![]() ![]() The cent is a logarithmic unit of measurement. The standard system for comparing interval sizes is with cents. For a comparison between the size of intervals in different tuning systems, see § Size of intervals used in different tuning systems. For instance, an equal-tempered fifth has a frequency ratio of 2 7⁄ 12:1, approximately equal to 1.498:1, or 2.997:2 (very close to 3:2). ![]() As a consequence, the size of most equal-tempered intervals cannot be expressed by small-integer ratios, although it is very close to the size of the corresponding just intervals. Most commonly, however, musical instruments are nowadays tuned using a different tuning system, called 12-tone equal temperament. Intervals with small-integer ratios are often called just intervals, or pure intervals. When a musical instrument is tuned using a just intonation tuning system, the size of the main intervals can be expressed by small- integer ratios, such as 1:1 ( unison), 2:1 ( octave), 5:3 ( major sixth), 3:2 ( perfect fifth), 4:3 ( perfect fourth), 5:4 ( major third), 6:5 ( minor third). The size of an interval between two notes may be measured by the ratio of their frequencies. 13 Alternative interval naming conventions.10 Size of intervals used in different tuning systems.9.2 Deducing component intervals from chord names and symbols.9.1 Chord qualities and interval qualities.The importance of spelling stems from the historical practice of differentiating the frequency ratios of enharmonic intervals such as G–G ♯ and G–A ♭. These names identify not only the difference in semitones between the upper and lower notes but also how the interval is spelled. Examples include the minor third or perfect fifth. In Western music theory, the most common naming scheme for intervals describes two properties of the interval: the quality (perfect, major, minor, augmented, diminished) and number (unison, second, third, etc.). For this reason, intervals are often measured in cents, a unit derived from the logarithm of the frequency ratio. This means that successive increments of pitch by the same interval result in an exponential increase of frequency, even though the human ear perceives this as a linear increase in pitch. For example, any two notes an octave apart have a frequency ratio of 2:1. ![]() In physical terms, an interval is the ratio between two sonic frequencies. Intervals can be arbitrarily small, and even imperceptible to the human ear. Some of the very smallest ones are called commas, and describe small discrepancies, observed in some tuning systems, between enharmonically equivalent notes such as C ♯ and D ♭. They can be formed using the notes of various kinds of non-diatonic scales. Intervals smaller than a semitone are called microtones. The smallest of these intervals is a semitone. ![]() Intervals between successive notes of a scale are also known as scale steps. In Western music, intervals are most commonly differences between notes of a diatonic scale. Īn interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord. In music theory, an interval is a difference in pitch between two sounds. ![]()
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