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The consensus in piano tuning philosophy explains the stretched tuning scale by the inharmonicity of piano strings. This study aimed to examine how variable inharmonicity influences the result of the piano tuning process, compare the tuning curves of aurally tuned pianos with the curves derived from subjective octave enlargement experiments, and evaluate whether the pitches of inharmonic or harmonic versions of the same tone are perceived differently. In addition, the influence of strings of other piano keys on the measured inharmonicity of a single piano string was investigated. The inharmonicity of all individual strings was measured on a Steinway D grand piano. Variable inharmonicity was implemented by additive synthesis with frequency-adjusted sinusoidal partials. Fifteen piano tuners and 18 orchestra musicians participated in the experiments. The results indicate that the inharmonic piano tones produced a keyboard tuning curve similar to the Railsback curve and differed significantly from the harmonic counterpart. The inharmonic tuning curve was reminiscent of the subjective octave enlargement curve. Inharmonic tone pitches were perceived to be higher than harmonic tones up to C ♯ 7. The covibrating strings of the other keys did not exhibit any meaningful effect on the measured inharmonicity of a single string of the played key. [ABSTRACT FROM AUTHOR]

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Piano tuning is known to be difficult because the stiffness of piano strings causes the tones produced to be inharmonic. Aural tuning is time consuming and requires the help of a professional. This motivates the question of whether this process can be automated. Attempts at automatic tuning are usually assessed by comparing the Railsback curve of the results with the curve of a professional tuner. In this paper we determine a simple and reliable rule for tuning the high tones of a piano with the help of a listening test. This rule consists of matching the two tones in an octave interval so that the first partial frequency of the upper tone becomes exactly the same as the second partial frequency of the lower tone. This rule was rated best among four tuning rules that were compared in the test. The results found are explained using a beat-based analysis, and are consistent with some previous studies. They are also tested against the existing method of using Railsback curves, and it is shown that comparison using Railsback curves is an unreliable method of assessing different tunings. The findings from this paper can be used to create a complete automatic tuner that could make the process of piano tuning quick and inexpensive. [ABSTRACT FROM AUTHOR]

For decades, the phenomenon of subjectively enlarged octaves has been investigated using sinusoidal and synthesized complex tones. The present study elaborates the topic with samples of real orchestra instruments in successive tone listening experiments. Compared to previous research, this study also included a substantially larger number of subjects (N = 36). Examined instrument tones were categorized into five groups based on their acoustic principles. In addition, each group was assessed at three dynamic levels (pp-mf-ff). Collected data were analyzed with tuning stretch curves by applying generalized additive models in the manner of the Railsback curve used to characterize piano tuning. Although the tuning curve modeled for the orchestra instruments was observed to differ slightly from the Railsback curve and typical Steinway D grand piano tuning (Steinway, New York), the stretching trends were qualitatively similar. Deviation from a mathematical equal-tempered scale was prominent. According to statistical analyses, dynamics or musical background of the participant did not affect results significantly, but some instrument groups exhibited differences in the curve extremities. In conclusion, the stretched scale is natural for a human listener and should be used as a reference scale in tuning machines instead of the mathematical equal-tempered scale. [ABSTRACT FROM AUTHOR]

Nowadays, the development of electronic technology is changing every day. Computer technology has been widely used in various fields; therefore piano tuning teaching needs to keep pace with the social pace, and the tuning industry needs to be updated and explored to make it step on a new stage. In this study, the Fast Fourier Transform, Auto-correlation and Cepstrum feature extraction algorithms for audio visualization software were used to extract and visualize the audio features of seven piano tones from G4 to A4, and according to the characteristics the frequency was calculated and contrasted with the standard audio. Through the sound visualization analysis, it was found that the Auto-correlation algorithm was more consistent with the standard frequency. The use of sound visual tuning detection can plays an auxiliary role in piano tuning teaching. [ABSTRACT FROM AUTHOR]

