Spiritus:
You are wrong.
The quality of melody, which a tune has, is not found in any of the component notes.
Here’s another.
A parabola on a Cartesian plane has a quality not found in any of its points, its curve.
O R G A N I Z A T I O N.
Organization determines the melody and defines the curve. In music it can be represented with a score. In mathematics it can be represented with an equation.
The best lack all conviction
The worst are full of passionate intensity.
*
melody: Music.
a) A rhythmically organized sequence of single tones so related to one another as to make up a particular phrase or idea.
b) Structure with respect to the arrangement of single notes in succession.
c) The leading part or the air in a harmonic composition.
parabola: A plane curve formed by the locus of points equidistant from a fixed line and a fixed point not on the line.
The best lack all conviction
The worst are full of passionate intensity.
*
Lib: “I am just trying to establish an informal debate on the topic of gestalt in the hopes of, for one thing, clearing up just what gestalt is. But I don’t find all the Clintonesque definition of is stuff to be helpful.”
Lib, you seem to want to dismiss discussion over your definition of “gestalt” as trivial. Let me break something to you: IT IS STILL NOT CLEAR IF YOU BELIEVE THAT ORGANIZATION IS SUFFICIENT TO ACCOUNT FOR THE GESTALT PHENOMENON. You can try to dismiss everybody as trying to pester you with insignificant details, but when it isn’t clear what you mean on this fundamental point in contention then it is very, very difficult to hold a reasonable discussion with you. It is not clear what you are trying to say. I am not being contrary, I am not “out to get you” or anything like that. I would very much like to have a reasonable discussion, but when you refuse to come out and say what you mean it is very difficult. I thought I was finally getting your message when you said
. I agree with that 100%. I also agree with Spiritus’s response 100%. The “gestalt” perception of “melody” comes because we percieve the organization of the notes. Similarly, a single star can’t be a constellation, but a group of stars can when they are organized in a particular way. Please respond as clearly as you can to Spiritus, because he has gotten right to the heart of the matter.
Lib, I’ll tell you what I think about von Ehrenfel: he didn’t understand music. Let’s take a simple six note melody:
do do me do la sol
That’s the first measure of “Happy Birthday”. It can be played in any key and is still very recognizable. Why? Not because of some seventh element of complex construct. It is recognizable because we have a ‘do’ then the second ‘do’ ‘me’ ‘do’ are all a major third apart and the ‘la’ is a major sixth removed, and finally the ditty resolves itelf with a perfect fifth.
The mathematical organization of frequency is the only property missing. Spiritus & Erratum are right on the money. That organization is essential to our recognition of the melody. Feed those notes into a computer and let it randomly play them back. You will eventually hear “Happy Birthday”. I fail to see any missing properties.
Yet to be reconciled with the reality of the dark for a moment, I go on wandering from dream to dream.
Gentlepersons
Well, to the elbow maybe.
Organization is only ONE part of it. There can be no organization without an overall context. There can be no organization into melody without scales. In fact, unless a melody is a scale, it respresents a disorganization of scale. There can be no organization into an equation without algebra. And unless your equation is an identity, it is disorganized until you solve it.
Sake
Actually, the first note in Happy Birthday is not the tonic note. If you start on C, you’re in the key of F. F will be the last note of the song.
So its — sol sol la sol do ti
“There can be no organization into an equation without algebra.”
If you show a parabola to a three-year-old, it will still be a parabola, even if the kid doesn’t know algebra. You are attributing properties of the observer to the object again. It doesn’t matter what we use to describe a parabola (and, by the way, there are non-algebraic ways to define a parabola, such as the one Spiritus Mundi gave), it only matters how the points are arranged. Same for music.
Erratum
No, it doesn’t.
It also matters what they’re arranged on. A parabola drawn on a coordinate system other than a Cartesian one might not even have a curve.
No, it isn’t.
Erratum beat me to it this time.
