Periodic table
The organization of the periodic table can be used to derive relationships between the various element properties, and also to predict chemical properties and behaviours of undiscovered or newly synthesized elements. Russian chemist Dmitri Mendeleev published the first recognizable periodic table in 1869, developed mainly to illustrate periodic trends of the then-known elements. He also predicted some properties of unidentified elements that were expected to fill gaps within the table. Most of his forecasts proved to be correct. Mendeleev's idea has been slowly expanded and refined with the discovery or synthesis of further new elements and the development of new theoretical models to explain chemical behaviour. The modern periodic table now provides a useful framework for analyzing chemical reactions, and continues to be widely used in chemistry, nuclear physics and other sciences.
Harmonic table note layout
The structure and properties of the Harmonic Table have been well known since at least the 18th century. Indeed, as a pitch space, the Harmonic Table is topologically equivalent to Euler's Tonnetz, discovered by the Swiss mathematician Leonhard Euler in 1739. The two pitch arrays are trivially obtained from each other by direct shear mapping. This note layout created by Euler is utilised in Neo-Riemannian theory to geometrically model its musical ideas.