Thursday, December 1, 2016

Octaves Above Milstein's Prokofiev is...Sort of the Same Prokofiev

It is not too far-fetched, or at least not unprecedented, to identify an even division of time too slow to be heard as a pitch with a label that customarily is assigned to a pitch. For example, the sound waves emanating from a black hole in the Perseus Cluster have been identified as a B flat, although they are too low to be heard: indeed, the crests of the waves are millions of years apart. But to label this frequency with a pitch is simple enough. Multiplying or dividing a frequency by 2n moves it up or down, respectively, by n octaves. This transfer by one or more octaves both preserves its letter name and potentially puts it within the range of human hearing where we typically categorize frequencies with letters. For example, 440 Hz is an A, and so is 880 Hz, 1760 Hz, 220 Hz, 110 Hz, and the rate at which the moon goes around the earth (the sidereal month of 27.321661 days). Well, actually the sidereal month is a rather high A (30 octaves lower than ~459 Hz); in fact, it is closer to the black hole's B flat (of which one is ~466 Hz).

With this in mind, consider the opening of Prokofiev's Second Violin Concerto in G minor, which was premiered in Madrid on this day 81 years ago. It begins with a G, B-flat, D, E-flat, C sharp, and another D played by the soloist, and then this rising motive repeats in its entirety. The frequency at which the rising motive appears can also be labeled as a pitch. Prokofiev indicated a tempo of quarter = 108, which makes the motive's frequency a slightly low F sharp. While some commercially recorded performers roughly take that tempo, many others tend to go slower: around an F or even around an E for the rising motive. But Nathan Milstein, in a live recording from 51 years ago, not only plays it faster than what Prokofiev requests (and with relatively little rubato), but also plays the rising motive "at a G," several octaves below the open-string G he plays to begin the concerto, a G that matches the opening tonal center of the concerto.

Prokofiev follows this rising motive and its repetition with a descending motive (D-C-Bb) and its embellished repetitions that extend the motive lower and longer by one suffixed note with each repetition. However, thanks to durational reductions of interior notes, each descending motive still takes up the same amount of time; therefore, the frequency of the descending motive can still be labeled by a single pitch letter. Milstein's tempo for this portion puts the descending motive's frequency at around a B. Although the descending motives neither contain a B nor are in B, the immediately following orchestral statement of the ascending and descending motives is transposed to start on, and position the tonal center on, B.

The movie below demonstrates these pitch-tempo relationships.


Thanks to Debbie Rifkin for encouraging me to think about this concerto.

Friday, November 4, 2016

Some Unused Counterpoint in Brahms's First Symphony

Brahms's First Symphony in C Minor premiered 140 years ago today. Its first movement finds ingenious ways to combine its motives and themes together in counterpoint. (Julian Horton's video for the Society for Music Analysis provides an insightful introduction to these motives, themes, and combinations.)

In the exposition, Brahms shows how an inverted form of the main theme meshes well with the closing theme. In the instance below, the inverted main theme is in the bass, while the closing theme is in the treble. Eight measures later, he swaps their registral positions.




In the development, Brahms shows how the closing theme can be well combined with itself in canon at the octave a half-measure later. In the instance below, the dux (leading voice) is in the treble, while the comes (the imitating voice) is in the bass. Eight measures later, he swaps their registral positions.



What Brahms never does in the symphony is combine these two instances of two-part counterpoint into an instance of three-part counterpoint, which works quite well in forming seven complete triads while maintaining independence among all three voices. One possible version, transposed to the key of the symphony, is below.

Tuesday, October 11, 2016

Carter Burwell's Musical Accuracy in The Chamber

Perhaps the most appreciated part of The Chamber, a film adaptation of the John Grisham novel by the same name that was widely released in theaters exactly twenty years ago today, was the musical score by Carter Burwell. One of the parts of Burwell's score that I especially appreciate is the music that accompanies the end of an impassioned closing argument (around 1:09:00) that young lawyer Adam Hall (Chris O'Donnell) is making in court on behalf of his client and grandfather Sam Cayhall (Gene Hackman), who is scheduled to be executed for a racially motivated murder.

The musical content is quite straightforward: it is in E-flat major, the harmonies alternate back and forth between an E-flat major triad and a G-minor triad, the melody rises do-re-mi three times, and the texture thickens and dynamics rise gradually over the course of the cue. The tonal-harmonic aspects involve what I have called a "loss gesture" and have written about here and here and demonstrated here.

But that's not what I especially appreciate. The "loss gesture" works well when a listener well perceives the transition from one triad to another. The soundtrack is dominated by Chris O'Donnell's dialogue. What I admire is how Burwell's harmonic changes find holes in the dialogue. He finds not only big holes in between sentences, of course, but also two smaller holes within sentences: the 0.8-second hole between "It's a tragedy that" and "has destroyed three lives already," and the even smaller 0.4-second hole between "He was" and "raised by his family and this state to become the man that he became."

Below is a transcription of the music and the dialogue that notates time exactly proportional to space. (Sts. = strings, Brs. = brass, +W.W. = woodwinds are added.) The holes are indicated with enclosures whose color matches the description above.


Sunday, September 4, 2016

Folding Phish's Tweezer

At Dick’s Sporting Goods Park in Commerce City, CO, the rock group Phish is playing their last show of their 2016 summer tour as I post this. As phish.net says, "If there is a single Phish song that can be said to evolve with and exemplify Phish’s sound and artistry over the decades, it’s 'Tweezer.'" Below is a simplification of the famous opening lick, in "Tweezer Reprise"'s key of D. Here is a recording.

