OVERTONES – Music, Phonetics, ... and Maths intertwined

[Skye Løfvander]

OVERTONE SINGING
INTERTWINES MUSIC, MATHS, ... AND LANGUAGE!

Hopefully the above statement doesn't sound too overrating for anyone who personally has given attention to overtone singing, where the music very obviously is expressed through number and wovel sounds.
Two days ago I appealed for assistance to translate the interface of the Overtone Spiral program, and I am overwhelmed by the kind and generous responses, which may lead to a German, a Spanish, a Romanian, and maybe even a Finnish version.

I also shared a link to the program in various music theory and microtonal groups, and the respons was great. One of the most pleasing things was how Paul Christian from Minneapolis within minutes was able to write about 100 lines code, which could not only render the Ari graphic (Ari for 'arithmetics') I have used for representation of numbers in the app, but it included four different ways of systematisation.

LEARN TO COUNT WITH OVERTONE SINGING
Overtone singers ought to be aware, that each new prime number introduces a new musical function through the harmonic series.
Ari is not a number system like the [2, 5] base 10 system which forms the basis of most modern number culture, or like the sexagesimal [2, 3, 5] system used in ancient Mesopotamia. Ari is a representation of the essence of number analysis, the prime factorization. As such it is also a representation of music.

Brief introduction:
- The numbers appear as circles/wheels which are divided by 'spokes'.
- Prime numbers (2, 3, 5, 7, 11, 13, 17, 19, ...) appear as wheels with a number of spokes/radials going all the way from perimeter to center.
- Each added concentric ring indicates that the number consist of one further factorization element.

Example:
15 = 3x5 may be a good place to start as it is composed by the two first odd primes, 3 (perfect fifth in music) and 5 (just major third in music). A perfect fifth interval plus a just major third interval gives us the just major seventh (=15).
The circle representation shows four versions, different ways of systemising.
In the two upper ones all 15 subdivisions can be seen in the outer ring.
In the two lower ones the rings only illustrates the primes, 3 and 5 in different order.