The repeating bass line when Angelica Schuyler identifies with Hamilton in “Satisfied” (you can hear these notes in the opening of the track, but it’s easier to hear them as a bass line around 1:07): The chord progression/bass line in the track when we meet Burr, “Aaron Burr, Sir”: ![]() Someone should probably write a dissertation on this, but for now here are some brief snapshots. Hamilton’s bass line from “My Shot” (Do Me Fa Le Ti) and Burr’s chord progression from “Wait For It” (I vi iii) are everywhere in the musical. But if you take a look at a set of reasonably-accurate chord symbols, you’ll notice that almost every “Ab” has a “ sus” after it, meaning that they leave out the leading tone–the defining note of this chord that gives it its sense of striving! There’s certainly tension in the song, but it’s a simmering tension, hidden underneath this seemingly placid surface–at least until Burr finally lets it out at 1:31. Technically, it does have V chords, rooted on A-flat. (Music theory tidbit: of all the chords in a major key, the iii and vi chords are the only two with “minimal voice leading” from the I, each differing from it by only a single note.)Įven when “Wait For It” deviates from this I-vi-iii chord progression, it never gives us the goal-direction associated with Hamilton. This repeats over and over, each voice moving as little as possible–never going anywhere, unwilling to take a risk. Each line moves as little as possible: the low notes simply go Do, Do, Ti the top notes go Sol, La, Sol, and the middle notes are stuck on Mi the whole time. Imagine connecting all the high notes (designated with squares) as a line of music, all the middle notes (triangles) as another, and all the low notes (normal noteheads) as a third. Here’s the repeating riff underneath Burr’s big solo, “Wait For It.” There are three notes in each measure: one low, one high, and then one in the middle. I won’t get too much into why these chords are more static and ambiguous, but the way they generate this effect in Hamilton is at least in part through “voice leading,” how individual notes in each chord relate to individual notes in the surrounding chords. If the dominant chord and the leading tone have well-defined goals and a strong sense of striving, then on the other end of the spectrum are the iii and vi chords. The line basically goes Do, Me, Fa, Le, Ti, with a few short striving notes in between. Like the previous one, it ends with an augmented interval reaching up for the leading tone (Le to Ti is an augmented second). This one’s also in minor, but strives upward the whole time. Of course, Hamilton’s first chance to shine is in his big song, “My Shot,” which also has a repeating bass line, and this is the one that Miranda most strongly associates with Hamilton throughout the musical. (The interval from Me up to Ti is an augmented fifth–an unusual interval in music, and one that I hear as effortful.) The first four notes of the bass line are pulled inexorably down, until that last note forcefully reaches back up to the leading tone to pull us into a repeat. That reaching is also clear in the repeating bass line that follows (which I’ve notated twice as fast, just to avoid a bunch of ties). Hamilton never quite reaches the goal he’s striving for–he just keeps reaching throughout the musical. The high A# is left hanging way up high as our resolution comes several octaves down. But while it achieves its goal–that last note is indeed “do”–it’s not the right one. This A# is scale degree 7, the “leading tone,” “ti,” a drink with jam and bread and the note that will “bring us back to do, do, do, do.” If V is the tensest chord in the classical tradition, the leading tone is the tensest note in the scale. In a way, it’s the satisfying “resolution” of the really high A# right before. ![]() ![]() Look at that last note, the really low B in the third measure (I promise it’s a B, no need to count ledger lines). ![]() Certain chords in the classical tradition are strongly expected to progress to certain other chords, giving them a sense of tension until they “resolve.” The quintessential example is the dominant or “V,” the chord we get right at the beginning of the musical. Composer Lin-Manuel Miranda uses music to portray these characters right from the beginning.
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