The System of the Mbira
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Mathematics in African History and Cultures
Paulus Gerdes & Ahmed Djebbar MATHEMATICS IN AFRICAN HISTORY AND CULTURES: AN ANNOTATED BIBLIOGRAPHY African Mathematical Union Commission on the History of Mathematics in Africa (AMUCHMA) Mathematics in African History and Cultures Second edition, 2007 First edition: African Mathematical Union, Cape Town, South Africa, 2004 ISBN: 978-1-4303-1537-7 Published by Lulu. Copyright © 2007 by Paulus Gerdes & Ahmed Djebbar Authors Paulus Gerdes Research Centre for Mathematics, Culture and Education, C.P. 915, Maputo, Mozambique E-mail: [email protected] Ahmed Djebbar Département de mathématiques, Bt. M 2, Université de Lille 1, 59655 Villeneuve D’Asq Cedex, France E-mail: [email protected], [email protected] Cover design inspired by a pattern on a mat woven in the 19th century by a Yombe woman from the Lower Congo area (Cf. GER-04b, p. 96). 2 Table of contents page Preface by the President of the African 7 Mathematical Union (Prof. Jan Persens) Introduction 9 Introduction to the new edition 14 Bibliography A 15 B 43 C 65 D 77 E 105 F 115 G 121 H 162 I 173 J 179 K 182 L 194 M 207 N 223 O 228 P 234 R 241 S 252 T 274 U 281 V 283 3 Mathematics in African History and Cultures page W 290 Y 296 Z 298 Appendices 1 On mathematicians of African descent / 307 Diaspora 2 Publications by Africans on the History of 313 Mathematics outside Africa (including reviews of these publications) 3 On Time-reckoning and Astronomy in 317 African History and Cultures 4 String figures in Africa 338 5 Examples of other Mathematical Books and 343 -
Archiving the Cultural Legayc of Mbira Dzavadzimu in the Context of Kuriva Guva and Dandaro Practices
ARCHIVING THE CULTURAL LEGAYC OF MBIRA DZAVADZIMU IN THE CONTEXT OF KURIVA GUVA AND DANDARO PRACTICES By Perminus Matiure A Thesis submitted to The University of KwaZulu-Natal in fulfilment of the requirement of the Degree of Doctor of Philosophy In the Faculty of Humanities, Development and Social Sciences School of Music November 2013 Supervisor: Dr Patricia Opondo ACKNOWLEDGEMENT I am grateful to all participants who provided both data and archival materials for this study. Members from Hwedza District and Gweru urban provided very valuable information which made this thesis a success, I thank them all. I give special thanks to Tichaedza Mauraya, Reverend Basera and Muhwati Chinyanga, who were the major consultants of this study. I would like to extend my profound gratitude to the various mbira ensembles that managed to participate during mbira shows. These include Maungira Enharira, Mhembero Mbira Ensemble, Dzimbabwe Mbira Ensemble, Ras Diva Mbira Ensemble, Senga Primary School, Cecil John Rhodes, Thornhill and United College of Education. Particular mention goes to Mbira Dzenharira for being support in both the Mbira Conference and the Mbira Symposium. I also thank members of the Department of Music and Musicology for supporting me during my research especially members of Zvirimudeze Mbira Ensemble. Not forgetting the Research board of University of Kwa-Zulu Natal and Midlands State University for the unwavering financial support they provided. My supervisor, Dr Patricia Opondo is a supervisor of a class of her own. Her professional wisdom, integrity, collegial and motherly attitude made consultations and supervision easy. I also would like to thank colleagues who provided me with courage and advice who include Sailas Mangwende, Dr Jerry Rutsate, Dr Sheasby Matiure, Richard Muranda and Claudio Chipendo. -
MASHONALAND EAST PROVINCE - Basemap
