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[July 18, 2016 12:36 pm] « » [music21]
Despite the author name, this is a guest post from Christopher Witulski; he can be reached at  chris.witulski at gmail.com.  We thank him for sharing this exciting pre-publication work. -- MSC

Last year I learned about music21 and ever since I have been wondering how I can use it to learn more about the Moroccan musical repertoires that I study. Long story short, I ended up building a tool for creating interactive web-based contour visualizations from the command line and I'd like to share it here.

Climbing out of a rabbit hole

I was working through a project and struggling to keep track of things. The paper was an analysis of a genre of Moroccan sung poetry called malhun for the 2016 Analytical Approaches to World Music conference. The performance of each poem can last twenty-ish minutes and contains a number of repetitions of the refrain text. These refrains are short (roughly eight 2/4 measures long) and modulate through repetitive--but different--melodies. I had transcribed over sixty of them in an attempt to understand how they worked, how they changed, and how they were related to each other.

Musicians on stage, with a solo singer in front and the author among five violinists holding his in Western style
Malhun Performance in Fez, Morocco

Having performed this music in Morocco (I'm the lone violinist in the photo who can't quite figure out how to play while holding the instrument upright on my knee), I was constantly struck with this feeling of déjà vu. New melodies felt so similar to old ones, but I could not put my finger on how or why. The problem was simple: I could not keep sixty or seventy different transcriptions in my head at once. Comparing them was getting tricky. I wanted a way to stack them on top of each other, almost as if I could print the transcriptions on a transparency and show them all at once on an overhead projector.

Over the previous months, I had been teaching myself Python in an effort to learn more about music21 and what it could do. It was time to try and build the tool that I needed instead of wishing I could find it.

Visualizing contours

For the presentation, I put together a small library that carried out two main tasks. First, it used music21 to parse my transcriptions, normalize the length of each melody, and build a dataset. Using offsets, frequencies, and distances from the final note of each melody, it turned note objects into a JSON of coordinates. At 1,000 different y values (each corresponding with 1/1,000th of the length of the total melody), it measured an x value for the frequency and one for the "distance from the root," the distance in steps above or below the melody's final pitch.

Visualization of 68 Melodic Contours from Malhun overlaid with one labeled in bold red
Malhun Contour Example

The JSON was passed to another library that I had been recently learning and working with called D3.js. It is written in JavaScript and designed for creating powerful interactive data visualizations. I supplemented my presentation with an online chart of each of my malhun transcriptions: by grouping contour lines within each poem, I was able to easily see the source of my déjà vu. Despite changes in pitch content, range, root motion, and a host of other things, the contours themselves often stayed strikingly consistent throughout the long performances. You can see the visualization and click through the different poems online, though be aware that some parts (like the "Next" button) are artifacts of the paper presentation.

Building a tool

Maybe two weeks ago I decided to try my hand at creating a Python library of my own. I simplified the chart, creating a sort of template, remove the stepwise element of the visualization, and fought my way through learning to upload a project to PyPI. The result is ContourViz... I didn't give much thought to the name, my apologies.

"Three Melodic Contours" -- one is shown in blue.
ContourViz, simple example

The tool takes, as an argument, either a music notation file or a directory with many of them. It parses these files and creates a JSON structure of 1,000 coordinates for D3.js to work with. It then copies a folder called results that includes an index.html file and a folder of JavaScript and CSS files that the generated web page will use into the current directory. Finally, it runs the Python SimpleHTTPServer and opens the new page, parsing the JSON to create the visualization.

You can install ContourViz using the following in your terminal:

pip install contourviz

It runs from the command line, so creating a visualization of multiple melodies, like the one above, is as easy as:

chart-single-contour '/path/to/file.xml'

Working with a directory is similar:

chart-contours '/path/to/directory/full/of/xml/or/mxl/files'

6 Melodic Contours -- more complex chart showing 2 x three overlapping contours from Damlij-Bouzouba
ContourViz, more complex example
I'm still toying with the system and it has a number of issues. For example, I would love for it to parse voices as individual melodies if they are present. Instead, it only works with monophonic lines, meaning that each voice has to be in an individual file if you wanted to visualize voice leaning or other contrapuntal patterns. There are smaller issues: I still need to set up the Y axis to render note names properly.

Please feel free to check out the GitHub repo and suggest any other changes or ways in which it could be more helpful. This is my first go around at building a tool of this sort, so I am eager to hear if it is helpful and how it could be improved. And thank you for allowing me to join the community.



[July 12, 2016 18:08 pm] « » [music21]
The following is a guest post from Daniel McGillicuddy, alias Basso Ridiculoso.  He can be reached at daniel.mcg [at] gmail.com.   -- MSC

Hello all!

I am a gigging musician and bass player who has discovered music21, but, alas, I am certainly not a musicologist or academic.

I have seen many of the amazing examples that showcase music21’s capabilities with classical and twentieth-century music, and wanted to show how I use music21. Hopefully these examples show that music21 can also be used to explore jazz and popular music, either via analysis for educational purposes or for developing improvisational ideas.

Jazz Standard Voice Leading Lines

Music21 has an amazing corpus of public domain classical music, but most jazz standards are not available for inclusion. But, since music21 has an understanding of seventh chords and reads MusicXML, a virtual corpus of jazz standards is available for analysis and exploration via another application called IRealPro. IRealPro is a virtual accompanist software program that has chord charts for over 3000 jazz standards, and which can export the chord progressions in MusicXML, a format that will allow music21 to understand the harmony. Once we have that outline of a jazz standard's harmonic structure, music21 can be turned loose.

