N-Boc stuff

Dearest People of the alternative tuning list,

You know, its really really funny,-I have, actually, learnt more about
mathematics and social interaction from the Internet that any formal course
could have taught me.

I often wounder why this is, I mean, is this just because of me?

Another thing that really occurred to me, was my inability to essentailly
predict the future, and also difficulty I have planning ahead.

Sometimes mathematics can prove counter-intuitive,-I have difficulty
predicting EXACTLY how such-and-such will trun out, and I thought that this
next little project would turn out a lot easier than what I had anticipated,
but this wasn't the case, it was actually qite difficult.

One such example is what happened to me when I tryed to formulate rules for
the FUNDAMENTAL THEOREM OF ARITHMETIC variants,-this is, more correctly, my
proposed experiments with the use of the n-bocinni series to essentially act
as the prime number series, a sort of "stnad in", when it comes to useing
these numbers as a product series for designateing tuning ratios based on
just intonation.

May I ask you: IS IT POSSIBLE TO USE THE N-BOCINNI SERIES TO ACT AS A
PRODUCT SERIES WHEN EACH N-BOCINNI MEMBER IS RASIED TO A NUMBER AS A
COEFFICIENT, AND ESSENTIALLY THUS, TO GIVE ANY NUMBER IN OUR JUST INTONATION
RATIO?

Thus:

t(n) t(n+1) t(n+2) t(n+3) t(n+4)........ t(n+a)
^+/-A ^+/-B ^+/-C ^+/-D ^+/-E ^+/-N = X/Y

.......essentially these numbers as terms of the n-bocinni series, instead
of the prime number series.

I must ask, using MULTIPLICATION and multiplication alone, how effective are
the terms of the n-bocinni series, and terms of the series n^2 as compared
to the primes?

I know that 2^n is utterly useless, it merely gives a series full of holes
when these are multiplied, the effect is even more pronounced when
superpowers are used.

As I said, Joe Monzo has shown me now, the basic procedure for application
of the prime number series for making lattices, and I got to woundering
about the use of other seires.

Given the:

Fibonacci series: t(n+1)=t(n-1)+t(n), essentially
term(new)=term(old)+term(older), we get the well known: 1, 1, 2, 3, 5, 8,
13, 21, 34, 55, 89, 144....

Tribonacci series t(n+2)=t(n+1)+t(n)+t(n-1): 1, 1, 2, 4, 7, 13, 24, 44, 81,
149, 274, 504....

Quadbonacci series t(n+3)=t(n+2)+t(n+1)+t(n)+t(n-1): 1, 1, 2, 4, 8, 15, 29,
56, 108, 208, 401, 773.....

Pentbonacci series t(n+4)=t(n+3)+t(n+2)+t(n+1)+t(n)+t(n-1): 1, 1, 2, 4, 8,
16, 31, 61, 120, 236...

I am thinking about the different tuning and JI lattices that could be made
from, and for the interaction of the prime number series, as from this
FUNDAMENTAL THEOREM OF ARITHMETIC, and when playing around with the concept,
I have thought of something.

If I list some matrices, using the n-bocinni and the prime number series, I
can perhaps, at least for most of them, get a system which uses ta product
of these numbers, rasied to a power coefficient, and, I have choosen a juicy
temperament that I liked the look of, -a temperament, that is, based on
these numbers, but when I actually sat down to do this, it turned out to be
a lot more difficult to do than I first thought.

So, is there any one here who is a dab hand at computer programming, and
could acess the effects of all the possible combinations of the n-bocinni
series, when these are multiplied by each other, and put to ratios, and as
to the lowest possible terms of these ratios to approximateing the JI ratios
used?

The reason that I ask this is because it will be painstakeing work to do
this by sight, and hand,-it could very well take months.

I have now, by the way, found a power seire that generates the golden
proportion.

****The Bohlen-Pierce scale structures site gives the following diatonic
scale -- the "Lambda scale":

1/1 25/21 9/7 7/5 5/3 9/5 15/7 7/3 25/9 3/1

Thus, to place this in the prime number series, the Fibonacci number series,
the tribonacci number series, and the quadbocinni and pentbonacci series:

2 3 5 7 11 13 17 19 23
-1 2 -1
2
1
1
2
1 1
1
2
1

| 1 2 3 5 8 13 21 34 55 |
-------------------------------------------
|
|
????

n
C Best approximates x/y by multiplication

r
|1 2 4 7 13 24 44 81 149|
------------------------------------------
|
|
?????

|1 2 4 8 15 29 56 108 208 |
-------------------------------------------
|
|
????????

|1 2 4 8 16 31 61 120 236|
------------------------------------------
|
|
????????

I thought that it would just be a matter of having the JI intonation ration
of this Bohlen-Peirce intonation's ratios compared individualluy to the
specific n-bocinni's ratios as multiplied combinations, and when these
ratios are simplified, we could acess the closeness of each.

The next part, having done this, is the fun bit!

We then can interpolate each with other n-bocinnis and make lattices from them.

Any ideas??

---Sarn.