crazy, man... crazy

This is crazy... but doesn't "Irrational" music mean we should all be
using "decimal points??"

I guess that belongs on the "Tuning Math" list...

___________ ______ _____
Joseph Pehrson

[Joe:]
> This is crazy... but doesn't "Irrational" music mean we should
> all be using "decimal points??"

> I guess that belongs on the "Tuning Math" list...

Joe, don't you remember in practicalmicrotonality
there were discussions about renaming the group from
various factions.

Mary had the suggestion of 'Irrational Microtonality'
which I thought was great and worth preserving because
of the multiple meanings.

(BTW, real numbers with decimal points _are_ rational.
I thought irrationals were transcendental numbers like
pi that could not be represented in a whole number base
by using fractions and also includes complex and imaginary
numbers (does it?))

- Jeff

In-Reply-To: <200106011622.JAA09104@...>
Jeff wrote:

> (BTW, real numbers with decimal points _are_ rational.
> I thought irrationals were transcendental numbers like
> pi that could not be represented in a whole number base
> by using fractions and also includes complex and imaginary
> numbers (does it?))

My, how quickly *this* list turned into numerological babble :)

A rational number is a fraction composed of two integers, so yes any
finite decimal is in this category. A transcendental number can't be the
solution of a polynomial equation of integers. So pi is transcendental,
but phi is merely irrational. I think complex and imaginary numbers
would be "complex" and "imaginary".

Graham

--- In crazy_music@y..., "X. J. Scott" <xjscott@e...> wrote:

/crazy_music/topicId_65.html#68

> (BTW, real numbers with decimal points _are_ rational.
> I thought irrationals were transcendental numbers like
> pi that could not be represented in a whole number base
> by using fractions and also includes complex and imaginary
> numbers (does it?))

Hi Jeff,

"Irrational" means exactly what the word says: any number
which cannot be represented as a fraction comparing two
integer terms as a ratio.

If you multiply the number by any integer denominator and
you can't get rid of the decimal in the numerator, it's
irrational.

-monz
http://www.monz.org
"All roads lead to n^0"

--- In crazy_music@y..., "X. J. Scott" <xjscott@e...> wrote:

/crazy_music/topicId_65.html#68
> (BTW, real numbers with decimal points _are_ rational.
> I thought irrationals were transcendental numbers like
> pi that could not be represented in a whole number base
> by using fractions and also includes complex and imaginary
> numbers (does it?))
>
> - Jeff

I'm sure you're right, Jeff. That's why I'm posting over here on
the "Crazy Music" list rather than on the "Math Tuning" list. I know
where I belong!

_________ _____ _____
Joseph Pehrson

[monz:]
> "Irrational" means exactly what the word says: any number
> which cannot be represented as a fraction comparing two
> integer terms as a ratio.

OK yes I really should have said 'irrationals *include*
transcendental numbers'.

And imaginary and complex numbers can be irrational or
rational I suppose: 3i vs 2i/3 + 1/4.

Not sure if imaginary numbers are or are not
transcendental. Graham says "A transcendental number
can't be the solution of a polynomial equation of
integers." which if that is a sort of definition
would separate the two since complex numbers obviously can
be soch a solution.

> If you multiply the number by any integer denominator and
> you can't get rid of the decimal in the numerator, it's
> irrational.

Not following this, I think you meant to say something
else.

Also, when Graham said "A rational number is a fraction
composed of two integers" I think he meant "A rational
number is a fraction composed of whole numbers", since 0/0
and 1/0 are not rational.

*** Any follow ups please to metatuning, since we are
basically talking about the name of this group and not
about actual music. Sorry I brought it up in this group.

- Jeff