MASHONALAND EAST PROVINCE - Basemap Mashonaland Central Karanda Chimandau Guruve MukosaMukosa Guruve Kamusasa Karanda Marymount Matsvitsi Marymount Mary Mount Locations ShinjeShinje Horseshoe Nyamahobobo Ruyamuro RUSHINGA CentenaryDavid Nelson Nyamatikiti Nyamatikiti Province Capital Nyakapupu M a z o w e CENTENARY Mazowe St. Pius MOUNT DARWIN 2 Chipuriro Mount DarwinZRP NyanzouNyanzou Mt Darwin Chidikamwedzi Town 17 GoromonziNyahuku Tsakare GURUVE Jingamvura MAKONDE Kafura Nyamhondoro Place of Local Importance Bepura 40 Kafura Mugarakamwe Mudindo Nyamanyora Chingamuka Bure Katanya Nyamanyora Bare Chihuri Dindi ARDA Sisi Manga Dindi Goora Mission M u s e n g e z i Nyakasoro KondoKondo Zvomanyanga Goora Wa l t o n Chinehasha Madziwa Chitsungo Mine Silverside Donje Madombwe Mutepatepa Nyamaruro C o w l e y Chistungo Chisvo DenderaDendera Nyamapanda Birkdale Chimukoko Nyamapanda Chindunduma 13 Mukodzongi UMFURUDZI SAFARI AREA Madziwa Chiunye KotwaKotwa 16 Chiunye Shinga Health Facility Nyakudya UZUMBA MARAMBA PFUNGWE Shinga Kotwa Nyakudya Bradley Institute Borera Kapotesa Shopo ChakondaTakawira MvurwiMvurwi Makope Raffingora Jester H y d e Maramba Ayrshire Madziwa Raffingora Mvurwi Farm Health Scheme Nyamaropa MUDZI Kasimbwi Masarakufa Boundaries Rusununguko Madziva Mine Madziwa Vanad R u y a Madziwa Masarakufa Shutu Nyamukoho P e m b i Nzvimbo M u f u r u d z i Madziva Teacher's College Vanad Nzvimbo Chidembo SHAMVA Masenda National Boundary Feock MutawatawaMutawatawa Mudzi Rosa Muswewenhede Chakonda Suswe Mutorashanga Madimutsa Chiwarira -
THE ORIGINAL AFRICAN MBIRA? (See Map)
A/-^ <-*■*■*. g , 2 ' A 9 -1-2. THE ORIGINAL AFRICAN MBIRA ? THE ORIGINAL AFRICAN MBIRA? h §§* ANDREW TRACEY ft may be possible to show, one day, that all the different mbiras1 of Africa are descended from one another, and that all stem from one particular type, which can then te assumed to be the form of the instrument as it was originally invented. I would like D present here some evidence to show that in one large part of Africa at least all the ■any types of mbiras can be traced back, with greater or lesser degrees of probability, IB one type which must, at least, be very ancient, and at most, if connections with, or distribution to other mbira areas of Africa can be proved, may be the nearest we will get to knowing the earliest form of the mbira in Africa. The area comprises most of Rhodesia, central Mozambique, and southern and eastern and parts of southern Malawi, southern Mozambique, and northern Transvaal, >m Zunbia, Sooth Africa. Or, to put it more simply, much of the lower Zambezi valley, with a spill ell ire ant towards the south (see map). tl On first considering the bewildering variety of different types of mbiras played in this m, taking into account the different reed arrangements, methods of construction, tone anilities and musical techniques, it is hard to find any consistent family relationships. Bat if only one feature is taken as the main indicator, namely the arrangement of the •otei in the keyboard, which, as it appears, turns out to be a remarkably constant factor, Kreral interesting and far-reaching relationships come to light. -
Midlands State University Faculty of Arts
MIDLANDS STATE UNIVERSITY FACULTY OF ARTS DEPARTMENT OF HISTORY AND INTERNATIONAL STUDIES AN EXAMINATION OF TACTICS USED BY ZANLA TO PROMOTE THEIR IDEOLOGY AND AGENDA FOR THE LIBERATION OF ZIMBABWE. A CASE STUDY OF MUZARABANI (1972-1979) By THELMA B BOMANI R144662M Being a dissertation submitted in partial fulfilment of the requirements of the BACHELOR OF ARTS DEGREE IN HISTORY AND INTERNATIONAL STUDIES at Midlands State University JUNE 2018 ZVISHAVANE- ZIMBABWE SUPERVISOR: MR G.T NCUBE APPROVAL FORM The undersigned certify that they have supervised the student Thelma B Bomani (R144662M)’s dissertation entitled “An examination of tactics used by ZANLA to promote their ideology and agenda for the liberation of Zimbabwe. A case study of Muzarabani (1972-1979)” Submitted in Partial fulfilment of the requirements of the Bachelor of Arts Honours Degree in History and International Studies offered by Midlands State University. MR. G.T. NCUBE …………………………. SUPERVISOR DATE DR. J. CHAKAWA …………………………. CHAIRPERSON DATE .................................. …………………………… EXTERNAL EXAMINER DATE i DECLARATION I, Thelma B Bomani, hereby declare that this dissertation is my original work which has never been submitted to any university. All sources used in this dissertation which is not mine have been acknowledged to show that it is the work from other scholars in accordance to copy right law. This is submitted in partial fulfilment of the requirements of Bachelor of Arts Honours Degree in History and International Studies offered by the Midlands State University. Thelma B Bomani ………………….. June 2018 ii DEDICATION This dissertation is dedicated to my family. iii ACKNOWLEDGEMENTS There are a number of individuals who are worthy to be acknowledged in the completion of my degree. -