For this example, lets export the chord chart to the standard “Alone Together” and generate a 3rd to 7th voice-leading line through the entire tune, based on this concept by Burt Ligon, as described here.

(links: Alone Together.XML and Guide Tone Lines with Music21.py)

Since music21 understands harmony, any kind of voice leading line is possible, for instance the 5th resolving to the 9th. Now these voice leading lines can be generated for any jazz standard (or for any chord progression) that can be exported as MusicXML format and these lines can be used as jumping off points for making solos or studying voice leading.

Jazz Solo Analysis 

Analyzing jazz solos from the masters is another way to get improvisational material, but it is better known as stealing someones licks! Since music21 can understand the relationship of any note to any chord, it can be used to analyze the functional relationship of the notes in a solo.

Here is an example of Miles Davis’s solo on “Freddie Freeloader” with the notes being labeled so they represent their function against the chord being played, for example, an F note on a Bb7 chord being the fifth.

(links: Miles Solo XML  and Melodic Labeler.py)

This same Music21 code was used to analyze Charlie Parker's solo on Bloomdido, and a walking bass line over F blues by Ron Carter.

Now any solo line that can be exported as MusicXML can be analyzed by music21 and then explored even further. What notes are favored? What beats of the bar do certain notes get played on? How many times do certain notes get played? Are there repeating phrases that a certain player uses over and over? All of this can be cataloged or graphed once it has been brought into the music21 world. The included code needs a chord symbol over every measure.

Hopefully these examples show that music21 is not only for musicologists exploring the pitch class space of Bartok's string quartets or for twelve-tone row composers! Students and musicians can use it for very useful and practical purposes as well. Many thanks to Michael for allowing this guest posting from big music21 fan!

(Ed: Thanks Dan! The examples included here are copyrighted by their respective composers and publishers. We believe their inclusion here for educational and instructional purposes are supported by all four factors of the Fair Use test).
[June 26, 2016 16:18 pm] « » [prolatio]
For the past few years, I've been trying to use the Getting Things Done philosophy with Cultured Code's application Things to manage my tasks and todos.

My two biggest problems preventing success have been (1) Maintaining an Inbox Zero philosophy, where at least daily, I get my Inbox to zero, by deleting messages, doing a very quick reply, or immediately creating a task for a message that requires more than 2–5 minutes to take care of, and (2) being realistic about the number of tasks that I can possibly say yes to and have the time to actually do.

Sometimes, I can maintain Inbox Zero for six or eight months.  Other times, I get way behind on Inbox Zero and need to resort to an Inbox DMZ to reset the obligations that I have. Usually the thrill of an empty inbox at that point will let me get out of DMZ in a few weeks.  Maybe someday I'll write about how this happens to me and how I break the cycle (at least so I can read this post again later), but at this moment, I'm almost out of Inbox/Email Hell.  So my big problem lately is the second one.

When I was a graduate student, or just starting out as a professor, I was so thrilled that someone was asking little ol' me to be on a committee, help them with a problem in my field ("Can you transcribe this medieval song?"), or, big honor, fly out and give a talk at their school.  I am still honored to be asked, but fortunately or unfortunately, at this point in my career, I'm asked to do far too many things that I could possibly do.

One of the hardest parts about saying "no," is that I have always been far too much of an optimist about how long a particular task will take.  Sure, it'd just take twenty minutes to write that recommendation letter, IF I were in the right mental state, not distracted, had all my ducks in a row, etc.  Realistically, I've never gotten one done in under an hour, and three hours is more usual.  An article review? I need to learn that I write far too many notes to the author, duplicate too much of the research, order sources from ILL, etc., and so eight hours is a realistic timeline for me for a twenty-page review.

I've figured that I have about sixty hours of work in me per week (not just academic work but also counting certain stressful obligations, such as being a trustee, dealing with a plumber, etc. that I don't consider fun time). Of those sixty hours, I know that recurring obligations such as teaching and advising will take up about 30 hours a week most of the year.  This leaves about 30 hours per week (1500 hours per year) to do everything else I've either agreed to do, or need to do to continue to develop as a professor (researching and writing articles and books, developing music analysis software, etc.).  Twenty letters of recommendation and ten article reviews per year eats up 10% of that time.  Joining a board is probably 50 hours a year.  Etc. etc.  Adding it all up and it's easy to see why the years when I say "No" often, I can write, say, two chapters and three articles, and those that I don't, I'm lucky to get a single article out.

(And then there's the damage I do to others when I say "Yes, sure!" and then end up stretching or breaking deadlines or needing to cancel later; this is the worst of all possible options.)

I've been trying to find tools to help me manage this time better, but there's nothing I could find, so I finally took four of those 1500 hours and wrote a script to help me.  (Maybe I'll get half those hours back since I did learn a new skill of Javascript for Automation).  

Each day I try to create a realistic plan for the day during a morning review.  It always begins with Inbox zero as a task.  (Since 2012, I've tried to make every task begin with an action verb. "Inbox zero" has somehow remained as an exception, since I always know what to do about it).  Each task usually has two tags attached to it, a location tag ("@Any" is the most common.  "@Home", "@MIT" also appear), and a time tag ("5 min," "15 min", "1 hr", etc.).  When I've organized the ToDos in a good order for the day, and adjusted the times to what I think are realistic, I run the thingsToCal.scpt which puts all the todos on the calendar, making sure that they don't interfere with any events already in the calendar.   The results are below:



I can now see that, hmm... given that it's my turn to cook, I'm going to need to be willing to work until around 9:30 if I'm going to get all these things done; for a weekday, that's fine.  For Sunday night, I think I'd rather not.  Something (probably that "Get an Outline" for Tuesday's talk event) will need to go till to tomorrow.  (And that was before I added an hour-long "Blog about this system" todo).  After rearranging, etc., I rerun the script and the events for the day get removed and readded in the new order.

