In Western classical music, an augmented second is an interval created by widening a major second by a chromatic semitone, spanning three semitones and enharmonically equivalent to a minor third in 12-tone equal temperament.<ref name="B&S">Benward & Saker (2003). Music: In Theory and Practice, Vol. I, p.54. Template:ISBN. Specific example of an A2 not given but general example of major intervals described.</ref><ref>Hoffmann, F.A. (1881). Music: Its Theory & Practice, p.89-90. Thurgate & Sons. Digitized Aug 16, 2007. Archaically: redundant or extreme sharp second.</ref> For instance, the interval from C to D is a major second, two semitones wide, and the interval from C to DTemplate:Music is an augmented second, spanning three semitones.
UsageEdit
Augmented seconds occur in many scales, including the various modes of the harmonic minor and double harmonic scales. In harmonic minor, the augmented second occurs between the sixth and seventh scale degrees. For example, in the scale of A harmonic minor, the notes F and GTemplate:Music form the interval of an augmented second. This distinguishing feature of harmonic minor scales occurs as a consequence of the seventh scale degree having been chromatically raised in order to allow chords in a minor key to follow the same rules of cadence observed in major keys, where the V chord is "dominant" (that is, contains a major triad plus a minor seventh). An augmented second also appears in the diminished seventh chord (in 1st, 2nd, and 3rd inversion) between the diminished seventh and the root, and in the German sixth chord between the Template:MusicTemplate:Music and Template:MusicTemplate:Music degrees.
TuningEdit
An augmented second is enharmonically equivalent to a minor third in 12-tone equal temperament ({{#if:Minor third on C.mid|{{#ifexist:Media:Minor third on C.mid|<phonos file="Minor third on C.mid">Play</phonos>|{{errorTemplate:Main other|Audio file "Minor third on C.mid" not found}}Template:Category handler}}}}), but is distinguished in other tunings. In tunings near quarter-comma meantone it approximates the septimal minor third of ratio 7:6 ({{#if:Septimal minor third on C.mid|{{#ifexist:Media:Septimal minor third on C.mid|<phonos file="Septimal minor third on C.mid">Play</phonos>|{{errorTemplate:Main other|Audio file "Septimal minor third on C.mid" not found}}Template:Category handler}}}}). In pythagorean tuning and schismatic temperament, however, it closely approximates the classical minor third of ratio 6:5 ({{#if:Just minor third on C.mid|{{#ifexist:Media:Just minor third on C.mid|<phonos file="Just minor third on C.mid">Play</phonos>|{{errorTemplate:Main other|Audio file "Just minor third on C.mid" not found}}Template:Category handler}}}}). In superpyth temperament, the fifth is sharpened so that the augmented second reaches the classical major third of ratio 5:4 ({{#if:Just major third on C.mid|{{#ifexist:Media:Just major third on C.mid|<phonos file="Just major third on C.mid">Play</phonos>|{{errorTemplate:Main other|Audio file "Just major third on C.mid" not found}}Template:Category handler}}}}).
The 75:64 just augmented second ({{#if:Just augmented second in scale.mid|{{#ifexist:Media:Just augmented second in scale.mid|<phonos file="Just augmented second in scale.mid">Play</phonos>|{{errorTemplate:Main other|Audio file "Just augmented second in scale.mid" not found}}Template:Category handler}}}}) arises in the justly tuned C harmonic minor scale between ATemplate:Music (tuned to 8:5) and B (tuned to 15:8).<ref>Paul, Oscar (1885). A manual of harmony for use in music-schools and seminaries and for self-instruction, p.165. Theodore Baker, trans. G. Schirmer.</ref> It is very close to the 7:6 septimal minor third, differing by a septimal kleisma.
ReferencesEdit
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