Hello Filip,
Thank you for your reply!
One thing I didn't include in my last comment is that actually for the time being the system that you already have elaborated to me seems pretty close to the most practical. If someone has come to a point where the accentuation of overtones becomes part of a score I guess he needs to take the trouble to learn the language. I feel much in accord with Jan Heinkes comments.
One reason for taking the discussion to more philosophical perspectives is that human language is always created in a tension field and sometimes it is not very practical to aim for the optimal.
If the type characters on our computers were positioned optimally we would be able to write considerably faster. The arrrangement we use is a gigantic waste of time just imagine everyone spending 50% less time typing! But obviously it is too big a practical problem to implement a different system.
Another point is that what seems optimal today may definitely not be optimal tomorrow. Many technically orientated people where optimistic during the 7oes by the perspectives of digitally displaying the time: 10:14:27, and many of them hoped that the sexigesmal (60-) base for time registering could be replaced by a more logical decimal (10-) base. But nowadays again everyone is back to the round watches with hands revolving. Maybe they have only subconsciously realized that it is question of two ideas which we cannot just replace: 1) time is cyclic 2) the round watches actually teaches us how to divide a larger whole - whether you interprete it as time or geometry. I shouldnt like even to imagine a society governed by a linear, decimal interpretation of time!
So when I present the idea of numbers as pattern I need to have realistic expectations. Actually I once spend most of a year developing a music notation system which - if not exactly optimal - in my view surpasses the staff notation we use at a number of points, but how to make the world adapt to the idea?
There is an ocean of examples of confusion and ambiguity (a word which may mean at least two things which are partly contradictory/ ambigious!) in all human languages, also those related to music, to my knowledge there are at least tree different ways of using solfege to mention one.
The harmonic series has its roots deep in universality and offers a genuine holistic approach to the universe with mathematic, phonetic, physical and musical perspectives and now it is our challenge to develope the language - or languages - and I am pretty convinced that this will not happen without much confusion.
Hopefully it is our privilege to deal with it!
Best,
Skye

Thank You, Skye.

I am honored that You consider "my optimal notation sys." practically good enough for today-world.

Language indeed is created in a tension field. (unless it is artificial - created by some great Great Master linguist like for example J.R.R.Tolkien)

OK, I will let "My Optimal Notation system" sleep for a while.

One day, when it will not be good enough for someone, he/she will just improve it and make it better. (like a language that evolves in time... )

Well, not exactly notation in the traditional sense, but maybe useful for conducting and practice:



What may be the most remarkable about overtone singing is that it unites some very fundamental elements of speech (phonetics), music (intervals) and ... mathematics: each prime number incarnates a new tonal function through the harmonic series. The three fields share a common and very deep offspring which we may contact through our practice.
One of the oldest ways to indicate tonal functions is by hand and fingers (the guidonian hand etc.). And fingers have always been used to indicate numbers (a digit may be numerical or anatomical!).

Octaves are actually mirrored in the arithmetic series 1-2-4-8-16-... so it is obvious to find a finger counting system which may bridge the numbers and the tonal functions. The most interesting in my view would be to utilize the binary counting, where each digit position is exactly the 1-2-4-... (whereas the positions of our common 10-digit system are 1-10-100-1.000-...).

In practice it can be used by choir leaders to indicate which harmonic should be amplified, and for establishing awareness in personal practice... developing a harmonic finger language.
One hand can indicate numbers from 0 to 31 which should be sufficient for most overtone singers (and those who need wider frames don't need the fingers). This also gives the choir leader the opportunity to indicate two different harmonics for two different voice groups within one choir.