jwilzewske: algorithm

Showing posts with label algorithm. Show all posts

Sunday, June 7, 2009

Early-Music Aleatorics: Mozart’s Macrogranular Minuet Generator

T he piece starts with a recognizably Mozartean voice, but as different versions of the minuet are superimposed, the textures become complex and passingly dissonant. Soaring themes, too, and bits of poignancy, rise. There’s much to arrest the ear.”
— Scott Cantrell, Dallas Morning News, 21-APR-2006, review of Robert Rodriguez’s ‘Mozart Dice Game’.

A nleitung:
Walzer oder Schleifer mit 2 Würfeln zu componieren,
ohne Musikalisch zu seyn,
noch von der Composition etwas zu verstehen.”

[Instruction:
To compose a waltz or a schleifer / landler with two dice,
without being musically gifted,
nor knowing anything about composition.]
— W.A. Mozart.

S ometime around 1775—when is not known with certainty—Mozart wrote the measures and instructions for a musical compositional method using dice, a table of numbers, and a set of cards. On each card was printed one measure of music and a number to identify that measure. You randomly select from these pre-written measures of music based on rolls of the dice. With each dice roll, you do a table look-up to find out what card (measure) you are to select from the deck. Then you put the cards together to create new Menuets. It was possibly the first [published] algorithmic stochastic composition.

T here are 176 possible Menuet measures and 96 possible Trio measures to choose from. The results of the 32 dice rolls and the pretty large set of pre-written measures give a quite large number of different compositions that could be generated by Mozart’s rules.

B ut there are not 11¹⁶ + 6¹⁶ = 4.6 * 10¹⁶ possible compositions as some claim. [My god, there is an error on the internets!]

N or is it ₂₇₂C₃₂ (176 + 96 things, taken 32 at a time) = 4.6 * 10⁴¹ possible menuets.

I nstead, what you have with Mozart’s menuet generator are 11¹⁶ * 6¹⁶ = 1.3 * 10²⁹ possibilities. That’s because his rules specify a menuet as a segmented number (string-vector) comprised of 16 base-11 (undecimal [Babylon5 ‘minbari’]) digits concatenated with 16 base-6 (hexal) digits, where each digit indexes into a separate list of permitted measures. Only members of the specific subset of measures that Mozart enumerated in a given roll’s list are permitted (table column look-ups), not just any from the whole set of all 176 Menuet measures or all 96 Trio measures.

I f you fail to preserve it [the sequence of 32 numbers from your dice rolls, or the sequence of measures you get], it will be a menuet that will [probabilistically speaking—] never be heard again.”
— Martin Gardner, Scientific American, 1970.

The Menuet section is in the tonic key and the Trio section is in subdominant.
Measure numbers are indicated in the top row.
Outcome of each dice roll is indicated in the left-most column (2 to 12 for the Menuet roll with two dice; 1 to 6 for the Trio single-die roll).
For example, for the first measure (Menuet) if you rolled “snake-eyes” you would play measure #96 of the 176 possible Minuet measures. If in bar 17 (Trio) you rolled a “6” you would play measure #18 of the 96 possible Trio measures.

I n 2005, the Dallas Symphony Orchestra commissioned a ‘new version’ of K. 516f in honor of the 250th anniversary of Mozart’s birthday.

Robert X. Rodriguez, photo (c) Schexnyder

M usical Dice Game’ begins with the first solo quartet playing the first half of one minuet; both quartets then join to play all eleven versions of those bars at once; the second solo quartet continues with the second half of the minuet, followed by all eleven versions of those bars, again played by all forces simultaneously. Eleven continuous variations follow, based on the harmonies and principal melodic motifs of the original dice game. I most often used the game’s versions for throwing a five, six, eight, nine or, particularly, a seven. Since, by the laws of probability, those numbers are the most likely to be thrown, they have the most melodically distinctive variants. In the first few variations, the themes and harmonies are given in their simple, original forms; then, as the piece progresses, the minuets are disguised, and the music grows more and more chromatic, complex and rhythmically asymmetrical. In the final variation, a synthesis is reached between the Mozartean themes and their transformed versions, as the original minuets return, superimposed over the varied material in a festive musical layer cake.”
— Robert Xavier Rodriguez, score notes, 2005.

