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The union of two intervals is an interval if and only if they have a non-empty intersection or an open end-point of one interval is a closed end-point of the other, for example (,) [,] = (,]. If R {\displaystyle \mathbb {R} } is viewed as a metric space , its open balls are the open bounded intervals ( c + r , c − r ) , and its closed balls ...
Examples of perfect subsets of the real line are the empty set, all closed intervals, the real line itself, and the Cantor set. The latter is noteworthy in that it is totally disconnected. Whether a set is perfect or not (and whether it is closed or not) depends on the surrounding space.
For example, the ascending interval from C to the next F is a perfect fourth, because the note F is the fifth semitone above C, and there are four staff positions between C and F. Diminished and augmented fourths span the same number of staff positions, but consist of a different number of semitones (four and six, respectively).
A major triad can also be described by its intervals: the interval between the bottom and middle notes is a major third, and the interval between the middle and top notes is a minor third. By contrast, a minor triad has a minor third interval on the bottom and major third interval on top. They both contain fifths, because a major third (four ...
Pages in category "Perfect intervals" The following 5 pages are in this category, out of 5 total. This list may not reflect recent changes. F. Fifteenth; O. Octave; P.
In music theory, a perfect fifth is the musical interval corresponding to a pair of pitches with a frequency ratio of 3:2, or very nearly so.. In classical music from Western culture, a fifth is the interval from the first to the last of the first five consecutive notes in a diatonic scale. [2]
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Because of this, we say that a number without a flat represents a major (or perfect) interval, while a number with a flat represents a minor interval. In this example, the numbers mean: 1 = (perfect) unison; 2 = major second ♭ 3 = minor third; 4 = perfect fourth; 5 = perfect fifth ♭ 6 = minor sixth ♭ 7 = minor seventh; 8 = (perfect) octave