The historical context of the Lambdoma matrix and its applications

Recently there has been a renewed interest in pure harmonic representations of music and other man-made systems. The Lambdoma matrix is such a representation that was introduced in the 4th century EC. This matrix has had impact over the centuries on mathematics, music and engineering. An electronic interface called the Pythagorean Lambdoma harmonic keyboard (PLHK) has been developed by a team of engineers to facilitate the study of these representations by musicians, psycho acousticians and other researchers.