This letter extends our prior work on context-dependent piano transcription to estimate the length of the notes in addition to their pitch and onset. This approach employs convolutional sparse coding along with lateral inhibition constraints to approximate a musical signal as the sum of piano note waveforms (dictionary elements) convolved with their temporal activations. The waveforms are pre-recorded for the specific piano to be transcribed in the specific environment. A dictionary containing multiple waveforms per pitch is generated by truncating a long waveform for each pitch to different lengths. During transcription, the dictionary elements are fixed and their temporal activations are estimated and postprocessed to obtain the pitch, onset, and note length estimation. A sparsity penalty promotes globally sparse activations of the dictionary elements, and a lateral inhibition term penalizes concurrent activations of different waveforms corresponding to the same pitch within a temporal neighborhood, to achieve note length estimation. Experiments on the MIDI aligned piano sounds dataset show that the proposed approach significantly outperforms a state-of-the-art music transcription method trained in the same context-dependent setting in transcription accuracy. [ABSTRACT FROM PUBLISHER]

Following the theoretical study of the Complexity Features in the Computer-aided piano tuning reported in 2014 to the SISOM Conference [1], this work focuses on the technical part of frequencies determination and of the frequencies bands identification, for a specific grand piano (the 5’3” Kohler- Campbell one). Using a Fast Fourier Transform (FFT) treatment (by means of computers) of the acoustic pressure determined by microphones, the frequencies of the first 6 partials of all 88 keys of the grand piano were determined, as well as the identification rule of the keys belonging to each frequency band of a piano instrument. There were identified so 90 frequencies bands: 57 central ones involving 6 rather near partials frequencies (NPF), 15 bands with 5 NPF, 6 bands with 4 NPF, 5 bands with 3 NPF and 7 bands with only 23 NPF, adding the 12 bass solitary fundamentals frequencies: A0 … G1#. [ABSTRACT FROM AUTHOR]

The perceptual results of Plomp and Levelt [J. Acoust. Soc. Am. 38, 548-560 (1965)] for the sensory dissonance of a pair of pure tones are used to estimate the dissonance of pairs of piano tones. By using the spectra of tones measured for a real piano, the effect of the inharmonicity of the tones is included. This leads to a prediction for how the tuning of this piano should deviate from an ideal equal tempered scale so as to give the smallest sensory dissonance and hence give the most pleasing tuning. The results agree with the well known "Railsback stretch," the average tuning curve produced by skilled piano technicians. The authors' analysis thus gives a quantitative explanation of the magnitude of the Railsback stretch in terms of the human perception of dissonance. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we studied the failure cause of two types of piano strings. The numerous problems which make it difficult to quantify the string life are systematically analyzed. The strings in question, made of spring steel (cold drawn wires with different thickness), are bass strings and acute strings of a piano concert. SEM analysis and Energy dispersive X-ray analysis (EDS) were made. Related questions were taken into account: [•] the connection of the string at the “tuning pin”; [•] string wear produced in its anchor point “agraffe”; [•] the bending in the compression points; [•] the environment where the piano is located, the relative humidity and the strings corrosion phenomena that might trigger stress-corrosion cracking; [•] the surface finish of the cold drawn string. Besides these factors, it is necessary to consider the different tuning performed on a concert grand piano. [Copyright &y& Elsevier]

