*12-minute except from the 32-minute cycle. The lowest frequency in this work is 30 Hz and a good subwoofer is required to reproduce the full range of the work.*

*Tonecycle Base 30 Hz, 2:3:7 Sine Wave Version*

*2012, sound environment: the linear superposition of 77 sine wave frequencies set in ratios based on the harmonics 2, 3 and 7 imperceptibly ascending toward fixed frequencies and then descending toward the starting frequencies, infinitely revolving as in circles, in parallel and various rates of similar motion to create continuous slow phase shift with long beat cycles*

*Tonecycle Base 30 Hz, 2:3:7 **Sine Wave Version* consists of the linear superposition of 77 sine wave frequencies based on the invariant harmonic ratios of 2, 3 and 7, 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 sound interacts with physical objects and other sound waves, and the energy flow of the sine waves is preserved and continues to propagate, the waves interfere with each other at any given point in space and the algebraic sum of this simple linear equation of frequencies and amplitudes creates very complex interference patterns. Depending on the relative phase and the distance each wave has to travel in the space, the placement of the waves varies according to their wavelengths and the phase relationships between the waves also vary spatially.

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 120 Hz ascended at specific rates to reach 122 Hz, 124 Hz, 126 Hz, 128 Hz, 130 Hz, 132 Hz, 134 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 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 120 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) |

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 |

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 |

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.

Since all tones are ascending or descending together, some in fixed ratios to create parallel motion and some not in fixed ratios to create similar 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.

Copyright © Jung Hee Choi 2007-2014