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Under that convention, a fourth is an interval encompassing four staff positions, while a fifth encompasses five staff positions (see interval number for more details). The augmented fourth (A4) and diminished fifth (d5) are defined as the intervals produced by widening the perfect fourth and narrowing the perfect fifth by one chromatic ...
Conversely, no augmented or diminished interval is diatonic, except for the augmented fourth and diminished fifth. A ♭-major scale. The distinction between diatonic and chromatic intervals may be also sensitive to context. The above-mentioned 56 intervals formed by the C-major scale are sometimes called diatonic to C major.
[1] [3] For instance, the interval from C to G is a perfect fifth, seven semitones wide, and both the intervals from C ♭ to G, and from C to G ♯ are augmented fifths, spanning eight semitones. Being augmented, it is considered a dissonant interval. [4] Its inversion is the diminished fourth, and its enharmonic equivalent is the minor sixth.
diminished fifth (6 semitones), and; augmented fifth (8 semitones). After the unison and octave intervals, the perfect fifth is the most important interval in tonal harmony. It is highly consonant. Its implementation in equal temperament tuning is highly accurate, unlike the major third interval, for example.
The Pythagorean diminished fourth (F ♭--, 8192:6561 = 384.36 cents), also known as the schismatic major third, is closer to the just major third than the Pythagorean major third. In just intonation the usual diminished fourth: the interval C ♯ to F, a diatonic minor second plus a pure minor third, or the interval C to F ♭ , a minor third ...
The augmented-fourth interval is the only interval whose inverse is the same as itself. The augmented-fourths tuning is the only tuning (other than the 'trivial' tuning C-C-C-C-C-C) for which all chords-forms remain unchanged when the strings are reversed. Thus the augmented-fourths tuning is its own 'lefty' tuning." [2]
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
(hence the seven 'interval classes') The tonal interval names 'minor 2nd' and 'major 7th' both correspond to "interval class 1" for example, this is because both are composed of one semitone and directional order is unimportant when the criteria become to select the smallest interval. Similarly, the 'augmented fourth' and the 'diminished fifth ...