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Augmented second

From Wikipedia, the free encyclopedia
Musical interval
Augmented second
Inversediminished seventh
Name
Other names-
AbbreviationA2[1]
Size
Semitones3
Interval class3
Just interval75:64,[2] 81:68, 125:108, 7:6, 19683:16384
Cents
12-Tone equal temperament300
Just intonation275, 253, 267, 318

InWestern classical music, anaugmented second is aninterval created bywidening amajor second by achromatic semitone, spanning threesemitones and enharmonically equivalent to aminor third in12-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]

Augmented seconds occur in many scales, including the various modes of theharmonic minor anddouble 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 allowchords in a minor key to follow the same rules ofcadence observed in major keys, where the V chord is "dominant" (that is, contains a major triad plus aminor seventh). An augmented second also appears in thediminished seventh chord (in1st,2nd, and3rd inversion) between the diminished seventh and the root, and in theGerman sixth chord between thescale degree 3 andscale degree 4 degrees.

Tuning

[edit]

An augmented second isenharmonically equivalent to aminor third in12-tone equal temperament (Play), but is distinguished in other tunings. In tunings nearquarter-comma meantone it approximates theseptimal minor third of ratio 7:6 (Play). Inpythagorean tuning andschismatic temperament, however, it closely approximates theclassical minor third of ratio 6:5 (Play). Insuperpyth temperament, the fifth is sharpened so that the augmented second reaches theclassical major third of ratio 5:4 (Play).

The 75:64 just augmented second (Play) arises in the justly tuned Charmonic 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 aseptimal kleisma.

References

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  1. ^abBenward & 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.
  2. ^Haluska, Jan (2003).The Mathematical Theory of Tone Systems, p.xxvi.ISBN 0-8247-4714-3. Classic augmented second.
  3. ^Hoffmann, F.A. (1881).Music: Its Theory & Practice, p.89-90. Thurgate & Sons. Digitized Aug 16, 2007. Archaically:redundant orextreme sharp second.
  4. ^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.
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