I'm hoping that this system works well.  If you are geeky and want to try it out, the code is at this link. It runs only with Things (if Time tags are set up properly) and OS X/macOS Calendar (with a calendar called Things) and you'll need to use it at your own risk (Sorry if something gets screwed up in your calendar), hence I'm not providing installation instructions beyond this link. But if I can get it to run faster (currently, figuring out my existing schedule on Calendar takes 20-30 seconds) and perhaps to work with next items beyond today (and maybe preserving non-working hours, etc.) then I'll make it a nicer script.

Wish me luck! Especially if you've been waiting on a reply or for me to do something for you.


[December 12, 2015 12:18 pm] « » [prolatio]

Note

Please see the Preface to this Series to understand the goals of putting up this unpublished work and the general apologies for not citing a more up-to-date bibliography.

This paper is a (mostly unedited) seminar paper presented to Reinhold Brinkmann's seminar on twentieth-century opera (Fall 1999). Thus no bibliography or citations post 1999 are included.  It was also written at a time when many musicologists could have not known the basics of Einstein; now this view seems a little obsolete. The only changes (beyond fixing of typos) in this version are the YouTube clips that have been added where easily found.

It Could Be Very Fresh: 

Structure, Repetition, and Reception in Einstein on the Beach (1999; part 2)

Glass's Analysis

Glass has chosen to base much of his analysis of the work on the harmonic features of the music.  The introduction of harmonic shifts within sections, begun with Music in Twelve Parts (1971-4) and continued in Another Look at Harmony (1975) which Einstein grew out of was for Glass a significant change in his musical style in the years preceding the opera.  It is understandable that since most common tools for analyzing Western music rely on harmonic structure he would employ these methods in looking at his own now harmonically shifting works.13  However, a look at Glass’s harmonic analysis of a single motive, five, reveals how little roman numeral analysis of his motivic idea tells us about the work.


13 Other conventional analytical tools would present other problems; Schenkerian and other voice-leading analysis techniques, even if they were available to a composer who received his musical training in the 1950s, can readily be seen to hold little promise for understanding this work.

If as Glass has said “process here is the subject rather than the source of the music” and “the noticing of process itself becomes exhilarating,”14 then an analysis which focuses on one iteration of a process is missing some of the most salient features of the piece.  Glass has pointed out that the motive, f-minor, D-major, A-major, B-dominant7, E-major can be heard as i-VI-IV♭ in f with IV♭ being heard as a pivot to IV-V-I in E.  He has further stated that since the motive ends a half-step below where it began it “provides the leading tone for the original i (f).  As it is a formula which invites repetition, it is particularly suited to my kind of musical thinking.”15

14 Robert Wilson and Philip Glass, Einstein on the Beach, edited by Vicky Alliata, (New York : EOS Enterprises, 1976(?)), [n.p., center of book]. The quotations sound more like Reich than what we are used to hearing from Glass in their emphasis on the perception of process.
15 Philip Glass, “Einstein on the Beach,” essay printed in liner notes to recordings of Einstein on the Beach and in Music by Philip Glass. Part 2, paragraph 6.

While he is correct in stating the five chords can be heard as a modulation from f minor to E major, it is certainly questionable whether any listener will hear it as such, or especially whether the twentieth repetition of the cell will produce such an effect on the listener.16  The ability to hear this passage tonally is particularly hampered by the voice-leading from the fifth chord to the first chord of the repetition.  While the other four transitions between chords followed traditional four-part voice-leading rules,17 the motion from E major to f minor contains three major “errors”: There are parallel octaves between the “alto” and “bass” voices, parallel fifths between the “tenor” and “bass”, and a doubled leading tone.  After hearing this non-common practice transition, it is unlikely that the listener will perceive further repetitions tonally; the use of IV♭ as a pivot chord was already a stretch to hear the first time.

16 The sections of five in “Train 1” have 39 repetitions each. “Knee 2” has 44 repetitions of five (22 + 22). The 158 repetitions in “Spaceship” dwarf any other section of five in the opera. I will be using the term “cell” to refer to a specific instance of a motive in which the motive may be rhythmically or melodically altered.
17 This statement notes but takes exception to the doubling of the bass a fifth higher which, everywhere except in the score, is heard as an acoustical effect of the electric organs and not an independent voice.

If we do not hear this progression as a tonal modulation (at least after the first presentation) it makes sense to ask whether Glass’s choice of chords has any bearing on our perception of the music.  I will argue that does using two alternative versions as counter-examples:

Purely tonal variation

Non-tonal variation


The version above is a strictly tonal version of five, grounded in E major.  The lower version is an atonal rendition of the theme, not cadencing in any key.  Both versions preserve the general bass contour of five, use triadic harmony, and retain three of the chords of five.18  Yet neither alternative is satisfying under repetition the way five can be heard to be.  In the tonal version the listener becomes frustrated because there is a strong unfulfilled expectation that the music will “go somewhere” harmonically yet there is a feeling of sameness because the music does not—it is simply E major followed by E major.  The atonal version distances the listener for the opposite reasons.  Without any cadential formula there is no harmonic expectation created and little (harmonic) reason to continue concentrating on the music.  It is the version in Einstein which balances these listening concerns.  The final three chords (IV-V7-I) form the most efficient establishment of tonal center possible while the augmented triad formed by the first three is an effective way of eliminating a possible key—the only triad not able to be constructed from diatonic scales.19  The listener tries to make tonal sense of the progression only to realize in the next repetition that this is futile.  Later, the strength of the IV-V7-I cadence invites him or her to try again, repeating the process many times throughout the piece.

