Greetings,
Ran across an interesting site: If the button on the bottom won't work
for you, the address is
http://www.speech.kth.se/music/smac03/abs03_link.html
ORAL
Modeling the longitudinal vibration of piano strings
B Bank, L Sujbert
Budapest University of Technology and Economics, Department of Measurement
and Information Systems, Budapest, Hungary
This paper is about the physical modeling of the longitudinal string
vibrations in the piano. Informal listening tests show that the longitudinal
vibrations play an important role in attack of the sound, and are responsible for the
metallic character of low notes. However, their modeling has not yet been
considered in the literature.
First, a simple mathematical model is developed for qualitative
understanding. The longitudinal vibration is made up of the free vibration of the
longitudinal modes, and a forced vibration coming from a second-order nonlinearity. For
the latter, a closed-form solution is given in the case of sinusoidal
transversal displacement with non-rigid termination. To investigate how these effects
develop in more natural circumstances, finite difference string and hammer
models are used, with parameters taken from real pianos. The results are
compared to piano measurements.
The aim of this study, besides a better insight to the underlying physics, is
to develop sound synthesis methods. Therefore, an efficient modeling approach
is presented, which can be used with digital waveguide string models. The
approximation is based on neglecting those effects, which have less importance
from the perceptual point of view. Sound examples will be presented as a part of
the talk at the SMAC2003 Conference.
POSTER
Quality of treble piano tones
A Galembo
Sechenov Institute of Evolutionary Physiology and Biochemistry, Russian
Academy of Sciences, Lab 32, St. Petersburg, Russian Federation
In this study it is shown that the quality of a treble tone of the piano is
defined primarily by the temporal dynamics of the perceptually competing impact
noise ("knock") and the string-born tonal element (the partials responsible
for pitch sensation). The relation between the two elements depends primarily
on the parameters of the hammer-string contact, and not so much on the
soundboard properties. The knock component is "colored" by the metal frame, in
particular by the choice of material. Two ways (mechanical and electronic) of
experimentally separating the knock and the tonal element in a real piano tone for
listening tests and demonstrations are shown. (The paper presents results of
previous industrial research conducted in the acoustic laboratory of the
Leningrad Piano Factory, Russia to English readers.)
POSTER
Phase randomisation in piano bass tones
A Galemboÿ, A Askenfeltÿ
ÿSechenov Institute of Evolutionary Physiology and Biochemistry, Russian
Academy of Sciences, Lab 32, St. Petersburg, Russian Federation; ÿKTH, Dept. of
Speech, Music and Hearing, Stockholm, Russian Federation
It has been shown that the timbre of synthesized multi-component harmonic
bass tones with steady magnitude spectrum depends on the phase spectrum,
particularly on the randomness of the relative phases between partials [Galembo et al,
JASA 110, 1649-1666]. For inharmonic spectra (as in the piano), the waveform
will be non-stationary due to the temporal evolution of the phase relations.
This creates audible attack transients which are characteristic for the
particular starting phases. The relevance of these findings for the perception of
real piano tones has been unclear. A piano tone shows a complex dynamic evolution
of the spectrum during attack and decay, which besides inharmonicity, is
influenced by the properties of the sound board and room reverberation. In this
pilot study it is shown that frequency sweeps and associated pitch glides due to
phase rotation introduced by string inharmonicity are present in real piano
bass tones. The evidence is clear in the string and bridge velocities, and also
in the radiated sound close to the piano, although to a lesser extent.
POSTER
Measurement and reproduction accuracy of computer-controlled grand pianos
W Goeblÿ, R Bresinÿ
ÿAustrian Research Institute for Artificial Intelligence, Vienna, Austria;
ÿRoyal Institute of Technology (KTH), Department of Speech, Music, and Hearing
(TMH), Stockholm, Sweden
The recording and reproducing capabilities of a Yamaha Disklavier grand piano
and a Bösendorfer SE290 computer controlled grand piano were tested, with the
goal of examining their usefulness for performance research. An experimental
setup consisting of accelerometers and a calibrated microphone is used to
capture key and hammer movements, as well as the acoustic signal. Five selected
keys are played by pianists with two types of touch ('staccato - legato').
Timing and dynamic differences between the original performance, the corresponding
MIDI file recorded by the computer-controlled pianos, and its reproduction are
analyzed. The two devices performed quite differently with respect to timing
and dynamic accuracy. The Disklavier's onset capturing is slightly more
precise (+/-10 ms) than its reproduction (-20 to +30 ms), the Bösendorfer performs
generally better, but its timing accuracy is slightly less precise for
recording (-10 to 3 ms) than for reproduction (+/-2 ms). Both devices exhibit a
systematic (linear) error in recording over time. In the dynamic dimension, the
Bösendorfer shows higher consistency over the whole dynamic range, while the
Disklavier performs well only in a wide middle range. Neither device is able to
capture or reproduce different types of touch.
