2. Statement of the Problem
The Structural Set Theory is a convincing
and fascinating document capable of
solving outstanding issues raised by earlier
scholars in African rhythm, but the theory
not known to many.
There is a body of knowledge about African
music, but the question is still often asked:
“What is African music?”
“What makes a music African?” …
No one has tested the theory with African
Art music.

3. Research Questions
1. Are the rhythmic structures used in African Art
music compositions really set based?
2. Is the structural set theory relevant for analysing
other music than drum ensemble music?
3. Which aspects of the theory are functional in
African Art music, and which are not?
4. Are there any peculiarity in rhythm with one
composer to the other?
5. Are there structural differences and similarities
between African drum ensemble music and African
Art music.
6. Are there any rhythmic ideas and other attributes
peculiar to art composers differently from drum
music performers?

4. Objectives
To verify whether the rhythmic structures
used in African Art music compositions
are set based.
To identify the aspects of the theory that
are functional in Art music and those
which are not.
To find out if the structural set theory is
relevant for analyzing African Art music.
To demystify the theory for common
knowledge and use.

5. Delimitation
Compositions of
J.H.K. Nketia:
• Monkanfo no - Choral piece
• Play Time - Piano piece
Kenn Kafui:
• Pentanata 1 - Piano piece
• Migli - Choral piece

6. The Theoretical Framework
Elaborately expatiate on the SST
Use the under-listed SST components to
analyze the Research Samples:
1. Sets and its properties
2. Ostinato and Ostinato Background
3. Extrapolations: Successive sets, Masking, Subsets &
Supersets
4. Master drummer’s Role in the Art music compositions
5. Interpolations
6. Bridge Procedures
7. Cross Sets
8. Regulative Time Point (RTP)
9. Total Organizational Inference
10. Codification and Formulae
11. Linear and Circular Analysis

7. Importance of the Study
The study will help expand knowledge of the
Structural set theory.
The research findings will be an important
contribution to the theoretical sources for music
analysis.
The research will be a useful reference material
for comparative study and appreciation in high
music institutions of learning in ethno-
musicological research but especially for the
study of music across Africa.
It will accelerate the theory’s becoming a universal
tool for analyzing, understanding and explaining
rhythm in African music.

8. Review Of Related Literature
1. The writings of some historians on
African music, and that of ethno-
musicologists have been studied:
E.g. Jones A. M, Kauffman, Koetting James,
Kubik Gerhard, Rahn John, Agordoh A. A,
Agawu Kofi, Nketia JHK, Ward Williams,
Hombostel, John Blacking and others
2. Apart from the author Willie Anku, these
persons did a study on the theory:
 Dr.Kongo Zabana,
 Paddy J.N. Moonlit, and
 Entsua-Mensah Theodora

9. METHODOLOGY
(Research Design)
Data collection
By the Delimitation, one choral composition
and an instrumental piece (piano), each from
the scope
Compilation and transcription of the pieces on
computer using finale
Descriptive
General conventional overview of the pieces
and the profile of the composers, and
Hypothesis

10. HYPOTHESIS
Explanatory
Critical study and comprehensive
presentation and explanation of the theory
in simplest terms with few original and
new simpler examples.
Analytical
Analysis of the pieces using the Structural
set theory.

11. DISCUSSIONS
African beliefs and the theory
Music – Exhibit of culture
Beliefs –
 Communalism
 Supreme God
 Duality
 Spiritual guide (Fetish priest)
 Circular concept of life

12. Principles of the theory
1. Time line or Time cycle
2. Regulative Beat/Regulative Time Point (RTP)
3. Master drum/Ostinato
Background relationship

13. Properties of the Set
4 BEATS SPAN -Time line or Time cycle
2 SYMETRICAL HALVES
REGULATIVE TIME POINT (RTP)

14. Three Set Types
1. 16-Set
Semiquaver grids -
2. 12-Set
Quaver grids –
3. Cross Set Ye υ e
1. Akpi

15. Cross Rhythm Effect: Akpi (Asafo dance - Gbi Hohoe)

16. MASTER DRUM
Set manipulation procedures
A. Isostructure and Multi-structures
B. Successive sets:- Dual representation of sets
C. Extrapolation:- Repetition, Masking, Subsets
and Supersets
D. Staggered Rhythms
E. Interpolation and Nested Interpolations
F. Waiting Patterns
G. Bridges (Transitional patterns)