18 With the hindsight of knowing his future output, one might wonder if the atonal version is actually a plausible alternative Glass could have written. It should be remembered, however, that in 1976 the last major work by Glass was Music in Twelve Parts which ended with a complete twelve-tone row in the bass.
19 Another piece from the 1970s which achieves its harmonic interest through a contrast between two contrasting harmonic areas within a repetition is Reich’s Four Organs (1970). An example of a piece which uses harmonic material related to the “atonal” theme is Louis Andriessen’s Hoketus (1977), sections A-D. As in the alternative Einstein version, the two and later four non-tonally directional chords of Hoketus cause the listener not to derive interest from the pitches played within a section. In Andriessen’s work this is intentional and a way of directing the listener toward the rhythmic and antiphonal features of the piece.

These harmonic aspects of the motive, while containing some interest in themselves, are subservient to the process of development the cell undertakes over time.  When presented as part of the train “still-lives” (Train 1, Night Train, the coda of Building, and Spaceship), each of the five chords has a different meter which changes throughout the section.20  This is the process of primary musical interest:



20 In the knee plays, five maintains a constant meter within a repetition but changes meter between repetitions. This process as carried out in “Knee 4” is examined below.

The numbers in the table represent the number of eighth notes in each cell.  A few characteristics of the rhythmic process are immediately apparent.  From section B to K, with the exception of the fourth chord of F all rhythmic processes are strictly prolonging.  Each repetition chord is as long or longer than the previous repetition of it.  Another property of the process is that each chord is held for either 3, 4, (3+3), or (4+3)♪ . ; that is to say, the chords with 6 or 7♪ introduce no new figurations not heard in the 3 or 4♪ sections.21

21 Later presentations of five will be have lengths of 5 and 8 (Knee 3) and will have 6 figures which are not literal repetitions of 3 (see "Knee 4," second cell, below).

The lengthening of chords (and thus cells) follows two distinct processes and thus divide the section.  The first cell, A (repeated three times) acts as an introduction and a presentation of what becomes the standard form of the motive—when five is heard at the end of “Building,” A is the only form presented.  The next five cells, B-F, present the process of lengthening the motive from 3 to 4♪ beginning with the fifth chord and progressing toward the first.  Cell F alters the process slightly by reducing the fourth chord to 3 while augmenting the first to 4.  Avoidance of the projection of regular meter within a cell seems to be the overriding reason for this decision.

The next five cells, G-K, present a similar process, lengthening from 4 (or 3) eighth notes (via 6 ) to 7♪ beginning with the first chord and moving roughly from front to back: 1, 2, 4, 3, 5.  The cell which at B lasted 16 is expanded by K to 33.  The shift back to the quick transitions between chords of L feels like a tightly stretched rubber band being suddenly released.  Without a change of tempo, the speed of the cell has been dramatically increased and, with the return of the rhythmic profile of the introduction, the process feels complete.  By repeating L six times rather than three Glass makes the coda more satisfying to the listener: while each chord is much faster (3 or 4 rather than 6 or 7), by the fourth repeat (which does not exist in any other cell) we are able to hear the cell not as a five-chord motive but as two five-chord motives, a total of 36.  Thus rather than lessening the tension of increased cell length (B-K), L acts as a culmination of this process.  By focusing our aural “gaze” on two different levels of activity, the pattern can be heard as both accelerating and broadening simultaneously and without contradiction.

(The analysis of Einstein will continue in the next blog post)

[November 21, 2015 16:38 pm] « » [prolatio]

Note

Please see the Preface to this Series to understand the goals of putting up this unpublished work and the general apologies for not citing a more up-to-date bibliography.

This paper is a (mostly unedited) seminar paper presented to Reinhold Brinkmann's seminar on twentieth-century opera (Fall 1999). Thus no bibliography or citations post 1999 are included.  It was also written at a time when many musicologists could have not known the basics of Einstein; now this view seems a little obsolete. The only changes (beyond fixing of typos) in this version are the YouTube clips that have been added where easily found.

It Could Be Very Fresh: 

Structure, Repetition, and Reception in Einstein on the Beach (1999; part 1)


December 1976 witnessed the dropping of a new work, startlingly unusual in many ways, on a mostly unsuspecting Metropolitan Opera public.  Einstein on the Beach, a collaborative opera by artist/director Robert Wilson and composer Philip Glass brought the worlds of extreme avant-garde theater and repetitive minimalist music to the conservative opera hall for the first time.  Five hours without intermissions, omitting identifiable characters or narrative structures, and based on a tiny melodic and harmonic vocabulary, Einstein’s fundamental elements had all been developed in experimental theatre and music during the previous decade, but their union in Glass and Wilson’s opera resulted in a work whose impact has changed new music and especially new opera for the last quarter-century.

This paper asks what this impact has been and why this work has come to have such an influence.  It is an attempt to explain some of how Einstein works and how the piece came to exist at this point in Glass and Wilson’s creative output.  To present this study, some new and slightly unusual analytical tools are employed which rest on my ideas about how we listen to and perceive minimalist music.  While there is certainly not space to even attempt at a complete analysis of the work, it is my goal to use examination of a few representative sections to get at some of the underlying structures of Einstein, an opera I see as, if not flawless or totally without precedent, nonetheless remarkable and original in its musical and theatrical conception.

