The Musical Expression of Numbers, natural base systems

Imagine hearing music when other people would otherwise count.

What is counting?
We humans appear to be constantly counting.  However, what exactly is the act of counting?  We humans tend to enjoy music in most cultures too.  The act of counting seems to be integral to music in a unique way. 

What is counting as distinct from music?  Why do we count and not express music, to achieve the same ends? 

I do not know the answer to those questions but I want to explore their essences and how they can be beautifully brought together.

The act of counting inherently presumes separation of state as an axiom.  For instance, we count a dozen eggs because we subconsciously define that one egg is a separate entity.  We choose to identify individuality this way before we count.  However, if we were counting toad eggs --- usually they are spawn linked together in a messy chain --- we would be at a loss of how to separate entities.  Even if we had a microscope, we are still presuming that one toad egg is a separate entity.  Yet, we know that was not always the case.  A single egg is the product of two different objects that magically fuse together.  The separate gametes are the product of much more complicated assemblies if we were to continue retracing the steps which produced the single egg. How and where and when we define the separation of one single entity from any other is our choice --- a choice that is a reflection of the natural world as well as a reflection of our own perception, however our perception may have arisen. 

Musical scales are physically different but universally recognized aesthetically.  Musical scales are mathematical assemblies of objectively separated harmonies of physics.  Doubling the frequency of a note, will produce its octave --- "the only interval to appear as a constant in the musical scales of nearly every culture." By tripling the note, we arrive at the fifth step along the scale transposed up an octave.  If all of the natural harmonies are transposed down to the base fundamental range, we arrive at all of the steps of the diatonic scale in perfect temperament. 

This analysis can be done in reverse.  Instead of doubling the frequencies, we could cut them in half and transpose the undertones up.   This eliminates our axiom of separation of state and assumes that everything is divisible.  Instead of assuming one egg is distinct from any other egg, we could assume that a dozen eggs is a single unit.  My example of the eggs seems absurd however, most of the rest of our environment is devoid of clear delineations.  Thus, we could think of counting as the reverse of dividing larger entities.  For instance, counting trees in a forest is largely a useless task compared to measuring the volume occupied by the forest.  It makes more sense to treat an individual tree as a cell within an entire organism.   However, that is still an arbitrary distinction engrained through arbitrary customs.  Many indigenous peoples see themselves as one with nature.  Separation of state is variable and arbitrary for what we commonly identify as living entities.  However, the musical scale is neither variable nor arbitrary.  The physics of music are not by chance. 

The decimal system is a commonly accepted language of numbers.  We use ten different digits that are technically words.  Each word/digit has a specific definition associated with a different quantity.  Everybody in the world happens to follow the same specific set of rules of assembling these words to convey clear meaning.  Counting to ten seems likes a law of nature much like humans all assume the force of "gravity" will always and everywhere keep them planted on the ground. 

The decimal system seems intuitive since we all have ten fingers.  However, the choice of a decimal system --- as opposed to an octal system or a binary system or as strange as this may sound, a non-linear base system for people who need to think faster than most other people --- is completely arbitrary.

I wonder if there any mathematical savants who translate numbers from the decimal system to other base systems with ease.  This sounds like a great feat but I believe the potential for musical expression in different number bases to be too beautiful to dismiss the mental possibility of any human being.

My dream is greater.  I wonder if there are any mathematical savants who could hear numbers as digits each representing separate words which sound like notes upon a scale --- any scale (or all scales!) of the auditor's choice.  The steps of the musical scale are all a part of nature as is the geometric perfection of a snowflake.  Would it not be fascinating to express numbers as melodies?

Instead of speaking numbers, we could sing them.  Each base system can be expressed as a different scale and thus, as a different language.  The different modes of each scale would be different dialects.  The key of the music becomes immaterial.  The possibilities for musical expression and representation through numbers are endless. 


Imagine translating a number from one base system to a different base system with as much ease as common linguists do so in verbal expression.  Imagine if such translations/calculations could be facilitated through the synesthesia of music and numbers.  Could there be any use for such a calculation?  Maybe not.  However, I am imagining a musical ensemble performing as a calculator.  

If we counted in the octal system instead of the decimal system, I wonder if we would encounter savants naturally expressing and hearing numbers in musical expression since the natural scales have eight steps.  However, semi-tones would be ignored. 

We could translate numbers into a duodecimal system with each semi-tone interval representing the accidental notes of the scale.  This would limit the melodies of numbers to a single octave.  

The pentatonic scale is commonly heard in oriental cultures.  They could seamlessly express the digits of our common decimal system across two octaves in that limited style of music.  I am not sure how that would work. 

Of course, this could all be easily programmed with a computer and a sound card.  I wonder how much more beautiful humanity would be if we could sing our counting and this was a natural trait of our race as much as speaking is to us now. 

I posit that the decimal system is an unfortunate historic development for mankind and a product of our evil opposable thumbs.  Imagine how peaceful and beautiful primate life would be without them.  I wonder if our chosen decimal system stunts the musical wisdom of every individual by clashing with the physical harmonies of nature. 


This dream was inspired by Daniel Tammet, a mathematical savant and multi-linguist who lives numbers through multi-dimensional visual artistic expression.  If you want to understand how arbitrary our decimal system happens to be, ask him what pictures he would imagine in a different base system.  He expressed a unique attraction to the number nine --- I found this odd because it would not necessarily exist in an octal base number/musical/perfectly harmonious language.  Thus, the synaesthesia appears to be one of unique individuality and would imply infinite possibility. 
I wonder if he has ever experienced or witnessed musico-numerical synaesthesia.  If the infinite number "Pi is life." then I would imagine that a duodecimal or even an octal base translation into melody must be a most beautiful sound we may be missing. 

In my own personal philosophy of life, there is no separation between individuals, matter, energy, magnetism and the magic that God gave us to keep it all together: faith.  Man can not live knowing everythig.  He needs to believe to be true certain axioms he can not objectively prove.  For instance, the sun will rise tomorrow and there is no sense counting the stars in the sky. 

Counting through musical expression provides 2 parallel subjective experiences for every sequence in nature: 1 from the undertones and 1 from the overtones.  We choose whether we want to separate from entities or whether we want to bring them together.