ninths

Ninths are a way to divide a whole into nine equal parts. In fractions, a ninth is 1/9, and the set of ninths consists of numbers k/9 for k = 1 through 8. The decimal expansion of 1/9 is 0.111..., a repeating decimal. As a rational number, 1/9 is in simplest terms and cannot be reduced.

In measurement and technical fields, ninths may be used to describe fractional dimensions, such as 1/9 inch. This subdivision is less common than halves, quarters, eighths, or sixteenths, but can appear in engineering drawings, machining, and layout work where precise fractional dimensions are required.

In music, a ninth is an interval that spans nine diatonic scale degrees, effectively an octave plus a second. The quality can be major or minor: a major ninth is 14 semitones above the root, while a minor ninth is 13 semitones. In chord notation, a ninth indicates adding that interval above the root, producing chords such as dominant ninth, major ninth, or minor ninth, often used to create color and extension beyond the triad.

The term ninth is the ordinal form of nine, used for sequencing, lists, calendars, and various scholarly and practical contexts. The plural ninths refers to multiple such divisions or intervals.