# Augmented second

> Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Augmented_second
> Markdown URL: https://mediated.wiki/source/Augmented_second.md
> Source: https://en.wikipedia.org/wiki/Augmented_second
> Source revision: 1334433702
> License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/)

{{Infobox Interval|
main_interval_name = Augmented second|
inverse = [diminished seventh](/source/diminished_seventh)|
complement = [diminished seventh](/source/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> 81:68, 125:108, 7:6, 19683:16384| 
cents_equal_temperament = 300|
cents_24T_equal_temperament = |
cents_just_intonation = 275, 253, 267, 318
}}In [Western classical music](/source/Western_classical_music), an '''augmented second''' is an [interval](/source/Interval_(music)) created by [widening](/source/augmentation_(music)) a [major second](/source/major_second) by a [chromatic semitone](/source/chromatic_semitone), spanning three [semitones](/source/semitones) and enharmonically equivalent to a [minor third](/source/minor_third) in [12-tone equal temperament](/source/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.

:<score sound>
{
\override Score.TimeSignature
#'stencil = ##f
    \relative c' {
        \time 4/4
        \set Score.tempoHideNote = ##t \tempo 1 = 20
        <c dis>1
    }
}
</score>
== Usage ==
Augmented seconds occur in many scales, including the various modes of the [harmonic minor](/source/harmonic_minor) and [double harmonic](/source/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 [chords](/source/chord_(music)) in a minor key to follow the same rules of [cadence](/source/cadence_(music)) observed in major keys, where the V chord is "dominant" (that is, contains a major triad plus a [minor seventh](/source/minor_seventh)). An augmented second also appears in the [diminished seventh chord](/source/diminished_seventh_chord) (in [1st](/source/First_inversion), [2nd](/source/Second_inversion), and [3rd inversion](/source/Third_inversion)) between the diminished seventh and the root, and in the [German sixth chord](/source/German_sixth_chord) between the {{music|flat}}{{music|scale|3}} and {{music|sharp}}{{music|scale|4}} degrees.

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

==References==
<references/>

{{Intervals}}

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

---
Adapted from the Wikipedia article [Augmented second](https://en.wikipedia.org/wiki/Augmented_second) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Augmented_second?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.