The U.S. wine making industry is poised to take a big hit from global warming in the coming decades. A climate model shows that premium wine growing regions — warm areas that suffer little frost or extreme heat — could decline by as much as 81 percent by the end of the century.

In western music, certain arrangements of chords and melodies sound “right” and others don’t. Musical theorists have long employed mathematics to try to understand harmony and melody, and particularly why only some sequences of notes lead from one specific chord to another in an aesthetically acceptable manner.

An advanced mathematical analysis uses a theoretical space in which all chords are points and sequences of notes connecting chords are lines between the points. The analysis shows that western music — even dissonant avant-garde compositions — use one of only three geometrical symmetries in the notes leading from one chord to another. This geometry of chords also provides a better understanding of consonance and dissonance, differences among musical genres and strategies of particular composers.