Barbershop Arranging — Part 5: Breaking the Circle
Resolving the Dominant 7 tension in new and unexpected ways
This is Part 5 of a 10-part series on barbershop arranging. The full guide is here.
Our toolbox at this point is looking solid. We know how the innate tension in Dominant 7 chords resolves in an intuitive and predictable way around the Circle of Fifths. We know how to use this framework to harmonize a melody. We know how to weasel our way out of tougher situations when the melody note doesn’t quite fit into our desired chord. And we know how to spell chords to maximize harmonics while also maintaining thoughtful voice leading for each singer. We’ve come along way, and we should feel proud!
We can move mountains with Circle of Fifths progressions alone, but occasionally we’ll need or want to break ranks. Not all songs follow the Circle of Fifths perfectly—or even remotely—so additional progressions might be required to keep the original character of a song intact. Further, just as important as tension and release in music is another pair of concepts: surprise and delight. Audiences love when arrangers make creative, bold, thoughtful new choices. Fortunately, tension can resolve in more ways than meet the eye.
Tritone resolution, revisited
In our initial discussion of Tritone Resolution, we said that the most intuitive resolution is to the key that contains the 3 and the flat-7. This gave us our hallowed V7 → I progression upon which we built the entire Circle of Fifths. However, like a poorly scripted sequel to a perfect original film, the plot has thickened, and we’re about to meet a whole new cast of characters.
Recall that “releasing” tension means going from a place of dissonance to a place of consonance. If we allow ourselves to surprise the listener, there are actually many different places of consonances to which we can resolve!
Consider a G7 chord. Let’s focus on the Tritone between its B and F. Typically, we’d resolve this tritone inward, the B ascending by one half step and the F descending by one half step, to a C Major Triad. But we can do so much more. For the following explorations, we’ll isolate the B and the F and observe where else these two notes might resolve to release their tension.
The members of this sequel squad are radically different in character and charisma. Some are stronger, while some pride themselves on their subversive nature. Here for their first table read is the whole eclectic bunch.
Note: Each video will depict how the red G7 tritone resolves to the blue pitches of the following chord, but all pitches in both chords will be played.
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Inward resolutions
The following resolutions resolve the tritone inward, with the 3rd ascending and the 7th descending.
G7 → C (V7 → I)
3rd up 1 half-step.
7th down 1 half-step.
The tried and true progression the ear will always appreciate. The old friend, warm and helpful, always ready to offload your tension and give you the simple peace you desire.
G7 → A (V7 → VI)
3rd up 2 half-steps.
7th down 1 half-step.
The celebrated action hero called to arms, taking flight and piercing through the clouds to save the day. A leader through and through, proclaiming that victory is all but certain.
G7 → Ab (V7 →♭VI)
3rd up 1 half-step.
7th down 2 half-steps.
The littlest lift, but one that could not have come at a better time. A mentor you spot briefly in the distance, whom you resolve to reach anew after nearly losing hope.
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Outward resolutions
The following resolutions take a different approach, resolving the tritone with opposing, outward motion. This time, the 3rd descends, and the 7th ascends.
G7 → F# (V7 → #IV)
3rd down 1 half-step.
7th up 1 half-step.
The clever scientist determined to extend the corpus of human knowledge and experience. The breakthrough: something uncannily familiar, but flipped on its head, vibrant and fresh.
G7 → Eb (V7 →♭III)
3rd down 1 half-step.
7th up 2 half-steps.
The lifelong friend. A light in your life who will support you unfailingly in a time of need. Always ready with a reassuring smile and a comforting mantra to put you at ease.
G7 → D (V7 → II)
3rd down 2 half-steps.
7th up 1 half-step.
The revelrous partygoer, thrilled at any opportunity to gather with friends known and yet to be met. Inclusive and invigorating, yet the probable culprit for all the sticky floors after a lit fest.
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3-stagnant resolutions
Next, we move on to a class of resolutions that leave the 3 in place, and let 7 alone bear the responsibility of resolving the pair into a consonant interval.
G7 → B (V7 → VII)
3rd stays.
7th up 1 half-step.
The former underdog who just gave the knockout blow to a far superior opponent. Collapsing in exhaustion, breathing heavily amidst an oncoming rush of achievement and relief.
G7 → E (V7 → III)
3rd stays.
7th down 1 half-step.
The wily Monte dealer who makes a living outfoxing passersby. Serves inevitable defeat with a fiendish grin and a cunning lift of the eyebrow.
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7-stagnant resolutions
Finally, we visit a set of resolutions that do the reverse of the previous set, leaving the 7 in place and letting the 3 achieve consonance on its own terms.
G7 → Bb (V7 → ♭VII)
3rd down 1 half-step.
7th stays.
The revolutionary mobilizing a group of comrades. Willing to die for the cause, and likely to motivate the rest to the same mindset. Shouts of “Carpe Diem” will erupt at any moment.
