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The Study 21 is not based on a continuum acceleration process, but on very fast discrete, high resolution, acceleration process. The 21’s roll is the first one Conlon marked with template lines. (Earlier Studies were punched using the rhythm scale on the machine, based on octave-oriented traditional music values (wholes, halves, quarters...)  I checked out all the original rolls in his studio in Mexico city in 1993:

 

Rolls without template marks:

1, 2ab, 3abcde, 4, 5, 6, 7, 8, 9,10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

 

Marked rolls: 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 40ab, 41abc, 43, 44, 46, 47, 50, tango?

 

In the Studio 21 Conlon used for the first time his new punching machine. This machine allowed te composer to freely move the “time” car, avoiding the “octave” time regime of wholes, halves, quarters, etc. (Figs. 1 and 2).

 

Figure . 1

 

The old punching machine

A: the "rhythm car" is attached to a fixed duration scale, octave-oriented:

wholes, quarters, eights. One represents the shortest value possible. 

B : The pitch car is attached to chromatic-scale values.

C: The paper-roll.

 

 

Figure  2:

 

The new punching machine

A : A thin steel wire is part of the machine. Each line of a template on the roll (C) should coincide with the wire before punching.

B : The pitch car is attached to chromatic scale values.

D : The paper-roll.


Conlon used a common “reference unit” template on the roll for both voices. We can associate the distance between two lines with the number "1". (Note: Conlon defined a "bar" each 12 lines). The composer also used an "in-between" value  (“0.5”, the F sharp falls between the lines, see figure), so that the real resolution of the 21 is 0.5 not “1”. The use of a "0.5" value proves the use of the new machine.

In terms of tempo relationships, both Gann’s and Tenney’s descriptions were made, I think, from the final score and therefore are not quite precise.

The composer used a single tempo-template for both voices: Both voices have the same "time resolution”, and this resolution is very high. Nancarrow manage to create acceleration or de-acceleration evolutions by assigning different distances between notes, departing from the minimum resolution value, and sometime less. What is important here, also, is the speed and the perception factors. We don’t realize the terrace effect here because of both, the high speed of the notes in the fast texture (due to our perception's limitation and averaging-capacity, we tend to convert discontinuous information into continuous information, just like when we see a video or film and do not perceive the frame-rate, but a continuous movement), and the long distance between notes, in the slower texture (due to our pattern-recognition-oriented perception, we tend to "pixelate" continuous information and create recognizable patterns with it). This canon is a good example how our perception of music works, related to our perception’s physical limitations and wonderful capacity of synthesis. Nancarrow's genius manages to play with both at the same time in this piece

The philosophical conception of the piece was a brake-point in his work, a new esthetical thought, a  new vision which required a new operational context, a new machine.

By the way: The Wergo’s 1990 edition have minute mistakes, I don’t know if Wergo reconsidered this in further editions. VOL II, cd 2, the real track-to-piece numbering is:

 

Track 1: Study 4

Track 2: Study 5

Track 3: Study 6

Track 4: Study 14

Track 5: Study 22

Track 6: Study 26

Track 7: Study 31