Structure of the Opera

Any analysis of the musical structure of Einstein must begin with Glass’s own comments on the subject given in the essay “Einstein on the Beach”, included in both recordings of the work.  In his essay, Glass describes the opera as being divided into sections defined by the number of distinct chords in them.  The opening “Knee 1” is obviously a three-chord section, A minor, G major,1 C major.  Glass asserts that sections from one chord (Trial 1) to five chords (Spaceship and similar sections) are present in the opera.2  While an examination of the score according to tonal conceptions supports his arguments, whether the listener actually perceives changes in the pitch content of chords as the primary organizing feature of the music will be examined and challenged below.

1 We do not know for certain that this chord is major until it appears in altered form in Knee 3 and 4 and in the recap in Knee 5. The dominant-tonic motion suggested by G-C allows us to hear G-major in the absence of evidence to the contrary.


2 Throughout this paper, small caps will be used to denote motives in the opera. These motives can be found in charts in the appendix.



Addition of Wilson's Comment


Wilson has stated that his musical theater has its roots in the visual arts—especially painting and drawing.  As such, he has organized his use of theatrical space according to the way space is used in three different styles of painting: portrait, still-life, and landscape.  In a portrait, the focus of the observer is nearly completely taken in by the subject.  A still-life, while still having a main subject, derives much of its visual force through the relationship between that subject and the sounding context.  A landscape takes this sounding region and makes it the subject; while there may be different levels of foreground and background within a landscape, there is not a sharp distinction between subject and context as there is in the other two forms.

Wilson applied these concepts to Einstein by distinguishing three different uses of the stage.  He treated the knee plays as portraits: the action is limited to a small part of the stage, the actors are the focus of the scene, and what little “scenery” there is consists of chairs, slabs of glass, etc. at the same spatial distance as the actors.  The train and trial scenes (including “Building” and “Spaceship”) form the second of Wilson’s three divisions of theatrical space.  Actors are seen in relation to larger backdrops at the back of the stage and smaller props are placed throughout the stage.  The longer title of the two dance scenes, “field with spaceship” confirms their place as the two landscape sections of the opera.3  The entire field of the stage is used as the dancers move about causing the viewer’s eyes to continually shift from one actor to another.

3 There would be some question whether the spaceship scene in Act IV is also a landscape had Wilson not stated (in Einstein on the Beach, the Changing Image of Opera, 1986) that there were only two landscape scenes in the opera. Although the entire stage is used in “Spaceship” and the back of the stage, rather than being a backdrop, forms an integral part of the action (the musicians are placed there), the isolation of action in only a few places on stage at any particular moment distinguishes it from the other dance works.

Wilson’s portraits, still-lives, and landscapes are distributed symmetrically throughout the opera:



The opera can be symmetrically divided in several ways.  First, the knee plays divide the opera into four parts—the four acts—each of which contains two or three still-lives or landscapes.4  The landscapes divide the opera again into three sections as bracketed in the figure above.  The titles in italics are grouped together by their similarity in style: texts based on counted quarter notes.  These sections further divide the opera into two sections.

3 The musical material in “Building” and “Spaceship,” being derived from “Train 1” allows us to consider them as a unified section interrupted by “Bed.” With this conception, the symmetry is preserved to an ever greater degree.

The division of the opera into five knee plays,5 four acts, three sections articulated by Wilson’s “landscapes,” two sections divided by the recurrence of the counted quarter notes in “Prison,” and one unity parallels Glass’s contention that the musical material is made up of sections consisting of five, four, three, two, and one chord.  The symmetric divisions of the opera stand in contrast to the asymmetric rhythms and phrases of much of the work, reversing the standard of Western classical music.

5 Glass has stated that the most important musical material is introduced in the knee plays and has asserted that their structure structures the opera. Although I do not agree entirely with this statement, it is supported by the parallelism indicated above.

Visual and Non-musical Structures

Wilson and Glass have emphasized that they conceived of Einstein on the Beach as a “portrait” opera, where the scenes and staging would be composed of elements which related to the subject, Albert Einstein.  By choosing one of the most well-known and important figures of the twentieth century—the figure of the century according to Time magazine—the two creators did not need to present the story of a person’s life, but instead to present images on the stage and allow the audience to relate these images to the knowledge of the subject that they brought with them to the piece.  Musically, this took the form of a solo violin in the orchestra, since Einstein was a violinist, and possibly the prominent use of numbers as a foundation for the sung text.6  The visual references to Einstein are both more numerous and more difficult to connect to the subject.7  While other commentators have identified many of the references to his biography, references to his work in physics have been much more elusive for writers.  K. Robert Schwarz, for example, identified the train, one of the most important symbols in Einstein as simply a vague reference “back to a pre-atomic era.”8 

6 The numbers were not originally planned to be part of the sung text and were inserted for aid in memorization of rhythms. However, that they remained in the opera in the end and only in certain places argues for a connection between their presence and the subject of the work.
7 In many ways, they were also the most important for the first viewers of the opera, who came mostly to see a Wilson production and probably did not know SoHo’s Philip Glass. As John Rockwell wrote in 1978:
To be fair, ‘Einstein’ was a co-creation of Mr. Wilson and Philip Glass, the composer. But most people not only saw it as basically Mr. Wilson’s work—so much so that Mr. Glass was openly aggrieved, and has declined further collaboration with Mr. Wilson—but as the capstone to a series of remarkable large-scale Wilson theatrical creations that dated back to the 1960s. (New York Times, 26 November 1978, p. 5)
There is a certain irony that in America today the work is mostly viewed as not the capstone of Wilson’s creations but the starting block for Glass’s first operatic trilogy.
8 K. Robert Schwartz, Minimalists (London: Phaidon Press Ltd. 1996), p. 131.