G7 → F (V7 → IV)
3rd up 1 half-step.
7th stays.
The portly companion with a lazy gaze. Asked to devise a creative plan, will share the first idea that comes to mind, then have a seat nearby and stare aimlessly at a bug on the wall.
G7 → C# (V7 → #I)
3rd up 2 half-steps.
7th stays.
The pesky 10th-grader whose aim in life is to subvert rules and expectations. Hides your keys and ties your shoelaces together. The house cat of humans, but admirably spicy and deliberate.
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Each of the chord progressions above evokes different sentiments and colors (some synesthetics literally see different colors when they hear triads in different keys). But all obey the principle of Tritone Resolution: they see a Tritone and resolve it to a more consonant interval, letting the other two pitches from the G7 chord go where they may to complete the Triad.
Tritone substitution
Breaking with our B-movie metaphor for a moment, let’s discuss the G7 → C# (V7 → I#) progression in more detail. A Tritone is special for its functional qualities, but it is also unique in another way: the Tritone is the only interval that is symmetric.
Interval inversions
In the previous post, we discussed how the Half-Diminished 7 and the Dominant 7 can function as “fraternal twins,” such that the former can be substituted for the latter in a progression. There is another class of fraternal twins in music as well: interval pairs.
An interval, a pair of two notes, may in some sense be sung either “right side up” or “upside down.” Consider the interval between C and G. Sung with the C on the bottom, we have a Perfect 5th. But what if we invert the interval, lifting the C an octave up and leaving the G on the bottom? Suddenly we have a Perfect 4th! We call this an interval inversion.
Below is a visual of all intervals together with their inverted variants. The Minor 2nd inverts into a Major 7th and vice versa. The Major 2nd inverts into a Minor 7th. The Minor 3rd inverts into a Major 6th. The Major 3rd inverts into a Minor 6th. The Perfect 4th inverts into a Perfect 5th, as we’ve just seen (interval inversion is a commutative property). And lastly, we see that a Tritone inverts to itself—making it not a fraternal, but an identical twin.
Exploiting Tritone symmetry
The Tritone is the only interval whose inversion is the same as the original. This has a powerful implication with respect to V7 resolutions. Consider the Tritone between B and F within the G7 chord again, built on scale degrees 3 and 7 relative to the G root.
If we isolate the Tritone and invert it in place, we’re left with the same Tritone—complete with all the same character and progressional proclivities—except with the scale degrees reversed. That is, 3 becomes 7, and 7 becomes 3. This suggests that we can find a completely different Dominant 7 chord in which the F is scale degree 3 and the B is scale degree (flat) 7.
Ignoring enharmonic spellings, that chord is C#7, a tritone away from our original G7 chord! Here’s a visual of the process:
Since the original Tritone is unchanged, we can just as easily progress from this new C#7 chord to G7’s preferred destination: a C Major Triad. Or we could follow the Circle of Fifths forward from C#7 and proceed to F#. The most astonishing part is that G7, as the mirror image of C#7, can do the same! This makes G7 and F# Major unlikely bedfellows, more so than any other of the new V7 resolutions we’ve just enumerated.
Substituting V7 for I#7, and vice versa, is called tritone substitution. Either chord may progress to its own tonic as well as the tonic preferred by the other, since they share a common Tritone.
Tritone substitution creates a particularly exciting and unexpected harmonic effect that is quite common in the initial cadences of barbershop up-tempo arrangements, not least because two voice parts can “post on” (sustain) the dissonant Tritone pitches while the other two voice parts shift to reveal the new chord. See if the effect sounds familiar:
Progressing to other seventh chords
Tritone substitution is a special benefit of barbershop’s tendency to resolve from one Dominant 7 chord directly to another. Above, we progressed from V7 to a series of new Major-chord destinations, but we can also decorate the destination chords with flat 7s of their own.
Persisting the tension
Tacking the 7th onto each of our non-standard V7 destinations somewhat diminishes the unique character that we described for each progression. The tension injected by the flat-7 tends to dominate in the following chord, putting every V7 → ?7 progression on seemingly equal footing. In some sense, the ear simply hears a pair of barbershop chords, more than it hears the unique character of the progression between them.
Stitching arbitrary Dominant 7 chords together can help arrangers persist the tension while adding harmonic variety or wiggling out of a tricky melodic spot. With a Tritone on every chord in an intentionally over-the-top and unpredictable cadence, for instance, the audience will be practically begging for a resolution into a Major Triad. When dialed to 11, this tension persistence might sound like this:
Paying attention to pivot notes
Tritone substitution is so effective partly because of the excitement that two voices can stay put while other voices move around them to fashion a new chord. It’s like doing a magic trick with one hand tied behind your back. In classical music theory, we might call this modulation around a pivot note.
