Strange ears

I have to admit, I was never one to let practical limitations stand in my
way, and I will not bow to
mathematical experimentation being too impractical to use in
temperaments!!!!!!!!!!!!!!!!!!!!!!!!!!!

Sure, imaginary numbers used in calculateing termperaments would most likely
give us:

e^{cos(x)+sin(x)i}, and a lot of complex numbers would probably be
generated/outputted, but we can manipulate the sounds involved, and get
thinking creatively!!!

Thus, imaginary numbers could have the sound reversed, or time stretched, as
also could negative numbers.

An exobiological entity would have a fine old time, or a Polyversal entity
from another Universe, would also, and supposedly, reversed sound is what
"tachyons" would sound like!!!!!!!!!

:o)

There is a theorem related to DeMoivre's theorem, or so I have heard, that
states that we will not actually get anything more fantastic than imaginary
numbers from ordinary algebras, in effect, we are "traped" to:

reals:+/-, imaginarys:i/-i, and complex numbers: R+i, R-i, -R+i, -R-i, and
hypercomplex numbers cannot arise out of these algebras, altho I have seem
them emulated with Hermitean matrices, on a website once, and I am still
looking for information about these matrices, as I have lost the darned
website!!!

Please, PLEASE, P-L-E-A-S-E, ---if somebody, anybody, could calculate:

a) (2i^(1/12)^n
b) (2i^(1/12i)^n
c) (2^(1/12i)^n
d) (2i^(1/12)^in
e) (2i^(1/12i)^in
f) (2^(1/12i)^in

for me, I would be endebetted to them!!!!!

I will, as I said, need to take a formal course, and some mathematics papers
to help me understand the convention for calculateind complex, and imaginary
exponents, logarithms, and roots, but I really want somebody to give me a
tad of advice!!!!

Also, I have made some temperaments out of the "pluperfect square" aka the
"squared square".

Anybody interested????????????????????????????????????????

Sincerely,

Sarn Richard Ursell.

In-Reply-To: <200006060730.TAA31696@smtp1.ihug.co.nz>
Sarn Ursell wrote:

> There is a theorem related to DeMoivre's theorem, or so I have heard,
> that
> states that we will not actually get anything more fantastic than
> imaginary
> numbers from ordinary algebras, in effect, we are "traped" to:
> reals:+/-, imaginarys:i/-i, and complex numbers: R+i, R-i, -R+i, -R-i,
> and
> hypercomplex numbers cannot arise out of these algebras, altho I have
> seem
> them emulated with Hermitean matrices, on a website once, and I am still
> looking for information about these matrices, as I have lost the darned
> website!!!

Perhaps you mean quaternary numbers. Here's the best link I could find
quickly:

http://forum.swarthmore.edu/dr.math/problems/rosequater.html

Then again, it may have been Clifford algebra, as featured in the Dirac
wave equation. Who knows? There's plenty of weird stuff out there!

> Please, PLEASE, P-L-E-A-S-E, ---if somebody, anybody, could calculate:
>
> a) (2i^(1/12)^n
> b) (2i^(1/12i)^n
> c) (2^(1/12i)^n
> d) (2i^(1/12)^in
> e) (2i^(1/12i)^in
> f) (2^(1/12i)^in
>
> for me, I would be endebetted to them!!!!!

Get Python: http://www.python.org

Then, to generate the first one, where n is an integer, you write

pow(2j,n/12.0)

where j here is like i was before. For n=0 to 12, this gives:

(1+0j)
(1.05039924072+0.138287683504j)
(1.08421508149+0.290514555507j)
(1.09868411347+0.455089860562j)
(1.09112363597+0.629960524947j)
(1.05899965706+0.812599017122j)
(1+1j)
(0.912111557213+1.18868692422j)
(0.793700525984+1.374729637j)
(0.643594252906+1.55377397403j)
(0.461163111024+1.72108416092j)
(0.246400639937+1.87159867418j)
2j

Get the interpreter, and you can work out the rest yourself.

Graham