1. Understanding the score of PNO2
An introduction to the structural background of the piece and instructions on how to prepare a version for performance.
Rob Canning 2009

2. These instructions as well as a pdf version of the instructions and a copy of the score are available for download from:

3. It is also performable from a digital projection.
The score in hardcopy is printed on a single sheet of A1 paper – if you would like to be sent a copy please contact :
It is also performable from a digital projection.

4. Soloist and live electronics Soloist, live electronics and tape.
The piece is performable in many different configurations – it can be for:
Soloist
Soloist and Tape
Soloist and live electronics
Soloist, live electronics and tape.
Multiple performers
Multiple performers and tape.
Multiple performers, live electronics and tape.

5. Purely acoustic versions are also possible...
All equipment needed to execute a version employing, tape and/or live electronics, and/or spatialised surround sound can be provided by the composer (based London UK).
Purely acoustic versions are also possible...

6. The score is a semi-indeterminate score where the performer/performers prepares a version of the piece in advance of a perfomance...

7. There are many levels of freedom you have as a performer but in order for the piece to work you must have an understanding of the rules of the game...

8. To undertand how the piece works you need to understand a little bit about Magic Squares....

9. A magic square is a grid of numbers where the sum of all the colums, rows and diagonals all add up to the same number...

10. 4 9 2 3 5 7 8 1 6 3x3 “Lo Shu” Magic Square Horizontal Vertical
Diagonal
All sum to 15
This is know as the magic sum.

11. magic numbers control duration4 9 2 3 5 7 8 1 6
The magic numbers control the duration of the piece.
Lets say each number represents seconds or pulses.
Each horizontal, vertical or diagonal can be seen as a structural unit of equal duration.
15 seconds

12. 4 9 2 3 5 7 8 1 6 Each cell in the square contains a musical fragment
These musical fragments are played for the duration given by the number in that square 4 9 2 3 5 7 8 1 6

13. 2 performers playing from the same square will synchronise every 3 units4 9 2 3 5 7 8 1 6
If two performers play different routes they will change cells at different times but will sychronise every 3 units or 15 seconds
Or if one performer plays with a 15 second delay effect then the start of each route of three will synchronise.

14. We use a 8x8 magic square
3x3 gives us only 9 pieces of musical material and short phrases of 15 seconds
8x8 gives us 64 pieces of material and a magic sum of seconds
4 mins 20 seconds

15. Some magic squares are more interesting than others52 61 4 13 20 29 36 45 14 3 62 51 46 35 30 19 53 60 5 12 21 28 37 44 11 6 59 54 43 38 27 22 55 58 7 10 23 26 39 42 9 8 57 56 41 40 25 24 50 63 2 15 18 31 34 47 16 1 64 49 48 33 32 17
Many different types of magic square
This one is the Franklin magic square and has many unique ways it can be navigated
Horizontal = yes
Vertical = yes
Diagonal = no
Many other ways...

16. Other possible routes...

17. Bent diagonals 52 61 4 13 20 29 36 45 14 3 62 51 46 35 30 19 53 60 5 12 21 28 37 44 11 6 59 54 43 38 27 22 55 58 7 10 23 26 39 42 9 8 57 56 41 40 25 24 50 63 2 15 18 31 34 47 16 1 64 49 48 33 32 17

18. Bent diagonals 52 61 4 13 20 29 36 45 14 3 62 51 46 35 30 19 53 60 5 12 21 28 37 44 11 6 59 54 43 38 27 22 55 58 7 10 23 26 39 42 9 8 57 56 41 40 25 24 50 63 2 15 18 31 34 47 16 1 64 49 48 33 32 17

19. Bent diagonals 52 61 4 13 20 29 36 45 14 3 62 51 46 35 30 19 53 60 5 12 21 28 37 44 11 6 59 54 43 38 27 22 55 58 7 10 23 26 39 42 9 8 57 56 41 40 25 24 50 63 2 15 18 31 34 47 16 1 64 49 48 33 32 17

