a Latin particle, signifying a whole and a half; which, joined with altera, terza, quarta, &c. is much used in the Italian music to express a kind of ratios, particularly several species of triples.

SESQUI-Alterate, in Geometry and Arithmetic, is a ratio between two lines, two numbers, or the like, where one of them contains the other once, with the addition of a half.

Thus 6 and 9 are in a sesqui-alterate ratio; since 9 contains 6 once, and 3, which is half of 6, over; and 20 and 30 are in the same; as 30 contains 20, and half 20 or 10.

SESQUI-Duplicate ratio, is when of two terms the greater contains the less twice, and half the less remains; as 15 and 6; 50 and 20.

SESQUI-Tertional proportion, is when any number or quantity contains another once and one third.