TOPIC:

APPLICATION OF THE STRUCTURAL SET THEORY TO AFRICAN ART MUSIC COMPOSITIONS

A CASE STUDY OF SELECTEDWORKS OF J.H.K. NKETIA AND KENN KAFUI

by SAMUEL HEMAN AGBEVOHIA

MPhil, Music Candidate

Statement of the ProblemThe 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.

Research Questions1. 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?

ObjectivesTo 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.

DelimitationCompositions of J.H.K. Nketia:• Monkanfo no - Choral piece• Play Time - Piano pieceKenn Kafui: • Pentanata 1 - Piano piece• Migli - Choral piece

The Theoretical FrameworkElaborately expatiate on the SSTUse the under-listed SST components to analyze the Research Samples:

1. Sets and its properties2. Ostinato and Ostinato Background3. Extrapolations: Successive sets, Masking, Subsets & Supersets4. Master drummer’s Role in the Art music compositions5. Interpolations6. Bridge Procedures7. Cross Sets8. Regulative Time Point (RTP)9. Total Organizational Inference10. Codification and Formulae11. Linear and Circular Analysis

Importance of the StudyThe 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.

Review Of Related Literature1. 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

METHODOLOGY(Research Design)

Data collectionBy the Delimitation, one choral composition and an instrumental piece (piano), each from the scopeCompilation and transcription of the pieces on computer using finale

DescriptiveGeneral conventional overview of the pieces and the profile of the composers, and

Hypothesis

HYPOTHESISExplanatory

Critical study and comprehensive presentation and explanation of the theory in simplest terms with few original and new simpler examples.

AnalyticalAnalysis of the pieces using the Structural set theory.

DISCUSSIONSAfrican beliefs and the theory

Music – Exhibit of culture

Beliefs – Communalism Supreme God Duality Spiritual guide (Fetish priest) Circular concept of life

Principles of the theory1. Time line or Time cycle

2. Regulative Beat/Regulative Time Point (RTP)

3. Master drum/Ostinato Background relationship

Properties of the Set 4 BEATS SPAN -Time line or Time cycle

2 SYMETRICAL HALVES

REGULATIVE TIME POINT (RTP)

Three Set Types1. 16-Set

Semiquaver grids -

2. 12-Set

Quaver grids –

3. Cross Set Ye υ e

1. Akpi

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

MASTER DRUMSet manipulation procedures

A. Isostructure and Multi-structuresB. Successive sets:- Dual representation of setsC. Extrapolation:- Repetition, Masking, Subsets

and SupersetsD. Staggered RhythmsE. Interpolation and Nested InterpolationsF. Waiting PatternsG. Bridges (Transitional patterns)

Set manipulation proceduresSAMPLES

BRIDGES

Intervals created when changing from one rhythmic orientation (RTP) to another

2 types – Normal and Idiomatic bridge

Codification and Formulae There are 5 Attributes of the CODE (Formular)

1. SET-TYPE - 16 or 12 set2. Number of ATTACK POINTS - How many strokes3. Rearrangement in PRIME FORM - Rearrangement in Magnitude4. ROTATION NUMBER - Arrangement back, from Prime F. 5. RTPExample 1: Borborbor subsidiary time line

4 4 4 (4)

16/3[4 4 4 (4)] RTP9, R0

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

Codification-Formula in ReverseTo 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

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 ROPattern:

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 --- ---

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 BHBar 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.

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

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 R0Pattern:

Bar 5-6: Soprano Alto share Master drum roleby imitation. Flexible transitive set: They form a set of same cells symmetrically Kongo

describes as dimorphic. Bar 9-12: Successive sets, modifiedBar 13-21: Successive sets,Bar 22: Bridge to RTP1Bar 23-47: Successive sets with contrapuntal entries.Bar 47-76: No new development SST-wise.

CONCLUSIONPart 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 relevant, 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 evidence of maximum use of extrapolation and staggering of sub and supersets, interpolations and nested interpolations to achieve high level of drum-mastership; Perhaps because Kenn Kafui is a traditional drummer born and bred in the Gbi Togbe Gabusu royal family lineage and a member of the Asafo company.

5.All SST attributes discovered by Anku pertains to African Art music. More attributes of the SST is revealed. Some of the newly uncovered attributes in African art music are possibly practiced in drum ensemble music but not discovered and named by Anku. The newly discovered attributes in this study include the flexible set, transitive set and shifting set. These call for the study of their existence in the drum ensemble music.

Part 2 - Structural Similarities/Peculiarities1. 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.

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.

Thank you.