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The Studies 37 and 21 for Player Piano are perhaps Nancarrow's most impressive and well known pieces.  Due to its importance, I decided to clear out some issues regarding the 21. 

 

Nancarrow punched this study two times: the  first one he departed from a punching score based on the old punching machine but before the punching process was finished, he realized that the rhythm pinions didn't fit with the roll lenght and the desired performance speed for this studio (1). Later on he punched a second roll, using the new punching machine. Here the main differences between both punching machines.

 

 
Old design   New design
Pitch and Rhythm are based on discrete scales. Both pitch and rhythm cars are suited with fixed-position pinions.   Only pitch is based on pinions. A cable is attached and the tempo marks are draw on the paper roll itself.

 

 

The old design was based on octave-oriented, Western-music rhythm notation values. The rhythm car was "attached" to

these rhythm pinions. In-between values were not possible.

 

 

 

Old design with fixed rhythm values to be seen at

the left side. In this photo the machine was already

adapted with the steel cable. (3)

 

New design: very simple but efficient one: a steel cable

at 90° to be used as reference to punch each different

tempo layer even with irrational tempo ratios. (3)

 

Nancarrow's player piano Studies may be divided indeed in two "punching-machine" groups: Rolls with no template tempi marks (Nancarrow wrote these pieces with the usual rhythm values) and rolls with tempo template markings on the roll. I personally identified both groups around 1994 in his studio in Mexico City. These are my results (they coincide with Jürgen Hocker findings.)

 

Rolls without any rhythm scale (the scale was built in the punching machine)

1, 2ab, 3abcde, 4, 5, 6, 7, 8, 9,10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
Rolls with marked rhythm templates or tempi layers:

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

 


 

 

The Study 21

 

 

The study is based in two kinds of acceleration priciples: a pitch acceleration and a tempo acceleration.  The pitch acceleration is conceptual in this case. This piece  is a 2-voice canon using a single 54-notes melody which "accelerates": by each repetition the melody looses the final note and therfore becomes shorter and in fact,  accelerates. Red and blue lines above become shorter each time.


"... Then what I do is I take the roll and I draw out of that these tempo relations with the smallest unit, lets say a 16th note or whatever..." (Interview with Charles Amirkahnian, Radiom.org, "Speaking of Music Conlon Nancarrow", 1984)

Conlon used a common Time-Unit (TU) on the roll for both voices. Lets arbitrary associate the distance between two of the illustrated lines with the number "1" as TU.  (Note: Conlon defined a "bar" each 12 TUs). The composer used also an in-between “0.5 value.  (Observe how the F-sharp falls between the lines and how often is this "0.5" value used in the Study. Table below, ".5" values).  If  the Study 21 were punched with the old machine using the shorter value (or highest resolution), this "in-between value" would be impossible to punch. There is the possibility Conlon used the old machine for this Study only if he decided to use the machine highest resolution for exceptional notes like this one, but considering the hyper-massive quantity of notes to be punched, this would be an unpractical decision. Conlon punched this study twice, I ignore the reasons.


In terms of tempo relationships, both Gann’s and Tenney’s descriptions were made, I think, from the final score using arbitrary measurements. The actual tempo ratios displayed in Study 21 can be seen below:  (Thanks to Bertram Hansum for twice-checking these numbers). Values in parenthesis, right column: how many times does this ratio appear in this study? Outstanding symmetries are to be seen at the first part of the studio, before the "coda", which is more "musical"  than systemic, less consequent, more climatic.  The two  "o.75" values  at the coda are exceptional and might be a mistake.
 

Time-Units ("1") relationship

Slow voice begining U.T.