Early in Wilhelm Heinse's eccentric novel Hildegard von Hohenthal (1796) his characters confront the problem of how music works on the senses. The novel's hero, Kapellmeister Lockmann, tunes a piano--to an idiosyncratic temperament of his own invention--as he proposes an intensely physical model for musical listening. He uses this demonstration, while simultaneously trying to start a love affair with the novel's heroine, Hildegard von Hohenthal, to reclaim older ideas about natural temperaments and key characteristics in an era of heightened interest in the anatomy of cognition. But Heinse's own opinions are not always the same as those of his characters. Drawing on his notebooks, I trace how Heinse struggled to come to terms with opposing views of his friend and colleague, the anatomist Samuel Thomas Soemmering, and of the philosopher Immanuel Kant of how sound affects the body. Soemmering's Uber das Organ der Seele (1796) and Kant's Critique of Aesthetic Judgment (1790) both act as intertexts and paratexts to the novel, and Heinse more than once splits his own opinions about both books between his characters. The tuning scene addresses important questions about the hierarchy of the senses, the creation of musical meaning, and the freedom of performers and listeners to form their own interpretations of music. Heinse's naturalist ideas about musical agency rub against the grain of a narrative--still current today--dominated by a transaction between heroic composers on the one side and awe-struck listeners on the other. To re-assess these ideas is to re-imagine a crucial hinge in music history. [ABSTRACT FROM AUTHOR]

The article discusses how mathematical concepts can be used to interpret music. It cites ideas from David Wright's book "Mathematics and Music" and "Music: A Mathematical Offering," by David Benson. It offers a review of basic concepts such as the physical aspects of sound and the basic layout and tuning of the piano keyboard. The article also explains how the equal spacing of twelve semitones of an octave can be interpreted through ratios and exponentials.

A letter is presented from theoretical physicist Richard Feynman to piano tuner Howard McQuigg which is related to the nonzero stiffness of piano strings affecting tuning and how piano tuners should give significance to ear-created harmonics. INSET: How to tune a piano.

Abstract: The tuning system of a piano has remained relatively unchanged since the instrument’s inception. A piano’s tuning system has been designed to be both inexpensive to manufacture and to preserve the tension and thus pitch of each string over long periods of time. This tuning system requires such a high degree of skill to manipulate that only trained professionals are able to tune pianos. This paper presents a novel adjustable impact tuning hammer and a reinforcement learning control system that may allow piano owners to tune their own pianos in the future. [Copyright &y& Elsevier]

The low frequency broadband vibrational behavior of a piano soundboard is considered. Attention is focused on the ability of finite element models and analytical models to predict precisely the behavior of such a complicated structure—especially with its orthotropy and rib effects. In order to validate these abilities, an experimental modal analysis, considered as the reference, is compared first with a numerical calculation and then with an analytical modeling of the modal basis of the same soundboard. The high structural complexity of the soundboard exceeds the analytical capabilities, but agreement is very good for the numerical model, in the frequency domain, and equally in the spatial one. The final aim is to generate a numerical tool for designing and optimizing piano soundboards. [Copyright &y& Elsevier]

This paper presents an intelligent permanent magnet synchronous motor-based servo drive system used in automated piano tuning applications. The permanent magnet synchronous motor-based drives are able to improve the accuracy of the piano tuning process in comparison with the traditional direct-current motor-based and step motor-based servo drives. To explain the techniques, firstly, the structure and principles of the automated piano tuning devices with a surface-mounted permanent magnet synchronous motor-based drive system integrated are introduced, illustrating that it is feasible to implement the proposed piano tuning strategy. Secondly, the piano tuning devices have two functions: low-speed rotation and position holding. To ensure that the surface-mounted permanent magnet synchronous motor can rotate stably over the low-speed range with strong anti-interference capacity, a double closed-loop speed-regulation-based control scheme is employed. And to ensure high position control performance, a fuzzy-adaptive triple closed-loop position-regulation-based control scheme is employed. It terms of the control schemes, it deserves to be mentioned that main contributions include, firstly, the parameters of the proportional integral controllers in the double closed-loop speed-regulation structure is tuned relying on both stability and bandwidth analyses. Then, a fuzzy-adaptive proportional integral controller is specially-designed for the triple closed-loop position-regulation to adapt to the piano tuning applications. Simulation is conducted on a 20 rpm three-phase permanent magnet synchronous motor servo drive-based piano tuning system to validate the proposed piano tuning method and to verify the proposed control techniques. [ABSTRACT FROM AUTHOR]