its groups of 6 actually (you don't include the first integer!)
Checkout the hexachord;
http://en.wikipedia.org/wiki/Hexachord
Can you explain a little bit more about what you mean by that? Are you saying to do a fibonacci, of the golden ratio? Anyway, ed leedskalnin writes in his book you need a sound base. I agree.next octave starts at phi or fibonacci factor times base frequency
waiting on some bright ideas from someone, I'm a bit stumped quite how to take it from here (by the way i've not implemented the addition in my app - yes, i added them long strings up all by hand urghh) - it was worth it though.
Your right, 10th always is balanced. Perhaps thats because the unit size (harmonic base) just completed +1 (1+0). It's a rare number. It only comes round once, then it's gone. In fact, you'll never see another number that adds up quite like 10. Not anywhere. Every other number has very _VERY_ different properties (see Fibonacci) - it'll never add up like any other number. Which is why the exception is mnemonically simple to accommodate in base 10. It may also be a direct proof for the cosmological reasons for the number of digits on a human being, (Vitruvian universe, and da vinci's cosmografia del minor mondo)
and why the decimalization, digital computing was a marked revolution in mans understanding of maths.
Of course, they will never replace the irrational fractions. It's decimal we use to _propagate them_ co-incidence? I think not. "need eachother" seems like a good way to look at human beings, perhaps the same thing applies to maths, and physics, perhaps? ;-)
yours truly,
A

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