"warm fuzzy feelings"

Isn't "elegance" a quality of certain mathematical proofs? Unless you define
this solely as brevity or conciseness, isn't this another form of the "warm
fuzzy feeling" that was mentioned recently? So, a JI guitar would be
"elegant" because the acoustics of the vibrating string is reflected in the
tuning. Thats what I was trying to express when I said it gives me a "warm
fuzzy feeling". I believe in mathematics, "elegance" is a real component of
what makes a good proof, or at least an aesthetically attractive proof.
Tuning theory is not about "proofs" but it certainly is about aesthetics.

Dante

Rosati wrote,

>I believe in mathematics, "elegance" is a real component of
>what makes a good proof, or at least an aesthetically attractive proof.

Science is often about aesthetics because the simplest explanation is
usually the most beautiful, the best epistemologically (leading to the most
insight), _and_ the most likely to be correct.

>Tuning theory is not about "proofs" but it certainly is about aesthetics.

For a piece of aesthetically beautiful tuning theory, see Balzano's paper
_The Group-theoretic Description of 12-Fold and Microtonal Pitch Systems_.
This has got to be the most elegant and aesthetically attractive proposal of
a new tuning system that I've ever seen. In fact, it's so well-constructed
that some of our finest minds have been convinced by it. But does that make
it in any way a "proof" or "scientific"? It almost appears to be, but I've
spent some time on the list exposing its holes, and ultimately it's a house
of cards that comes tumbling to the table.

If you want the fretting of your guitar to stand as a work of art aside from
the music it makes, that's fine, but I don't care about that. What I care
about is the _sound_ it makes, and that's what tuning theory is really
about.

What's behind this, Dante? You're the only JI composer I've ever heard
claiming that JI intervals aren't sonically "special" in some way. Are you
dissatisfied with your guitar?

----- Original Message -----
From: Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>
> What's behind this, Dante? You're the only JI composer I've ever heard
> claiming that JI intervals aren't sonically "special" in some way. Are you
> dissatisfied with your guitar?

????? not at all! I just mean that JI intervals are "sonically special" JI
intervals, and ET intervals are "sonically special" ET intervals. I play
both kinds of guitars and I don't see it as a competition. Of course there
is a difference, otherwise why bother, but can't they both be "special"? I
don't feel like ET is a "compromise" or "degredation", it is what it is and
you can make great music using those intervals just as with JI intervals.
viva la difference!

Dante

>????? not at all! I just mean that JI intervals are "sonically special" JI
>intervals, and ET intervals are "sonically special" ET intervals.

Well, you (or anyone) can tune simple JI intervals by ear with far more
accuracy than you can tune ET intervals by ear, right? That makes the former
more "sonically special" to me.

>I play
>both kinds of guitars and I don't see it as a competition. Of course there
>is a difference, otherwise why bother, but can't they both be "special"? I
>don't feel like ET is a "compromise" or "degredation", it is what it is and
>you can make great music using those intervals just as with JI intervals.
>viva la difference!

That's fine! But then the only point of referencing the natural harmonic
series, to me, would be to explain the "specialness" that I eluded to above.
Otherwise, it's just a house of cards.

Dante Rosati wrote,

> JI intervals are "sonically special" JI intervals, and ET intervals
are "sonically special" ET intervals.

Not to deny the fuzzy purr of periodicity, which I'm sure your not,
but this kinda says it all for a lot of folks I'm sure! I'm don't
quite get what Paul's talking about ("You're the only JI composer I've
ever heard claiming that JI intervals aren't sonically "special" in
some way"), but most anyone who routinely composes in a wide variety
of tunings is bound to be of the 'both are sonically special' opinion
I would have to think.

Anyway, it's always a good thing, well to my ears and aesthetic
anyway, to hear it from someone else on this list.

--d.stearns

----- Original Message -----
From: Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>
> That's fine! But then the only point of referencing the natural harmonic
> series, to me, would be to explain the "specialness" that I eluded to
above.
> Otherwise, it's just a house of cards.