RAFOC REMINISCENCES and RAMBLINGS - WEEK 62 – 11Th JUNE 2021
ROYAL AIR FORCE OFFICERS’ CLUB Johannesburg P.O. Box 69726 BRYANSTON 2021 [email protected] www.rafoc.org President: David MacKinnon-Little Vice Presidents: Basil Hersov, Colin Francis, Geoff Quick, David Lake Chairman: Bruce Harrison [email protected] Tel: 011 673 0291 Cell: 083 325 0025 Vice Chairman: Jon Adams [email protected] Tel: 011 678 7702 Cell: 082 450 0616 Hon. Secretary: Colin Ackroyd Tel: 012 942 1111 Cell: 082 800 5845 Hon. Treasurer: Jeff Earle Tel: 011 616 3189 Cell: 083 652 1002 Committee Members: Russell Swanborough Tel: 011 884 2611 Cell: 083 263 2740 Karl Jensen Tel: 011 234 0598 Cell: 082 331 4652 Jean-Michel Girard Cell: 083 659 1067 Geoff Fish Tel: 012 667 2759 Cell: 083 660 9697 Web Master: Hanke Fourie Tel: Cell: 082 553 0210 Bank Account: Nedbank - Melrose Arch Br: 19 66 05 Account 19 66 278 063 RAFOC REMINISCENCES AND RAMBLINGS - WEEK 62 – 11th JUNE 2021 GREETINGS: Day 442... More snow on the Berg, extended Eskom load-shedding and water cuts continue in many residential areas... Eskom denies secretly launching stage 6 load-shedding... Ramaphosa places health minister Zweli Mkhize on special leave... Massive increase in criminals trying to steal your identity in South Africa... more than half of all South Africans (36 million) benefitting from government grants in some manner. South Africa’s shrinking tax base is too strained to fund the NHI experts say... Wildlife, bribery and cigarettes part of latest Op Corona successes... Hmm... Rassie upbeat about the 45-man Springbok squad announced for the three-Test series against the British Lions in South Africa. -
Bishop Knight-Bruce (1891–1894)
CHAPTER ONE OCCUPYING THE GROUND: BISHOP KNIGHT-BRUCE (1891–1894) In 1891 the Church of the Province of South Africa (CPSA), a daughter church of the Church of England, expanded into Central Africa. A diocese was created by the Provincial Synod for an area north of the Diocese of Pretoria, which ended at the Limpopo River. This diocese, “for Mashonaland and the surrounding territories”,1 was one of the largest Anglican dioceses in the world. It was roughly the size of France, two-and-a-half times the size of Great Britain (see Map 1, p. xx). The central area of the original diocese is today divided into the fi ve dioceses of the Anglican Church in Zimbabwe (Harare, Matabeleland, Mutare, Central Zimbabwe and Masvingo). Mashonaland itself was little known to the outside world in 1891 and undefi ned, other than by its general topography and the distribu- tion within it of Shona-speaking peoples (‘the Mashona’). At its centre was a large, high plateau, well-wooded and watered. To the north, the land fell away to the Zambezi River; to the east, in the region of the Manyika people rose a mountainous barrier beyond which lay the colony of Portuguese East Africa. Much of the area was dominated by two peoples of Southern, Nguni, origin: the Gaza, in ‘Umzila’s country’ to the south-east;2 and the Ndebele (‘Matabele’), in the south-west (see Map 2, p. xxi). Ndebele territory (Matabeleland) was itself bordered to the south- west, across the Ramokwebana and Shashe Rivers, by territory known as ‘Khama’s country’: Khama was the leading chief of a number of native polities which had come under British infl uence, as the Bechuanaland Protectorate, in 1885.3 To the south-east of Matabeleland and south- west of Gazaland ran the Limpopo River, which served not only as an ecclesiastical boundary between the new Diocese of Mashonaland and 1 ‘The Bishop’s Letter: Resolutions: Section VII’, CMSA 6:64 (April 1891), xxxi. -
Relationship with Percussion Instruments