B eautiful! Having been persuaded/challenged by the DSO to go where angels fear to tread, Rodriguez created a composition guided by Mozart’s stochastic wurfelspiel rules that is notable for its novelty and sheer musicality. It does not have too much emphasis on ‘bar-lines’, despite the ‘measure-wise’ macro-granularity of the stochastic engine (dice-rolling selection of single measures by table look-up). It’s superbly constructed... a moving piece of music in its own right, and one that also invites us to critically rethink Mozart’s own compositional methods and computational composition in general.

I n light of the Schick/ICE Xenakis concert in Chicago earlier this week and my previous CMT post speculating about algorithmic composition methods’ begging for human editing/finishing, I thought I’d mention Mozart’s own experiments, as well as Robert Rodriguez and his Mozart Reloaded.

M usic is meaningless noise unless it touches a receptive mind.”
— Paul Hindemith.

P otential for banality, or beauty

What are avatars of impendingness?
After Verdi died in 1901 (January, in Milan, of complications from a single, deterministic stroke), Italy suffered a cardiac/cultural arrest of confidence.
After Xenakis died in 2001 (February, in Paris, of complications from multiple stochastic ailments he had been enduring), Greece suffered nothing, at least not right away.
But soon after each event, the protean exuberance of the respective century collapsed; emergent self-absorption papered over with frenzied ornamentation.
No such country as “Homeland”... non-existence hardly ameliorates its artistic self-glorification.
You know, things that happen according to Markovian rules can be changed without loss of overall meaning, and likewise without gain of overall meaning.

What are Markov melody engines?
Stochastic algorithms who have had a recurring, salacious role in western music composition for more than 200 years...
Who do not want the listener to be aware of their forms and metabolisms.
Mozart’s ‘Musikalisches Wurfelspiel’ K.516f is well-known. But other composers, including Haydn and C.P.E. Bach, fooled around here.
Recombining humanly-composed motifs in random orders, first for the novelty of it, but then as friends/accomplices, then as crutches/co-dependents, and finally as addictions.
Mozart wrote (or [at least] Peter Welcker published in 1775, in London) a ‘Tabular System Whereby Any Person without the Least Knowledge of Musick May Compose Ten Thousand Different Menuets in the Most Pleasing and Correct Manner’.
‘Pleasing’, maybe, sometimes. ‘Correct’, leave it for the first violin to say.”

Tuesday, March 10, 2009

Canonical Form as Social Networking (Reply re: Canonical Form as Epidemic Contagion)

Y our infectious/epidemiology model may be the first theory of canonical form that says that voices engaged in canon are passive ... coerced, so to say. As though the neighboring parts had some sort of apraxia until infected. But they are not at a loss for words. They are not passive [respondents]. And you obviously do not have anything like the release of tension, which is the conclusion of normal classical music composition structure.”
— Anonymous email to CMT.

I agree with some of the emailer’s observations about the earlier CMT post: the players are not ‘passive’ or ‘inert’. Each is receptive to stimulation and, after being stimulated/infected by those around them, engages in ‘speculative’ or ‘expansive’ elaboration upon what they’ve received.

B ut I disagree about the ‘tension’ point. There’s no ‘law’ that says that all musical events must be deliberative or rational or intended. Individual players may emit sounds that have unintended [but wonderful—] consequences or inadvertent meanings. Players have a possibility for automatic or pre-conscious improvisational sonic production, which the composer can call upon if she/he wishes (think Stockhausen or Nancarrow or Tenney). There may be hyper-structural or obsessive features that are far from ‘rational’ (think Feldman or Babbitt or Cage). Stochastic/random elements don't mean that a piece defies analysis—only that the analytical approach has to change to address the content. It’s not a music theory dead-end.

I n fact, I think that the indeterminacy/stochastic elements tend to make the music more ‘listener-centric’ rather than ‘performer-centric’ or ‘text/composer-centric’. We are on ‘edge’ in part because of the greater indeterminacy/unpredictability that it has, compared to conventional forms. The indeterminacy itself is a kind of ‘structure’ or ‘form’. And, so long as the player or listener understands the relationships of the structures and mechanics of the thing—how the stochastic events and mechanisms fulfill the roles of themes and modulations in traditional music—then the thing can be comprehensible and emotionally accessible, just as any other piece of music is.

