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2.2 – rhythmic matrices

The rhythmic aspect directly deals with cultural differences that reverberate with the musical information in transit between the musical contexts of each realization.

Consider the question that is a permanent issue of restlessness for musicians and that has been present throughout this study. Such issue is introduced by the statement of Egberto Gismonti to Arrigo Barnabé, which is transcribed below. [i]



The German musical culture is grounded in “march”;
whereas the Brazilian musical culture whether it be more or less “cult”,
is grounded in that the low frequency (of the surdo drum) that sounds in the second beat of the measure
and in the syncope, whose division is never where it should be. [i]

Since our syncope…

[sings the following rhythms]

…undergoes a dislocation and is felt by the German orchestra as “march”, in the musical figure…[i]

… and by the French – despite the fact of having been Africa’s colonizers – as triplet.  


The issue is presented when we realize a significant difference between a rhythmic approach that feeds itself on the “tempo” stability, more present in the musician that has been nurtured by popular practices – not written down –, and another, connected to the written tradition, which develops through the “expression” ruled exactly by devices based on tempo variation. […]

The fertile conflict to which we refer is verified in the very nature of the Brazilian popular music, which fully feeds itself on the tension resulting from the encounter between the  rhythmic management of African and European musical matrices.

Polarity strategically established by the present study facing the fact that the indigenous musicianship – which completes the Brazilian constituent triad – “is found diffuse and its elements are hard to point out”, even within the “caipira music”, which might be the main musical derivation resulting from the encounter between the Portuguese men who grounded in Brazil at the beginning of colonization and the indigenous women. [i]

Thus, the mameluco, people who settled and shaped the region known as Brazil’s center-south, are who start assimilating and gathering that musicianship. It is the mameluco who incorporate the indigenous music structures in an intuitive manner, listening to it sounding in their mother’s voice. Today this musicality is found diffuse and its elements are difficult to pinpoint within the caipira music because due to the almost total extermination of the Tupi nation the references to the music produced by these peoples were lost, remaining to us today to discover it through the elimination of musical elements inherent to the white and black cultures, by means of a truly musical archaeological work. (VILELA, 2004, p.175)

Our research contributes to that archaeological work insofar as it studies the relation between the written tradition – European – and the oral tradition (not written down) – African – in Brazil. [i] Revealing polarity of the core of the question that is herein introduced.



00:00 00:00 In a pagode in Planaltina (Marco Pereira)

00:29 00:00 slap on the guitar

01:25 00:00  the rhythmic precision and the syncopation

If you keep the precision, you understand the syncopation,

if you play in an imprecise manner,
sort of a little “loose”,
which the erudite musician in general applies when playing,
you miss the syncope notion.

[sings a syncopation]

You understand the syncopation only when the pulsation gets clear. [i]


02:56 additive rhythm


The western rhythm is divisive, because it is based on the division of certain duration in equal values. Thus, as all manuals of music theory teach, a semibreve is divided into two minims; each of these divided into two semiminims, and so on. The African rhythm is additive, because it reaches certain duration through the sum of smaller units, which group forming new units that may not have a common divisor (it is the case of 2 and 3). (JONES, 1959, p. 210 apud SANDRONI, 2001, p. 24)



03:20  melodic division x rhythmic pulsation

03:40  “the smallest figure” in music and Nico Assunção

05:37 mathematical perfection and expressivity


This manner of listening to the musical stuff resonates in Marco Pereira’s executions, which equilibrate the timbre quality, characteristic of his erudite formation, with the rhythmic precision – at the same time “mathematical” and “swinglike” – whose popular song accompaniment masters he has studied. [i]

A study that in this case includes a view linked with the written music, in which the score itself represents a graphic system that demands the clarification of such mathematical relations.

João Bosco, with whom the same bass player Nico Assunção worked for years, follows as interlocutor in a dialogue that goes deep into the management of rhythm. Guitar-player endowed with natural domain of contrametricity, which in Brazil so many times is based on the simple binary compass, prefers to present “rhythmic matrices” as examples that work this same “asymmetry” in drawings developed in wider structural segments. João Bosco “feels” and assimilates such segments in his very way – with a commitment that differs from the commitment of who reads – to express them with the “naturalness” distilled through listening to his masters.



00:00  how do you work with rhythm in a conscious level?



00:30 Moacir Santos and Dave Brubeck

I’ve listened to two very good guys in my life,
one was Dave Brubeck [i] with his quartet,
with two records, Time Out (1959) and Time Further Out (1961),
and after that Moacir Santos [i] with Coisas (1965). […]

Brubeck and Moacir worked out a very impressive polyrhythmia
with the advantage that is marked by simplicity.
They were great teachers.


The score album entitled Coisas: cancioneiro Moacir Santos – launched by Jobim Music in 2005 as an initiative of an ample process of “rediscovery” of the conductor from Pernambuco, supported by musicians Mário Adnet and Zé Nogueira from Rio de Janeiro – brings preface by critic Hugo Suckman:

Moacir would later reveal that he liked those pieces he was writing so much that he would like them to be given numbers in the same way as composers do in erudite music. Thus, instead of Opus n.1, Opus n.2, Opus n.3, as the classical compositions are ordered, Moacir opted for Coisa n.1, Coisa, n.2, Coisa n.3, subtitling that first series of ten, African-Brazilian Things. It would also be Baden Powell the first musician to let himself be grabbed and influenced by “Coisas”. Many of the famous African-sambas being composed at the time and which would be launched in a series by Forma records were exactly born in the music classes with exercises proposed by Moacir. The African character of “Coisas” is the reason for Baden’s and Vinícius de Moraes’s African-sambas to come to life. (SUCKMAN, 2006, p.23)



01:08 complexity and comfort

02:25 I don’t feel 13, I feel good.

