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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]
Augmented fourth between C and F ♯ and the diminished fifth between C and G ♭ are enharmonically equivalent intervals. Both are 600 cents wide in 12-TET. Since a chromatic scale is formed by 12 pitches (each a semitone apart from its neighbors), it contains 12 distinct tritones, each starting from a different pitch and spanning six semitones
C2–F ♯ 2–C3–F ♯ 3–C4–F ♯ 4 and B1–F1–B2–F3–B3–F4 etc. Between the all-fifths and all-fourths tunings are augmented-fourth tunings, which are also called "diminished-fifths" or "tritone" tunings. It is a repetitive tuning that repeats its notes after two strings. With augmented-fourths tunings, the fretboard has ...
[1] [3] For instance, the interval from C to E is a major third, four semitones wide, and both the intervals from C ♭ to E, and from C to E ♯ are augmented thirds, spanning five semitones. Being augmented, it is considered a dissonant interval. [4] Its inversion is the diminished sixth, and its enharmonic equivalent is the perfect fourth.
The augmented fourth (A4) is the only augmented interval that appears in diatonic scales (in D ♭ major it occurs between G ♭ and C). The standard abbreviations for augmented intervals are AX, such that an augmented third = A3. [7]
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).
This is often interpreted as a quartal hexachord consisting of an augmented fourth, diminished fourth, augmented fourth, and two perfect fourths.The chord is related to other pitch collections, such as being a hexatonic subset of the overtone scale, also known in jazz circles as the Lydian dominant scale, lacking the perfect fifth.
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