On counting and other musical mathematics in oriental dance

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.

From Topkapi Palace, Istanbul

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.

From Topkapi Palace, Istanbul

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.

From Topkapi Palace, Istanbul

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!

From Topkapi Palace, Istanbul

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.