Entries tagged with “Chance Operations”.


John Cage

Happy Birthday!

Below is a score I wrote in tribute to John Cage, in this his centenary year. I may not get a chance to realize this score so I’m posting it up here for anyone to utilize. If anyone does realize this score let me know via the comments or an email. I’d certainly love to see and/or hear anyones attempts.

In recognition of John Cage’s frequent use of the I Ching for his ‘chance operations’ I chose to use it as a randomizing element for this score. I tend to not use the I Ching in my compositions; in the scores where I have used stochastic means I have only one other time used the I Ching (that was for Mid-Spring (rock, breath, 12kHz) which like all of the Eleven Clouds releases was dedicated to an inspirational artist, in this case John Cage). For this piece this would require tossing coins, or yarrow stalks three hundred times (for this year only, +3n for each subsequent year).  However one could easily automate the generation of I Ching values in such a way to accurately capture the randomness of tossing the yarrow stalks. This page covers the mathematics quite well and there are definitely apps and webpages out there to get these values. If I get a chance to work on this (perhaps later in the far) I’d implement this in a spread sheet where one could automate the entire generation process. Then one could print it out or preferably use it as a guide to creating the performance score with brush and ink.

I’m definitely free to answer any questions in order to improve understanding of how to construct or perform the score. Comments on overall clarity are appreciated even if one isn’t going to perform it.

One^n
(for John Cage on the occasion of his hundredth birthday)

 

Composed in memoriam of John Cage in his centenary year.

Constructing the score

where n = the number of years since the birth of John Cage

1) Take a large sheet of paper, the larger the better, and mark from 1-64 on the left edge and top edge. The marks should be equidistant apart with the same spacing on the top and bottom. For instance each mark could be 1″ apart making for a 64×64 inch grid. The spacing that you choose is the scale for this score.

2) Using the I-Ching (or anything that captures the probabilities correctly see: http://www.dentato.it/iching/) generate four numbers for each value of n:  i.e.:

1 – 23, 42, 9, 17

If there are moving lines then you should generate both values putting the second into parenthesis. i.e.:

2 – 61 (37), 45, 19, 40

3 – 29 (54) ,12(19), 4, 8

4 – 8, 13, 49 (3), 36 (23)

5 – 26, 50 (38), 13 (2), 12

and so on

These numbers should be labeled x,y, z,w where the four numbers are: x, y: coordinates, z: orientation and w: magnitude.

3) Place a dot of ink, ideally with a brush, but at least in some way that they are not uniform, at the coordinates of the first two numbers as x, y. If there is already a dot here, proceed as if there isn’t perhaps creating a larger, darker, thicker or completely subsumed dot. If there is a parenthetical value for x, y or both x and y place a second dot at that those coordinates.

Note: If one were to automate this with software cast an additional I Ching value to be used as the diameter of the dot. You should map the the value in the range of  1-64 to 4 x your scale. Changes in this case should either be applied to the second dot if it exists or added to the diameter of this dot.

4) Next mark the angle from z using the following formula using 6 degrees for each count of the generated number. Values greater than 60 should have no angle marked. If there is a parenthetical value then mark a second angle following the same system for the first.

5) Finally draw a line using either pencil or ink (or both) from the center of the dot at the marked angle the length of which is determined by w using the scale set in the grid markings (see 1). If no angle has been marked, no line should be drawn. If there is a parenthetical value then there are two conditions. If there are two angles then the two magnitudes are used for them in a one to one correspondence (and on all dots if there are more than one). If there is only one angle then add the two values together. This may extend beyond the marked boundaries or even off the paper.

Examples

With a scale of 1=1″

Ex. 1: 23, 42, 9, 17

Here there would be a dot at  23, 42 with at line at 454 degrees extending 17“.

Ex. 2:  61 (37), 45, 19, 40

For this case there would be a dot at  61, 45 and at 37, 45 with at line at 114 degrees extending 40“.

Ex. 3:  29 (54) ,12 (19), 4, 8

In this example there would be a dot at  29, 12 and at 54, 19 with at line at 24 degrees extending 8“.

