VISUAL REFERENCE FOR MUSICIANS

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1 VISUL RRN OR MUSIINS Y MILS OKZKI 2014 ITION

2 TWO NOT STRUTURS The intervallic relationship between any two different pitches within an octave will form one of these 6 shapes.

3 THR NOT STRUTURS The intervallic relationship between any three different pitches within an octave will form one of these 19 shapes.

4 OUR NOT STRUTURS The intervallic relationship between any four different pitches within an octave will form one of these 43 shapes.

5 TL O MLOI LMNTS XPLNTION: Pitches are shown as a chromatic circle, ascending in a clockwise direction. One circle represents all transpositions - pitches can be assigned in any rotation. or example: b b b b b b... and so on. b b b b b b b b b ach pitch collection is shown as a shape formed by connected dots. major triad looks like this: This figure represents all transpositions of the same intervallic relationships: & b b # n n b b # n n n bb b nn n b b 5th # n n b root # n # 3rd ll inversions and octave displacements are considered equivalent. The same figure above also represents any of these, in any transposition, or any other larger range of pitches: & Pitch sets can be simultaneous (chords) or sequential (melodic). The same figure above also represents any of these, in any transposition, in any rhythm: & ll unique pitch formations in 12-Tone qual Temperament containing a number of pitches from 0-12 are listed. Only one rotation of any formation is listed. Rotation is equivalent to transposition. or example, is listed, but its rotation is redundant and not listed. The total of 352 pitch formations are derived from 122 prime forms (this includes the empty set, with no pitches). Prime form is the arrangement of pitches starting at 12:00 on the circle that has the smallest intervallic span. prime form can produce three other formations through these operations: 1) Reflection (reversing the intervallic order) 2) omplement (the negative space of the Prime orm) 3) Reflected omplement (the negative space of the Reflection, or the Reflection of the omplement) ach row of the table shows a Prime orm and its related formations. If one of the operations does not produce a new formation, the space is left blank. or example, upon reflection makes which is the same as the original formation in rotation. (this is the case with any symmetrical shape) nd the complement of is which, when rotated, is the same as the reflection: (this can only happen with six note formations)

6 PRIM ORM RLTION OMPLMNT RLT OMPLMNT 0 pitches 12 pitches 1 pitch empty set chromatic scale 11 pitches single pitch 2 pitches 10 pitches semitone / major 7th tone / minor 7th minor 3rd / major 6th major 3rd / minor 6th perfect 4th / perfect 5th tritone

7 PRIM ORM RLTION OMPLMNT RLT OMPLMNT

8 PRIM ORM RLTION OMPLMNT RLT OMPLMNT 3 pitches 3 pitches 9 pitches 9 pitches minor triad major triad diminished triad augmented triad

9 PRIM ORM RLTION OMPLMNT RLT OMPLMNT 4 pitches 4 pitches 8 pitches 8 pitches

10 PRIM ORM RLTION OMPLMNT RLT OMPLMNT 4 pitches 4 pitches 8 pitches 8 pitches all interval tetrachord {0,1,3,7} all interval tetrachord {0,4,6,7} all interval tetrachord {0,1,4,6} all interval tetrachord {0,2,5,6} major 7th

11 PRIM ORM RLTION OMPLMNT RLT OMPLMNT 4 pitches 4 pitches 8 pitches 8 pitches

12 PRIM ORM RLTION OMPLMNT RLT OMPLMNT 4 pitches 4 pitches 8 pitches 8 pitches minor 6th dominant 7th minor 7th diminished 7th octatonic

