The process of finding the difference in pitch between two tones, ordered from lower to higher (ascending) or higher to lower (descending), involves computation. These computations determine the specific musical distance, expressed numerically (e.g., a second, a third, a fifth), and qualitatively (e.g., major, minor, perfect, augmented, diminished). For example, measuring the span from C to G upward identifies a perfect fifth. Conversely, measuring from E to C downward yields a minor third.
Determining these musical distances is fundamental to music theory, composition, and performance. Accurately establishing intervals enables harmonic analysis, chord construction, melodic development, and transposition. Historically, various systems have been devised for this determination, evolving from Pythagorean ratios to modern equal temperament, each influencing the character and possibilities of musical expression.
