Handling inharmonic series with median-adjustive trajectories

A new method for the analysis of inharmonic instrumental tones is presented. The method exploits an equation derived from the well-know inharmonic series equation, where the inharmonicity coefficient is balanced with the frequencies and numbers of any two partials extracted from a pseudo-harmonic series. A serial search for increasingly deviating spectral peaks is aided with the integrated refinement of increasingly reliable inharmonicity coefficient and fundamental frequency estimates. This firsthand approach to the problem of evaluating inharmonic spectra brings about an unprecedented level of simplicity, efficiency and accuracy

A parametric method for pitch estimation of piano tones

The efficiency of most pitch estimation methods declines when the analyzed frame is shortened and/or when a wide fundamental frequency (F0) range is targeted. The technique proposed herein jointly uses a periodicity analysis and a spectral matching process to improve the F0 estimation performance in such an adverse context: a 60ms-long data frame together with the whole, 7 1 /4-octaves, piano tessitura. The enhancements are obtained thanks to a parametric approach which, among other things, models the inharmonicity of piano tones. The performance of the algorithm is assessed, is compared to the results obtained from other estimators and is discussed in order to characterize their behavior and typical misestimations. Index Terms — audio processing, pitch estimation 1

A Pitch Salience Function Derived from Harmonic Frequency Deviations for Polyphonic Music Analysis

In this paper, a novel approach for the computation of a pitch salience function is presented. The aim of a pitch (considered here as synonym for fundamental frequency) salience function is to es- timate the relevance of the most salient musical pitches that are present in a certain audio excerpt. Such a function is used in nu- merous Music Information Retrieval (MIR) tasks such as pitch, multiple-pitch estimation, melody extraction and audio features computation (such as chroma or Pitch Class Profiles). In order to compute the salience of a pitch candidate f , the classical approach uses the weighted sum of the energy of the short time spectrum at its integer multiples frequencies hf. In the present work, we pro- pose a different approach which does not rely on energy but only on frequency location. For this, we first estimate the peaks of the short time spectrum. From the frequency location of these peaks, we evaluate the likelihood that each peak is an harmonic of a given fundamental frequency. The specificity of our method is to use as likelihood the deviation of the harmonic frequency locations from the pitch locations of the equal tempered scale. This is used to cre- ate a theoretical sequence of deviations which is then compared to an observed one. The proposed method is then evaluated for a task of multiple-pitch estimation using the MAPS test-set

Multiple-F0 estimation of piano sounds exploiting spectral structure and temporal evolution

This paper proposes a system for multiple fundamental frequency estimation of piano sounds using pitch candidate selection rules which employ spectral structure and temporal evolution. As a time-frequency representation, the Resonator Time-Frequency Image of the input signal is employed, a noise suppression model is used, and a spectral whitening procedure is performed. In addition, a spectral flux-based onset detector is employed in order to select the steady-state region of the produced sound. In the multiple-F0 estimation stage, tuning and inharmonicity parameters are extracted and a pitch salience function is proposed. Pitch presence tests are performed utilizing information from the spectral structure of pitch candidates, aiming to suppress errors occurring at multiples and sub-multiples of the true pitches. A novel feature for the estimation of harmonically related pitches is proposed, based on the common amplitude modulation assumption. Experiments are performed on the MAPS database using 8784 piano samples of classical, jazz, and random chords with polyphony levels between 1 and 6. The proposed system is computationally inexpensive, being able to perform multiple-F0 estimation experiments in realtime. Experimental results indicate that the proposed system outperforms state-of-the-art approaches for the aforementioned task in a statistically significant manner. Index Terms: multiple-F0 estimation, resonator timefrequency image, common amplitude modulatio

A Model of Partial Tracks for Tension-Modulated, Steel-String Guitar Tones

This paper introduces a spectral model for plucked, steel string tones, based on functional models for time-varying fundamental frequency and inharmonicity coefficient. Techniques to evaluate those analytical values at different time indexes are reviewed and commented. A method to evaluate the unknowns of the fundamental frequency and inharmonicity coefficient functions and match the data of a given tone is presented. Frequency tracks can thereafter be deployed and traced for all values of time. Their accuracy is discussed, and applications for the model are suggested