Multimedia Figure X. Building a Relationship with Percussion Instruments Bill Matney, Kalani Das, & Michael Marcionetti Materials used with permission by Sarsen Publishing and Kalani Das, 2017 Building a relationship with percussion instruments Going somewhere new can be exciting; it might also be a little intimidating or cause some anxiety. If I go to a party where I don’t know anybody except the person who invited me, how do I get to know anyone else? My host will probably be gracious enough to introduce me to others at the party. I will get to know their name, where they are from, and what they commonly do for work and play. In turn, they will get to know the same about me. We may decide to continue our relationship by learning more about each other and doing things together. As music therapy students, we develop relationships with music instruments. We begin by learning instrument names, and by getting to know a little about the instrument. We continue our relationship by learning technique and by playing music with them! Through our experiences and growth, we will be able to help clients develop their own relationships with instruments and music, and therefore be able to 1 strengthen the therapeutic process. Building a relationship with percussion instruments Recognize the Know what the instrument is Know where the Learn about what the instrument by made out of (materials), and instrument instrument is or was common name. its shape. originated traditionally used for. We begin by learning instrument names, and by getting to know a little about the instrument. -
Interview with Diane Thram by Meredith Holmgren, in Conversation with Diane Thram
Spring 2014 Interview with Diane Thram by Meredith Holmgren, in conversation with Diane Thram The International Library of African Music (ILAM) at Rhodes University in Grahamstown, South Africa, is widely considered to be the oldest and largest repository of African music field recordings in the world. Founded in 1954 by Hugh Tracey as a research institution and archive, it preserves thousands of historical recordings going back to 1929 and continues to support contemporary fieldwork. Among its most renowned recordings is Hugh Tracey’s seminal Sound of Africa series—selections of which are available from Smithsonian Folkways Recordings—which remains among the most influential fieldwork in the field of African ethnomusicology. Smithsonian Folkways Magazine editor Meredith Holmgren corresponded with ILAM’s director Diane Thram about their impressive collections and projects. The following represents an abbreviated, edited version of the conversation. ***** MH: What are the main collections at the International Library of African Music (ILAM)? DT: ILAM’s major holding is the Hugh Tracey collection, but other holdings include the Andrew Tracey collection and Dave Dargie collection... We’ve recently processed Jaco Kruger’s field collection, which includes extensive research on Venda music, from the northern part of South Africa. And [we have] another collection from a sociologist here at Rhodes University [Michael Drewett] who did a lot of research on the censorship of popular music during apartheid. His field recordings are being processed now and digitized. It’s an ongoing thing. We receive deposits from researchers doing work with African music and one of our aims is to build the archive. -
Hmong Music in Northern Vietnam: Identity, Tradition and Modernity Qualification: Phd
Access to Electronic Thesis Author: Lonán Ó Briain Thesis title: Hmong Music in Northern Vietnam: Identity, Tradition and Modernity Qualification: PhD This electronic thesis is protected by the Copyright, Designs and Patents Act 1988. No reproduction is permitted without consent of the author. It is also protected by the Creative Commons Licence allowing Attributions-Non-commercial-No derivatives. If this electronic thesis has been edited by the author it will be indicated as such on the title page and in the text. Hmong Music in Northern Vietnam: Identity, Tradition and Modernity Lonán Ó Briain May 2012 Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Music University of Sheffield © 2012 Lonán Ó Briain All Rights Reserved Abstract Hmong Music in Northern Vietnam: Identity, Tradition and Modernity Lonán Ó Briain While previous studies of Hmong music in Vietnam have focused solely on traditional music, this thesis aims to counteract those limited representations through an examination of multiple forms of music used by the Vietnamese-Hmong. My