Fast voice begining U.T

Reflection symmetry 1 Reflection symmetry 2

Actual Ratios

32:3

16

1.5

 

32:3

32:3 (2)

31:3

15.5

1.5

 

31:3

31:3 (2)

31:4

15.5

2

 

31:4

31:4 (2)

30:4

15

2

 

15:2

15:2 (2)

30:5

15

2.5

 

6:1

6:1 (2)

29:5

14.5

2.5

 

29:5

29:5 (2)

29:6

14.5

3

 

29:6

29:6 (2)

28:6

14

3

 

14:3

14:3 (2)

28:7

14

3.5

 

4:1 )

4:1 (2)

27:7

13.5

3.5

 

27:7

27:7 (2)

27:8

13.5

4

 

27:8

27:8 (2)

26:8

13

4

 

13:4

13:4 (2)

26:9

13

4.5

 

26:9

26:9 (2)

25:9

12.5

4.5

 

25:9

25:9 (2)

25:10

12.5

5

  5:2

5:2 (2)

24:10

12

5

  12:5

12:5 (3)

24:11

12

5.5

Symmetry Anomaly  

24:11 (1)

23:11

11.5

5.5

23:11  

23:11 (3)

23:12

11.5

6

23:12  

23:12 (2)

22:12

11

6

11:6  

11:6 (2)

22:13

11

6.5

22:13  

22:13 (2)

21:13

10.5

6.5

21:13  

21:13

21:14

10.5

7

3:2  

3:2

20:14

10

7

10:7  

10:7

20:15

10

7.5

4:3

 

4:3

19:15

9.5

7.5

19:15

 

19:15

19:16

9.5

8

19:16  

19:16

18:16

9

8

9:8  

9:8 (2)

17:18

8.5

9

17:18  

17:18 (2)

JOINT   17:17

8.5

8.5

— Reflection Line  

1:1 (1)

18:17

8.5

9

17:18  

18:17 (2)

18:16

8

9

9:8  

9:8 (2)

19:16

8

9.5

19:16  

19:16

19:15

7.5

9.5

19:15  

19:15

20:15

7.5

10

4:3  

4:3

20:14

7

10

10:7  

10:7

21:14

7

10.5

3:2  

3:2

21:13

6.5

10.5

21:13  

21:13

22:13

6.5

11

22:13  

22:13 (2)

22:12

6

11

11:6  

11:6  (2)

23:11

5.5

11.5

23:11  

23:11 (3)

23:11

5.5

11.5

23:11  

23:11 (3)

24:10

5

12

Symmetry Anomaly  

12:5 (3)

24:10

5

12

  12:5

12:5 (3)

25:10

5

12.5

  5:2

5:2 (2)

25:9

4.5

12.5

 

25:9

25:9 (2)

26:9

4.5

13

 

26:9

26:9 (2)

26:8

4

13

 

13:4

13:4 (2)

27:8

4

13.5

 

27:8

27:8 (2)

27:7

3.5

13.5

 

27:7

27:7 (2)

28:7

3.5

14

 

4:1

4:1 (2)

28:6

3

14

 

14:3

14:3 (2)

29:6

3

14.5

 

29:6

29:6 (2)

29:5

2.5

14.5

 

29:5

29:5 (2)

30:5

2.5

15

 

6:1

6:1 (2)

30:4

2

15

 

15:2

15:2 (2)

31:4

2

15.5

 

31:4

31:4 (2)

31:3

1.5

15.5

 

31:3

31:3 (2)

32:3

1.5

16

 

32:3

32:3 (2)

CODA

 

 

   

 

32:2

1

16

   

16:1 (1)

34:2

1

17

   

17:1 (1)

68:3

0.75

17

   

68:3 (1)

24:1

0.75

18

   

24:1 (1)

36:1

0.5

18

   

36:1 (1)

38:1

0.5

19

   

38:1 (1)

40:1

0.5

20

   

40:1 (1)

42:1

0.5

21

   

42:1 (1)

44:1

0.5

22

   

44:1 (1)

44:1

0.5

22

   

44:1 (1)

46:1

0.5

23

   

46:1 (1)


Nancarrow managed to create acceleration or de-acceleration by assigning different distances between notes, departing from the minimum resolution value, and sometimes half. 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.


(1) Personal conversations with Conlon Nancarrow, Mexico City, Ca. 1993.

(2) Gann, Kyle, The music of Conlon Nancarrow, Cambridge Universtity Press, 1995. Tenney, James, "Study # 21", in "C.N. Studies for player piano", Wergo, wer60166/67 50, Booklet, p.p. 12-14),

(3) Photos by Jürgen Hocker and Jörg Borchardt, take form Jürgen Hocker's website.