What If...A Single Note Were Different? One Change Could Destroy the Entire Tonality

Marvel's "What If...Doctor Strange Lost His Heart Instead of His Hands?" was released on Disney+ eighteen days ago. (Warning: spoilers soon ahead.) Laura Karpman composes the music for the series. In scoring this episode, Karpman explains that she "started with these four really soft piano chords." This four-chord progression can first be heard at 7:22, during a montage in which Strange tries over and over again to stop Christine from dying. It is also heard at the end of the episode, when Strange's desperation leads to the end of his world, and the Watcher's voice-over concludes: "One life, one choice, one moment, can destroy the entire universe." The progression is shown on the first staff below; it is juxtaposed against one transposition of what Mark Richards calls the Axis-a progression, which I have shown to be an important signifier of the heroic and epic in scoring for recent film, film trailers, and television. 

These progressions differ by only a single note in a single chord: the F sharp in the last chord of the one-sharp version of Axis-a is an F natural in the last chord of Karpman's four. Not even the root changes: the D-major chord becomes a D-minor chord. And yet this smallest of changes transforms the music into something very different, like a negative image of Axis-a. 

Within a seven-note diatonic scale, there is a single tritone. For example, among the seven pitches of the one-sharp collection—like a G-major scale—the tritone is between F# and C. There are six consonant triads in any diatonic collection, but only two of them—one major, one minor—are "tritone-free," that is, they do not overlap with the tritone at all. For example, in the one-sharp collection, those two triads are G major and E minor. Diatonic and "classically" tonal music tends to favor these triads, using them more often than other triads, putting them at beginnings and endings of phrases, and placing them in more prominent metric locations.

The Axis-a progression, which presents all seven pitches of a diatonic scale, puts these two privileged triads in the first and third positions, which are the most metrically weighted in the four-chord loop. But Karpman's seemingly minute alteration shifts the diatonic scale, which then passes the twin mantles of "Privileged Chord" to two other triads. The second chord in Karpman's four-chord loop is one of these triads, which is arguably in the weakest metric position of the four, and the other triad is not in this progression at all. To attempt to hear the second chord as a privileged chord feels contrived, forced, even useless, like Strange's attempts to cheat death.

Musicellanea Sails Away

This will be my 88th and final musicellanea post. The total of 88 total posts matches the total of 88 keys of a standard modern piano keyboard. Furthermore, of the 12 equal-tempered pitches within an octave, C is understood as the (mostly arbitrary) starting point. Analogously, of the 12 months in the modern Western calendar, January is understood as the (mostly arbitrary) starting point. This blog's monthly posting schedule matches this mapping from C to January, since I began on October 2013 (analogous to A0, the lowest note on the modern piano) and ended on January 2021 seven years and three months later (analogous to C8, seven octaves and three half steps higher, the highest note on the modern piano).

I will conclude this blog with a lightning round of three unrelated miscellaneous musical observations.

1. The syntonic comma is the difference between four pure 3/2 perfect fifths -- like C4 up to E6, via G4, D5, and A5 -- and two pure 2/1 octaves plus a pure 5/4 major third -- like C4 up to E6, via C5 and C6. As a fraction, and as an ascending interval, the syntonic comma is 81/80, which is (3/2)^4 / ( (2/1)^2*(5/4) ). As a decimal, this is the rather humdrum 1.0125. As a fraction, and as a descending interval, the syntonic comma is 80/81. As a decimal, this is 0.987654320 repeating, but can be rounded to 0.987654321. How fun that humans have n digits, and one of the most significant musical commas is (n-1)^2-1 / (n-1)^2.

2. In Wagner's Tannhäuser, the title character sings his "Hymn to Venus" three times in Act 1. The first time, the music is in D-flat major with a tempo indication of half note = 69. The second time, the music is in D major with a tempo indication of half note = 72. The third time, the music is in E-flat major with a tempo indication of half note = 76. Not only is this music increasing in intensity by getting slightly higher and faster with each iteration, but the ratios by which each are increasing are rather close to one another: the pitch is increasing at a ratio of around 1.059 (the equal tempered half step), and the tempo is increasing first at a ratio of 1.043 (72/69) and then around 1.056 (76/72).

3. In the one-measure piano introduction to Ives's song "Tom Sails Away," my favorite moment is near the end of the measure, the moment occupied by the sole F, encircled in the music below. If I were playing this music, I would aim to use a slight change of dynamics and/or microtiming to give this seemingly uninteresting F some special treatment.

One the one hand, this F breaks a pattern. The image below teases out some three-note motives with a melodic major third (shown with a yellow arrow) in some direction overlapping with a melodic tritone (shown with a purple arrow) -- either before or after -- in the same direction. Two of these motives occur in the first half of the measure in immediate succession, the second a major seventh lower than the first. Had the F4 of my favorite moment been an F#4, then two versions of this same motive -- one retrograded, the other inverted -- would have occurred in the second half of the measure in immediate succession.

Furthermore, by using F natural instead of F# at this moment, the first measure contains all 12 pitch classes (the 12 pitches in the equal-tempered chromatic scale without attention to register) besides F#, as shown in the graphic below. (One octave of keyboard with the standard white-black key coloration is shown on the left. The image below also replaces the major-third yellow arrow with a minor-third green arrow.) The second measure completes the set of 12 pitch classes, with F#s prominently placed as the lowest note and the first note of the treble melody. Therefore, by breaking from a pattern, attention is drawn toward something that is incomplete that later music makes complete.

On the other hand, the F continues a pattern. The top voice in the first measure plays a mi-re-do dotted-rhythm motive that overlaps with its transposition down a major third -- again, this interval is shown with a yellow arrow -- producing five of the six notes of a whole-tone scale. As shown below, the F at my favorite moment completes this whole-tone scale, albeit down the octave. A continuation of this sequential pattern would transpose the motive down another major third to G to F to E flat. The vocalist enters with something very close to this -- G# to F# to E -- which is down a minor third (plus an octave) instead of a major third. Once again, the green arrow replaces the yellow arrow.

However, G to F to E flat does occur later, to begin the last vocal line, which occurs at the end of the song, as shown below. When the first vocal entry in the second measure breaks from a pattern, once again attention is drawn toward something that is incomplete that later music makes complete.

OK, that's it for this blog. I hope that you got something out of it. Thanks to Stephen Soderberg for suggesting this idea to me in the first place.

I have one last thing to share: hidden among some of the post titles of this blog is a message.