The visual representation described in this paper is the result of my own research and work, but does not constitute a novelty in its entirety. The ba

The Fine Art of Combining Harmonics

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2021-06-22 07:00:06

The visual representation described in this paper is the result of my own research and work, but does not constitute a novelty in its entirety. The basis, or underlying principle of this mathematical graph is a matrix of numbers with ancient history1 called “Lambdoma”, also known as the Lambdoid by Nicomachus, the Pythagorean ChiX, the Tetraktys by Plato, the Lambdoma Table by von Thimus, and the Cantor array.2 Other names include Mensa Pythagorica3 and combinations of the above terms, like Pythagorean Table. Whole-number systems that bear a one-to-one relationship with the Lambdoma matrix are the Farey series of gear ratios generated by a Diophantine equation4;5 and the Stern–Brocot tree. Related concepts include the Archetypal Splay–Tree or Co–Prime Pattern6 mapped by Ervin M. Wilson inside this grid of harmonic ratios, and the Partch–Meyer–Novaro tonality diamond structures which constitute a confined development of the original concept.

The novelty of my version consists in the accurate representation of musical entities, by using a graphical system mathematicians call “logarithmic”, which I call “sonic”, where the eye sees the distribution of tone-spaces in the same way as the ear hears them.