We’ll talk about modulation more in the next section, but the key is that we can move more seamlessly between chords that share one or two pitches between them. For instance, the reason we characterized G7 → E Major as a “wily Monte dealer” earlier in this post, is that when we move from G7 → E7, both the B and the D can stay put, much to the delight of the cunning arranger. (The coy half-step ascent from G to G# only adds to the effect.)
The strong pitch overlap between G7 and E7 is partly why we don’t see many deceptive cadences in barbershop arranging. (A deceptive cadence is a progression from V7 → vi, the relative minor chord of the tonic, instead of to the I chord itself.) Instead, with just a flick of the wrist, we can transform G7 into E7, which includes a strong leading tone into A and, indeed, moves naturally along the Circle of Fifths to A. Here’s an example of G7 → A and G7 → E7 → A played back to back. Note that the E7 “pivot” chord guides the ear much more strongly into A minor:
Tonicization
We’ve now seen new options for harmonization based on resolving tension to different places, inverting tritones, and pivoting using shared notes between sequential chords. We have one more topic to cover before we wrap this segment. We discussed G7 → E7 → A minor as a more effective barbershop progression from V to vi than the traditional deceptive cadence. This is because of tonicization.
Definition
Tonicization is the casting of a pitch other than the tonic as a “temporary tonic” for a few measures. In the example above, we started in C Major, then we tonicized the A in the A Minor Triad by moving through A Minor’s own dominant chord, the E7. We call E7 a secondary dominant here, because it is a dominant chord of a tonic other than the tonic of the original key. In particular, the G# leading tone and the dissonant Tritone it forms with the D, convince the ear that A minor is the new home base.
Tonicization is so effective that the ear may have a hard time remembering the original tonic at all. And if we stay in the new key area for a while, we can use an even stronger label: modulation. Modulation is the long-lived recasting of a pitch other than the original tonic as a new tonic.
As distinct from barbershop’s “warp-speed” Circle of Fifths, which is just a string of secondary dominant chords flowing into each other, tonicization and modulation often land on a Major or Minor Triad to firmly plant the new key’s flag in the ground.
In practice
When arranging for barbershop, the song may call for us to linger in a certain chord area along our Circle of Fifths progression, or we may encounter melody notes that don’t fit into the current chord—or any other seventh-chord variant of the current chord.
Another tactic we can try is to tonicize the current chord, treating that chord as our new home base, and “borrow” chords from the key built on that tonic in order to appropriately harmonize everything locally. (Recall that the triad built on the tonic is able to progress to any other chord—the same rules apply here, we’ve just changed our tonic!)
Here’s a contrived passage to demonstrate, with most of the arranging already done. Broadly, we start in C, progress through A7 along the Circle of Fifths into a D minor triad—our first minor chord of this series—and then resolve through G7 back to C along the Circle of Fifths. The lack of a seventh chord on the downbeat in D minor is a good indication that we’re tonicizing it. But how to handle the errant C# in that D minor chord area?
None of D minor’s common seventh-chord variants include C# (the Major 7 chord doesn’t exist in the minor scale, because the 3rd is flatted). However, the Dominant 7 of D minor, A7, does include C#! We can use A7 here and notate it according to its function as the dominant of D minor: V7/ii (“five-seven of two”):
It may seem like we’re moving backward along the Circle of Fifths from D to A7 to harmonize that one pitch. But in fact, we’re simply borrowing the V7 chord from the key of D minor—perfectly permissible to the ear given that the initial A7 so wonderfully tonicized the D-natural in the first place.
Reflection
We began this journey with a simple selection of Dominant 7 chords abiding by the Circle of Fifths. Now, we’ve uncovered a treasure trove of chord progressions that seemingly permit every motion under the sun. Here’s a quick summary of the V7 Resolutions alone:
This chart suggests that we can literally resolve the tension in a V7 chord into any of the 12 available keys. How does this help us, the ambitious budding arranger, know which chords to use when?
The answer is that the Circle of Fifths should always serve as our base, and the other V7 resolutions should serve as our spice. An unexpected progression can zap the palate with piquant finesse if peppered into a creative spot, but too many surprises will cause the flavor to lose its luster—if not confuse the senses entirely. In short, these new choices are best for (1) getting out of a harmonic pinch, and (2) enriching an arrangement with variety.
We have nearly all the tools we need to start arranging our own gold medalist barbershop charts. We’ve yet to discuss embellishments, but that is a topic we can discuss on the job. The meatiest question still at hand is actually, “How on earth do we use Diminished 7 and Half-Diminished 7 chords properly?” We’ve touched on the very basics of them, but these are some of the most impact chords we can have in our arsenal, so it’s worth understanding them fully. Onward.
Next: Part 6: Wrangling the Diminished Duo
Full guide: Barbershop Arranging: A Modern Guide