20. Bent diagonals 52 61 4 13 20 29 36 45 14 3 62 51 46 35 30 19 53 60 5 12 21 28 37 44 11 6 59 54 43 38 27 22 55 58 7 10 23 26 39 42 9 8 57 56 41 40 25 24 50 63 2 15 18 31 34 47 16 1 64 49 48 33 32 17

21. Bent diagonals with wraparound52 61 4 13 20 29 36 45 14 3 62 51 46 35 30 19 53 60 5 12 21 28 37 44 11 6 59 54 43 38 27 22 55 58 7 10 23 26 39 42 9 8 57 56 41 40 25 24 50 63 2 15 18 31 34 47 16 1 64 49 48 33 32 17

22. Any two 2x2 groupings 52 61 4 13 20 29 36 45 14 3 62 51 46 35 30 19 53 60 5 12 21 28 37 44 11 6 59 54 43 38 27 22 55 58 7 10 23 26 39 42 9 8 57 56 41 40 25 24 50 63 2 15 18 31 34 47 16 1 64 49 48 33 32 17

23. 2x2 with wraparound 52 61 4 13 20 29 36 45 14 3 62 51 46 35 30 19 53 60 5 12 21 28 37 44 11 6 59 54 43 38 27 22 55 58 7 10 23 26 39 42 9 8 57 56 41 40 25 24 50 63 2 15 18 31 34 47 16 1 64 49 48 33 32 17

24. Top corners units 52 61 4 13 20 29 36 45 14 3 62 51 46 35 30 19 53 60 5 12 21 28 37 44 11 6 59 54 43 38 27 22 55 58 7 10 23 26 39 42 9 8 57 56 41 40 25 24 50 63 2 15 18 31 34 47 16 1 64 49 48 33 32 17

25. ...and bottom corners 52 61 4 13 20 29 36 45 14 3 62 51 46 35 30 19 53 60 5 12 21 28 37 44 11 6 59 54 43 38 27 22 55 58 7 10 23 26 39 42 9 8 57 56 41 40 25 24 50 63 2 15 18 31 34 47 16 1 64 49 48 33 32 17

26. Four corners plus any 2x2 52 61 4 13 20 29 36 45 14 3 62 51 46 35 30 19 53 60 5 12 21 28 37 44 11 6 59 54 43 38 27 22 55 58 7 10 23 26 39 42 9 8 57 56 41 40 25 24 50 63 2 15 18 31 34 47 16 1 64 49 48 33 32 17

27. The score is an 8x8 grid...

28. You navigate your way though the musical score based on the routes allowed by the magic square

29. As a performer you choose which routes you take through the magic square / 8x8 grid

30. You decide how long the piece is going to be by deciding how many routes you choose to play.

31. This is done BEFORE a performance.
You must spend a some time preparing your own version of the piece.

32. Each route comprises 8 cells of music...

33. Once you have decided on how many and which routes you will play you must calculate the timings and mark them into your score as stopwatch cues.

34. More about this later...

35. The score is made up of 64 “cells” here is an examle of one cell from the score:

36. There are 8 distinct types of material in the piece – each row of the grid employs a similar mode of playing...

37. There are detailed instructions on how to approach the material in the pdf version of the instructions.... here I will only deal with how the piece is structured.

38. So far we have a score comprising 64 cells of musical material
Here is the score -->

40. And here is an example of one of the cells:

42. How we move from one cell to another is based on the possible routes through this type of magic square...

43. 52 61 4 13 20 29 36 45 14 3 62 51 46 35 30 19 53 60 5 12 21 28 37 44 11 6 59 54 43 38 27 22 55 58 7 10 23 26 39 42 9 8 57 56 41 40 25 24 50 63 2 15 18 31 34 47 16 1 64 49 48 33 32 17

44. 52 61 4 13 20 29 36 45 14 3 62 51 46 35 30 19 53 60 5 12 21 28 37 44 11 6 59 54 43 38 27 22 55 58 7 10 23 26 39 42 9 8 57 56 41 40 25 24 50 63 2 15 18 31 34 47 16 1 64 49 48 33 32 17

45. 52 61 4 13 20 29 36 45 14 3 62 51 46 35 30 19 53 60 5 12 21 28 37 44 11 6 59 54 43 38 27 22 55 58 7 10 23 26 39 42 9 8 57 56 41 40 25 24 50 63 2 15 18 31 34 47 16 1 64 49 48 33 32 17

