Polyphony and monophony in instruments harpejji and the Chapman stick). Multiphonics can be used with many regular wind instruments to produce two or more notes at once, although this is considered an extended technique. Explicitly polyphonic wind instruments are relatively rare, but do exist. The standard harmonica can easily produce several notes at once. Multichambered ocarinas are manufactured in a number of varieties, including double, triple, and quadruple ocarinas, which use multiple chambers to extend the ocarina's otherwise limited range, but also enable the musician to play more than one note simultaneously. Harmonic ocarinas are specifically designed for polyphony, and in these instruments the range
Quadruple product Quadruple product In mathematics, the quadruple product is a product of four vectors in three-dimensional Euclidean space. The name "quadruple product" is used for two different products, the scalar-valued scalar quadruple product and the vector-valued vector quadruple product or vector product of four vectors . The scalar quadruple product is defined as the dot product of two cross products: where a, b, c, d are vectors in three-dimensional Euclidean space. It can be evaluated using the identity: or using the determinant: The vector quadruple product is defined as the cross product of two cross products: where a, b, c, d