Puoliautomaattisen pianonviritysjärjestelmän signaalinkäsittely

Tuning a piano is a complicated and time-consuming process, mostly done by professional tuners. To make the process faster and non-dependent on the skills of a professional tuner, a semi-automatic piano tuning system is developed. The system composes of a stepper motor, an aluminium frame, an Arduino Uno, a microphone and a computer. The stepper motor changes the tune of piano strings by turning pins connected to them, the aluminium frame holds the motor in place and the Arduino controls the motor. The microphone and the computer are used as a part of a closed loop control system to tune the strings automatically. The control system requires the current fundamental frequency as well as the optimal, “in tune”, fundamental frequency. In this thesis, literature as well as algorithms on finding the current fundamental frequency are reviewed and a novel tuning process for calculating the optimal fundamental frequency is developed. The novel tuning process is compared against a tuning done by a professional tuner. The process is well suited for the tuning of a piano, as there is very little difference between the tuning done by the process and the tuner. Between keys A0 and G#5 the difference between the tunings is 2.5 cents and above that, in a region where the pitch of a string is much harder to hear, the difference is 8.1 cents.Pianon viritys on monimutkainen ja aikaa vievä prosessi, jonka pääosin tekevät ammattilaisvirittäjät. Pianon virittämisen helpottamiseksi sekä viritysajan lyhentämiseksi on kehitetty puoliautomaattinen pianonviritysjärjestelmä. Järjestelmä koostuu askelmoottorista, alumiinikehikosta, Arduino Uno mikroprosessorista, mikrofonista sekä tietokoneesta. Askelmoottori ja alumiinirunko mahdollistavat pianon kielien vireen säätämisen ja Arduino, mikrofoni sekä tietokone toimivat osina takaisinkytkettyä säädintä, jonka avulla kielet pystytään virittämään automaattisesti. Kielen virettä hallitaan säätämällä kielen perustaajuutta. Tässä työssä tutkitaan miten pianon kielen perustaajuuden saa selvitettyä sekä kehittää uuden menetelmän, jonka avulla saadaan laskettua perustaajuus, jossa kieli on parhaassa mahdollisessa vireessä. Kun tätä menetelmää verrataan ammattilaisvirittäjän tekemään viritykseen, niiden välillä on eroa vain 2,5 senttiä koskettimien A0 sekä G#5 välillä, sekä 8,1 senttiä koskettimien A5 ja C8 välillä. Ylemmillä koskettimilla oleva suurempi ero johtuu siitä, että kielien virettä on vaikeampi kuulla näillä koskettimilla

The Temperament Police: The Truth, the Ground Truth, and Nothing but the Truth

The tuning system of a keyboard instrument is chosen so that frequently used musical intervals sound as consonant as possible. Temperament refers to the compromise arising from the fact that not all intervals can be maximally consonant simultaneously. Recent work showed that it is possible to estimate temperament from audio recordings with no prior knowledge of the musical score, using a conservative (high precision, low recall) automatic transcription algorithm followed by frequency estimation using quadratic interpolation and bias correction from the log magnitude spectrum. In this paper we develop a harpsichord-specific transcription system to analyse over 500 recordings of solo harpsichord music for which the temperament is specified on the CD sleeve notes. We compare the measured temperaments with the annotations and discuss the differences between temperament as a theoretical construct and as a practical issue for professional performers and tuners. The implications are that ground truth is not always scientific truth, and that content-based analysis has an important role in the study of historical performance practice. 1

A digital waveguide-based approach for Clavinet modeling and synthesis

The Clavinet is an electromechanical musical instrument produced in the mid-twentieth century. As is the case for other vintage instruments, it is subject to aging and requires great effort to be maintained or restored. This paper reports analyses conducted on a Hohner Clavinet D6 and proposes a computational model to faithfully reproduce the Clavinet sound in real time, from tone generation to the emulation of the electronic components. The string excitation signal model is physically inspired and represents a cheap solution in terms of both computational resources and especially memory requirements (compared, e.g., to sample playback systems). Pickups and amplifier models have been implemented which enhance the natural character of the sound with respect to previous work. A model has been implemented on a real-time software platform, Pure Data, capable of a 10-voice polyphony with low latency on an embedded device. Finally, subjective listening tests conducted using the current model are compared to previous tests showing slightly improved results

Statistical Spectral Parameter Estimation of Acoustic Signals with Applications to Byzantine Music

Digitized acoustical signals of Byzantine music performed by Iakovos Nafpliotis are used to extract the fundamental frequency of each note of the diatonic scale. These empirical results are then contrasted to the theoretical suggestions and previous empirical findings. Several parametric and non-parametric spectral parameter estimation methods are implemented. These include: (1) Phase vocoder method, (2) McAulay-Quatieri method, (3) Levinson-Durbin algorithm,(4) YIN, (5) Quinn & Fernandes Estimator, (6) Pisarenko Frequency Estimator, (7) MUltiple SIgnal Characterization (MUSIC) algorithm, (8) Periodogram method, (9) Quinn & Fernandes Filtered Periodogram, (10) Rife & Vincent Estimator, and (11) the Fourier transform. Algorithm performance was very precise. The psychophysical aspect of human pitch discrimination is explored. The results of eight (8) psychoacoustical experiments were used to determine the aural just noticeable difference (jnd) in pitch and deduce patterns utilized to customize acceptable performable pitch deviation to the application at hand. These customizations [Acceptable Performance Difference (a new measure of frequency differential acceptability), Perceptual Confidence Intervals (a new concept of confidence intervals based on psychophysical experiment rather than statistics of performance data), and one based purely on music-theoretical asymphony] are proposed, discussed, and used in interpretation of results. The results suggest that Nafpliotis\u27 intervals are closer to just intonation than Byzantine theory (with minor exceptions), something not generally found in Thrasivoulos Stanitsas\u27 data. Nafpliotis\u27 perfect fifth is identical to the just intonation, even though he overstretches his octaveby fifteen (15)cents. His perfect fourth is also more just, as opposed to Stanitsas\u27 fourth which is directionally opposite. Stanitsas\u27 tendency to exaggerate the major third interval A4-F4 is still seen in Nafpliotis, but curbed. This is the only noteworthy departure from just intonation, with Nafpliotis being exactly Chrysanthian (the most exaggerated theoretical suggestion of all) and Stanitsas overstretching it even more than Nafpliotis and Chrysanth. Nafpliotis ascends in the second tetrachord more robustly diatonically than Stanitsas. The results are reported and interpreted within the framework of Acceptable Performance Differences