Editing Augmented second

{{Infobox Interval|
main_interval_name = Augmented second|
inverse = [[diminished seventh]]|
complement = [[diminished seventh]]|
other_names = -|
abbreviation = A2<ref name="B&S"/>|
semitones = 3|
interval_class = 3|
just_interval = 75:64,<ref name="Haluska">Haluska, Jan (2003). ''The Mathematical Theory of Tone Systems'', p.xxvi. {{ISBN|0-8247-4714-3}}. Classic augmented second.</ref> 125:108, 7:6, 19683:16384| 
cents_equal_temperament = 300|
cents_24T_equal_temperament = |
cents_just_intonation = 275, 253, 267, 318
}}
[[File:Augmented second on C.png|thumb|right|Augmented second on C {{audio|Minor third on C.mid|Play}}.]]

In [[Western classical music]], an '''augmented second''' is an [[Interval (music)|interval]] created by [[augmentation (music)|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. {{ISBN|978-0-07-294262-0}}. 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 D{{Music|sharp}} is an augmented second, spanning three semitones.

== Usage ==
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{{music|sharp}} 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 [[chord (music)|chords]] in a minor key to follow the same rules of [[cadence (music)|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 [[First inversion|1st]], [[Second inversion|2nd]], and [[Third inversion|3rd inversion]]) between the diminished seventh and the root, and in the [[German sixth chord]] between the {{music|flat}}{{music|scale|3}} and {{music|sharp}}{{music|scale|4}} degrees.

==Tuning==
An augmented second is [[enharmonically equivalent]] to a [[minor third]] in [[12-tone equal temperament]] ({{Audio|Minor third on C.mid|Play}}), but is distinguished in other tunings. In tunings near [[quarter-comma meantone]] it approximates the [[septimal minor third]] of ratio 7:6 ({{Audio|Septimal minor third on C.mid|Play}}). In [[pythagorean tuning]] and [[schismatic temperament]], however, it closely approximates the [[Minor third|classical minor third]] of ratio 6:5 ({{Audio|Just minor third on C.mid|Play}}). In [[22 equal temperament|superpyth temperament]], the fifth is sharpened so that the augmented second reaches the [[Major third#Harmonic_and_non-harmonic_thirds|classical major third]] of ratio 5:4 ({{Audio|Just major third on C.mid|Play}}).

The 75:64 just augmented second ({{audio|Just augmented second in scale.mid|Play}}) arises in the justly tuned C [[harmonic minor scale]] between A{{music|b}} (tuned to 8:5) and B (tuned to 15:8).<ref>Paul, Oscar (1885). ''[https://books.google.com/books?id=4WEJAQAAMAAJ&q=musical+interval+%22pythagorean+major+third%22 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]].

==References==
<references/>

{{Intervals}}

{{DEFAULTSORT:Augmented Second}}
[[Category:Augmented intervals]]
[[Category:Seconds (music)]]