Lib, you seem to be confusing a particular scheme of organiztion with the quality of being organized. Eastern and western scales differ, yet both organize notes into melodies. The “context of organization” which you seem to be requiring is the perception of an observer. You say that “unless a melody is a scale, it respresents a disorganization of scale”. This is your perception, and it is shaped by your culture and your experiences. If you hand me a guitar and I start plucking strings at random while inexpertly fingering frets (which is about all I would be able to do–well, I could probably smash it dramatically over an amplifier, but I digress) I will be creating a melody. Now, I grant that it will not be euphonius and people are unlikely to ask me for a repeat performance, but it is still a melody. Whether you can map it to any particular musical scale is irrelevant.
The case for algebra is even simpler. There are multiple ways to define a parabola without reference to algebra. I gave one above. Another is through conic sections. Algebra is simply another tool we have to describe a particular arrangement of points.
The best lack all conviction
The worst are full of passionate intensity.
*
“A parabola drawn on a coordinate system other than a Cartesian one might not even have a curve.”
A parabola is not defined as “y=x^2”, it is defined as Spiritus defined it. In a cartesian coordinate system, that happens to be equivalent to “y=x^2”. If you aren’t talking about y and x in cartesian coordinates, then you aren’t talking about a parabola with that equation. With a little bit of thought or a search of the net, I could find the equation for a parabola in polar coordinates. Would that convince you? You can change the coordinate system all you want, you can’t change the shape. Similarly, in base 10, pi is roughly 3.14159… You can’t change the value of pi by representing it in binary. You want to assign the properties derived from the medium of communication to the object itself. That doesn’t fly. A parabola is a parabola is a parabola, and is so because of its shape. A parabola was a parabola before analytic geometry was invented. When you cut a cone in the right way, you see a parabola, whether you know it or not. A parabola is a shape, an arrangement of points.
Erratum already gave the correct answer to this one, so let me just add:
Then it won’t have the “gestalt” property of curve, will it? 
The best lack all conviction
The worst are full of passionate intensity.
*
Y’all are exasperating.
The shape property of a cone depends entirely on its context, in this case, its topology.
See Extension theory The interface between set-theoretic and algebraic topology by Jerzy Dydak of the University of Tennessee, 1995.
I never said anything equivalent to the notion that the value of pi changes in some other base. What I was saying implied that the value of pi would change if space-time were shaped differently.
Lib:
If I take a sphere and squeeze it into a torus, the properties of the shape change. It is also no longer a sphere. To say the shape is dependent upon the topology makes sense only if you are speaking about the mathematical representation not the object itself.
To illustrate:
I have a graph of a parabola on a cartesian plane. I erase x & y axes and superimpose a polar graph. I have the same parabola, but I will need a different equation to describe it in this context. This is a way to speak about parabolas.
I have the equation y==x**2. On a cartesian plane, this graphs as a parabola. If I change the topological context, it may graph sa a different shape. This is a way to talk about equations.
The best lack all conviction
The worst are full of passionate intensity.
*
Spiritus
I know, I know. Like I told you in the Ethics of Gestalt Thread, we don’t disagree on what you’re saying, but only what you’re meaning by it.
Yes, if you a roll a sphere into a torus it is no longer a sphere.
But if you roll your whole frame of reference, your whole context, your whole coordinate system then what somebody else sees as a twisted up mess, you still see as a sphere.
So you are again speaking about a perceptual quality, Lib.
Wheeeee… this debate’s sliding around like greasy ice.
Lib - Is this a bad-but-acceptable paraphrase of what you’re saying?: Let’s say I generated a random pattern of pixels on my monitor. In the pattern I’m seeing, the pixels are of a specific number, location, size and color. But they’re not organized, they’re random. Now this JPEG I just opened also has pixels of a specific number, location, size and color. But in these pixels I see the Mona Lisa, that is, there is a context within which these pixels have organization, hence the “Mona Lisa gestalt”. So, context determines organization (no context for organization = no organization).
Spiritus - Is this a bad-but-acceptable paraphrase of what you’re saying?: Same song and dance I gave Lib, in reverse… organization generates context (no organization = no context).
Other-wise
You have it essentially right.
All of reality exists in the context of reference frames; conversely, nothing is real, and cannot be organized, outside a perceptual context. It is a simple matter of fundamental thermodynamics and elementary relativity.
What a lovely piece of scrap irony!! 
Huh?