Related papers: A New Keyboard for the Bohlen-Pierce Scale
A new musical scale devised by the author, based on natural logarithms, is described. Most of the logarithmic pitches bear no correspondence to the twelve tones of the ancient tuning system attributed to Pythagoras, based on ratios of whole…
In piano playing, different ways of touch lead to different tones. The effects of changing forces on keys are presented by changing interaction between hammer and string. The thesis focuses on several important variables in hammer-string…
Humans have been developing and playing musical instruments for millennia. With technological advancements, instruments were becoming ever more sophisticated. In recent decades computer-supported innovations have also been introduced in…
This paper aims to develop a comprehensive physical model and numerical simulation schemes for a grand piano. The model encompasses various subsystems, including hammer felt, hammer shank, string, soundboard, air and room barriers, each…
For around 300 years, humans have been learning to play the modern piano either with a teacher or on their own. In recent years teaching and learning have been enhanced using augmented technologies that support novices. Other technologies…
The aim is to explore new opportunities of the pitch organization of the musical scale. Specifically, a numerical comparison of the different musical temperaments among themselves in the degree of approximation of the Pythagorean scale is…
In classical music and in any genre of contemporary music, the tonal elements or notes used for playing are the same. The numerous possibilities of chords for a given instance in a piece make the playing, in general, very intricate, and…
Both, human appreciation of music and musical genres, transcend time and space. The universality of musical genres and associated musical scales is intimately linked to the physics of sound and the special characteristics of human acoustic…
A set of basic notes, or `scale', forms the basis of music. Scales are specific to specific genre of music. In this second article of the series we explore the development of various scales associated with western classical music, arguably…
The mathematics of musical intervals and scales has been extensively studied. Vastly simplified, our ears seem to prefer intervals whose frequency ratios have small numerator and denominator, such as 2:1 (octave), 3:2 (perfect fifth), 4:3…
The perception of consonance/dissonance of musical harmonies is strongly correlated with their periodicity. This is shown in this article by consistently applying recent results from psychophysics and neuroacoustics, namely that the just…
In this work we present a new approach for the task of predicting fingerings for piano music. While prior neural approaches have often treated this as a sequence tagging problem with independent predictions, we put forward a checklist…
A method is proposed which enables one to produce musical compositions by using transposition in place of harmonic progression. A transposition scale is introduced to provide a set of intervals commensurate with the musical scale, such as…
We develop aspects of music theory related to harmony, such as scales, chord formation and improvisation from a combinatorial perspective. The goal is to provide a foundation for this subject by deriving the basic structure from a few…
A keyboard is the most important input device for a computer. It is used with various types and sizes of computer. But the same standard keyboard will not work efficiently with different types of computers at different environments. There…
This paper aims to develop a holistic evaluation method for piano sound quality to assist in purchasing decisions. Unlike previous studies that focused on the effect of piano performance techniques on sound quality, this study evaluates the…
Why are white and black piano keys in an octave arranged as they are today? This article examines the relations between abstract algebra and key signature, scales, degrees, and keyboard configurations in general equal-temperament systems.…
We investigate correlations among pitches in several songs and pieces of piano music by mapping them to one-dimensional walks. Two kinds of correlations are studied, one is related to the real values of frequencies while they are treated…
In order to explore tonality outside of the `Pythagorean' paradigm of integer ratios, Robert Schneider introduced a musical scale based on the logarithm function. We seek to refine Schneider's scale so that the difference tones generated by…
Piano tones vary according to how pianist touches the keys. Many possible factors contribute to the relations between piano touch and tone. Focusing on the stiffness of string, we establish a model for vibration of a real piano string and…