The train meant far more than this for Einstein’s work in physics.  The train was a recurring subject in his explanations of special relativity, almost a leitmotiv for showing that the concept of simultaneity is not universal but particular to every observer.  The image Einstein evoked, which recurs in practically every physics textbook today, was that of a train car being struck by lightning at least twice:9

9 Examples from physics books are reproduced from Douglas C. Giancoli, Physics: Principles with Applications (Upper Saddle River, N.J.: Prentice Hall, 1997), however they could have been taken from any number of physics texts.

“Train 1,” a bar of light cuts through the train backdrop twice, in the sections where the process of cyclical motives of different lengths (cyc) gives way to music in E♭ based on additive processes (add).10  It certainly could not have escaped the notice of Glass that his musical stretching and contracting of our perception of time, through repetition and additive structures, was carried on against the backdrop of a proof that time has no absolute reference point.


(2015: Video clip showing the striking of lightening on a train)



10 David Cunningham, “Einstein on the Beach,” Musics 12 (May 1977), reprinted in Writings on Glass (q.v.), pp. 155-156. Cunningham is one of the few writers to note the train’s importance in relativity demonstrations. He also recognized the allusion to Einstein’s question about riding on a beam of light in “Spaceship”.

The transformations of the train into building and spaceship in Act 4 also have their roots in relativity thought experiments.  The building, seen from both the front and side simultaneously, is a demonstration of how observers at rest see light reflected off objects moving at high speeds.11


11 I have photo-reversed the image of the building from the opera to make the similarity to the physics text’s diagram. Note that the front of the building is not rotated in either image, the important distinction between a relativity demonstration and a standard perspective drawing.

The spaceship image, in addition to being a standard demonstration of relativistic length contraction (along with a rotating ruler or stick or an oblong clock which are also seen in the opera) hints at the prospects for future nuclear apocalypse which Einstein’s work on nuclear physics made a frightening possibility.12


12 Glass, in Music by Philip Glass, has denied that Nevil Shute’s 1957 post-apocalyptic novel On the Beach was a conscious influence on Glass or Wilson. There are several other music compositions having “on the beach” in their titles which could have influenced Glass (and possibly even Wilson’s) choice of titles. The second movement of Ralph Vaughn William’s Sea Symphony (c. 1909) is titled “On the Beach at Night Alone.” The similarly titled “On the Beach at Night” by Andrew Imbrie (1961) is scored for vocal ensemble with string orchestra. Roger Session’s song “On the Beach at Fontana,” (1967) taking its words from James Joyce, is another possible influence. All three of these works begin “on the beach at” somewhere, which is a closer parallel to the opera’s original title, “Einstein on the Beach at Wall Street” than is the Shute novel. The connections are unlikely, but Glass and Wilson would be the last to deny that meaning in the opera could be constructed for a listener via past experience with the novel.

The length contraction demonstrated by the spaceship manifests itself in several other ways in the opera.  The tall, narrow chairs used throughout the opera are examples of this physical phenomenon on stage.  Further analysis of how the staging parallels the teachings and life of Einstein will have to await a video viewing of the opera.

(The paper will continue in a coming blog post with musical analysis of the opera. The "further analysis," even several live and video viewings later will still need to wait.)

[November 21, 2015 12:34 pm] « » [prolatio]

Preface

From 1998 to 2006, I worked extensively on Minimalist music as a secondary field to my main research on fourteenth-century music. Under the caring guidance of Reinhold Brinkmann, I gave several papers on the topic, considering a dissertation on Glass's Einstein on the Beach and the analysis of minimalist music. 

By the end of my Ph.D., I had three mostly written articles which needed the sort of fleshing out to turn conference paper into publication. Good events, such as having many obligations at MIT, discovering computational musicology/music21, and having more to say on medieval music, conspired to make it so these articles never got polished nor made it into print in any way beyond the few people who still had handouts from random conferences where I presented the work.

It is nearly 2016 and I have not worked in minimalist circles for almost ten years now. During this time, minimalist studies have exploded: the Society for Minimalist Music has been founded, numerous conferences have taken place, and whole monographs on significant works such as Nixon in China, De Staat, and so on have been published. Minimalism has gone from being a research area to sneer at to one of the foundational parts of modern music studies. Thus, my work was becoming more and more dated with each year that I did not keep up with new bibliography, new terminology, and new discoveries.

It has become time to admit that it's extremely unlikely that I will ever work up these thoughts into a format that could be published in a significant journal. I can already imagine the "revise and resubmit" requests to cite so many people whose work is relevant to my own, but which I don't know now and was not written when I wrote the words below. I have tenure now, so formal publication is less important to my career than it was a couple of years ago. Yet I do think that there are probably some tidbits of theories here that might still be useful to someone. What I present below are unrevised (except in the case of typos or sentences that trailed off or references to video clips etc.) versions of talks given between 1999 and 2005. I would welcome comments on places where I can add bibliography and cite others who published this work first  (which I will update with a note) and I apologize in advance for all the already published work that is not included. If there is interest (by a journal that does not mind that this has appeared on the web), I could revise later, but none of this information was doing anyone any good sitting on my hard drive, so might as well get it up where maybe it could help someone.

Given the best traditions of blogging, I will try to break these posts into approximately 1,000 word chunks. The label "minimalist publication project" will help find other contributions to this series as they are uploaded.

Ambiguity and Certainty in Minimalist Processes

Dublin Conference on Music Analysis, June 2005

A useful way of looking at repeated processes in minimalist music is to consider the amount of ambiguity or certainty they introduce.  This view moves beyond description of the mechanisms of processes (additive, divisive, cyclic) and focuses on their effects on the form of a work or a section of a work, and from there on the expectations of listeners.  I begin by discussing how some processes have the potential to create ambiguities in perception.  We will then observe the opposite case: pieces where we are able to perceive order in the midst of a highly complex or seemingly somewhat homogenous texture.