Is there a difference between "conceptual specialness" (elegance) and "sonic
specialness"? Or are they the same thing, one perceived with the conceptual
mind, and the other with the aural mind?

Dante Rosati wrote,

>Is there a difference between "conceptual specialness" (elegance) and
"sonic
>specialness"? Or are they the same thing, one perceived with the conceptual
>mind, and the other with the aural mind?

Sure they're different. Milton Babbitt's music, for example, is
"conceptually special" but I would argue that it fails to get most of that
across aurally because our hearing apparatus is biased toward picking up
certain types of information and making certain types of simplifications,
while other types of information are nearly impossible to process aurally,
and Babbitt's theory failed to take any of this into account.

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:
> http://www.egroups.com/message/tuning/14771
>
> For a piece of aesthetically beautiful tuning theory, see
> Balzano's paper _The Group-theoretic Description of 12-Fold and
> Microtonal Pitch Systems_. This has got to be the most elegant
> and aesthetically attractive proposal of a new tuning system
> that I've ever seen. In fact, it's so well-constructed that some
> of our finest minds have been convinced by it. But does that make
> it in any way a "proof" or "scientific"? It almost appears to be,
> but I've spent some time on the list exposing its holes, and
> ultimately it's a house of cards that comes tumbling to the table.

Boy, the coincidences on this list sure are coming thick and fast!
Just this morning, I found out that Balzano teaches here in
San Diego, and so I've started looking for stuff, so that I'll
be familiar with his work when we meet face-to-face. I have
indeed been very impressed by the elegance of what I've read
so far.

Paul, I've seen only a few little tidbits from you about Balzano
since I've been on the list, so my guess is that it's stuff that
you posted back when Mills College was the list server. If you'd
be willing to put it all together in one posting, I'll upload it
to my site. Perhaps if it refers to Onelist/eGroups postings
you can just make a list of the relevant links.

-monz
http://www.ixpres.com/interval/monzo/homepage.html

Hi Monz,

Did you try a search on Balzano on the Onelist/eGroups server? That should
get you everything you need -- though there's not much of interest in the
first (most recent) page of search results -- keep going from there. Feel
free to ask me for clarifications.

-Paul

>>I believe in mathematics, "elegance" is a real component of
>>what makes a good proof, or at least an aesthetically attractive proof.
>
>Science is often about aesthetics because the simplest explanation is
>usually the most beautiful, the best epistemologically (leading to the most
>insight), _and_ the most likely to be correct.

The last two are the same, and the first is a behavior-creating emotion we
evolved because being correct is good for survival.

>For a piece of aesthetically beautiful tuning theory, see Balzano's paper
>_The Group-theoretic Description of 12-Fold and Microtonal Pitch Systems_.
>This has got to be the most elegant and aesthetically attractive proposal of
>a new tuning system that I've ever seen. In fact, it's so well-constructed
>that some of our finest minds have been convinced by it. But does that make
>it in any way a "proof" or "scientific"? It almost appears to be, but I've
>spent some time on the list exposing its holes, and ultimately it's a house
>of cards that comes tumbling to the table.

Perhaps I never understood Balzano's paper, Paul, but I'm going to have
to disagree. He makes an awful lot of assumptions... and when did you
ever expose any holes? The only arugment I can remember you making was on
the failure of the scheme to produce consonant chords -- something which
Balzano lists as one of his goals in his introduction.

-Carl

>Perhaps I never understood Balzano's paper, Paul, but I'm going to have
>to disagree. He makes an awful lot of assumptions... and when did you
>ever expose any holes? The only arugment I can remember you making was on
>the failure of the scheme to produce consonant chords -- something which
>Balzano lists as one of his goals in his introduction.

He makes you believe that the familiar properties of scales, keys, and
triads come from, and belong only to, a certain kind of 4-by-3 group
(4*3=12). It's so convincing, you almost have to believe it . . . until you
remember that the very same properties, at least for music until Beethoven,
also arises in 19 and 31 -- smashing his whole argument.