13 PRIM ORM RLTION OMPLMNT RLT OMPLMNT 5 pitches 5 pitches 7 pitches 7 pitches

14 PRIM ORM RLTION OMPLMNT RLT OMPLMNT 5 pitches 5 pitches 7 pitches 7 pitches

15 PRIM ORM RLTION OMPLMNT RLT OMPLMNT 5 pitches 5 pitches 7 pitches 7 pitches

16 PRIM ORM RLTION OMPLMNT RLT OMPLMNT 5 pitches 5 pitches 7 pitches 7 pitches harmonic major harmonic minor

17 PRIM ORM RLTION OMPLMNT RLT OMPLMNT 5 pitches 5 pitches 7 pitches 7 pitches melodic minor pentatonic diatonic

18 PRIM ORM RLTION OMPLMNT RLT OMPLMNT 6 pitches 6 pitches 6 pitches 6 pitches

19 PRIM ORM RLTION OMPLMNT RLT OMPLMNT 6 pitches 6 pitches 6 pitches 6 pitches

20 PRIM ORM RLTION OMPLMNT RLT OMPLMNT 6 pitches 6 pitches 6 pitches 6 pitches

21 PRIM ORM RLTION OMPLMNT RLT OMPLMNT 6 pitches 6 pitches 6 pitches 6 pitches

22 PRIM ORM RLTION OMPLMNT RLT OMPLMNT 6 pitches 6 pitches 6 pitches 6 pitches whole tone

23 RNOMIZ HROMTI PITH SP Two diagrams of twelve tone rows arranged in large 12x12 Latin Squares made of smaller 3x4 Latin Rectangles. ach complete row, column, and small 3x4 rectangle formed by dotted lines contains 12 tones. There are 479,001,600 possible 12 tone rows, and there are billions of possible versions of these diagrams. b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #

24 TRII PITH SP Three axis lattice, connecting pitches by Minor Thirds, Major Thirds, and Perfect ourths. Major Triad Semitones Minor Triad 3rd Root 5th Root 5th 3rd b b b b b b b b b b b b b b b b b b b b b b b b b b

25 MIX SYMMTRY PITH SP onnected Whole Tone, iminished, and Pentatonic shapes. Opposing tonal areas connected in the center by Perfect ourths. Name: xes of Symmetry: Whole Tone 12 iminished 4 Pentatonic 1 b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b

26 OLN RTIO PITH SP periodic Penrose Tiling with Pentatonic pitch assignments (shown in corners). s the number of tiles increases, the ratio of Kite to art shapes approaches the olden Mean. b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b

27 POLYPULS The 28 possible polypulses created by using subdivisions of the beat 2-8, shown in reciprocal pairs. Large dots are sounded events, small dots are rests, and arcs show subdivision groupings. (turn the page upside down to reverse orientation) 7:8 2:3 2:5 3:2 4:3 5:2 2:7 3:4 3:5 7:2 4:5 5:3 3:7 5:4 8:3 7:3 4:7 3:8 6:5 7:4 5:7 5:6 8:5 7:5 6:7 5:8 8:7 7:6

28 POLYPULS The 28 possible polypulses created by using subdivisions of the beat 2-8, showing pulse ratio and size of upper note in relation to lower note. 2:7 (3.50).. 3:8 (2.67) 3 3 j j 2:5 (2.50) 3:7 (2.33) 3 3 j j 4:7 (1.75).. 3:5 (1.67) 3 3 j j 5:8 (1.60) r r..

29 2:3 (1.5) 5:7 (1.40) r r.. 3:4 (1.33) 3 3 j j 4:5 (1.25).. 5:6 (1.20) r r.. 6:7 (1.17) j j.. 7:8 (1.14) r j j r....

