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The extremes of the meantone systems encountered in historical practice are the Pythagorean tuning, where the whole tone corresponds to 9:8, i.e. (3:2) 2 / 2 , the mean of the major third (3:2) 4 / 4 , and the fifth (3:2) is not tempered; and the 1 ⁄ 3-comma meantone, where the fifth is tempered to the extent that three ...
The intervals of 5-limit just intonation (prime limit, not odd limit) are ratios involving only the powers of 2, 3, and 5.The fundamental intervals are the superparticular ratios 2/1 (the octave), 3/2 (the perfect fifth) and 5/4 (the major third).
Instead, the inequalities must be solved independently, yielding x < 1 / 2 and x ≥ −1 respectively, which can be combined into the final solution −1 ≤ x < 1 / 2 . Occasionally, chained notation is used with inequalities in different directions, in which case the meaning is the logical conjunction of the inequalities ...
In summary, a set of the real numbers is an interval, if and only if it is an open interval, a closed interval, or a half-open interval. [ 4 ] [ 5 ] A degenerate interval is any set consisting of a single real number (i.e., an interval of the form [ a , a ] ). [ 6 ]
Interval class Play ⓘ.. In musical set theory, an interval class (often abbreviated: ic), also known as unordered pitch-class interval, interval distance, undirected interval, or "(even completely incorrectly) as 'interval mod 6'" (Rahn 1980, 29; Whittall 2008, 273–74), is the shortest distance in pitch class space between two unordered pitch classes.
Interval class table for [0,1,4,6] ic notes of [0,1,4,6] built on E diatonic counterparts 1: E to F: minor 2nd and major 7th 2: A ♭ to B ♭ major 2nd and minor 7th 3: F to A ♭ minor 3rd and major 6th 4: E to G ♯ major 3rd and minor 6th 5: F to B ♭ perfect 4th and perfect 5th 6: E to B ♭ augmented 4th and diminished 5th