03:10 5/4 : Lília (Milton Nascimento)

05:05 when you divide the music, it settles and stays comfortable.


At this point, João Bosco presents us the “division” that he “feels” in a 4/4 groove that he uses in several compositions and rereadings [i]. Such a division seems to work as reference like a timeline [i], which João Bosco transmits using resources that are not related to the western written tradition, but rather, according to Kubik,  to orality and the way the matter is taught in Africa: “A referential rhythmic phrase is the structuring heart of a musical piece (…) The rhythmic motifs of reference are transmitted from the teacher to the student through syllables or mnemonic phrases” (KUBIK, 1981, p.93).

Division that João Bosco “sings” to convey his sensation [i], which could be noted in the following ways:

Thus, João Bosco shows that his references are more ample structures so as to reach the wished inflection in the minimum parts of “time”. Inflection reached sometimes just by subverting a rhythmic “precision” referenced in the proportions reproduced by the metronome. As in the case of hitting a note that would be the last eighth note from the first beat of the measure (sung in t’), which in this context happens “delayed” and with clear attraction to gravity in relation to the note that we write as being the fourth sixteenth (hit by the guitar and sung in “ka”).  In this way, syllable “t’ka” presents us the inflection point in the rhythmic articulation that will make the difference for a “natural” execution.



06:17 each one feels polyrhythmia in a specific way


The musical figure that tries to represent this indetermination taking place in the rhythmic subdivision is noted by Mário de Andrade in this way:


Subversion of the western rhythmic division principle that in a lively fraternity harmonizes with the eighth note interpreted with “jazz felling”[i]. A resource that takes on the condition of approximated writing [i] and refers to the development of all the musical culture born in North America as a result from the encounter between the European and African musical traditions.

If the relation with the written rhythmic inflection – marked by styles of each period of the western music history – undergoes transformations over the centuries as it molds the “cult” music tradition, another dynamics is established by means of the readjustment of rhythmic written resources to the popular music that reaches its hegemonic expression through the pact shaped around the word “swing”. This pact is directly related to the body in movement that is marked at the top left corner of the page with scores with the following indication:

  1. Part presented at 24m03s in the second program with the interview with Egberto Gismonti – recorded in 2004 – given to the “Supertônica”  program, conceived and presented by composer Arrigo Barnabé, broadcast by Rádio Cultura FM de São Paulo.

    Available at: Accessed: Sept. 2013.

  2. In this fashion Gismonti exemplifies, through the Brazilian characteristic syncope, the concept of contrametricity – that is, musical figures that question the bar – in contrast with the rhythmic figure associated to the German “march” which is an example of cometricidade – since it confirms the beats of the bar.

    Concept presented in Feitiço Decente (SANDRONI, 2001, p.27).

  3. LINK with the idea “you understand the syncope only when the pulsation gets clear” presented in  – 2.2 – rhythmic matrices – in the statement of Marco Pereira.

    LINK with the central idea presented in – 5.2 – a question for Browuer – in the dialogue with Sérgio Assad.

    1. LINK with idea presented in – 5 – MESTIZO BLOOD: FIVE SOLOS
  4. LINK with the idea “that is not so African, it is more indigenous” presented in – 5.5 – “Boi de Mamão” – in the statement of P. C. Pinheiro.

    1. LINK with the central idea presented in – 2 – a question for Browuer.
  5. LINK with the idea “João Gilberto (has a) taken that has such precision and constancy that it virtually does not change” presented in – 2.2 – Rhythmic matrices – in the statement of Marco Pereira.

  6. Dave Brubeck (1930-2012), American pianist and composer who was a jazz icon. A musician whose mother was a piano teacher, but who avoided reading the scores, and even so, graduated in 1942, in the University of the Pacific, in Stockon, California.

  7. Moacir Santos (1926-2006), Brazilian musical arranger, composer, conductor, and multi-instrumentalist, born in Pageú (Pernambuco), who moves to Los Angeles in 1967, settling down in Pasadena – California – where he lived composing soundtracks for the cinema and teaching music.

  8. A rereading that uses the “taken” presented in the sequence by João Bosco is Se você jurar ( If you swear) (Ismael Silva/Francisco Alves/Nilton Bastos), in the album Dá licença meu senhor (Excuse me sir)launched in 1995 (Epic/Sony Music).

  9. “It (the timeline) may be defined as a rhythmic pattern in additive or divisive form that incorporates the basic pulse or the regulating pulsation, as well as the density referential. Instead of regular groups of four notes, groups of five, six or seven notes may be used in patterns of binary or ternary subdivision (simple or composed bar)”. (NKETIA, 1974, p. 132)

  10. LINK with Chico Saraiva’s account in – 5.5 – “Boi de mamão” – with Paulo César Pinheiro : “I’ve ended up ‘rhythmically singing’ a melody that for not being any longer just a melody to be given lyrics, visited the rhythmic design of the referred key”.

  11. This convention always needs to be indicated in takens with jazz felling. It establishes that the eighth note should be interpreted not literally, but as a quialetrada figure above.” (ALMADA, C. 2000, p.45)

  12. LINK with the idea “the inflexions of the phrases count more on the experience of the performers in the genres interpreted than on the detailed articulation of the notation” presented in – 4.5 – playing together.