Small World

small world a random, connected graph with v vertices and e edges such that 5 ≤ v ≤ 79 and v – 1 ≤ e ≤ 2v. each vertex represents a pre-determined, distinct event. for example, an event might be a fragment or event of another piece by other composers including, but not at all limited to, joseph kudirka, johannes ockeghem, james orsher, michael pisaro mark so, tashi wada, christian wolff, etc. or the events may be differentiated by timbre, pitch, dynamic, duration, location, type of action or sound object, etc. perhaps explore events that may create an impasse. for example, assigning a vertex an event that must interact with an already occurring event or that can only occur after the occurrence of an event or succession of events within or without the set of events assigned to the vertices of the graph (see christian wolff’s for one, two, or three people). a starting vertex (or vertices for several voices; a voice being an individual path through the graph) is arbitrarily determined for the first occurring event of each respective voice (though each voice need not enter simultaneously). each successive event within a voice must be an event assigned to a neighboring vertex of the previous vertex/event. the exploration of voice following in moderation is encouraged the piece ends any time after each voice has played all the events or when an impasse has been reached. the following pages contain an example set of 20 events. also, a series of graphs (randomly generated by the first example algorithm provided below) all with 20 vertices but each with a different number of edges are provided. the graphs have been formatted for readability. distances between vertices do not indicate anything such as duration. all that matters is whether two vertices are connected implying a temporal succession. these examples are freely usable and changeable. it is also encouraged to create different graphs and event sets and to realize more than one graph simultaneously a random, connected graph may be generating using the following algorithms. example 1: 1) choose a number of vertices, v, and a number of edges, e, such that 5 ≤ v ≤ 79 and v – 1 ≤ e ≤ 2v; 2) initialize the graph by adding two vertices and connecting them; 3) add a vertex and connect it to a vertex already present in the graph; 4) repeat step 3 until v vertices are present in the graph. 5) choose 2 random vertices to connect such that the edge does not create a loop or a parallel edge; 6) repeat step 5 until the e edges are present in the graph. • note that steps 5 and 6 are not necessary if e = v – 1. example 2: 1) choose a number of vertices, v, and a number of edges, e, such that 5 ≤ v ≤ 79 and v – 1 ≤ e ≤ 2v; 2) generate all connected graphs with v vertices and e edges; 3) randomly select one of the graphs.

-mike winter (los angeles; september 2008)

1) successive subsets of a harmonic series; sounded melodically descending or ascending 2) stones; soft 3) a relatively loud burst of short percussive sounds followed by an indefinite duration of silence 4) many, many very small falling objects 5) a long continuous tone after at least 10 seconds of silence 6) the melody of a folk song with several notes replaced by silence or transposed by a small amount 7) several sine tones of random pitch with staggered, imperceptible entrances and exits 8) a very slow glissando 9) 10 to 20 seconds of a sound similar to white noise 10) a tangible gift; made during the piece; presented or displayed 11) a very slow glissando that intersects with a glissando already sounding 12) a resonator imposed over and activated by an already sounding event 13) a series of words generated from a markov chain of some high order 14) waiting; waitfulness 15) a distant sound 16) plucked; perhaps a cactus 17) bowed 18) a bell-like tone with relatively long decay; allowed to vibrate; followed by silence; possibly repeated several times with the same duration between the attack of each tone 19) silence followed by a repetition or mimicking of no less than 3, nor greater than 8, successive events of another voice 20) silence followed by a repetition or mimicking, irrespective of order, of no less than 3, nor greater than 8, of the events that have just occurred within or without the above listed events

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