ORAL
The piano action as the performer's interface: Timing properties, dynamic
behaviour and the performer's possibilities
W Goeblÿ, R Bresinÿ, A Galemboÿ
ÿAustrian Research Institute for Artificial Intelligence (ÖFAI), Vienna,
Austria; ÿRoyal Institute of Technology (KTH), Department of Speech, Music and
Hearing (TMH), Stockholm, Sweden
A concert pianist is able to produce every imaginable nuance of expression by
handling the 88 keys of his/her piano, no one of which travelling through a
greater distance than one centimeter. In this study, we investigate the
temporal behaviour of grand piano actions by different manufacturers with different
types of touch ('legato' versus 'staccato'). An experimental setup consisting
of accelerometers and a calibrated microphone was used to capture key and
hammer movements, as well as the acoustic signal. Five selected keys were played by
pianists with the two types of touch. The analysis of the three-channel data
was automated by computer software. Discrete measurements (e.g., finger-key,
hammer-string, key bottom contact times, hammer velocity) were extracted for
each of the 2563 recorded tones in order to study several temporal relations.
Travel times of the hammer (from finger-key to hammer-string) as a function of
hammer velocity varied clearly between the two types of touch, but only
slightly between the pianos. A travel time versus hammer velocity function found in
earlier work derived from a computer-controlled piano could be replicated. Key
bottom contact times exhibit larger variability between types of touch and
pianos. However, no effect of touch type was found in the peak sound level (in dB
as a function of hammer velocity). This finding raises once again the
question whether other factors than hammer velocity influence the tone of the piano.
Piano string vibration and problems of its numerical modeling
A Raffaj
Petrof, spol. s r.o., Research dept., Hradec Kralove, Czech Republic
The specifities of a piano string vibration and their influence on a final
piano sound timbre are summarized. The numerical model of a piano string was
created by means of the finite difference methods (FDM).
As piano hammer model which excites virtual piano string was used non-linear
hereditary (hysteretic) hammer model introduced by Stulov.
The dynamical force-compression characteristics of piano hammer are measured
on the special measuring apparatus, which will be described and compared to
the Stulov's apparatus. The measured results is compared to piano hammer
properties measurements which are done usually by hammer manufacturers.
A brief discussion of hammer properties influence on final piano timbre is
presented. For the simulation of reality the real soundboard was excited by
shaker which is supplied by computed signal. This signal is proportional to force
transmitted from string to the bridge. In this way is aurally judged the
influence of string qualities, way of hammer manufacturing and quality changes
during the voicing.
At the conclusion the possibilities of the numerical model improving by
addition of the longitudinal modes simulation and non-linearity transfer of string
vibration to the bridge is presented.
ORAL
The piano soundboard behaviour in relation with its mechanical admittance
J S Skala
Petrof , spol s.r.o., Research, Hradec Kralove, Czech Republic
Piano soundboard input mechanical admittance was investigated in wide
frequency range. In lower frequency range strong differences between peak and pit
values have been observed. With the increasing frequency, the wrinkled character
of soundboard admittance is changed to more smooth one, due to a coupling of
modes. The idea was to compare piano soundboard behaviour upon driving by
shaker supplied with simple harmonic force signal on near peak and pit (mode +
antimode) frequency. The measurement was made on soundboard fixed to backframe and
iron frame without strings. We expect that on antimode frequency the
soundboard radiation will be very poor. The final perceived sound volume differs less
than it has been expected. A discussion if rest of sound energy can be
leakaged out more either on other frequency partials by soundboard or by other piano
parts (iron frame, rim) is included. This effect is one (but not only one)
reason for we can hear a piano tone with frequency in which level of the
soundboard admittance is very low.
ORAL
Experimental and theoretical studies of piano hammer
A Stulov
Institute of Cybernetics at Tallinn Technical University, Centre for
Nonlinear Studies, Tallinn, Estonia
Based upon the large number of experimental data obtained using a special
piano hammer testing device, it has been shown, that all the present-day piano
hammers have as a quality the hysteretic type of the force-compression
characteristics. This not a chance because such a hysteretic character has been
developed step-by-step following the history of evolution of piano hammers since the
instrument was created. The dynamical behaviour of the contemporary piano
hammer can be described by different mathematical hysteretic models. In addition
to the four-parameter nonlinear hysteretic model of piano hammer, another new a
three-parameter hysteretic model was developed. This is very similar to the
nonlinear Voigt model and permits a description of the dynamical hammer felt
compression that is consistent with experiments. The both models are based on an
assumption that the hammer felt made of wool is a microstructural material
possessing history-dependent properties. The equivalence of these models is
proved for any realistic values of hammer velocity. The continuous dependencies of
the hammer parameters on the key number are obtained, which is the first
known case of such an analysis. The application of hysteretic models to numerical
simulation of the grand piano hammer-string interaction is demonstrated. The
flexible string vibration spectra excited by different piano hammers are
analysed. All that together, leads to a new method for piano stringing-scale design.
Click Here: <A HREF="http://www.speech.kth.se/music/smac03/abs03_link.html">
S M A C 0 3</A>
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Ed Foote RPT
http://www.uk-piano.org/edfoote/index.html
www.uk-piano.org/edfoote/well_tempered_piano.html
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