46. 52 61 4 13 20 29 36 45 14 3 62 51 46 35 30 19 53 60 5 12 21 28 37 44 11 6 59 54 43 38 27 22 55 58 7 10 23 26 39 42 9 8 57 56 41 40 25 24 50 63 2 15 18 31 34 47 16 1 64 49 48 33 32 17

47. 52 61 4 13 20 29 36 45 14 3 62 51 46 35 30 19 53 60 5 12 21 28 37 44 11 6 59 54 43 38 27 22 55 58 7 10 23 26 39 42 9 8 57 56 41 40 25 24 50 63 2 15 18 31 34 47 16 1 64 49 48 33 32 17

48. 52 61 4 13 20 29 36 45 14 3 62 51 46 35 30 19 53 60 5 12 21 28 37 44 11 6 59 54 43 38 27 22 55 58 7 10 23 26 39 42 9 8 57 56 41 40 25 24 50 63 2 15 18 31 34 47 16 1 64 49 48 33 32 17

49. 52 61 4 13 20 29 36 45 14 3 62 51 46 35 30 19 53 60 5 12 21 28 37 44 11 6 59 54 43 38 27 22 55 58 7 10 23 26 39 42 9 8 57 56 41 40 25 24 50 63 2 15 18 31 34 47 16 1 64 49 48 33 32 17

50. 52 61 4 13 20 29 36 45 14 3 62 51 46 35 30 19 53 60 5 12 21 28 37 44 11 6 59 54 43 38 27 22 55 58 7 10 23 26 39 42 9 8 57 56 41 40 25 24 50 63 2 15 18 31 34 47 16 1 64 49 48 33 32 17

51. 52 61 4 13 20 29 36 45 14 3 62 51 46 35 30 19 53 60 5 12 21 28 37 44 11 6 59 54 43 38 27 22 55 58 7 10 23 26 39 42 9 8 57 56 41 40 25 24 50 63 2 15 18 31 34 47 16 1 64 49 48 33 32 17

52. 52 61 4 13 20 29 36 45 14 3 62 51 46 35 30 19 53 60 5 12 21 28 37 44 11 6 59 54 43 38 27 22 55 58 7 10 23 26 39 42 9 8 57 56 41 40 25 24 50 63 2 15 18 31 34 47 16 1 64 49 48 33 32 17

53. 52 61 4 13 20 29 36 45 14 3 62 51 46 35 30 19 53 60 5 12 21 28 37 44 11 6 59 54 43 38 27 22 55 58 7 10 23 26 39 42 9 8 57 56 41 40 25 24 50 63 2 15 18 31 34 47 16 1 64 49 48 33 32 17

54. The duration each cell is played for is determined by the number in that cell....

55. In this example the chordal material is played for 24 seconds (or pulses)

56. As well as the main material each cell has a piece of introductory material called the magic note (MN)...

57. Each cell has a magic note...
If we add a number on to each cell the system still works
In this case we have added 10 to all cells 14 19 12 13 15 17 18 11 16

58. Each cell has a magic note...14 19 12 13 15 17 18 11 16
In the context of the score this means we can add some extra material to each cell
An event at the start of each cell (the magic note)
And silence at the end of each cell

59. We can see the magic note in the upper left corner
the pause is indicated by text at the end of the cell
In this case we have added 8 seconds on to each unit, 4 for the magic note and 4 for the end pause

60. YOU decide how to articulate this note, it could be, for example:
Played by you on an other instrument
Could be marked by striking a pitched gong or crotale
You could sing this note
You decide...
The only rule is that the magic note must stand apart significantly from the main material and must use the pitch indicated

61. It is the synchronisation of these magic notes that defines the structural outline of the composition
Due to the magical nature of the square, after every 8 cells played all the musicians involved will perform their magic note at the same time
In versions with tape and//or live electronics this synchronisation of elements will also occur

62. The magic note duration may change every 8 units.
Consider the structural building potential of this when making your version.
This will become clearer when we look at an example...

