Tonecycle for Blues Base 30 Hz, 2:3:7 Ensemble Version with 4:3 and 7:6

Tonecycle Base 30 Hz, 2:3:7 consists of the linear superposition of 77 sine wave frequencies, all ascending imperceptibly to fixed frequencies and then descending to the starting frequencies. In this composition, there are eleven groups of sine wave frequency components set in ratios based on the harmonics 2, 3 and 7. Each of the eleven groups has seven sine wave frequency components that have the same starting point. Each of these seven sine wave frequency components gradually separates from each of the other components over time while ascending at slightly different rates of speed, and then descending toward the starting frequencies, infinitely revolving as in circles. These extremely close frequencies and their harmonics constantly produce beat cycles that traverse through a continuum of phase angles.

Since all tones are ascending or descending together, all in fixed ratios to create parallel motion, and since there is no reference tone (drone) or fixed tonic with which to compare, the sense of the pitch shift is practically imperceptible. Instead, the gradual development of distinctive melodic and rhythmic patterns emerges over time as the result of the acoustical phenomenon of phase interference. Nonetheless, each melodic pattern (recognizable sequence of pitches) is infinitesimally higher and faster or lower and slower than the preceding pattern, while the pitch relationships within the pattern remain the same.

In this linear superposition of 77 sine wave frequencies, there is no traditional musical pitch, where pitch is defined to be a specific fixed frequency of at least a minimum duration. Further, although there is no fixed drone in this composition, a tonic is implied because the frequency ratios based on the harmonics 2, 3 and 7 remain invariant while tones are in motion. However, this sense of tonic is very subtle because the sine waves never stand on the lowest points of origin or the highest points of ascent. A frequency with the starting value of 60 Hz ascends 0.0000463 Hz per second and therefore is not in one place long enough to satisfy the definition of a traditional musical pitch.

Originally, the frequencies were programmed to move for six hours from the starting point to the ending point at constant rates. For example, seven frequencies starting at 60 Hz ascended at specific rates to reach 61 Hz, 62 Hz, 63 Hz, 64 Hz, 65 Hz, 66 Hz, 67 Hz in six hours (21,600,000 ms). However, I decided not to use the entire six-hour progression but rather to program the frequencies to circle back to the original starting frequencies after a shorter period of time to avoid including fast repetitive rhythmic combination tone beat patterns, which are eventually generated as part of the phenomenon. For the current version of the Tonecycle Base 30 Hz, 2:3:7, each cycle takes 32 minutes before starting a new cycle. Therefore, in the final composition the seven frequencies at 60 Hz ascend at the same original rate (used in the six hour version) to the following seven frequencies in sixteen minutes:

Starting Frequencies (Hz)	@ 16 minutes (Hz)	@ 6 hours (Hz)
60.0	60.044445	61.0
60.0	60.088890	62.0
60.0	60.133335	63.0
60.0	60.177776	64.0
60.0	60.222221	65.0
60.0	60.266666	66.0
60.0	60.311111	67.0
120.0	120.088890	122.0
120.0	120.177780	124.0
120.0	120.266670	126.0
120.0	120.355552	128.0
120.0	120.444442	130.0
120.0	120.533333	132.0
120.0	120.622222	134.0

The seven frequencies that start at 60 Hz will arrive at 1/2 of the above frequencies at the sixteen-minute point, and the seven frequencies that start at 30 Hz will arrive at 1/4 of the above frequencies at the sixteen-minute point. This process has been the fundamental compositional technique and structural determinant of the Tonecycle series, which I originally composed in 2006-2007. I have since composed numerous pieces using this technique incorporating various harmonic ratios.

Tonecycle Base 30 Hz, 2:3:7 Vocal Version has been used as the underlying cantus firmus-like drone for the live performance. For Vocal Version, I used the sound generated by the 77 sine wave frequencies and their gradual development of distinctive melodic and rhythmic patterns and added six channels of the overlaid voices of three performers, La Monte Young, Marian Zazeela and Jung Hee Choi improvising over the implied tonic in harmonic ratios based on 2, 3 and 7. The performers were asked to hold drones intuitively responding to the imperceptible movement of the tones and to each other. This combination of pitch material generated a remarkable array of harmonics. The relationships of the improvisations to the tones were constantly evolving since all tones are in motion and each melodic pattern is infinitesimally higher and faster or lower and slower than the preceding pattern, while the pitch relationships of the improvisations to the tones remain the same.

