In modern straight pianos and half-grand pianos the inharmonicity due to the bending stiffness of the strings makes the sound of lower notes of poor quality. The question of whether this can be ...corrected has been addressed in a previous paper and it was shown on the basis of numerical simulations that this might be possible. In the present paper we show using analytical models that fixing a single mass near the end of the string is a simple and efficient solution. Indeed, the experiments show that theoretical predictions are relevant. So, in practice, on the basis of a simple formula involving the inharmonicity coefficient, it is easy to deduce the position of a given mass in order to reduce significantly the inharmonicity of the bass strings.
In this work, we consider the problem of estimating the frequency content of inharmonic signals, i.e., sinusoidal mixtures whose components are close to forming a harmonic set. Intuitively, ...exploiting this closeness should lead to increased estimation performance as compared to unstructured estimation. Earlier approaches to this problem have relied on parametric descriptions of the inharmonicity, stochastic representations, or have resorted to misspecified estimation by ignoring the inharmonicity. Herein, we propose to use a penalized maximum-likelihood framework, where the regularizer is constructed based on optimal mass transport theory, promoting estimates that are close-to-harmonic in a spectral sense. This leads to an estimator that forms a smooth path between the unstructured maximum-likelihood estimator (MLE) and a misspecified MLE (MMLE), as determined by a regularization parameter. In numerical illustrations, we show that the proposed estimator worst-case dominates the MLE and MMLE, thereby allowing for robust estimation for cases when the inharmonicity level is unknown.
In this work, we consider the modeling of signals that are almost, but not quite, harmonic, i.e., composed of sinusoids whose frequencies are close to being integer multiples of a common frequency. ...Typically, in applications, such signals are treated as perfectly harmonic, allowing for the estimation of their fundamental frequency, despite the signals not actually being periodic. Herein, we provide three different definitions of a concept of fundamental frequency for such inharmonic signals and study the implications of the different choices for modeling and estimation. We show that one of the definitions corresponds to a misspecified modeling scenario, and provides a theoretical benchmark for analyzing the behavior of estimators derived under a perfectly harmonic assumption. The second definition stems from optimal mass transport theory and yields a robust and easily interpretable concept of fundamental frequency based on the signals' spectral properties. The third definition interprets the inharmonic signal as an observation of a randomly perturbed harmonic signal. This allows for computing a hybrid information theoretical bound on estimation performance, as well as for finding an estimator attaining the bound. The theoretical findings are illustrated using numerical examples.
Polyphonic pitch transcription consists of estimating the onset time, duration and pitch of each note in a music signal. This task is difficult in general, due to the wide range of possible ...instruments. This issue has been studied using adaptive models such as Nonnegative Matrix Factorization (NMF), which describe the signal as a weighted sum of basis spectra. However basis spectra representing multiple pitches result in inaccurate transcription. To avoid this, we propose a family of constrained NMF models, where each basis spectrum is expressed as a weighted sum of narrowband spectra consisting of a few adjacent partials at harmonic or inharmonic frequencies. The model parameters are adapted via combined multiplicative and Newton updates. The proposed method is shown to outperform standard NMF on a database of piano excerpts.
Tension-resolution patterns seem to play a dominant role in shaping our emotional experience of music. In traditional Western music, these patterns are mainly expressed through harmony and melody. ...However, many contemporary musical compositions employ sound materials lacking any perceivable pitch structure, rendering the two compositional devices useless. Still, composers like Tristan Murail or Gérard Grisey manage to implement the patterns by manipulating spectral attributes like roughness and inharmonicity. However, in order to understand the music of theirs and the other proponents of the so-called “spectral music,” one has to eschew traditional categories like pitch, harmony, and tonality in favor of a lower-level, more general representation of sound—which, unfortunately, music-psychological research has been reluctant to do. In the present study, motivated by recent advances in music-theoretical and neuroscientific research into a the highly related phenomenon of dissonance, we propose a neurodynamical model of musical tension based on a spectral representation of sound which reproduces existing empirical results on spectral correlates of tension. By virtue of being neurodynamical, the proposed model is generative in the sense that it can simulate responses to arbitrary sounds.