17. Set manipulation procedures
SAMPLES

18. BRIDGES
Intervals created when changing from one
rhythmic orientation (RTP) to another
2 types – Normal and Idiomatic bridge

19. Codification and Formulae
There are 5 Attributes of the CODE (Formular)
1. SET-TYPE - 16 or 12 set
2. Number of ATTACK POINTS - How many strokes
3. Rearrangement in PRIME FORM - Rearrangement in Magnitude
4. ROTATION NUMBER - Arrangement back, from Prime F.
5. RTP
Example 1: Borborbor subsidiary time line
4 4 4 (4)
16/3[4 4 4 (4)] RTP9, R0

20. Example 2: Borborbor/Kpalogo time line
16/5[2 4 3 3 2 (2)] RTP1,R2
NOTE: The 1st prime form number is always =0.
Count; [2º 4¹ 3² 3 2 (2)] (3² was the Original Start) =R0

21. Codification-Formula in Reverse
To reverse from the formula (CODE):
You may start from the rotation (R2).
E.g. The formula 16/5[2 4 3 3 2 (2)] RTP1 R2,
R2 gives us [2º 4¹ 3² 3 2 (2)]
The RTP always show the bar line position. E.g.
Additive form
Original form

22. ANALYSIS DISCUSSION OF FINDINGS
Pentanata I
•OPENING BAR 1-6: Tertiary structure
Bar 1-2: Complete set, RTP1; Isostructure,
Formular:12/4 [1211(1)(6)]RPT1 RO
Pattern:
Set type: Flexible set (Not named by Anku’s) Set with a
definite beginning, “a call” open to any suitable response to
complete. E.g. Tomekume --- ---

23. Bar 8-9: Complete set, RTP7; Pattern:
Set type: Transitive set (Not named by Anku’s) Set with
shifting RTP.
Bar 7-12: Master drum role appears taken by LH.
Bar 20-25: Double Interpolation: 2 successive sets within an
interpolation.
Bar 26-29: Master drum role appears changed to RH.
Bar 30-37: Successive sets in BH
Bar 38: Bridge to a restatement of the theme in BH with RTP1.
Bar 39-52: Extrapolations in BH.
Bar 53-60: Master drum role shared by both hands consecutively by
Imitation.

24. Bar 53-54: Staggered Subsets, 57-60: Hemiola

25. Monkanfo No
•OPENING BAR 1-4: RTP1, Dual structure; Flexible and
complimentary sets,
Bar 3-5: Complete set, RTP1; Alteration set,
Formular:12/5 [122216]RPT8 R0
Pattern:

26. Bar 5-6: Soprano Alto share Master drum role
by imitation. Flexible transitive set: They form
a set of same cells symmetrically Kongo
describes as dimorphic.
Bar 9-12: Successive sets, modified
Bar 13-21: Successive sets,
Bar 22: Bridge to RTP1
Bar 23-47: Successive sets with contrapuntal entries.
Bar 47-76: No new development SST-wise.

27. CONCLUSION
Part 1 – General Research Findings
1. The rhythmic structures used in
African Art music compositions are
set base.
2. The analysis made in this study
was solely based on the structural
set theory. This is how releant,
the theory is for analysing other
music than drum ensemble music
3. All aspects of the theory are
functional in African Art music.
4. There are peculiarity in
rhythm with one composer to the
other based on their life
background and experience. For
example Migli shows the eidence
of maximum use of extrapolation
and staggering of sub and
supersets, interpolations and nested
interpolations to achiee high
leel of drum-mastership; Perhaps

28. Part 2 - Structural Similarities/Peculiarities
1. Both African Art music and drum ensemble music are set
based.
2. African beliefs have great influence on the music.
3. The five principles of the structural set theory: timeline,
regulative beat, ostinato background/master drum and
the set of four equidistant beat span divisible into two
symmetrical halves apply to both African art music and
drum music.
4. All set manipulations apply to both types of music.
5. The master drum and ostinato background relationship
is not favourable for homophonic music.
6. Some African art compositions need modification of
length with structural bridges of a bar rest to fit timeline.

29. RECOMMENDATIONS
• Further research should be conducted into
the theory for possible more revelations.
• Funds should be made available for the
repackaging of the structural Set Theory to
be taught under music and cultural studies
in the basic schools.
• The set theory should be made a core
subject in the university music curriculum
to promote and enhance creativity in
African music studies.