I've spent some time on this blog analogizing pitch and time. Here's one way that they are related:

The gamut of pitch register lays out linearly, from low to high, but it also circles back on itself via the concept of the octave: "do-re-mi-fa-so-la-ti...do." Even though the second "do" is higher than the first, we still call them both "do." In fact, of all of these notes within the octave, this "do" is special: it is the tonic, the note toward which all of the others are oriented.

The expanse of chronological time lays out linearly, from earlier to later, but it also circles back on itself via the concept of the measure: "1-2-3-4...1." Even though the second "1" is later than the first, we still call them both "1." In fact, of all of these beats within the measure, this "1" is special: it is the downbeat, the beat toward which all of the others are oriented.

Now these five notes from "Tweezer"' have a rare property, and they have this property not only because of how far apart they are from one another in pitch and in time, but also because of what the tonic and the downbeat are.

This video describes this property.


This was the "one from rock music" I was referring to a year ago here. The first four notes of Gershwin's "I Got Rhythm" have the same property, but I hope I explained it better this time around. I can think of another song released in 2015 with a similar lick and the same tonal and metric orientation.

Sunday, August 14, 2016

In Die Walküre, Space Becomes Time

Wagner's complete tetralogy Der Ring des Nibelungen was first presented 140 years ago yesterday. The one part of this music that has probably embedded itself into Western cultural consciousness the most is the beginning of the third act of the second opera Die Walküre, the so-called "Ride of the Valkyries." The image below provides a notation of the first presentation of the melody. While the severe distortion of the notation makes it harder to read, it makes the distance that a measure of time and a semitone of pitch takes up on the image more equal to one another. All of the melody's local maxima (B3-D4-F4#-A4-C#5) divide this 14-semitone span into a 3+4+3+4 organization. The dominant-(5)-to-tonic(1) moments of the melody divide this 14-measure span into a 3+4+3+4 organization.


P.S. My post title cheekily refers to the fact that, in Wagner's last opera Parsifal, Gurnemanz tells Parsifal that that in this realm time becomes space ("Zum Raum wird hier die Zeit").

Sunday, July 31, 2016

Film Music Style as Guide for Late Beethoven

There is something entertaining, if not a little anachronistically naughty, about hearing a kind of more recent music in the music of someone like Beethoven (like hearing this in Beethoven's 7th symphony, or hearing this in Beethoven's 8th piano sonata). But here's an instance where it can be quite helpful. (There's a relevant cognition experiment of mine here that I invite you to try, but, if you decide to take part, do so before reading on.)

A year ago on this blog, I shared this trend about recent popular film music: "When two major triads whose roots are four semitones apart are adjacent, the triad with the root four semitones above is significantly more likely to be the tonal superior." This happens particularly when the two chords have been isolated from other tonal obligations and, without such obligations to gain tonal meaning, instead look toward one another.

In measure 13 of the first movement of Beethoven's op. 109 piano sonata, the notes of a D-sharp-major triad fill up most of the register of the piano and our attention with its sonorous and solid proportions, blocking from view much of what had occurred before. Then its firm surface suddenly shimmers and transforms into a B-major triad. To some film-music ears, this is a departure from stability and security: since B is four semitones lower than D-sharp, B is demoted in this two-character drama within a drama. I indicate this visually with a red arrow that fades into purple.
In sonata form -- a drama which this drama is within -- the recapitulation is both a return to and a reworking of the material from the exposition. In the first movement of Beethoven's op. 109, measure 62 in the recapitulation corresponds to measure 13 in the exposition. This time, it is a C-major triad that floods our senses much the same way that the D-sharp-minor triad did before. But its corresponding transformation is to an E-major triad, whose root is four semitones higher. The same harmonic conversion is now a homecoming, which I show with an arrow that changes from purple to red.
To be sure, this harmonic scheme is rather standard: the sonata is in E, and B is accustomed to its subservient role when E is the tonal sovereign. But local harmonies, together with a future music's chromatic tendencies, enrich this relationship and even offer a guide, however anachronistic, to the work's overall tonal plot.

Monday, June 27, 2016

Muse's Voice Leading at the Olympics

The 2016 Olympics are around the corner. The official song of the 2012 Olympics— “Survival,” by the British alternative rock band Muse—premiered on the radio on this day four years ago.

The lyrics of the opening are “Race, life’s a – race, That I’m gonna – win, yes I’m gonna – win, And I’ll light the – fuse, and I’ll never – lose…” The music accompanying these lyrics uses the triadic progression of BbM – Bb+ – Ebm – CbM – GbM, where M is major, m is minor, and + is augmented. The progression can also be considered in terms of smooth voice leading. First, one by one, each of the three voices in the BbM triad—on Bb, D, or F—moves up by a semitone, achieving the CbM triad. After this, two of the three voices in the CbM triad slip back down to make the GbM triad. Only the voice that started on the F and moved up to Gb never retreats, at least not until the progression starts over. Therefore, one can say that only this voice “wins,” as animated below, with the gold-colored figure as the winning voice.



What makes this more fitting is that, at least at the beginning of the song, Muse’s lead singer, Matt Bellamy, is intoning his first-person account of victory using precisely the notes of the “winning” voice. Now this, literally, is…VOICE…LEADING.