<12 19 28|-4 4 -1>=0

Is this equation like the e=mc^2 of music?

-Mike

Depends on whom you ask.

http://www.encyclospace.org/tom/artikel.pdf

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Is this equation like the e=mc^2 of music?
>
> -Mike
>

--- In tuning@yahoogroups.com, "hstraub64" <straub@...> wrote:
>
> Depends on whom you ask.
>
> http://www.encyclospace.org/tom/artikel.pdf
>

Mensch, was liest du da?! LOL.

Whatever the formula for music may be, the formula for music theory is sadly no mystery: I > U.

Hi Lobawad,

Am 06.03.2012 10:47, schrieb lobawad:
>
> Whatever the formula for music may be, the formula for music theory is sadly no mystery: I > U.

What do you mean by I > U -> "Intention > Understanding" ?

Best,
Wolf

--- In tuning@yahoogroups.com, Wolf Peuker <wolfpeuker@...> wrote:
>
> Hi Lobawad,
>
> Am 06.03.2012 10:47, schrieb lobawad:
> >
> > Whatever the formula for music may be, the formula for music theory is sadly no mystery: I > U.
>
> What do you mean by I > U -> "Intention > Understanding" ?
>
> Best,
> Wolf
>

That was a joke: "I am more (better) than U (you)". Maybe it is more funny if you read a lot of Taruskin, hahaha!

Hello Hans,

You changed the subject, so did you get this formula 5*d+2 ? - I'm not.
I read the article, but its writer seemed also uncertain in this point.

Thanks in advance for clarification :-)
Wolf

Am 06.03.2012 10:27, schrieb hstraub64:
> Depends on whom you ask.
>
> http://www.encyclospace.org/tom/artikel.pdf
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>>
>> Is this equation like the e=mc^2 of music?
>>
>> -Mike
>>
>
>
>

--- In tuning@yahoogroups.com, Wolf Peuker <wolfpeuker@...> wrote:
>
> Hello Hans,
>
> You changed the subject, so did you get this formula 5*d+2 ? - I'm
> not.
> I read the article, but its writer seemed also uncertain in this
> point.
>
> Thanks in advance for clarification :-)
> Wolf
>

I know the outlines of the theory (not from that article, though, which does not really go into technical details).

The formula is applicable to intervals in 12edo, represented mathematically as Z12 (integers modulo 12). The function f(x) = 5*x+2 (to be interpreted in modular artihmetics) has the property that it maps the set of intervals that are consonant according to Fuxian counterpoint (i.e. 0, 3, 4, 7, 8, 9) to its complement in Z12, and, moreover, it is the only affine function on Z12 with that property. Functions and partitions of this kind are the basis for Mazzola's counterpoint model, which - as often with Mazzola - consists of a lot of quite weird-looking mathematics, but, interestingly, produces quite accurately the rules of Fuxian first species counterpoint. How relevant this is is open to debate - and also, whether this is comparable to e=mc^2, of course. The magazine, I assume, wanted to squeeze a cartchy title out of it.

An interesting property of that counterpoint model is that it is applicable to arbitrary n-equal temperaments for even n. I have been planning for a while to try it out, for 22edo, for example - this would be a nice test for the relevance of the formula (if it sounds shitty, this would be a kind of falsification). But I haven't found the time yet...

The formula I>U, BTW, shines through in the article, too...
--
Hans Straub

Am 19.03.2012 17:04, schrieb hstraub64:
>
> I know the outlines of the theory (not from that article, though, which does not really go into technical details).
>
> The formula is applicable to intervals in 12edo, represented mathematically as Z12 (integers modulo 12).

Ah, this makes things clear! Thanks!
...and 5 (semitones, 5\12, aka fourth) is dissonant - as usual...

>
> An interesting property of that counterpoint model is that it is applicable to arbitrary n-equal
> temperaments for even n. I have been planning for a while to try it out, for 22edo, for example -
> this would be a nice test for the relevance of the formula [...]

I would expect that there is a similar formula for each edo - And I
would not be surprised if it turned out, that (basically) dissonance and
consonance are balanced...

Best,
Wolf

I would say there are cultures where the entire scale is set up in a way where the each tone is near equal in consonance and disonance to all the others. This has the property of allowing complete freedom in melodic independence. One can hear this in the music of the Pygmies, as well as in gamelan music.

,',',',Kraig Grady,',',',
'''''''North/Western Hemisphere:
North American Embassy of Anaphoria island
'''''''South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria
',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

-----Original Message-----
From: Wolf Peuker [mailto:wolfpeuker@...]
Sent: Monday, March 19, 2012 03:49 PM
To: tuning@yahoogroups.com
Subject: Re: [tuning] Re: k = 5*d+2

--- In tuning@yahoogroups.com, kraiggrady@... wrote:
>
> I would say there are cultures where the entire scale is set up in a
> way where the each tone is near equal in consonance and disonance to
> all the others. This has the property of allowing complete freedom in
> melodic independence. One can hear this in the music of the Pygmies,
> as well as in gamelan music.
>

The case of the perfect fourth, which is not allowed in Fuxian first-species counterpoint despite being counted as ("acoustically") highly consonant, can lead to reasoning that "acoustic" (or however you want to call it) consonance is not even that important in counterpoint... In the mathematics of Mazzola's model, "consonance" in the general meaning of the word is not important at all - all that counts is a special kind of symmetry, as the formula k = 5*d+2 summarizes. You can derive rules with dissonant intervals alone - how that sounds is another question. Well, maybe I should finally start exploring more seriously in that direction...
--
Hans Straub