For the live performance of Tonecycle for Blues Base 30 Hz, 2:3:7 with 4:3 and 7:6, I added two frequencies to the lower tetrachord: the septimal minor third, 7:6, and the perfect fourth, 4:3, which yield the septimal second, 8:7 between the 7:6 and the 4:3 frequency ratios of the scale. These successive superparticular ratios, 7:6 and 8:7 make the lower tetrachord symmetrical to the upper tetrachord divided by a whole tone, 9:8, such that the tonic, the septimal minor third and the perfect fourth degrees of the lower tetrachord are symmetrical to the perfect fifth, the septimal minor seventh and the octave of the upper tetrachord. These musical proportions of the scale have a close relationship to the ascending form of Raga Bhimpulasi and America’s own Blues.

In 2015 The Sundara All-Star Band premiered Tonecycle for Blues Base 30 Hz, 2:3:7 Ensemble Version with 4:3 and 7:6. Three vocalists—La Monte Young, Marian Zazeela, and Jung Hee Choi—and just intonation fretless guitar and bass—Jon Catler and Brad Catler—will improvise harmonically related frequency ratios accompanied by tabla master, Naren Budhkar.

The Ensemble Version has a parallel structure to Indian traditional raga and consists of three sections that emulate the life and creation cycle based on Hindu thought: alap, ektal vilampit (12-beat slow tempo) and ektal madhyalaya (12-beat medium tempo).

Alap is the slow unmetered exposition section during which the introduction of the pitches and the intervallic ratios of the musical mode take place with subtle shades and characteristic nuances. As the performers improvise, they gradually work their way up the scale, and the mood is developed in a continuous procession to bring out the essence of the music.

The first vilampit composition of Tonecycle for Blues metaphorically venerates death and a new cycle of life. This composition was inspired by a Korean traditional folk ballad “Hanobaeknyeon”. The mood of the original song expresses the sorrow and mournful profundity of death and separation. I took a few melodic lines from Hanobaeknyeon and rearranged these lines within the Tonecycle for Blues modal scale, and structured the rhythm in the traditional Indian tala, ektal vilampit, slow tempo 12-matra cycle, which is a much slower tempo but also parallels to a 12-bar blues.

The second madhyalaya (12-beat medium tempo) composition is a typical 12-bar blues composed by La Monte Young for this performance. The performers improvise over a medium tempo 12-bar cycle with traditional blues licks. This has a very lively, uplifting swing feeling that celebrates life.

Even though the first and the second compositions are in the same modal scale and both are in a 12-matra cycle, they emphasize contrasting moods that complement each other. The first composition articulates the sorrow and longing of separation, but also accepting death as a part of life. The second composition articulates joy and happiness in the release of the soul from the body with the prospect of new freedom through a continuous life cycle.

While traversing the common ground of improvisational phrases rooted in Indian raga, American blues techniques, Korean traditional folk ballads and musical Minimalism, this work creates a highly original sound that is based on just intervals.

Music is a relationship of sounds. In Indian music and all modal music, each pitch of a modal scale is determined in relation to the tonic. In Indian classical music, a pitch is not always a fixed frequency but its relationship to the drone determines the musical meaning of the pitch. This openness and wide range of possibilities allows improvising performers to have some control over the scale and to express subtle microtonal articulations of the pitches of the mode in which the raga is set.

The harmonic series extends beyond the limits of our perception and each set of harmonically related pitches produces a particular set of combination tones that together create a unique musical essence. Amidst the infinite shift of tones in Tonecycle Base 30 Hz, 2:3:7, both the fundamental and its relative pitches in invariant ratios, can be considered isomorphic to the infinite possibilities of a unique essence.