Ex. 4: 8, 13, 49 (3), 36 (23)

You would have a dot at 8, 13 and then two lines extending out  at 294 degrees for 36″ and 18 degrees for 23″.

Ex. 5:  26, 50 (38), 13 (2), 12

You would have a dot at 26, 50 and 26, 38 and then two 12″ lines from each dot  at 78 degrees and 12 degrees.

 

Performing the Score

If playing electronics the score should be interpreted as an Electric Score. For acoustic instruments it should be interpreted as a Pool of Sound (a Musical Pattern variant), for which see the specific instructions below. It can be play simultaneously with other instances of this score, for which each performer should generate their own score.  A duration should not be set for performance, the performance should continue until all the material is performed.

 

I. Playing as an Electric Score

  • For live electronics setup configured in response to the score.
  • Markings are not indications of sounds to played but of overall effect.
  • Whitespace must be taken into account
  • There is not a one to one mapping of length and duration; duration should be sufficient to realize the affect of the markings.
  • Always move in clusters.

 

II. Playing as a Pool of Sound

  • Pools of sound arise from the space in which they are set.
  • Each pool should be approached individually with common or connecting elements providing the structure.
  • The path through the score is up to the performer.
  • Spaces between the pools must be observed and should be also be a structural element.
  • A pool should be thought of as a system which can have multiple elements: a sound, but also its duration, repetition, dynamic and so on.
  • How the characteristics are determined is up to the performer but whatever structure is applied should form the basis for those that share symbolic features.

 

john Cage Etudes Boreales

John Cage Etudes Boreales / Harmonies / 10’40.3″ (Wergo)

John Cage used star charts as a source of randomness most famously in Atlas Eclipcalis, Etudes Australes, the Freeman Etudes and Etudes Boreales. This is in my mind an interesting technique for achieving a goal of integrating nature into ones composition. Cage of course most famously used the I Ching as his source of randomness, which is effect but basically he was using it to pick the numbers 1-64. You generate each line on its own and there are four states: solid, open, solid changing to open or open changing to solid.  After you work out each line you generally end up with two hexagrams, the starting one and the one you end up with after you have calculated the changing lines.  From there if you are practicing the divination, or are simply looking for a randomly selected philosophical message you consult the text and the various commentaries. Now how you apply this to composition is up to the composer and Cage used many different methods to do so.  This really was Cage’s art and genius; he set up systems that could take a known range of randomness and produce highly successful results.

Excerpt from the piano part of Etudes Breales

Overlaying barlines onto star charts and using the stars as notes (with magnitude as duration of the note perhaps) is really far more random and cedes far more control from the composer.  There are a lot of stars and thus these pieces are a lot more dense.  When Cage composed these works (the 1970s) he began to tackle a number of areas of composition he’d previously avoided such as harmony and virtuosistic pieces (for non david Tudor musicians).  Etudes Boreales is an example of a virtuosistic that in this particular recording doesn’t necessarily sound so.  The piece is for ‘cello and/or piano and this disc contains both a solo ‘cello version and a version for solo ‘cello and piano.  The piano part is actually a percussion score and it is the ‘cello part has all all aspects of the sound making meticulously notated including pitch, duration, articulation, color and dynamics.

Etudes Boreales is played twice on this disc, once for a percissionist  using a piano and the second for ‘cello solo and piano solo. The first version is the percussion version and I have to say this is fantastic.  The sounds are mostly short events that come in and out of spaces of varyin lengths (though none of epic length).  The sounds come from all over: hitting of one to many keys, tapping, rubbing, hitting the body of the piano, striking, rubbing, etc the strings, using mallets on the metal frame and so on. There are sounds that are muted and sounds that overlap with other sounds, use of the pedal for sustain and decay, sounds so faint as to barely register and achingly resonant chords. The video above is the first two of the four parts of the piece performed by Mark Knoop who is the pianist on this recording, so that is very representative of the disc under discussion here and nice to see as well as hear it performed. Below is a video of Knoop playing parts three and four to allow for a complete performance to be viewed.