I suggest that Ferneyhough’s ‘Chûte d’Icare’ and other recent compositions that employ canonical structures actually do permit significant run-time indirection. Furthermore, I suggest that such compositions are analogous to social networking and micro-blogging service. Canonical-form compositions like these are neither more nor less coercive than contemporary Web 2.0 apps and the canonical exchanges that arise in those.

Y es, canonical forms are inherently replicative. This cuts out a lot of the ‘me-too’ chatter and dilatory utterances among the parts, by definition. But there is nonetheless a lot of within- and between-channel complexity. The entropy of the signals is high, even though the signals are canonically structured! And in the Ferneyhough—or in, say, James Tenney’s ‘Postal Pieces’—the parts have to decide whether to ‘resist’ or instead ‘give in’/’succumb’ to the neighboring canonical utterances/viruses. There is the text of the score, and then there is each performer’s free-will...

C learspace uses an unconventional, passive ‘friending’ model. Other users can assert themselves as your friends with or without requiring or permitting your active assent or declining. Your only choice is to remove them (socially awkward), when all you maybe want to do is clear up your “activity feeds” so that you don’t have to drink from such a big fire-hose of information when all those people who friended you generate activity that doesn’t interest you. Facebook and other social networking apps have active/consensual assent-or-decline friending—so filtering/throttling the fire-hose is easier. In the Facebook and other active-friending apps, reciprocal friending is expected, and friend relationships are hard to break. By contrast, in Twitter the ‘following’ relationship comes without connotations of friendship (and less hesitation about unfollowing to control your attention).

W hat would be useful would be if canonical-form compositions were written like Twitter—and offered the notion of ‘following’ a part as an alternative to ‘friending’ or passively ‘subscribing’ as in conventional canonical-form compositions. That way each performer could retain some autonomous control of her/his social filter without having to ignoring feeds or corrupting the composer’s text with individual expressions/interpretations or out-of-band [a-canonical] irruptions.

Y ou can get around this by subscribing separately to each person’s activity RSS feed, but I have found no way to easily aggregate those into a single ‘river of activity’ stream other than creating a combined folder in my feed reader. By contrast, the ‘broadcast’ nature of sound means that we automatically aggregate the acoustic feeds of the other parts around us. (With my chronic hearing loss, I just have a hard time hearing the harpsichord...)

I suppose a non-broadcast canon could be composed and performed. Actually, tape loops and other electroacoustic media are in that vein. Or we could update Tenney’s postcards, and compose a canon where each performer goes into the studio alone and lays down a single track: each person/part is entirely at liberty to listen or not listen to a headphone ‘mix’ of one or some or all of the tracks that have been recorded by other performers. Then the engineer/producer/composer do the edit and post-production. Still canonical form—only off-line!

T witter itself is a great social filter. It has ‘lower friction’ than blogging, and the 140-character limit per tweet makes it less cognitively intrusive/absorptive than blogging or RSS feeds. It’s a shared party-line, and users tend to tweet things that preserve the signal-to-noise ratio for everybody on the party-line. (If they don’t, they can be un-followed without any concern.) Like blogging, Twitter allows you to time-shift your participation (something you can’t do with IM). And like ‘Chûte d’Icare’ or ‘Postal Pieces’, it permits stochastic run-time indirection.

A bout 20% of my Twitter followers are people I know. For better and worse, the rest are a wonderfully-varied ... canonical, stochastic ... Fire-Hose...

H ow does it feel to perform ‘Chûte d’Icare’ or ‘Postal Pieces’, I wonder?

T hank you for the email, and for the privilege of exchanging ideas about these things here!

I think of ‘form’ on a larger temporal scale—as what’s called ‘content’ on a smaller scale. That old ‘form-content’ dichotomy is, to me, a spurious one, because they involve the same thing at different hierarchical levels of perception. What we take to be substance or content—say, a string quartet—is really the result of forms—formal shapes and structures at a microscopic level: particular envelopes, waveforms, and sequences of these—detailsin the signal. All ‘form’ is just the same thing at a larger level,involving spans of time over, say, five minutes or more.”
— James Tenney, interview with composer Gayle Young, 1978.

Stravinsky, ‘Threni’, virulent tenor infector and susceptible bass, minor 6th below, canonically making and breaking the score’s rules