Re: ¿ cents value for 1048576/531441?

In a message dated 2003:05:03 09:07:50 AM, monz quotes paul & writes:

>"wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>

>> if you know that the pythagorean comma is 23.5 cents,
>> then you can see this is just 1200 - 23.5 = 1176.5 cents.
>
>Micosoft Excel gives me this:
>
>1048576/531441 = (2^20)*(3^-12) = ~1176.53999 cents.

Yick, MikroSoviet ;)

>you could pretty much say that it's 1176.54 cents.

I might be horrible at higher math (but, hey, I am improving... look at
what I know about microtonal concepts compared to 2-3 years ago
[Shit-crikey!, some things I wrote back then under the "zHANg" identity just
make me cringe in my seat today]), but at least I can round, cut corners ;)

>Excel often truncates long strings of decimal
>places to 7 or 8 decimal places, but here it
>only rounds to 5.

And my "freebie" calculator freaks at 3-4 decimal places... and somehow I
don't exactly wanna trust it's square root function (besides I rather open my
lil math book than turn the calculator on).
I have this old, old freeware kiddie math education program (high school
level) for Mac (System7!!!) * that is called MacChord which is a "digital
monochord" that supposedly calculates ratios and cents - it seems to only
calculate 5-limit, part of the 7-prime ratio spectrum and most of the common,
low-complexity Pythagorean - as well as compare them to 12tET monochord
positions, cents and decimals.
In another words, even this education program is entirely geared/biased
toward 12tET. In the readme file there is only a footnote on meantone scales.
There is an implicit subtext that makes it seem like 12tET is the
zenith-point of musical evolution.

* I am amazed it works on my PowerMac (OS9). My copy of JICalc (for
pre-PowerMacs) doesn't fair as well- it doesn't even "read"...

>to explain what paul said:
>
>(2^-19)*(3^12) is the prime-factorization of
>the Pythagorean comma, very nearly 23.46 cents.
>
>inverting the signs of the exponents,
>(2^19)*(3^-12) is a "negative Pythagorean comma",
>approximately -23.46 cents.
>
>adding an "8ve" (1200 cents) to this,
>-23.46 + 1200 = 1176.54 cents.
>
>algebraically, -23.46 + 1200 simplifies to
>1200 - 23.46, which is basically what paul wrote.

Aw, that makes it much easier to understand or at least follow
::scrambles to math reference books, i.e. _Math for Dummies_ and _Introducing
Mathematics_, etc.::

Thanx, Monz. And you, too, Paulie.

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& Gatherer of Extremely Enlightening Knowledge (or GEEK, for short ;)
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