View source for Diminished seventh

{{About|the interval|the chord|Diminished seventh chord}}
{{Infobox Interval|
main_interval_name = Diminished seventh|
inverse = [[Augmented second]]|
complement = [[augmented second]]|
other_names = -|
abbreviation = d7<ref name="B&S"/>|
semitones = 9|
interval_class = 3|
just_interval = 128:75,<ref name="Haluska">Haluska, Jan (2003). ''The Mathematical Theory of Tone Systems'', p.xxvi. {{ISBN|0-8247-4714-3}}. Diminished seventh.</ref> 216:125,<ref>Haluska (2003), p.xxvi. Acute diminished seventh.</ref> 32768:19683, 26:15|
cents_equal_temperament = 900|
cents_24T_equal_temperament = |
cents_just_intonation = 925, 947, 882, 952.3
}}

[[File:Diminished seventh on C.png|thumb|right|Diminished seventh {{Audio|Major sixth on C.mid|Play}}.]]

In [[classical music]] from [[Western culture]], a '''diminished seventh''' ({{Audio|Dim seventh on C.mid|play}}) is an [[interval (music)|interval]] produced by [[Diminution|narrowing]] a [[minor seventh]] by a [[chromatic semitone]],<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 d7 not given but general example of minor intervals described.</ref><ref>Hoffmann, F.A. (1881). ''Music: Its Theory & Practice'', p.89-90. Thurgate & Sons. Digitized Aug 16, 2007.</ref> and its [[Inversion (interval)|inversion]] is the [[augmented second]]. For instance, the interval from A to G is a minor seventh, ten semitones wide, and both the intervals from A{{Music|sharp}} to G, and from A to G{{Music|b}} are diminished sevenths, spanning nine semitones. Being diminished, it is considered a [[consonance and dissonance|dissonant]] interval.<ref>Benward & Saker (2003), p.92.</ref>

The diminished seventh is used quite readily in the [[minor key]], where it is present in the [[harmonic minor]] scale between the seventh scale step and the sixth scale step in the [[octave]] above.

In 12-tone [[equal temperament]], a diminished seventh is equal to nine semitones, a ratio of 2<sup>9/12</sup>:1 (approximately 1.6818), or 900 cents, and is [[enharmonic]]ally equivalent to a [[major sixth]]. There is no standard [[just intonation|just tuning]] of this interval, but one possibility, assuming the flat submediant is a perfect (5:4) major third below the octave, and the leading tone to be 15:16, would lead to an interval of 128:75, about 925 cents; another interval is 216:125, which is three minor thirds. However, in [[19 equal temperament]], it is enharmonically equivalent to an [[augmented sixth]], having a ratio of 2<sup>15/19</sup>:1 (approximately 1.7284), or 947 cents.

The 128:75 just diminished seventh arises in the C [[harmonic minor scale]] between B and A{{music|b}} by combining B-D, D|F, F-A{{music|b}}.<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> {{audio|Just diminished seventh in scale.mid|Play}}

==Usage in musical expression==

Since the Baroque era, Western European composers have used the diminished seventh as a melodic interval to convey intense, sometimes troubled emotion.  [[Richard Taruskin]] (2010, p.&nbsp;258) draws attention to the falling melodic figures in the bass (pedal) part of J. S. Bach's organ chorale prelude from the ''[[Orgelbüchlein]]'', "Durch Adam's Fall":[[File:Durch Adams Fall.png|thumb|center|500px|J.S.Bach, "Durch Adam's Fall" from ''Orgelbüchlein.'' [https://www.youtube.com/watch?v=k3Ck0ij_I84 Listen]]]

"What is a powerful surprise, and further evidence of Bach’s unique imaginative boldness, is the specific form the obbligato pedal part takes in this chorale setting: almost nothing but dissonant drops of a seventh – Adam’s fall made audible!  And not just the fall, but also the attendant pain and suffering are depicted (and in a way evoked), since so many of those sevenths are diminished."<ref>Taruskin, R. (2010), ''The Oxford History of Western Music'', Vol. 2.  Oxford University Press.</ref>
The expressive potential of the interval was not lost on Mozart, especially when, as Dennis Matthews (1971, p. iii) puts it, "Mozart reserved a minor home-key for his most disquieting utterances."<ref>Matthews, D. (1971) Introduction to score of Mozart Piano Concerto for Piano and Orchestra in C minor, K491. London, Eulenburg.</ref> The opening theme of the [[Piano Concerto No. 24 (Mozart)|Piano Concerto in C minor K491]], features rising diminished sevenths:[[File:Mozart K491 opening theme.png|thumb|center|500px|Mozart, Piano Concerto in C minor, K491, opening theme. [https://www.youtube.com/watch?v=PftH8FVzIRY Listen]]]

More startling is the finale of [[Symphony No. 40 (Mozart)|Mozart's G minor Symphony No. 40]], K550, which critic [[Charles Rosen]] (1971, p324) calls "a work of passion, violence and grief."<ref>Rosen, C. (1971) ''The Classical Style''. London, Faber.</ref> The development section features a disorienting sequence of diminished sevenths:[[File:Mozart K550 finale bars 125-30.png|thumb|center|500px|Mozart, Symphony No. 40, finale, bars 125–130. [https://www.youtube.com/watch?v=FdXgijZVdPs&t=3m36s Link to passage] ]]

The dramatic clout of the interval was further exploited by operatic composers during the nineteenth century.  Robert Donington (1963, p.&nbsp;175) heard the dark, atmospheric Prelude to [[Wagner]]’s opera ''[[Siegfried (opera)|Siegfried]]''  as "a kind of elemental brooding…Its material is an uneasy sequence of thirds low in the bass, and separated by a diminished seventh.":<ref>Donington, R. (1963) ''Wagner’s Ring and its Symbols''. London Faber.</ref>[[File:Siegfried Vorspiel.png|thumb|center|500px|Wagner, Siegfried, opening prelude. [https://www.youtube.com/watch?v=M_LrHBPfeas Listen]]]

==See also==
*[[Diminished seventh chord]]

==References==
<references/>

{{Intervals}}

[[Category:Diminished intervals]]
[[Category:Sevenths (music)]]