63. An example...

64. A version that uses three routes (each route is 8 cells long) with a magic note value of 10 seconds and a pause value of 5 seconds.

65. The first 8 units will be the four corners and the central 2x2 ...

66. 52 61 4 13 20 29 36 45 14 3 62 51 46 35 30 19 53 60 5 12 21 28 37 44 11 6 59 54 43 38 27 22 55 58 7 10 23 26 39 42 9 8 57 56 41 40 25 24 50 63 2 15 18 31 34 47 16 1 64 49 48 33 32 17

67. 1 2 6 7 5 8 4 3 3

68. From here on we will discuss rows and colums of the score like this:
row/column
1/1 = first row, first column i.e top left
1/8 first row, last column i.e. top right
etc.

69. This will be all more clear when you look at the paper documentation – for now have a quick look at some of these calulations...

70. Preparing a version: Play 1/1 for 52” 1/8 for 45” 8/8 for 17”61 4 13 20 29 36 45 14 3 62 51 46 35 30 19 53 60 5 12 21 28 37 44 11 6 59 54 43 38 27 22 55 58 7 10 23 26 39 42 9 8 57 56 41 40 25 24 50 63 2 15 18 31 34 47 16 1 64 49 48 33 32 17
Play 1/1 for 52”
1/8 for 45”
8/8 for 17”
1/8 for 16”
5/4 for 10”
4/4 for 54”
4/5 for 43”
5/5 for 23”

71. We must also add in the durational value of the magic note (MN )and the pause (P)

72. Add in the magic note (MN) and pause values you have chosen
Play the MN of 1/1 for 10”
Play cell 1/1 for 52”
Pause for 5 seconds
Play the MN of 1/8 for 10”
Play 1/8 for 45”
Play the MN of 8/8 for 10”
8/8 for 17”
1/8 for 16”
Etc. etc.

73. Calculating the duration:
Magic sum = 260” = 4 minutes 20 seconds
Magic note = 10” Pause = 5”
Each group of 8 cells has 8 MN and 8 pauses
= 15 * 8 = 120” = 2 minutes
So we add 2mins onto each group of 8”
4'20” + 2' = 6' 20”
So each group of 8 units will take:
6minutes and twenty seconds
In this example we choose to have 3 of these 8 units sections
3 * 6' 20” = 19'
Total duration based on these decisions:
19 minutes

74. Once you have decided on the way you will make your piece then you can add up all the values and calculate your stopwatch settings...
Here are the timings calculated for the first 8 units we chose earlier...

75. 1 2 6 7 5 8 4 3 3

76. Example timings for first 4 cells...10
00:00:00
Play MN of 1/1 10” 52
00:00:10
Play cell 1/1 for 52” 5 62
00:01:02
Pause 5” 67
00:01:07
Play MN of 1/8 10” 45 77
00:01:17
Play cell 1/8 for 45”
122
00:02:02
127
00:02:07
Play MN of 8/8 10” 17
137
00:02:17
Play cell 8/8 for 17”
154
00:02:34
159
00:02:39 16
169
00:02:49
Play cell 8/8 for 16
185
00:03:05

77. … and for the first 8 cells ...10
00:00:00 52
00:00:10 5 62
00:01:02 67
00:01:07 45 77
00:01:17
122
00:02:02
127
00:02:07 17
137
00:02:17
154
00:02:34
159
00:02:39 16
169
00:02:49
185
00:03:05 10
190
00:03:10
200
00:03:20 5
210
00:03:30
220
00:03:40 54
274
00:04:34
279
00:04:39
289
00:04:49 43
332
00:05:32
337
00:05:37
347
00:05:47 23
370
00:06:10
375
00:06:15

78. Blank timing tables are provided with the score...

79. When you have done the timings you can then mark these into the score

80. You might prefer to have the score projected onto a large screen with a data projector where it can be viewed by all performers (and audience)...
On your instrument you might just have the timing sheet and a stop watch rather than the large score which can impede lines of vision between you and the other perfomers.
In this case you dont mark the timings into the score but only on your timing sheet.

81. Now look at the paper documentation on:
You will find there everything you need in order to prepare a version.
If you are interested in preparing a verison and doing a performance or making a recording please contact me: