Walladah How is your relationship with mathematics? If you are a musician or a dancer
reading this, I am sure and please, be sure that your relationship with
mathematics is from good to BFFE (Best Friends For Ever). If you remember
yourself struggling with math at school, stop right there and admire how
mathematics found you and how you found it through performance arts
because other pathways were closed to both of you.
This is an article about education methods in oriental dance, but it is written
while having in mind broader issues concerning education in mathematics and
arts.
Dance involves various types of mathematics. Here we focus on mathematics
of music, how music and its math are connected to dance and how oriental
dancers connect to the music.
By the term oriental I translate raqs sharqi as an umbrella term representing
various styles of dance in Eastern and South Mediterranean as Amani of
Lebanon defines the term (1). I also include styles that were developed
elsewhere based on Mediterranean dance styles that the diaspora of the
region brought with them.
The question this article deals with is about counting in oriental dance as a tool
to get a grip of the music and whether counting helps us to dance in a beautiful
and culturally relevant and appropriate way.
For years I have seen a lot of discussions about counting: counting the beats,
counting the measures, counting the steps, counting the movement sequence.
It seems there are those who count and those who don’t. Same are those who
teach with counting and those who don’t count when they want to make a
piece of music accessible to students, especially students who might not be
familiar with the music traditions of the dance.
If you are wondering, I can assure you that everybody is counting, in the sense
that every musician and every dancer has a part of their music and dance that
is very mathematical. However, with counting here I mean the usual 1-2-3-4 or
1-2-3-4-5-6-7-8 that we can see and hear very often in our dance, particularly
in western settings. In mathematical terms, this is only one form of counting or
making mathematical representations of the music and the dance.
So, this linear counting with digits one after another is not discussed enough in
our art, i.e. how appropriate it is. We don’t discuss enough about its
alternatives either because this has as a prerequisite the discussion of the
current practices of counting.
We discuss even less how the dancers of the cultures, whether community
dancers or famous professional dancers, approach the mathematical aspects of
the music they dance to and of their dance as such. The colonial assumption
that the dancers of the cultures are not analytical enough (lol) or that they are
not good enough teachers (lol lol lol) led to a peculiar situation in which 4/4
rhythms might have very different dance expression, but in many occasions
outside the cultural contexts of the dance we end up hearing, or worse,
watching an 1-2-3-4. Because, 1-2-3-4 is thought of as a good representation of
a 4/4 rhythm. Same thing happens with 8/8. Other rhythmic categories are not
so popular and easy to count, which saves us from many instances for
example, of bad 10/8 (I have seen this, true story, unfortunately). The idea that
seems to be proliferating is that as long as we end up with the correct sum of
counted beats, we are good.
Sorry, but we are not. I am writing this not to blame people. We cannot blame
ignorance for its ignorance of its ignorance. My intention is to showcase that
there is higher or deeper mathematics in our dance. I also want to showcase
that many good dancers, of the cultures or guests to the cultures of the dance,
respect this mathematics, either by knowledge or intuition. We can be more
observing towards their knowledge and appreciate it.
Example: Many people learn rhythmic styles with dum and tek combinations. It
is still counting but it puts the emphasis on the sound combined with its place
in the rhythmic flow. Most drum musicians will also communicate like this with
dancers.
Why? Because the use of dum-teks is more mathematical than 1-2-3-4. It adds
at least two more dimensions to the linear count of digits. It adds tonality of
sound (and movement) and when and where the weight of the sound or music
and of the body will fall during the dance.
A lot of people think that mathematics are digits, letters and symbols to
represent the direction(s) of equations. Well, math is way more than that. Just
like anything else, math is related to culture. Digital representation of a
rhythm, 1-2-3-4, is one form only among many other forms of depicting it. You
are a dancer or a musician and you are good in mathematics, otherwise you
would not be in the art all. Whether you represent the math you use with
digits or with dum-teks does not change your math genius.
It is also probable that digits are too limited to express the math you are using.
And if one persists to use digits 1-2-3-4, it is also probable that one will end up
with this form of representation of the math, instead of the math one needs,
and even more the math one is able to use and (a)d(v)ance.
My observation is that the linear counting in oriental dance should be used
with many caveats and only when it is necessary. We dance the way we
perceive the world. Our oriental dance math is complicated, so to speak. When
we dance, we need to account for the flow of the music and the weight and
volume of the sound in order to express those with our bodies. Especially if we
do this while we improvise with a musician playing live and improvising as well,
there is no digital sequence that can express discursively, abstractly or even
more in three dimensions (3D) the flow of movement and where the weight of
the body will be visibly placed in that flow.
So, what do we do?
First, when we learn oriental dance in our communities, we don’t count. Can
you imagine dancing with your cousins and friends in a wedding party and
counting 1-2-3-4? You don’t have time for that, but also you don’t need it. if it
was needed, we would count. The cultures of origin of the dance are very
much connected to mathematics culturally and socially and there is great
respect for the field (also, great jokes about mathematics).
Second, if we don’t count, how do we know when and how to move? Music
will tell you. The intensity and timing of the dance is already engraved in the
music. You need to be attentive to music, of course. Music is not 1-2-3-4 or 1-
2-3. We have a special term meaning music for a reason.
Third, this is a communal dance, which means the math of it is collective. You
learn by watching others and replicating not just the movement but their
listening of the music. Their mathematical minds are made visible through
their dance. Obviously, the 1-2-3-4 says nothing to distinguish between saidi
dance and tsifteteli. Yet, those who know the dances know how to show you
whether it is 3 that you put your emphasis on, or 1 or maybe 4.
Fourth, collective mathematics also means that you learn according to the
recognition that mathematics is something that is not universal (2). We have a
symbolic language for math (digits, letters and symbols) but anyone who
knows the basics of the history of math, knows that its development needed
and needs various concepts, languages and cultural understandings. It is the
same when we say that music is a universal language. The statement is true
but does not erase the fact that each community has its own perception about
music, and its own tonality systems, music creations and rhythmic patterns.
Fifth, the epistemological (3) differences are there, whether we like it or not. If
one wants to approach music or dance from another culture, one must enter
the culture with humility and ask “how do you learn this?” instead of saying “I
am a western mind, break it down the way I want it”. You can do the latter and
the dancers of the cultures do this all the time when they are asked to. But
why don’t so many western learners have the results they hope for? Because it
is the same as if you try to understand a complex function with 1-2-3-4. Will
you ever achieve it? Even if you do (any mathematician reading this should
take a deep breath, this is just a mental exercise), will it ever express what a
complex function expresses?
Sixth, you can understand the difference between 1-2-3-4 and function
because most people learn to respect mathematics or even be afraid of it.
However, they don’t show the same respect to the sophisticated knowledge –
mathematics, physics, biology or history – that our dance codifies on so many
levels. I don’t like that people are often made to be afraid of math, and I
believe this could be avoided. Still, we don’t get familiar with it if we don’t
teach it properly or if people don’t want to learn properly, i.e. the way it
works. Same with dance. All this discussion and my persistence in critiquing the
colonial misrepresentations of our arts is not to make people from colonial
countries afraid but to show that they need 1) to make an effort to learn
properly and 2) to understand that a different culture has different ways of
learning.
Seventh, because epistemologies are not respected, we also miss the
connections and similarities. Take as an example the Arabic digits, that are
nowadays used all over the planet for mathematics and discourse, much more
in performance arts. We should not use Arabic digits to misrepresent Arabic
dances, don’t you think? But, have you ever learned a bit of western European
music from any era between 15 th and 20 th century? What most people call
“classical music”, while the term is problematic and colonial as such, is
considered to be the best music western societies produced. Do you know how
much 1-2-3-4 counting we do when we learn the piano or we sing Bach or
Schubert? Minimal to none!
