Augmented second
| Inverse | diminished seventh |
|---|---|
| Name | |
| Other names | - |
| Abbreviation | A2[1] |
| Size | |
| Semitones | 3 |
| Interval class | 3 |
| Just interval | 75:64,[2] 81:68, 125:108, 7:6, 19683:16384 |
| Cents | |
| 12-Tone equal temperament | 300 |
| Just intonation | 275, 253, 267, 318 |
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.[1][3] For instance, the interval from C to D is a major second, two semitones wide, and the interval from C to D♯ is an augmented second, spanning three semitones.
Usage
[edit | edit source]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 G♯ 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 ♭scale degree 3 and ♯scale degree 4 degrees.
Tuning
[edit | edit source]An augmented second is enharmonically equivalent to a minor third in 12-tone equal temperament (Audio file "Minor third on C.mid" not found), but is distinguished in other tunings. In tunings near quarter-comma meantone it approximates the septimal minor third of ratio 7:6 (Audio file "Septimal minor third on C.mid" not found). In pythagorean tuning and schismatic temperament, however, it closely approximates the classical minor third of ratio 6:5 (Audio file "Just minor third on C.mid" not found). In superpyth temperament, the fifth is sharpened so that the augmented second reaches the classical major third of ratio 5:4 (Audio file "Just major third on C.mid" not found).
The 75:64 just augmented second (Audio file "Just augmented second in scale.mid" not found) arises in the justly tuned C harmonic minor scale between A♭ (tuned to 8:5) and B (tuned to 15:8).[4] It is very close to the 7:6 septimal minor third, differing by a septimal kleisma.
References
[edit | edit source]- ^ a b Benward & Saker (2003). Music: In Theory and Practice, Vol. I, p.54. Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).. Specific example of an A2 not given but general example of major intervals described.
- ^ Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxvi. Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).. Classic augmented second.
- ^ Hoffmann, F.A. (1881). Music: Its Theory & Practice, p.89-90. Thurgate & Sons. Digitized Aug 16, 2007. Archaically: redundant or extreme sharp second.
- ^ 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.