30 8:7 (.875) :6 (.857) r r j j j j r r.... 6:5 (.833) j j.. 5:4 (.800) r r.. 4:3 (.750).. 7:5 (.714) j r j.. 3:2 (.667) j j 3 3

31 8:5 (.625).. 5:3 (.600) :4 (.571) j r j j r j :3 (.429) :2 (.400) 5 5 8:3 (.375) :2 (.286) 7 7

32 OUR T RHYTHMI MOS XPLNTION: The vertical lines show a four beat space. The numbered box shows the beat subdivision. The number beside the box counts the modes below. Modes are created by grouping subdivisions in two ways: Short (2 subdivisions, indicated by an upward arc) Long (3 subdivisions, indicated by a downward arc) Rhythmic modes fill the space entirely, without gaps. ll possible four beat modes are shown for the first four prime number subdivisions of the beat (2,3,5 and 7). 2 (1-4) 3 (1-6) 3 (7-12)

33 5 (1-20) 5 (21-40) 5 (41-60)

34 5 (61-80) 5 (81-100) 5 ( )

35 7 (1-20) 7 (21-40) 7 (41-60)

36 7 (61-80) 7 (81-100) 7 ( )

37 7 ( ) 7 ( ) 7 ( )

38 7 ( ) 7 ( ) 7 ( )

39 7 ( ) 7 ( ) 7 ( )

40 7 ( ) 7 ( ) 7 ( )

41 7 ( ) 7 ( ) 7 ( )

42 7 ( ) 7 ( ) 7 ( )

43 7 ( ) 7 ( ) 7 ( )

44 7 ( ) 7 ( ) 7 ( )

45 7 ( ) 7 ( ) 7 ( )

46 7 ( ) 7 ( ) 7 ( )

47 7 ( ) 7 ( ) 7 ( )

48 7 ( ) 7 ( ) 7 ( )

49 7 ( ) 7 ( ) 7 ( )

50 7 ( ) 7 ( ) 7 ( )

51 7 ( ) 7 ( ) 7 ( )

52 7 ( ) 7 ( ) 7 ( )

53 TL O RHYTHMI LMNTS xplanation: Rhythms are shown as a circle to eliminate redundancies and visualize the shape. On the circular path, large nodes are sounded events, and small nodes are rests. One circle represents all rotations - rhythms can start at any point. or example: = or or or or = ll unique rhythmic figures built from lengths of 1, 2 and 3, with number of events from 2 to 7 are listed, with these exceptions: Rhythms that are equivalent to a constant pulse are not listed. or example: = = = pulse of 2 Only one rotation of a rhythm is listed. or example: (listed) = = = (not listed) (not listed) (not listed) Internally repetitive rhythms are not listed. or example: = = (not listed) (listed) (not listed) (listed) Rhythms are independent from any subdivision or time signature. or example, this figure played in different beat subdivisions could be: = The table shows the 505 rhythms with lengths of up to 7 events, where each event can be of length 1, 2 or 3. The number of possible rhythms with this system extended to 12 events would be: or vents: 2 Possible Rhythms: 3 or or or or ,184 5,880 or ,104 44, etc.

54 RHYTHMS WITH TWO VNTS Lengths = 3, 4, 5 RHYTHMS WITH THR VNTS Lengths = 4, 5, 6, 7, 8 RHYTHMS WITH OUR VNTS Lengths = 5, 6, 7, 8, 9, 10, 11

55 RHYTHMS WITH IV VNTS Lengths = 6, 7, 8, 9, 10, 11, 12, 13, 14

56 RHYTHMS WITH SIX VNTS Length = 7, 8, 9, 10, 11 (columns connected by brackets contain rhythms of the same length)

57 RHYTHMS WITH SIX VNTS length = 12

58 RHYTHMS WITH SIX VNTS Lengths = 13, 14, 15, 16, 17

59 RHYTHMS WITH SVN VNTS lengths = 8, 9, 10, 11 (columns connected by brackets contain rhythms of the same length)

60 RHYTHMS WITH SVN VNTS length = 12

61 RHYTHMS WITH SVN VNTS length = 13

62 RHYTHMS WITH SVN VNTS length = 14

63 RHYTHMS WITH SVN VNTS length = 15

64 RHYTHMS WITH SVN VNTS length = 16

65 RHYTHMS WITH SVN VNTS Lengths = 17, 18, 19, 20

Week 3 Plan: Session Structure. Session 5 Session 6

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