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A new algorithm is presented for estimating the inharmonicity coefficient of slightly inharmonic stringed instrument sounds. In the proposed partial frequencies deviation method, the inharmonicity is estimated in an intuitive way by minimizing the deviation of the expected partial frequencies compared to the frequencies of the high amplitude peaks in the spectrum. This is done in an iterative process, where the algorithm converges towards the target estimation value. The algorithm is tested using both synthetic and recorded piano tones. The results show that the new algorithm produces accurate results with a small computation cost compared to other methods.

This paper investigates the audibility threshold of aliasing in computer-generated sawtooth signals. Listening tests were conducted to find out how much the aliased frequency components below and above the fundamental must be attenuated for them to be inaudible. The tested tones comprised the fundamental frequencies 415, 932, 1480, 2093, 3136, and 3951 Hz, presented at 60-dB SPL and 44.1-kHz sampling rate. The results indicate that above the fundamental the aliased components must be attenuated 0, 19, 26, 27, 32, and 41 dB for the corresponding fundamental frequencies, and below the fundamental the attenuation of 0, 3, 6, 11, 12, and 11 dB, respectively, is sufficient. The results imply that the frequency-masking phenomenon affects the perception of aliasing and that the masking effect is more prominent above the fundamental than below it. The A-weighted noise-to-mask ratio is proposed as a suitable quality measure for sawtooth signals containing aliasing. It was shown that the bandlimited impulse train, the differentiated parabolic waveform, and the fourth-order polynomial bandlimited step function synthesis algorithms are perceptually alias-free up to 1, 2, and 4 kHz, respectively. General design rules for antialiasing sawtooth oscillators are derived based on the results and on knowledge of level-dependence of masking.

This paper describes the main features of the sustain-pedal effect in the piano through signal analysis and presents an algorithm for simulating the effect. The sustain pedal is found to increase the decay time of partials in the middle range of the keyboard, but this effect is not observed in the case of the bass and treble tones. The amplitude beating characteristics of piano tones are measured with and without the sustain pedal engaged, and amplitude envelopes of partial overtone decay are estimated and displayed. It is found that the usage of the sustain pedal introduces interesting distortions of the two-stage decay. The string register response was investigated by removing partials from recorded tones; it was observed that as the string register is free to vibrate, the amount of sympathetic vibrations is increased. The synthesis algorithm, which simulates the string register, is based on 12 string models that correspond to the lowest tones of the piano. The algorithm has been tested with recorded piano tones without the sustain pedal. The objective and subjective results show that the algorithm is able to approximately reproduce the main features of the sustain-pedal effect.

This paper investigates the audibility of longitudinal components in piano string vibrations with listening tests. The recorded fortissimo sounds of two grand and one upright pianos have been resynthesized with and without longitudinal components and used in ABX type listening tests. Results suggest that the longitudinal components are audible up to note C 5 . However, a second test seeking the importance of the difference shows that the effect of longitudinal components for the range A 3 − C 5 is subtle. This means that modeling the phenomenon up to around note A 3 only is acceptable for sound synthesis applications.