The second version is for two solist playing the piece simultnously: ‘cello and percussionist playing a piano.  All of the charms of the previously discussed version are present, though Knoop seems to be mixing up the gestures. The ‘cello is a perfect counterpoint to this; often played high and with skittering attacks it could be another percussionist. But the longer tones, the rich tonality of the lower register of ‘cello, when these come in, the short bursts from the piano sink into them and the interpenetrations give life to a unique soundworld that is equal parts the two instruments. The two versions of this piece on this disc are worth it alone, but it also contains four more pieces for ‘cello and piano.

He counted the number of notes in a given voice of the piece [four-part choral music by William Billings -ed.], and then used chance to select from these. Supposing there were fourteen notes in a line, chance operations might select notes one, seven, eleven, and fourteen. In such a case, Cage would take the first note from the original and extend it until the seventh note (removing all the intervening notes); all the notes from the seventh to the eleventh would be removed, leaving a silence. Then the eleventh note would be extended to the fourteenth, followed by another silence. Each of the four lines thus became a series of extended single tones and silences. This was the version that Cage settled upon:

“The cadences and everything disappeared; but the flavor remained. You can recognize it as eighteenth century music; but it’s suddenly brilliant in a new way. It is because each sound vibrates from itself, not from a theory. . . . The cadences which were the function of the theory, to make syntax and all, all of that is gone, so that you get the most marvelous overlappings.”

-James Pritchett, from his Introduction to the Music of John Cage

This disc also contains three of the 44 harmonies from Apartment House 1776 (XXVII, XXIV and XIII) which is one of Cage’s musicirucus pieces in which many different types of events can take place simultaneously: 44 Harmonies, 14 Tunes, 4 Marches and 2 Imitations. He also stipluated that you can play any fraction of these and in the case of this disc they play three of the harmonies  for  ‘cello and piano.  The entirety of  Apartment House 1776 utilizes chance operations in the form of the I Ching in contrast to the star charts of Etudes Boreales. The disc opens with XXVII and its is short beautiful piece whose spare lines come in and out, widely spaced with that rich haunting ‘cello tone in almost transparent harmony with soft piano chords. Littlle bits of almost melody come in and out and there are the occaisonal burst of activity and of course short silences. The longest of these is less soft and has these real start stop feel. As if a player begins to play a melody and part way through stops and thinks a bit and then starts up. Which considering how it was composed makes perfect sense. Again the piano is more background and they tone of the two instruments creates a nice interplay. The final of the harmonies played here, XIII (which is also the 13th track on the disc) is almost a middle ground between the two. Shorter again, with more space than either of the previous, it has the stop and start feel of the middle one but with longer space more akin to the initial tracks.  I’m not much of a fan of the full on Apartment House 1776, but I really like these harmonies played in in this gentle, spacious style.

Friedrich Gauwerky

This middle track on the disc is an excerpt of  26’1.1499′” for a String Player of which cellist Friedrich Gauwerky chose to play the first 640.3 seconds of, thus giving the piece the title of 10’40.3′ (this as per Cage’s instructions on ways one can play the piece). The earliest piece on this disc and its construction utilized a third and pre-I Ching method of randomness: imperfections in paper. This method is utilized to generate highly specific locations on the strings of the instrument which allows for the pitch to be sounded. There also seems to be instructions for noises to be made of which I haven’t found much by way of specifics for. But  Gauwerky here chooses, for at least some of them, vocalizations which frankly I find to be one of the most dated of modernist classical cliches. The little yelps and guttural exclamations always sound the same as if the intense concentration of realizing the music just doesn’t allow for enough attention to be placed on this other activity. No matter when I’ve seen or heard it done and it is a string quartet trope in particular I’ve never liked it. Thus this is I’d say the only dud track here but really it’s 10 minutes doesn’t detract from the rest of the disc at all.

Knoop and Gauwerky are both well known and respected players of a wide variety of new music, so their top notch performance here is no surprise. The recording quality is pretty amazing as well, super transparent and close miked enough to pick up even the faintest sound. I didn’t hear any sounds of performer movement or breath so it really is just the sounds of the instruments and it really fills a room nicely. I’d been looking for a version of Etudes Borealis for while and this disc coming out this year fits the bill perfectly.