Modulation by enharmonic reinterpretation of a o7

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• 8 Comments sorted by Votes Date Added
• Scott Murphy

  October 2015 @sbmurphySend sbmurphy a private message.Vote Up0Vote Down

  Hi, David. So, to understand what you are looking for, would something like the music right after the cadenza in the last movement of Beethoven's Violin Concerto suffice? In this music, vii°7 of D -- the main key of the movement -- becomes vii°7 of A flat, which is briefly but thematically tonicized. In this case, the °7 chord (pcs 1, 4, 7, 10) is of tonic, not dominant, in both keys.

  -Scott M.
• Joel Lester

  October 2015 @JoelLesterSend JoelLester a private message.Vote Up0Vote Down

  In the recitative "Erbarm es Gott!" from Bach's St. Matthew Passion, the diminished seventh chord on the downbeat of m. 11 enters as vii7 of V in F# minor (a B# diminished seventh chord, which is equivalent to an F# diminished seventh chord), and resolves by moving to I6 in G minor. 

  In the overture to Wagner's Tannhäuser, the music in measure 204 follows a phrase in G major.  Over the next several measures, an embellishing diminished seventh chord (a diminished seventh with G in it) prolongs a G major chord, and then resolves to a B-flat major chord.  Presumably the B-flat major chord is a "tonic."  Thereafter, the same diminished seventh embellishes to a C# major chord which is locally treated as a tonic before eventually resolving as a dominant of F# in m. 220 to end this passage. 

  These passages are discussed in Chapter 29 of my 1982 text Harmony in Tonal Music (along with enharmonic reinterpretations of other sorts of chords that also sometimes move to non-dominant chords in the new key). 

  In the coda to the Allegretto vivace movement of Beethoven's op. 59 no. 1 string quartet, Beethoven in m. 442 begins a phrase in the tonic key of the movement, B-flat major.  Instead of a concluding tonic, that phrase ends with a repeated vii7 of vi (an F# diminished seventh).  After a GP, the same diminished seventh recurs, now with D# notated as its bass.  The next phrase is in E minor.  Before the D# diminished seventh resolves to the tonic E, the C in the diminished seventh moves down a semitone to B, turning the chord into a V6/5 of E. 

  Joel Lester
• Jena Root

  October 2015 edited October 2015 @jenarootSend jenaroot a private message.Vote Up0Vote Down

  Hi David,

  See page 2 of this worksheet (which you're welcome to print and use with your students. There's a treble staff under each system for the purpose of sketching the chords in simple position.). Beethoven, op. 2, no.2 goes from A major to F major via a dim7 which moves to a V7 in the new key, but the modulation back to A (final system of the excerpt)pivots via the same dim7 reinterpreted as viio6/5/ii in A. Hope this is helpful!

  https://drive.google.com/file/d/0B4ESzKhCMzrnZ25PTnRiZ1c0bW8/view?usp=sharing

  Jena Root
• Carson Farley

  October 2015 @carsonicsSend carsonics a private message.Vote Up0Vote Down

  According to Walter Piston the diminished 7th chord has 48 possible interpretations for modulation:

  Here is the passage from Walter PIston's Harmony, pg. 201:

  "The tonal ambiguity of the diminished seventh chord is turned to versatility when it is a question of modulation.  This versatillity is unmatched by any other chord.  A single diminished seventh chord, without enharmonic change , is capable, like any dominant chord, of the following analyses: V, V of II, V of III (in minor), V of III (in major), V of IV, V of V, V of VI (in minor), V of VI (in major), V of VII (in minor).  Add to these the nondominant forms II7 adn VI7, and the dominant of the lowered second degree (Vo/9 of N6), and we have twelve interpretations for the one chord.  Moreover, since the chord may be enharmonically written in four different ways without changing the sound, we may multiply the above by four, making a total of forty-eight possible interpretations."   

  I hope this is some help.  
• David Heetderks

  October 2015 @davidheetderksSend davidheetderks a private message.Vote Up0Vote Down

  Thank you, one and all, for the helpful information. Scott, in Beethoven's violin concerto, iii, the violin moves from E-natural to E-flat before the orchestra moves to A-flat major; thus the o7 first becomes a V6/5 of A-flat before resolving. Sorry if my question was not clear--I was looking for examples where the o7 moves directly to the new tonic without becoming a V first. Jena, your examples use similar voice leading, as does the Beethoven Op. 59 example.

  The Mozart Symphony #40 is a good example I wasn’t aware of. A colleague pointed out that “Dalla sua pace” from Don Giovannni uses a similar device: in mm. 28–29 a viio7/V in G minor is reinterpreted as viio6/5 in B minor and resolves directly to i6. The other examples (Bach, Wolf, and Wagner) are very interesting—thanks so much. We have looked at the common-tone o7s at the opening of the Allegro section of the Tannhäuser overture, and I was planning to show how they are repeated sequentially in the later passage.

  DH
• John Paul Ito

  October 2015 @itojpSend itojp a private message.Vote Up0Vote Down

  If this is for teaching, may be water under the bridge, but here are a couple more examples, or related examples.

  Parallel to Dalla sua pace but not as good a piece, Brahms, Triumphlied, 3rd mvt, 133-134, basically same chords, modulation is D major to F# minor.

  Brahms, C minor quartet, 1st movement, 1st and 2nd endings of exposition.  1st, to move from Eb back to c, vii7/V becomes on its second appearance "vii42/V" and signals the reinterpretation in the new key.  2nd, one note lowered by half-step to create Mm sonority, but this resolves as Ger+6/5, taking us to A minor.  So both qualify as not turning into V chords before they resolve.

  It's a nice example especially because of the prior history of the chord -- it started as an incomplete tonic plus an incomplete neighbor (m. 2), and was then a CTdim7 (m. 24) before becoming vii7/V in the codetta.

  If you have any interest in the opposite of what you describe -- moving between dominant sevenths that are related by shared enharmonically-equivalent vii7's -- the second phrase of Schubert's Bb trio is a great example.

  John
• Scott Murphy

  November 2015 @sbmurphySend sbmurphy a private message.Vote Up0Vote Down

  I'll take a shot at redeeming myself then:

  How about the casting of the seventh bullet in the Wolf's Glen scene from Der Freischütz? The music is in C minor before, and in F# minor after, and the four measures of °7 are "of tonic" in both keys. No smoothing of the °7 sonority to its more agreeable Mm7 sibling here, as to be expected at this wild moment.