research shows that in contemporary Vietnam, the lives and musical activities of the Hmong are constantly changing, and their musical traditions are thoroughly integrated with and impacted by modernity. Presentational performances and high fidelity recordings are becoming more prominent in this cultural sphere, increasing numbers are turning to predominantly foreign- produced Hmong popular music, and elements of Hmong traditional music have been appropriated and reinvented as part of Vietnam’s national musical heritage and tourism industry. Depending on the context, these musics can be used to either support the political ideologies of the Party or enable individuals to resist them. -
1 Evaluating Shona Liturgical Music in Localised Practices of Inculturation Within the Catholic Mass in Zimbabwe Submitted by Cr
Evaluating Shona Liturgical Music in Localised Practices of Inculturation within the Catholic Mass in Zimbabwe Submitted by Crispinah Machingura Submitted in partial fulfilment of the requirements for the degree of Master of Arts (Ethnomusicology) in the School of Arts, College of Humanities - University of KwaZulu-Natal, Durban, South Africa. November 2014 Supervisor: Doctor Sazi Dlamini 1 DEDICATION To God the Father our Lord Jesus Christ, be all glory, honour and praise through this work. Vana Vadiki VaMariya Musande, my dearest parents (Baba naMai Muketekesi), my brothers and sisters and all the Machingura grandchildren Nakeisha, Tanaka, Tinomudaishe, Chikomborero and Munashe, all for the love of you. i DECLARATION I declare that this thesis is my own original work. All citations, references, and borrowed ideas have been duly acknowledged. None of the present work has been previously submitted. Student name CRISPINAH MACHINGURA ………………………………………………………………… Date 14 NOVEMBER 2014 …………………………………………………. ii ACKNOWLEDGEMENTS I am most grateful to God for His sustaining treasures of unending mercies that kept me alive when I needed them most. Among the people who assisted me, I would like to express my most sincere gratitude to my supervisor, Dr Sazi Dlamini for his patience, academic prowess and unwavering mentorship. His keen interest in my work and encouragement were invaluable incentives towards the completion of this thesis. I am also indebted to the following people for their meaningful contribution to this study. A research project would never come to completion without information: I earnestly thank Prof David Dargie for directing me to invaluable literature about inculturation and Prof Andrew Tracey who also availed himself for interviews on Shona traditional music. -
University of the Witwatersrand
UNIVERSITY OF THE WITWATERSRAND AFRICAN STUDIES INSTITUTE African Studies Seminar Paper to be presented in RW 4.00pm AUGUST 1982 Title: The Making of Colonial Zimbabwe, Speculation and Violence 1890-1902. by: Ian Phimister No. 122 •UNIVERSITY OF THE WITWATERSRAND AFRICAN STUDIES INSTITUTE African Studies Seminar Paper to be presented at Seminar in RW 319 at 4.00 pm on Monday, the 16th August, 1982. THE MAKING OF COLONIAL ZIMBABWE, SPECULATION AND VIOLENCE 1890-1902. Ian Phimister NOTE This paper does not follow the usual seminar format as it is a chapter out of a forthcoming book by Dr. Phimister. ************************ THE MAKING OF COLONIAL ZIMBABWE: SPECULATION AND VIOLENCE 1890-1902 Ian Phimister 'The relationship between a good or bad share market on the one side and a British Colony in the stage of tender infancy on the other is to be studied, if anywhere, in this country of Rhodesia, Rhodesia is a country which, . almost avowedly is intended to be built up, or at least forced upward, by aid. of gold mining and land dealing on the £1 share limited lia- bility principle1 {Rhodesia Herald, 1898) The immediate genesis of colonial Zimbabwe grew out of the discovery of the main gold reef on the T-Jitwatersrand in 1886. When news of the find reached the diamond mining centre of Kimberley, reaction was mixed. Some entrepreneurs, particularly those bruised in the on-going fight to amalga- mate the diamond industry, made their way as fast as possible to the Rand. Others, with much less reason to gamble, like Cecil Rhodes, held back.