*Sound System Suggestions for Playback:
Since the lowest frequency in this work is 30 Hz, a very good pair of subwoofers is required to reproduce the full range of the work. Ideally, the sound system should be set to play at least 100 dB at the maxima of the standing wave antinodes.


This recording is a three-hour selection from the 24-hour full-length composition The Tone-field: Perceptible Arithmetical Relations in a Cycle of Eight Indian Raga Scale Permutations. As its title implies, the intervallic frequency relationships in this three-hour version were organized to create a musical equivalent of the sunset on the summer solstice day—the high position of the sun slowly setting as twilight passes into the evening. The summer solstice occurs once a year between June 20 and June 22 in the northern hemisphere, and sees the sun reaching its highest point. On this, the longest day of the year, the transition from day to night is also at its most extended.

There is an intrinsic and isomorphic relationship between sound and number, which can be precisely and reciprocally traversed in time. The ancient Indians and Greeks recognized music as numbers expressed in time and established a ratio theory where the tonal relation fundamentally corresponds with the number field, algebraic yantras. The Tone-field is a tonal-arithmetic frame of reference that converts the space into an audibly perceptible number field. The superimposed stationary standing waves in the space manifest the fundamental and nonlinear nature of time. Time and space are simultaneous and thus may be expressed in the equivalent frame. As time can only be measured through periodic phenomena, the periodicity of a sine wave has an intimate relation to time, through which its basic form can be expressed as a function of time (t); y(t) = A sin(2πft + Φ) = A sin(wt+Φ ). In this sound environment, space and the musical structure are concomitant such that the space itself becomes the musical scale. The listener’s body is completely enveloped by sound and shares its dimensions with the numerical structure of the present intervallic ratios. Any movement of one’s body causes a modulation of the chords in the space. Our bodies are connected and synchronized through sound. One’s relative motion not only changes the positional states but also enables the listener to experience the nonsequential sense of time in the space.

The full 24-hour version of The Tone-field orbits through eight modal scales based on ancient Indian raga systems. In the full composition, a day is divided into eight parts: pre-dawn (early morning), sunrise, morning, midday, afternoon, sunset, evening, and midnight. This 24-hour cycle consists of 16 distinctive sections: eight modal scale sections and eight transition sections. Each set of the modal scale comprises 45 to 64 continuous sine-wave frequencies precisely tuned to specific ratios stretched across nine octaves that are sustained as a simultaneous chord. During the transition sections, one set of sustained chords is superimposed upon the subsequent set of sustained chords, allowing the listener to experience the complex interrelationship of these two sets of intervallic frequency ratios as one set phases out and the other phases in over a period of time. The duration of each section, both of sustained chords and transitions, is relative to the length of the day. The 24-hour cycle is recalculated daily to select a modal scale appropriate for the time of day corresponding to the movement of the sun in a particular geographical space. All tones in the eight modal scales were born from the natural harmonic series of the same fundamental frequency and are mathematically related by whole number ratios. Therefore, the fundamental frequency and its multiples of first, second and higher-order combination tones become audibly contextualized and increasingly elaborate the musical meaning of each tone as the work progresses.

Due to the precise tuning of the intervals in just intonation, when presented at high volume, the complex intervallic ratios and their combination tones generate extremely rich tonal activity in the space and in the ear. As such, The Tone-field was originally written as a time-and-space-specific sound environment. Its first installation premiered in 2017 in the MELA Dream House, New York, as part of my multimedia installation, Ahata Anahata, Manifest Unmanifest XI, a series of environmental compositions presented with video, evolving light-point patterns, drawings, incense, performance and sound invoking the concept of Manifest Unmanifest. On August 17, 2017, for the first time, Dream House was open for a continuous 24 hours to experience a full cycle of The Tone-field.

I am deeply indebted to La Monte Young, from whom I learned everything about the most profound nature of sound. Young certainly comprehended and exploited standing waves, one of the most mysterious behaviors of sound within enclosed spaces. Continuous periodic composite waveforms and the reflection of their sounds create stationary patterns within a space, as standing waves do not appear to move in any direction but instead fabricate spatial regions of nodes (minimum amplitude) and antinodes (maximum amplitude) resulting from the interference of these sound waves.

The most exciting aspect of releasing the album The Tone-field: Perceptible Arithmetical Relations, Sunset on the Summer Solstice, New York for me is "releasing" this work publicly. The experience and perception of the work now become a relativistic and private process for the listeners. The listener uses the body, the whole body, as an instrument interacting with the sound and also uses the body as a means of perception. I sometimes visited my sound environment to observe how the audience is experiencing this work. I found it fascinating, wild and imaginative! Each element in the space, such as the dimensions of the room, angles of the speakers, objects, movement of the listener, etc., all affect the resulting structure of the standing waves and the perception of the chords. In The Tone-field one may experience the inseparable nature of the space-time continuum as modern relativistic physics informs us. One’s spatial movement can become an aural exploration, and aural perception can function as the coordinates of one’s spatial movement.

© Jung Hee Choi 2017, 2021

*included with purchase is a PDF of the original accompanying booklet*