Any interval intermediate between the Half Tone and the Whole Tone. [In just ratios,] Three-Quarter Tones range from about 13/12 (139 cents [¢]) to 11/10 (165¢).
Calculated as the 8th root of 2 -- 8√2, or 2(1/8) -- an irrational proportion with the approximate ratio of 1 : 1.090507733, and an interval size of exactly 150 cents. It is the size of one degree, and thus the basic "step" size, in the 8-edo (or 8-tET) scale.
The 3/4-tone occurs in all divisions of the octave which are multiples of 8 -- thus, it is a significant feature of the popular 24-edo quarter-tone scale, in which it traverses a pitch space of 3 degrees.