In music theory, an interval is a difference in pitch between two sounds. An 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 classical music from Western culture, a diesis is either an accidental, or a very small musical interval, usually defined as the difference between an octave and three justly tuned major thirds, equal to 128:125 or about 41.06 cents. In 12-tone equal temperament three major thirds in a row equal an octave, but three justly-tuned major thirds fall quite a bit narrow of an octave, and the diesis describes the amount by which they are short. For instance, an octave (2:1) spans from C to C', and three justly tuned major thirds (5:4) span from C to B♯. The difference between C-C' (2:1) and C-B♯ (125:64) is the diesis (128:125). Notice that this coincides with the interval between B♯ and C', also called a diminished second.
A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically. It is defined as the interval between two adjacent notes in a 12-tone scale. For example, C is adjacent to C♯; the interval between them is a semitone.
In music theory, a comma is a very small interval, the difference resulting from tuning one note two different ways. Strictly speaking, there are only two kinds of comma, the syntonic comma, "the difference between a just major 3rd and four just perfect 5ths less two octaves", and the Pythagorean comma, "the difference between twelve 5ths and seven octaves". The word comma used without qualification refers to the syntonic comma, which can be defined, for instance, as the difference between an F♯ tuned using the D-based Pythagorean tuning system, and another F♯ tuned using the D-based quarter-comma meantone tuning system. Intervals separated by the ratio 81:80 are considered the same note because the 12-note Western chromatic scale does not distinguish Pythagorean intervals from 5-limit intervals in its notation. Other intervals are considered commas because of the enharmonic equivalences of a tuning system. For example, in 53TET, B♭ and A♯ are both approximated by the same interval although they are a septimal kleisma apart.
Quarter-comma meantone, or 1⁄4-comma meantone, was the most common meantone temperament in the sixteenth and seventeenth centuries, and was sometimes used later. In this system the perfect fifth is flattened by one quarter of a syntonic comma (81:80), with respect to its just intonation used in Pythagorean tuning ; the result is 3/2 × 1⁄4 = 4√5 ≈ 1.49535, or a fifth of 696.578 cents. This fifth is then iterated to generate the diatonic scale and other notes of the temperament. The purpose is to obtain justly intoned major thirds. It was described by Pietro Aron in his Toscanello de la Musica of 1523, by saying the major thirds should be tuned to be "sonorous and just, as united as possible." Later theorists Gioseffo Zarlino and Francisco de Salinas described the tuning with mathematical exactitude.
In music, 31 equal temperament, 31-ET, which can also be abbreviated 31-TET or 31-EDO, also known as tricesimoprimal, is the tempered scale derived by dividing the octave into 31 equal-sized steps. Play (help·info) Each step represents a frequency ratio of 31√2, or 38.71 cents.
In music, septimal meantone temperament, also called standard septimal meantone or simply septimal meantone, refers to the tempering of 7-limit musical intervals by a meantone temperament tuning in the range from fifths flattened by the amount of fifths for 12 equal temperament to those as flat as 19 equal temperament, with 31 equal temperament being a more or less optimal tuning for both the 5- and 7-limits. Meantone temperament represents a frequency ratio of approximately 5 by means of four fifths, so that the major third, for instance C–E, is obtained from two tones in succession. Septimal meantone represents the frequency ratio of 56 (7 × 23) by ten fifths, so that the interval 7:4 is reached by five successive tones. Hence C–A♯, not C–B♭, represents a 7:4 interval in septimal meantone.
In music, 22 equal temperament, called 22-TET, 22-EDO, or 22-ET, is the tempered scale derived by dividing the octave into 22 equal steps. Play (help·info) Each step represents a frequency ratio of 22√2, or 54.55 cents.
A septimal comma is a small musical interval in just intonation that contains the number seven in its prime factorization. There is more than one such interval, so the term septimal comma is ambiguous, but it most commonly refers to the interval 64/63.
