Score Notes for Kenneth Peacock's Pibroch

Pitch and Waveform:

To create the piece, two FM sound sources are required. Both play a frequency of C2 (65.406 Hz), but one is detuned slightly (by about .1 Hz) to create a slowly swirling phase effect. Both operate with a very low Modulation Indexes in the range of 0.4 to 1.4, typically around 0.8. Fc:Fm Ratios (Carrier Frequency to Modulating Frequency) are chosen at random, allowing different combinations of sideband tones to be heard. By restricting these Fc:Fm Ratios to integer values, the sideband notes that result are harmonics of the Carrier Frequency. Since the Modulation Index determines the amplitude of audible sidebands, the low index limits the harmonic spectra to the harmonics adjacent to the modulating oscillator’s frequency. For example, if the modulating oscillator plays the fifth harmonic, and the ModIndex is 0.5, the output will consist of the fourth and sixth harmonics, in addition to the carrier tone.

Each sound source has its own sequencer to trigger these random note pairs. The rate of the sequencer is selected externally. The range of random Fc:Fm indexes is limited to 10, resulting in no higher than the eleventh harmonic. A triangular probability generator is used to weight the pitch range near the center. Occasionally, the same random number occurs in a sequence, resulting in notes which appear to be held for longer duration. This adds to the melodic interest.

Initially, the sequencer of the second voice is turned off, to allow a steady drone. After the third variation, it is started. This sequencer always runs at a slower rate than Voice 1. After Variation 20, it again assumes the role of a stationary drone.

Rhythm:

To achieve a sense of musical phrase, there is a third sequencer which stops and starts the sequencers of the two voices. This sequencer advances to the next variation every thirty-two beats. The voice sequencers have a duty cycle in which they are on for the first twenty-five beats, and hold for the next seven. In general, the beat-length of this sequencer is equal to that of Voice 1. However, when treble meters are used (for example, three against two), the beat rate is 1.5, (and sometimes 3) times the beat length of Voice 1 to accentuate the triplet feel. The rate of this sequencer is also selected externally.

Timbre:

By changing the Modulation Index ever so gradually, the timbre, and to some extent, the dynamics, of the piece can be given an overall shape. As implemented by the composer, a MIDI keyboard is used to increment the ModIndex in .05 steps per semitone. This way, notes on the keyboard can be struck in a chromatic sequence to gradually change the timbre. Additionally, a ramp generator can be used to increase and decrease this index. Increasing the index from 0.8 to 1.4 will create the effect of the sound source moving closer to the listener, while decreasing it from 0.8 to 0.4 (or less) will cause the source to recede.

Location:

The most interesting effects result if the two voices are "hard-panned" to the left and right speakers. Since there is an inherent, albeit slight, pitch difference between the two carrier oscillators, this wide panning exploits the slow phase shift that occurs. This is evocative of the phasing effects that might occur among a group of bagpipes droning. The piece will also benefit from a slight amount of reverberation. A bright reverb of moderate length, such as a chamber or plate reverb, is recommended.

Where surround sound playback is available, the difference channel (that is, the left channel minus the right channel) may be routed in mono to both rear channels. A mono sum of the left and right channels may be also routed to the center channel. Care must be taken, however, to prevent these channels from dominating the left and right. Properly set up, the additional channels will add a sense of motion between front and back.

Dynamics:

The piece begins with a moment of stasis, with both voices droning. This is meant to evoke the drone of a set of bagpipes. While a player can stop the flow of air to the chanter pipe (on which the melody is played), the drone pipes play continuously, and even the chanter will play non-stop, once the piece is underway. Likewise, the piece ends in a tableau. Instead of mimicking the abrupt starting and stopping of the drones as heard on the acoustic instrument, I have chosen to fade the drone in and out, so as not to interrupt the overall mood of the piece. Other than this, there are no dynamic changes. However, as mentioned, the timbre changes caused by gradually manipulating the Modulation Index give the ear the effect of increasing and decreasing loudness.

Compositional Structure:

This is the table of beat-lengths for each of the respective sequencers:

The piece is loosely modeled after a form for solo performer used in the Scottish Highland bagpipe music tradition, the Pibroch (in Gaelic, Piobreachad), in which a stately, melodic theme is repeated over a drone. In the Pibroch, it is the ornamentation of the melody that is the musical focus of the form. This ornamentation gradually evolves from simple to complex, and then returns to simplicity.

Since the Pibroch is slow and the musical materials used are minimal, the overall effect is somewhat solemn and contemplative. Pibrochs are often named for a fallen hero, but they are frequently named in honor of an event or a mentor, such as the patronizing laird, or a piping master. I have titled this piece in honor of Dr. Kenneth Peacock, Director of the Music Technology Program at New York University. He has broadened my compositional horizons considerably and without his input, this piece would not have been possible.