At a fundamental level, music may be described as a train of vibrations in the air. It can be further reduced to numbers — a string of binary digits (bits) that can be stored on a CD or sent around the world in a split second. But music carries enormous emotional content and can stir … Continue reading Music and Maths from Bach to Bacherach
Tag: Fourier analysis
Making Sound Pictures to Identify Bird Songs
A trained musician can look at a musical score and imagine the sound of an entire orchestra. The score is a visual representation of the sounds. In an analogous way, we can represent birdsong by an image, and analysis of the image can tell us the species of bird singing. This is what happens with … Continue reading Making Sound Pictures to Identify Bird Songs
Joseph Fourier and the Greenhouse Effect
Jean-Baptiste Joseph Fourier, French mathematician and physicist, was born in Auxerre 251 years ago today. He is best known for the mathematical techniques that he developed in his analytical theory of heat transfer. Over the past two centuries, his methods have evolved into a major subject, harmonic analysis, with widespread applications in number theory, signal … Continue reading Joseph Fourier and the Greenhouse Effect
Don’t be Phased by Waveform Distortions
For many years there has been an ongoing debate about the importance of phase changes in music. Some people claim that we cannot hear the effects of phase errors, others claim that we can. Who is right? The figure below shows a waveform of a perfect fifth, with components in the ratio $latex {3 : … Continue reading Don’t be Phased by Waveform Distortions
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