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**Posted 31 January 2005, 13:38**

A variation on La Monte Young’s *The Prime Time Twins in the Ranges 576 to 448; 144 to 112; 72 to 56; 36 to 28; with the Range Limits 576, 448, 288, 224, 144, 56, and 28*. An electronic piece written and realized with Scala, blue, and Csound.

Dedicated to La Monte Young in his 70th year.

Duration: 7 minutes 30 seconds.

Young’s *Prime Time Twins* is one of his continuous sine-tone installations. The twins of the title refer to pairs of numbers called “twin primes”: prime numbers that have a difference of two, such as 137 and 139. Young treats the set of twin primes listed in his title as overtones above a subsonic fundamental at 7.5 Hz. The piece consists of these ten pairs of pitches, which cover a five octave range, combined with seven other pitches (multiples of the seventh and ninth partials, the “range limits” of the title). The fundamental does not appear in any octave, but is implied by the resulting combination tones.

In preparing for my piece, I converted the PTT numbers into ratios, essentially reducing them to intervals within a single octave. Then I used Scala to gather these ratios, along with 9/8 and 7/4, into a “scale” (linked below). The fascinating thing when one considers the notes in this way is that it reveals very clearly that the PTTs are grouped into two tight clusters or ranges at the high and low ends of an octave: five pairs are located between 1/1 and 9/8, and the other five pairs are located between 7/4 and 2/1. Here is a table of the PTT “scale”, in ascending pitch order:

Ratio | Cents | Interval |
---|---|---|

1/1 |
0.000 | unison |

521/512 | 30.167 | 521-523 twins |

523/512 | 36.801 | |

269/256 | 85.755 | 269-271 twins |

271/256 | 98.579 | |

137/128 | 117.638 | 137-139 twins |

139/128 | 142.729 | |

281/256 | 161.312 | 281-283 twins |

283/256 | 173.590 | |

569/512 | 182.742 | 569-571 twins |

571/512 | 188.816 | |

9/8 |
203.910 | major whole tone |

7/4 |
968.826 | harmonic seventh |

227/128 | 991.858 | 227-229 twins |

229/128 | 1007.045 | |

461/256 | 1018.348 | 461-463 twins |

463/256 | 1025.842 | |

29/16 | 1029.577 | bottom of 29-31 twins |

59/32 | 1059.172 | bottom of 59-61 twins |

239/128 | 1081.040 | 239-241 twins |

241/128 | 1095.467 | |

61/32 | 1116.885 | top of 59-61 twins |

31/16 | 1145.036 | top of 29-31 twins |

2/1 |
1200.000 | octave |

In my piece, I use all of these pitches within the octave that starts at 240 Hz. The 1/1 and 2/1 are used as drones, as are 9/8 and 7/4, together serving as what Young calls range limits. The other tones enter gradually from low to high within the limits, and then gradually leave. As the texture thickens, the beating between tones forms a complex rhythmic pattern. Each pair of twins is played in stereo, with the pair members on opposite sides, which adds the element of binaural beating. All of the tones are simple sine waves, and no effects are used. The piece was composed using Steven Yi’s excellent program blue, which allowed me to work directly with the PTT scale I made in Scala.

The title *The Gemini Nebula* has several derivations. Gemini, of course, is a reference to twins. I used the word nebula because one of the effects produced by the piece reminds me of the “clouds” in the piano music of Young and Michael Harrison, but since I recently used the word “cloud” for another piece, I decided to use a related word. (By the way, it turns out that there really is an astronomical object called the Gemini Nebula.)

As with my previous piece that takes off from one of La Monte Young’s sine-tone works, I relied on Kyle Gann’s article “The Outer Edge of Consonance: Snapshots from the Evolution of La Monte Young’s Tuning Installations”.

Copyright © 2005, Dave Seidel. Some rights reserved. This work is licensed under a Creative Commons Attribution License.

MP3 (18MB)

blue project (text, 11KB)

Csound unified score file (text, 2KB)

Scala Prime Time Twins scale (text, 307B)

drones, just intonation, la monte young

Copyright © 2004-2014 Dave Seidel. Some rights reserved.

http://mysterybear.net by Dave Seidel is licensed under

Creative Commons BY-NC-ND 3.0 Unported.

http://mysterybear.net by Dave Seidel is licensed under

Creative Commons BY-NC-ND 3.0 Unported.

— 22 February 2005, 11:30 #