The Gemini Nebula

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.

Background & Technical Details

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 & Licensing

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)


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