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The perfect fourth is a perfect interval like the unison, octave, and perfect fifth, and it is a sensory consonance. In common practice harmony, however, it is considered a stylistic dissonance in certain contexts, namely in two-voice textures and whenever it occurs "above the bass in chords with three or more notes". [ 2 ]
For instance, the limit of the just perfect fourth (4:3) is 3, but the just minor tone (10:9) has a limit of 5, because 10 can be factored into 2 × 5 (and 9 into 3 × 3). There exists another type of limit, the odd limit , a concept used by Harry Partch (bigger of odd numbers obtained after dividing numerator and denominator by highest ...
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).
The size of an interval between two notes may be measured by the ratio of their frequencies.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 (), 2:1 (), 5:3 (major sixth), 3:2 (perfect fifth), 4:3 (perfect fourth), 5:4 (major third), 6:5 (minor third).
Standard tuning mixes a major third (M3) with its perfect fourths. Regular tunings that are based on either major thirds or perfect fourths are used, for example, in jazz. All fourths tuning E 2 –A 2 –D 3 –G 3 –C 4 –F 4 keeps the lowest four strings of standard tuning, changing the major third to a perfect fourth.
These three intervals and their octave equivalents, such as the perfect eleventh and twelfth, are the only absolute consonances of the Pythagorean system. All other intervals have varying degrees of dissonance, ranging from smooth to rough. The difference between the perfect fourth and the perfect fifth is the tone or major second.
"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." [23]
The previously discussed I–IV–V chord progressions of major triads is are a subsequence of the circle progression, which ascends by perfect fourths and descends by perfect fifths: Perfect fifths and perfect fourths are inverse intervals, because one reaches the same pitch class by either ascending by a perfect fourth (five semitones) or ...