Attempt at a New Theory of Music

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...we determined that sounds are pleasing when the ratio original: "ratio" - here meaning the mathematical relationship or proportion held between the numbers of vibrations produced in the same amount of time is perceived. Conversely, displeasure consists in this: when either no order is sensed, or that order which seems ought to be present is suddenly disturbed. Next, we explained how the order of sounds—which is contained in the ratio of vibrations produced simultaneously or in equal durations—is distinctly perceived. From this, it was soon possible to gather that some ratios are easier to perceive and others more difficult. Inquiring into the cause of this distinction, we have reduced the faculty of perception to degrees original: "gradus" - Euler's system for ranking the complexity of musical intervals; these are not only of the greatest importance in music, but can also bring immense utility to other disciplines and arts where beauty original: "venustas" - aesthetic elegance or charm is the goal. These degrees are arranged according to the simplicity of the ratios to be perceived, and all those ratios...