The wave equation for stiff strings and piano tuning

We study the wave equation for a string with stiffness. We solve the equation and provide a uniqueness theorem with suitable boundary conditions. For a pinned string we compute the spectrum, which is slightly inharmonic. Therefore, the widespread scale of 12 equal divisions of the just octave is not the best choice to tune instruments like the piano. Basing on the theory of dissonance, we provide a way to tune the piano in order to improve its consonance. A good solution is obtained by tuning a note and its fifth by minimizing their beats.Peer ReviewedPostprint (published version

Comparison of input devices in an ISEE direct timbre manipulation task

The representation and manipulation of sound within multimedia systems is an important and currently under-researched area. The paper gives an overview of the authors' work on the direct manipulation of audio information, and describes a solution based upon the navigation of four-dimensional scaled timbre spaces. Three hardware input devices were experimentally evaluated for use in a timbre space navigation task: the Apple Standard Mouse, Gravis Advanced Mousestick II joystick (absolute and relative) and the Nintendo Power Glove. Results show that the usability of these devices significantly affected the efficacy of the system, and that conventional low-cost, low-dimensional devices provided better performance than the low-cost, multidimensional dataglove

Significance of Harmonic Contents with Respect to the Timbre of the Violoncello

Harmonic contents (harmonic or inharmonic partials) is an important waveform characteristic that influences the timbre of musical tones. The first part of this research is aimed at finding out (through waveform analysis) the harmonic and inharmonic partials of four sampled violoncello (or cello) C#3 tones, each played using a different technique. The four different techniques studied are 'arco', 'spiccato', 'pizzzicato' and 'tremolando'. From the results of the waveform analysis, the difference in timbre between the four different playing techniques of the cello could be understood by comparing the harmonic contents of the four cello tones. The results of the waveform analysis generally showed that the four different playing techniques have different number of harmonic and inharmonic partials in their spectra. Both the 'spiccato' and 'tremolando' techniques produced more inharmonic compared to harmonic partials while the 'arco' technique produced more harmonic compared to inharmonic partials. The 'pizzicato' technique produced only harmonic partials. The results of the waveform analysis is then used in the second part of this research that is aimed at finding out the significance of various groups of harmonic or inharmonic partials in contributing to the timbre of the cello through a listening test. For this test, the results of the waveform analysis are used to modify the harmonic contents of the four cello tones. The timbres of the modified cello tones are then compared with the original cello tones by using short music sequences. Comparisons are then made between the four different techniques by using tables and graphs. Results indicate that different groups of harmonic or inharmonic partials affect the timbre of the cello in different ways. In other words, some groups of harmonic or inharmonic partials are more significant to the timbre of the cello compared to other groups. Besides, the timbres of the four different playing techniques are influenced by the harmonic contents modifications differently. The results generally showed the 'spiccato' technique as the technique that is influenced most significantly and the 'pizzicato' technique as the. technique that is influenced least significantly in timbre by the harmonic contents modifications executed. The timbres of both the 'arco' and 'tremolando' techniques are influenced moderately by the harmonic contents modifications. However, the timbre of the cello 'arco' technique is influenced more significantly by the harmonic contents modifications compared to the 'tremolando' technique

On inharmonicity in bass guitar strings with application to tapered and lumped constructions

In this study, the inharmonicity of bass guitar strings with and without areas of lowered and raised mass near the saddle is studied. Using a very high sample rate of over 900 kHz enabled finite difference time domain simulation to be applied for strings that simultaneously have nonzero stiffness and linear density which varies along the length of the string. Results are compared to experiments on specially constructed strings. Perturbation theory is demonstrated to be sufficiently accurate (and much more computationally efficient) for practical design purposes in reducing inharmonicity. The subject of inharmonicity is well known in pianos but has not been studied extensively in bass guitar strings. Here, the inharmonicity is found to be low in the lowest (open string) pitch on the five string bass guitar (B0) given typical standard construction. Conversely, the inharmonicity is high (around 100 cents at the 10th partial) when that string is sounded when stopped at the 12th fret and very high (around 100 cents at the 6th partial) when that string is stopped at the 21st fret. Bass guitar strings were constructed with three different constructions (standard, tapered and lumped) in order to demonstrate how incorporating a lump of raised mass near the saddle can achieve close to zero inharmonicity for the lower frequency partials. This also has potential in terms of improving the use of higher fret numbers for musical harmony (reducing beating) and also in controlling pitch glide that has, with some exceptions, often been attributed solely to nonlinear behaviour.Publisher PDFPeer reviewe

The spectral atom : cohesion of spectral particles in the music of Alvin Lucier.

Listeners often associate the music of Alvin Lucier with the practice of experimental music due to his unorthodox means of composition. By viewing his work in this way, whether consciously or subconsciously, his music is often treated as aleatoric. This classification ignores the compositional stimulus that fuels the creation of his music. Lucier’s compositions are driven by the exploitation of one facet (or phenomenon) of sound. These sound phenomena take the form of spectral particles: vibrating media, acoustics, and psychoacoustics. The spectral particles uncovered in his pieces combine to form a spectral atom. By analyzing four of Alvin Lucier’s works, Twonings,Silver Streetcar for the Orchestra,I am Sitting in a Room, andStill and Moving Lines of Silence in Families of Hyperbolas, I intend to extrapolate their spectral particles. A combination of these spectral particles will inform the spectral atom of the work in question