Favours and n-bocinnis

As I am now in the middle of frantically putting down information as to my
website, which I am hopeing to have up in one year, I wanted to ask you
people of the tuning digest to supply me with INFORMATION, as to:

*Webpages,
*Books,
*CDs and recorded music.

I was playing around with the n-bocinni seires just the other night, and
some very strange things took place.

The first thing that I noticed was the behaviour in sucessive ratios of
T(n-a)/Sum of all combinations of previous terms.

For the hexbocinni series, this behaviour was especially weird.

Using the golden proportion as a reference point, we can calculate the mean
errors, and things like the RMS error from this quasi-ratio, sure, I am well
aware of this, and even go as far as to use the lower ratios as the
Fibonacci series converges towards 1.61804....

However, the second weird thing that I noticed when experimenting with
higher n-bocinni ratios, was that there was a very real convergence in all
the subsequent ratios here to converge to 2^n, as in 1, 2, 4, 8, 16, 32....

This, incidentally, are the frequency intervals of the octaves in equal
temperaments.

Would it be possible to calculate the average error from each of these
n-bocinni series for each equal temperament and some JI temperaments?

Thus:

Fibonacci: *2
Tribonacci: *2, *4
Quadbonacci: *2, *4, *8
Pentbonacci: *2, *4, *8, *16
Hexbonacci: *2, *4, *8, *16, *32
Septbonacci: *2, *4, *8, *16, *32, *64

There is, also, as Warren Burt suggested, the possibilitys of the use of
irrationals from these *N terms (*=almost, but not quite this value), and
when I finally purchase a sampler, then I will experiment.

Also, in the back of my mind, I have plans for experimentation on n^2
sampling, or yranib gnielpmas, and I was woundering as to the effect of
taking the ratios of, say [2^(1/12)]^n, and "squeezeing/stretching" them to
fit n^2, thus:

1------>1
2------>1,
4------>4,
8------>9,
16---->16,
32---->25.

Effectively, this would be an "un temperament", and similar to:

(nth root 2)^12.

----Any comments?

---Sarn.

See http://mathworld.wolfram.com/GoldenRatio.html for formulae
relating phi (the golden section) to e, and for something very
relevant to the scales formed by the phi-octave-generator.

http://www.mathsoft.com/asolve/constant/gold/gold.html

--- In tuning@egroups.com, "Paul Erlich" <PERLICH@A...> wrote:

http://www.egroups.com/message/tuning/14195

> http://www.mathsoft.com/asolve/constant/gold/gold.html

Beautiful graphic, too. Now THERE'S a poster for a contemporary
music series (!!)
__________ ___ __ _
Joseph Pehrson

--- In tuning@egroups.com, Sarn Richard Ursell <thcdelta@i...> wrote:

http://www.egroups.com/message/tuning/14185

> Also, in the back of my mind, I have plans for experimentation on
n^2 sampling, or yranib gnielpmas,

Yranib gnielpmas (??) Are these really words, or are my eyes going
dyslexic (??)

___________ ___ __ __
Joseph Pehrson