 5, 2006, pp. 253-256.
[3] J. Rauhala, H.-M. Lehtonen, and V. Välimäki, ”Multi-ripple loss filter for waveguide piano synthesis,” in Proc. International Computer Music Conference, Barcelona, Spain, pp. 729-732, September 2005.
[4] J. Rauhala and V. Välimäki, "Parametric excitation model for waveguide piano synthesis," in Proc. 2006 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2006), Toulouse, France, May 14-19, 2006.
[5] Original piano sample from University of Iowa Electronic Music Studios,

Demo tone details

Case I:
Fundamental frequency = 65.4 Hz (C2)
Beating frequencey = 1 Hz

Case II & III:
Fundamental frequency = 61.7 Hz (B1)
Beating partial indices and frequencies (in order of appearance):
Partial index Beating frequency
3 0.63 Hz
4 0.67 Hz
5 0.83 Hz
8 0.50 Hz
11 0.80 Hz
12 0.95 Hz
13 0.77 Hz
14 0.20 Hz
16 1.05 Hz

More information

Homepage of Jukka Rauhala
Piano research at the Acoustics Lab
Modified: 19.5.2006