Eighth, even for beginners in western music, the teacher will explain the time
values of notes and basic rhythmic patterns so that we know the relative
duration of sound but they don’t make us pianists or singers count when we
make music. It would be absurd and we have no time for this, especially if we
want to go very quickly with our music. Yes, you read it correctly: any musician
of western European traditions will tell you they avoid counting because apart
from expression (the multi-aspect character of music), counting 1-2-3-4
reduces our mental and bodily abilities to play with the technical level a music
work requires.
As a pianist I can tell you that we count when we analyse something that
seems weird; when we make a repeated mistake and we slow down to use
arithmetics to make sure we did not misunderstand something; when the
composer plays with the rhythms changing them or using tricks to create
impressions of another rhythmic pattern than the real one. My teacher would
very rarely ask me to count but we would meticulously count when I seemed
not to grasp a phenomenon, e.g. when two voices play together with a
different rhythmic pattern each (western music is more rhythmically dissenting
than its reputation says). As a singer I can tell you that we count like the
pianists but we usually count with movement. Western singing uses arm
movement to count, if that reveals how much Western musical traditions trust
our bodies more than mathematical digits or the metronome (4).
Ninth, even the metronome ticking: we use it to check that we are able to keep
our rhythm of music steady; that we reached a level of velocity in our music
that we technically need; that we keep our notes having same time value when
they are played in rows or groups of notes. We don’t use the metronome for
playing music because music is more than steady or quick beat.
When my father brought me my metronome, he said “this will allow you to
play with an orchestra”. My father is a traditional musician. He learned both
Greek and Western tonality systems by ear. He is also a composer, singer and
dancer and he never counts 1-2-3-4 for anything in music when he plays or
dances. Neither any other musician in the extended family counts anything. He
knows however how Western traditions use counting: it is for basic
understanding among musicians. If I practise the piano for a concert, I know or
I have agreed with the other musicians, singers, dancers about the velocity of a
piece of music and I make sure that I am technically ready to rehearse with
them. However, the orchestra will not play with the metronome, because the
music has accelerating, slowing down and rubato (4) parts that the metronome
does not understand. This is why many orchestras work with a director so that
they have a human and not a machine ticking beats.
Finally, I invite you to look carefully at your own music traditions whatever
those are. I mentioned western music here not only because I love it but also
because it is a great example how arts are resisting mechanisation and linear
thinking more than other fields of knowledge. Listen to good music of any
tradition you like to get closer to the deep mathematics it contains. Speak with
musicians who give soul to the music and ask them whether and under which
conditions they use counting and even more linear counting. You will see that
linear counting is for checking mistakes and technical progress and for having
some starting point for collaborative projects.
You are a dancer or a musician. You know mathematics already. The task is to
get conscious of it and not get distracted or kept behind with shallow tools
that were not meant for your sophisticated skill.
Endnotes:
1. Amani’s CID-UNESCO lecture is accessible here .
2. There are people who believe that mathematics is universal because, they
say, it exists outside human society. They bring the paradigm that the
mathematical analogy of flower petals is there whether we humans observe it
or not. This however holds about biology, the weather, acoustics, speed of
light everything in nature. This does not mean that the disciplines who study
those phenomena are not socially created. What we humans know and
understand depends on our societies and the way we collective think.
2. Epistemology: the way a society thinks of knowledge, creates, improves,
disseminates and preserves it.
3. Metronome is a device, mechanical or electronic, that counts how many
times a note/beat we are interested in observing is played in a minute. We use
it to check our velocity or rhythmic steadiness in music making.
4. Rubato, a piacere or ad libitum, means that the rhythmic pattern is an
indication only, the composer wants us to improvise the rhythm (or more
aspects of the music) and we are free to play with the duration of notes and
rhythmic alterations. It is very close to the rhythmic logic of taqsim. Rubato is
also used by musicians of Western music on other occasions, even if the
composer does not notate this approach on the music sheet.
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