(2015): The paper began with several definitions of process in minimalism which were given in expanded form in other articles. They will be put in a separate post. It ended with discussions of process in Lucier and Beethoven, which will also be put in a separate post. What remains here are the elements of the paper that fit into the narrow niche of Ambiguity and Certainty.  For this reason, Figure numbers do not begin at 1.

I’m mostly going to confine myself to “top 40” minimalist pieces; the hits, in order to keep things in more familiar territory.  Let us consider a passage from Glass and Wilson’s Einstein on the Beach, given in a modified score as Figure 4.  The music is taken from the connecting passage between the first and second acts, Knee Play 2.






In this section, a series of additive and subtractive processes augment and diminish the lengths of the arpeggios. Let me focus on one place where I believe a clearly defined process can produce ambiguous results.

I believe no matter what, we have to hear the passage as a gradual change in tempo.  But we are given the opportunity to choose among two or more different tempo progressions.  In one of these ways of hearing, the beat of the passage is tied to the repetition of contour and its emphasis on the repeated bass note.  In this mode of listening, lines two and three have more but faster beats than the preceding lines.  This process is described by the line marked "contour" in Figure 5  What we hear is a subtractive process—a quickening of the tempo from six eighth notes per five beat section to four eighth notes per ten beat section.  The process continues now by removing a single eighth note and playing fifteen three-note beats per repetition.  Then one further eighth note is removed and we are left with two-note beats.4


4 After the two eighth-note contour, I have chosen six eighth notes to be the fundamental motivic beat for the final line of Figure 5's contour analysis rather than the one eighth-note beat. This choice was based on research that showed that tempos near to or father than 300 beats per minute are usually unable to be perceived as beats. See, for instance, Simon Dixon, "Automatic Extraction of Tempo and Beat from Expressive Performances," Journal of New Music Research 30 (2001).

Intriguingly, many listeners hear the passage in the opposite way, emphasizing the chord changes as primary over the repetition of contour. This hearing is given in the line marked "harmony" in Figure 5.  In this way of listening, the passage is primarily a large-scale ritardando except for the motion between passage 3 and passage 4 which is unambiguously an acceleration of beat no matter which mode of listening is chosen.*

* (2007/2015) In seven talks and classroom presentations I have conducted an experiment where I asked listeners to tap silently along with the changing beat of Knee 2 before giving this section of the paper. The results were always nearly evenly divided between those who chose the contour interpretation of the beat and those who chose the harmonic interpretation (a few listeners could not find a beat at all). In later talks I asked listeners to identify whether or not they had absolute pitch after conducting the experiment. The minority of listeners with absolute pitch always chose the harmonic interpretation over the contour interpretation, perhaps suggesting that the relationship between two motives with similar contours but different harmonies is much weaker for absolute pitch possessors than for the general population. I have been wanting to reproduce this experiment in a more formalized setting, but I admit now that this is not going to happen any time soon. In an April 13, 2005 interview with Philip Glass I conducted in Rome, I asked him about the changing beat and he said, "You mean where it goes 6, 4, 3, 2." I mentioned that some people hear it as slowing down because of the chords and he replied with some surprise, "Really?" but then returned to calmness saying that it was not too surprising because he tried to put ambiguous interpretation into his works and told the Beckett story with which this paper continues. I want to publicly thank Philip Glass for being so generous with his time and for JoAnne Akalaitis for facilitating the interview.

Ambiguity was a fundamental part of Glass’s musical philosophy in writing Einstein—he has frequently stated that he admired the quality of Beckett’s drama that each listener could experience the epiphany of the work in a different place; yet it is rare that a quality so fundamental and usually simple such as tempo can be experienced in opposing ways by different listeners.  The balance that allows ambiguous perception is also fragile.  The addition of a chorus sustaining the chords when the material returns in Knee 4, for instance, emphasizes the ritardando interpretation.





Stronger accidents at the beginning of each repetition of contour could have the opposite effect.  Once the ambiguity in the passage is noticed, there is also the possibility of consciously or unconsciously switching-gears at any moment from the contour to the harmonic interpretation or back to create other paths of acceleration and deceleration.

In Einstein, we have an ordered and predictable process which can create ambiguities in hearing a fundamental part of the music, the beat.  Conversely, some composers have paired minimalist processes which create surface disorder with compositional decisions which limit ambiguity.  Frederic Rzewski’s Les Moutons de Panurge is a piece for any number of players on any instruments consisting of a single melodic line.  First only one note of the line is played, then two, three, and so on until all sixty-five notes are played, after which notes are removed.  See the score and the realization of the opening in Figure 6.



As normally performed, due to rhythmic errors in playing, the musicians will make mistakes that cause them to temporarily be off from one other. Unlike standard performance situations, where the musicians would then get back in sync, the score tells the musicians to remain off from the others, eventually creating a jumble of different layers.




Although the work uses only two rhythmic values (quarter and eighth notes) and simple diatonic intervals favoring stepwise motion and motion by thirds--in a word, simple--the melodic line is constructed with practically no repetitions among various sections. The line has enough distinct material that even very short melodic sections played by any musician and which jump out of the texture give enough information to identify where each instrument is in the melody. Figure 7 gives a list of the places where hearing two or more notes is insufficient to precisely locate a player within the sixty-five-note score.