In music, the septimal minor third, also called the subminor third, is the musical interval exactly or approximately equal to a 7/6 ratio of frequencies. In terms of cents, it is 267 cents, a quartertone of size 36/35 flatter than a just minor third of 6/5. In 24-tone equal temperament five quarter tones approximate the septimal minor third at 250 cents. A septimal minor third is almost exactly two-ninths of an octave, and thus all divisions of the octave into multiples of nine have an almost perfect match to this interval. The septimal major sixth, 12/7, is the inverse of this interval.
In music and tuning, the ragisma is an interval with the ratio of 4375:4374, ≈0.396 cents. It is usually defined as the difference between the septimal minor third (7:6) and two Bohlen–Pierce small semitones. It is also the difference between minor Bohlen–Pierce diesis (245:243) and septimal semicomma (126:125), as well as the difference between the septimal third tone (28:27) and the greater diesis (648:625).
In music, septimal diesis is an interval with the ratio of 49:48 play (help·info), which is the difference between the septimal whole tone and the septimal minor third. It is about 35.7 cents wide, which is narrower than a quarter-tone but wider than the septimal comma. It may also be the ratio 36:35, or 48.77 cents. Play (help·info)
A septimal quarter tone is an interval with the ratio of 36:35, which is the difference between the septimal minor third and the Just minor third, or about 48.77 cents wide. The name derives from the interval being the 7-limit approximation of a quarter tone. The septimal quarter tone can be viewed either as a musical interval in its own right, or as a comma; if it is tempered out in a given tuning system, the distinction between the two different types of minor thirds is lost. The septimal quarter tone may be derived from the harmonic series as the interval between the thirty-fifth and thirty-sixth harmonics.
In music, 41 equal temperament, abbreviated 41-TET, 41-EDO, or 41-ET, is the tempered scale derived by dividing the octave into 41 equally sized steps. Play (help·info) Each step represents a frequency ratio of 21/41, or 29.27 cents, an interval close in size to the septimal comma. 41-ET can be seen as a tuning of the schismatic, magic and miracle temperaments. It is the second smallest equal temperament, after 29-ET, whose perfect fifth is closer to just intonation than that of 12-ET. In other words, is a better approximation to the ratio than either or .
A septimal tritone is a tritone that involves the factor seven. There are two that are inverses. The lesser septimal tritone is the musical interval with ratio 7:5. The greater septimal tritone, is an interval with ratio 10:7. They are also known as the sub-fifth and super-fourth, or subminor fifth and supermajor fourth, respectively.
A septimal 1/3-tone is an interval with the ratio of 28:27, which is the difference between the perfect fourth and the supermajor third. It is about 62.96 cents wide. The septimal 1/3-tone can be viewed either as a musical interval in its own right, or as a comma; if it is tempered out in a given tuning system, the distinction between these two intervals is lost. The septimal 1/3-tone may be derived from the harmonic series as the interval between the twenty-seventh and twenty-eighth harmonics. It may be considered a diesis.
Five-limit tuning, 5-limit tuning, or 5-prime-limit tuning (not to be confused with 5-odd-limit tuning), is any system for tuning a musical instrument that obtains the frequency of each note by multiplying the frequency of a given reference note (the base note) by products of integer powers of 2, 3, or 5 (prime numbers limited to 5 or lower), such as 2−3·31·51 = 15/8.
In music, a subminor interval is an interval that is noticeably wider than a diminished interval but noticeably narrower than a minor interval. It is found in between a minor and diminished interval, thus making it below, or subminor to, the minor interval. A supermajor interval is a musical interval that is noticeably wider than a major interval but noticeably narrower than an augmented interval. It is found in between a major and augmented interval, thus making it above, or supermajor to, the major interval. The inversion of a supermajor interval is a subminor interval, and there are four major and four minor intervals, allowing for eight supermajor and subminor intervals, each with variants.
In music theory, a neutral interval is an interval that is neither a major nor minor, but instead in between. For example, in equal temperament, a major third is 400 cents, a minor third is 300 cents, and a neutral third is 350 cents. A neutral interval inverts to a neutral interval. For example, the inverse of a neutral third is a neutral sixth.
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