An Analysis

In the previous essay a simple example of a complete musical expression was given.  This essay provides analysis of a real piece of music. For this analysis the composition Opening (from the album Emergent Musics) is used.

As for characterizing this composition as a real music, the proof of the pudding is in the eating, so readers are encouraged to listen to this piece if they have not already done so. A listener may or may not like this composition (this is guided by personal aesthetics, after all), but upon listening to it I believe most people will agree that it fits the category of a real music. As to whether or not is is an emergent music, hopefully this analysis will shed sufficient light on this question to demonstrate that it is.

(if you have not yet downloaded and listened to the piece, the following widget will stream it to your computer, if you have Flash and Javascript enabled:

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Spacial Definitions

As in all musics of this theory, the attributes of the space in which the composition will unfold (or at least in which the initial process executes) must be defined.  This is done with the following language statements:

set volume      100

set scale       (2 2 3 2 3) 50

set tempo       38

set wrapnotes   True

set maxnotes    5000

set duration    1.0

set timerange   (9 230)

set numtracks   10

set wraptracks  True

set pitchrange              (-8 16)

set trackpitchrange     2   (-3 11)

set trackpitchrange     6   (-3 6)

set trackpitchrange     7   (-3 6)

set trackpitchrange     9   (-3 6)

The scale defines a simple pentatonic scale, with the 0 note assigned to MIDI note 50.  This is shown in conventional notation below:

This stanza:

• Sets the positions of volume and duration for the initial rule execution (100 and 1 respectively).  As no time or track is defined, these take the default value of 0.
• Defines a tempo of 38 bpm, which relates musical time to human perceptual time.
• Defines the extent of time (from beats 9 to 230).
• Creates the voice space. This space has ten values (0 through 9) and wraps circularly.
• Creates the pitch space. This space is also wrapped circularly. Permissible default values are pitch number -8 through 16, except for voices 2, 6, 7, and 9,  which is defined to override the default.
• Limits the number of notes in the composition to 5000 (in reality the rules produce far fewer notes in the composition, so this line has no effect).

Melodic Fragment

There is one process which defines a simple melodic fragment of seven notes:

process melody {

    note time 0.0 pitch 4 duration 0.5 volume -10

    note time 0.5 pitch 8 duration 0.5 volume  10

    note time 2.0 pitch 4 duration 0.5 volume   0

    note time 3.0 pitch 6 duration 0.5 volume -10

    note time 4.5 pitch 4 duration 0.5 volume -20

    note time 5.5 pitch 3 duration 0.5 volume -30

    note time 6.0 pitch 1 duration 1.0 volume -40

}

This is shown in standard notation below:

Processes

The melody process is referenced by another process. This process executes the melody process 6 times, incrementing time by 3.25 beats and decreasing volume by 10 each time.

This process is coded in the language as follows:

process wrap {

    12 * (time 3.25 volume -10) melody

}

This process is in turn executed by another process, outerwrap. This process executes both the wrap process and the melody itself, and in doing so shifts time, pitch, and voice.

process outerwrap {

    6 * (time 6.125 pitch  4 track  1) wrap

    6 * (time 8.125 pitch -2 track -1) melody time 2

}

Lastly, this process (as well as the melody process) is called by another process, begin. As with outerwrap, shifts are made in time, pitch, and voice. Also, the time dimension is scaled by a factor of four in the execution of the melody process.

process begin {

    8 * (time 24 pitch 2 track  1) outerwrap

    4 * (time 12 pitch 2 track -1) melody tfactor 4

}

This process is the beginning process.

The Complete Score

The entire score is as follows:

start begin

### Spacial Definitions

set volume      100

set scale       (2 2 3 2 3) 50

set tempo       38

set wrapnotes   True

set maxnotes    5000

set duration    1.0

set timerange   (9 230)

set numtracks   10

set wraptracks  True

set pitchrange              (-8 16)

set trackpitchrange     2   (-3 11)

set trackpitchrange     6   (-3 6)

set trackpitchrange     7   (-3 6)

set trackpitchrange     9   (-3 6)

### Process Definitions

process begin {

    8 * (time 24 pitch 2 track  1) outerwrap

    4 * (time 12 pitch 2 track -1) melody tfactor 4

}

process outerwrap {

    6 * (time 6.125 pitch  4 track  1) wrap

    6 * (time 8.125 pitch -2 track -1) melody time 2

}

process wrap {

    12 * (time 3.25 volume -10) melody

}

### Melodic Fragment

process melody {

    note time 0.0 pitch 4 duration 0.5 volume -10

    note time 0.5 pitch 8 duration 0.5 volume  10

    note time 2.0 pitch 4 duration 0.5 volume   0

    note time 3.0 pitch 6 duration 0.5 volume -10

    note time 4.5 pitch 4 duration 0.5 volume -20

    note time 5.5 pitch 3 duration 0.5 volume -30

    note time 6.0 pitch 1 duration 1.0 volume -40

}

[Note: The score used for the recording sets some MIDI-specific values to aid in the production of sound (assigning programs to tracks and setting the pan and master volume of the tracks). These commands do not affect the score produced, and have been omitted for clarity.]

Summary

The piece Opening is composed of one simple seven note fragment and three process rules.  Upon listening, however, it is apparent that there is much going on, melodically, rhythmically, harmonically, and structurally. Truly, much emerges aesthetically from the score and theory.