Les jetons : partage équitable | Tangente

Pierre Boulez, mathematics and glory | Tangente

"Music is a hidden practice of arithmetic, the mind unaware that it is counting," said Leibniz. Pierre Boulez, who died on 5 January, conductor, composer and teacher of music and musical composition all at once, revealed to the whole world the hidden face of "his" music, in which mathematics runs through like a watermark.

Constructing musical chords | Tangente

Charles V's letter finally deciphered | Tangente

An encrypted letter from Charles V (1500–1558), Holy Roman Emperor, addressed in 1547 to Jean de Saint-Mauris, his ambassador to the king of France, and housed in the autograph collection of the Bibliothèque Stanislas in Nancy (Meurthe-et-Moselle), has just been not merely read but deciphered. Long passages in the letter are encoded.

Olivier Messiaen: music and congruences

Mathematics and music were intertwined for centuries before gradually going their separate ways. Yet many composers remain attached to the language of numbers. Olivier Messiaen is a notable example: congruences play a part in the construction of his modes.