There are fifteen two-note segments which do not identify the player's location. These represent thirty-three of the sixty-four possible two-note starting places, or about half.  If three contiguous notes can be heard from a single instrument in the texture, then there are only five segments that do not identify the location of the player. In fifty-five of the sixty-three possible places, the musician's position in the score will be known to the listener. With four contiguous notes, there are only two places of ambiguity, and with five notes, the listener always can have complete certainty of a musician's location.

I am not saying that Rzewski has purposely arranged his material to create maximum distinctiveness—in fact, I had a computer program generate 1000 random melodies, sharing only Rzewski’s notes and rhythms and his predilection for stepwise and 3rd motion, and the results were similar.5  The distinctiveness of short motives is not a result of his ordering, but rather of his choice of melodic material (non-tonally oriented skips and no apparent reason behind the choice of longer notes) and the lack of any distinctive ordering.  We can contrast the 65 notes of Moutons with the first 65 notes of the clarinet entrance of Mozart’s concerto.  Hearing any isolated note in Mozart’s work will give you a better idea of your location in the work, but there are many more locations where hearing three, four, or even five or six notes will not pinpoint your location.  A movement from a Bach solo ’cello suite would almost certainly have a lower level of distinctiveness by this metric.

5 A random distribution of the notes used by Rzewski was shuffled in a way that favored motion by seconds and third by having a 50% chance of reshuffling the notes if motion larger than a third was created, and a 75% chance of reshuffling if it was larger than a fourth. On average, this process resulted in 14 two-note matches per piece, 1 or 2 three-note matches per piece, a four-note match every six pieces, and a five-note match every fifty pieces

A similar effect can be heard in Satie’s oft-cited “proto-minimalist” work, Vexations, whose bass line is given in Figure 8.



Here Satie has composed the line out of extremely distinctive intervals, approaching the construction of an all-interval set.  Any two consecutive pitches or intervals in the bass will uniquely identify where the performer is within the line.  The piece is thus constantly sending signals about where the performer is in within this short line.  The larger form of the piece is completely different, consisting of 360 repetitions of this bass line organized into 840 larger repetitions played over 12 to 24 hours. Maddeningly, these interval-based signals constantly give localized information about the position in the line but give absolutely no information about where we are in the overall form of the work.

Ambiguities of perception and certainty within chaotic or hard to perceive processes are essential but overlooked components of minimalist music. Considering them in the light of previous characterizations of minimalist processes can bring out the many complexities hidden within seemingly simple pieces.

For older stories visit the Prolatio (general items) or music21 (computational musicology) blogs.

Michael Scott Cuthbert (cuthbert [at] mit.edu) is Associate Professor of Music and Homer A. Burnell Career Development Professor at M.I.T.

Cuthbert received his A.B. summa cum laude, A.M. and Ph.D. degrees from Harvard University. He spent 2004-05 at the American Academy as a Rome Prize winner in Medieval Studies, 2009-10 as Fellow at Harvard's Villa I Tatti Center for Italian Renaissance Studies in Florence, and in 2012–13 was a Fellow at the Radcliffe Institute in 2012-13. Prior to coming to MIT, Cuthbert was Visiting Assistant Professor on the faculties of Smith and Mount Holyoke Colleges. His teaching includes early music, music since 1900, computational musicology, and music theory.

Cuthbert has worked extensively on computer-aided musical analysis, fourteenth-century music, and the music of the past forty years. He is creator and principal investigator of the music21 project. He has lectured and published on fragments and palimpsests of the late Middle Ages, set analysis of Sub-Saharan African Rhythm, Minimalism, and the music of John Zorn.

Cuthbert is writing a book on Italian sacred music from the arrival of the Black Death to the end of the Great Schism.

Download what is almost certainly an out-of-date C.V. here (last modified June 2012)

2010
Changing Musical Time in the Renaissance (and Today), for Festschrift Joseph Connors (forthcoming)

Bologna Q15: the making and remaking of a musical manuscript, review for Notes 66.3 (March), pp. 656-60.

2009
Ars Nova: French and Italian Music in the Fourteenth Century, edited volume with John L. Nádas (Music in the Medieval World Reference Series vol. 6). London: Ashgate. Reviewed by Gary Towne, The Medieval Review, February 2010.

"Palimpsests, Sketches, and Extracts: The Organization and Compositions of Seville 5-2-25," L’Ars Nova Italiana del Trecento 7, pp. 57–78.

Der Mensural Codex St. Emmeram: Faksimile der Handschift Clm 14274 der Bayerischen Staatsbibliothek München, review for Notes 65.4 (June), pp. 252–4.

2008
"A New Trecento Source of a French Ballade (Je voy mon cuer)," in Golden Muse: The Loeb Music Library at 50. Harvard Library Bulletin, new series 18, pp. 77–81.

2007
"Esperance and the French Song in Foreign Sources," Studi Musicali 36.1, pp. 1–19.

2006
"Trecento Fragments and Polyphony Beyond the Codex", Ph.D. Dissertation, Harvard University (unpublished).

"Generalized Set Analysis and Sub-Saharan African Rhythm? Evaluating and Expanding the Theories of Willie Anku," Journal of New Music Research (formerly Interface) 35.3, pp. 211–19. [.pdf]

2005
"Zacara’s D’amor Languire and Strategies for Borrowing in the Early Fifteenth-Century Italian Mass," in Antonio Zacara da Teramo e il suo tempo, edited by Francesco Zimei. Lucca: LIM, pp. 337–57 and plates 10–13.

2001
"Free Improvisation: John Zorn and the Construction of Jewish Identity through Music," in Studies in Jewish Musical Traditions, edited by Kay Kaufman Shelemay (Cambridge, Mass.: Harvard College Library). pp. 1-31. [.pdf]

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