The prominent strategical approaches regarding the problem of guitar tablature transcription rely either on fingering patterns encoding or on the extraction of string-related audio features. The ...current work combines the two aforementioned strategies in an explicit manner by employing two discrete components for string-fret classification. It extends older few-sample modeling strategies by introducing various adaptation schemes for the first stage of audio processing, taking advantage of the inharmonic characteristics of guitar sound. Physical limitations and common standards of human performers are incorporated in a genetic algorithm which constitutes a second contextual-based module that further processes the initial audio-based predictions. The proposed methods are evaluated on both annotated guitar performances and isolated note recordings.
In this paper, a system for the extraction of the tablature of guitar musical pieces using only the audio waveform is presented. The analysis of the inharmonicity relations between the fundamentals ...and the partials of the notes played is the main process that allows to estimate both the notes played and the string/fret combination that was used to produce that sound. A procedure to analyze chords will also be described. This procedure will also make use of the inharmonicity analysis to find the simultaneous string/fret combinations used to play each chord. The proposed method is suitable for any guitar type: classical, acoustic and electric guitars. The system performance has been evaluated on a series of guitar samples from the RWC instruments database and our own recordings.
We evaluated whether task-irrelevant inharmonic music produces greater interference with cognitive performance than task-irrelevant harmonic music. Participants completed either an auditory ...(Experiment
1
) or a visual (Experiment
2
) version of the cognitively demanding 2-back task in which they were required to categorize each digit in a sequence of digits as either being a target (a digit also presented two positions earlier in the sequence) or a distractor (all other items). They were concurrently exposed to either task-irrelevant harmonic music (judged to be consonant), task-irrelevant inharmonic music (judged to be dissonant), or no music at all as a distraction. The main finding across both experiments was that performance on the 2-back task was worse when participants were exposed to inharmonic music than when they were exposed to harmonic music. Interestingly, performance on the 2-back task was generally the same regardless of whether harmonic music or no music was played. We suggest that inharmonic, dissonant music interferes with cognitive performance by requiring greater cognitive processing than harmonic, consonant music, and speculate about why this might be.
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With the increasing importance of smart gadgets in our daily lives, there is a need for an automatic piano transcription system in various multimedia services. For automatic piano transcription, the ...string inharmonicity coefficient (B) and fundamental frequency (f 0 ) should be detected robustly and accurately. The proposed triplet-sequentially additive partial (SAP) algorithm improves the current B estimation algorithm in terms of both performance and speed with less prior knowledge. Additionally, this joint (B, f 0 ) estimation algorithm is applied directly to the transcription of real piano recordings, and the 4.41% improvement of accuracy was achieved over another transcription system that had both similar processing steps and feature extraction method.
On Harmonic Approximations of Inharmonic Signals Elvander, Filip; Ding, Jie; Jakobsson, Andreas
2020 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2020,Barcelona, Spain,2020-05-04 - 2020-05-08
2020-May
Conference Proceeding
Open access
In this work, we present the misspecified Gaussian Cramér-Rao lower bound for the parameters of a harmonic signal, or pitch, when signal measurements are collected from an almost, but not quite, ...harmonic model. For the asymptotic case of large sample sizes, we present a closed-form expression for the bound corresponding to the pseduo-true fundamental frequency. Using simulation studies, it is shown that the bound is sharp and is attained by maximum likelihood estimators derived under the misspecified harmonic assumption. It is shown that misspecified harmonic models achieve a lower mean squared error than correctly specified unstructured models for moderately inharmonic signals. Examining voices from a speech database, we conclude that human speech belongs to this class of signals, verifying that the use of a harmonic model for voiced speech is preferable.
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