A = 432 or 440?

432 vs 440 - Harmony is determined by having low aliquot numbers. High aliquot numbers therefore equal discord. A frequency (cycles per second) is a composite or resultant of its aliquot parts. Composite or aliquot parts are found by factoring. [see overtone series]

432 = 2^4 * 3^3 all low numbers = (concord)
440 = 2^3 * 55 * 11 dangling higher numbers = (discord)
Therefore 432 has greater harmonicity than 440.
Of course, there is a lot more to this but the above ought to get you thinking. The true values here are to be found in the relationships between the overtone series of the fundamental of the scale, the notes on that scale and each of their overtone series. Computing the degree of harmonicity between all these notes and their secondary and tertiary harmonics/partials will show exactly how they do and do not harmonize. [see Law of Harmony]

Dougald Carmichael Ramsay
"Partials - Harmonics, so called because they are the parts of a sound." [Scientific Basis and Build of Music, page 63]

Schauberger
The outcome of this incessant reciprocal activity on the one hand is the reconstitution of the various kinds of water present in the individual zones, and on the other, the constant transformation of the species of vegetation in which water makes its way, ceaselessly moved by this inner interplay of forces. This inner, energetic interaction, however, is opposed by the effect of the water's weight. The alternating magnitudes of these component forces inevitably lead to the constant rising and falling of the water particles - the so-called pulsation of water. Every new formation and all growth is derived from the smallest beginnings. Continuing development in the early stages can only be accomplished if the circulation in the Earth's interior proceeds correctly. According to inner law, every higher form of vegetation is built up from the lower species preceding it. The carrier of the substances and the transmitter of the life-processes in the root-zone is the groundwater. The impulse for its movement is caused by a drop in temperature, to which the inner metabolic processes of the here decisive groups of basic elements give rise. The impulse for the movement of water is thus a product of the interactions between the opposites contained within it, which find their necessary resistance in the water itself. Through the resistance arising from the interactions between carbone and oxygen, fluctuations in temperature again occur and with them the impulse to move - the pulsation of water, which in this way at times dissolves salts and at others deposits them, transports them, creates energies and transforms them. The sense and purpose of these perpetual transformation processes is the creation and maintenance of the various types of vegetation and physical forms, which on their part again represent the bridges for the build-up and maintenance of the energies. [The Energy Evolution - Harnessing Free Energy from Nature, Conclusions]

See Also

432
Constituent
Fast Fourier Transform
partial
harmonic waveforms
harmonics
overtone
Table 11.05 - Comparison of Scale Structural Components and Relations
waveform

Frequency of A (Dale Pond; 2004, 07/06)
In the Schiller Institute article they make much of not using A=440 Hz because of its detrimental effects on the human voice. There are other issues too, I'm sure. I believe it was Pythagoras (who probably got it from Egypt) who first proposed or demonstrated A=432, in a "natural scale" scenario as pertains to vibrating strings. I concur with this finding or proposition insofar as it goes.

But, as always, there is far more to this issue than at first (even after 17 years of research!) meets the eye, ear and mind. Suffice it to say, for now, A=432 is more "natural" than other frequencies. Of course, most musicians will use whatever tonal frequencies best serve their specific purposes. And this is as it should be (IMHO) because having freedom to create something new and unique is important to us.

There are countless vibrations, oscillations and cycles moving among themselves constituting the rhythmic motions of the natural universe. Some researchers during the remote past have been sensitive to certain of these cycles and periodic motions sufficient to discern them and make other uses of them. So we see witnessed in ancient structures all sorts of numbers, number theories and relationships. Perhaps some numbers are more important than some other numbers IN CERTAIN CONTEXTS. But numbers like everything else are neutral possessing the meanings we have chosen to associate with them as also their relative standings amongst themselves within certain other relationships with each other.

I see the tension between A=432 or A-440 pretty much as written - but in a slightly different contextual expression. That A=432 leads to Concordant arrangement. If A=432 is concordant with nature then it participates in Concordant Chord Settings (what we would call today a Concordant Signature). A=440 is then a participant in discordant chord settings, by whatever degree of discord. So yes, as you say, A-440 is of the Terrestrial (material) realm whereas A=432 is of the Celestial (Divine) realm.

If we are to aspire to peace and harmony in life, as Keely said in his article "The Chord-Settings of Life" we must look within and cohere to concordance with the Celestial influences as evidenced by virtue of these concordant chord settings which are of the divine. In a sense then we "tune" our personalities to these centers.

"For the experience becomes rather as a very delicate instrument of music upon which the chords of life (which is God) are played." [Cayce (1436-2)]

It would behoove us then to compose and listen to music built upon this base of A=432 and shun music composed with anything else.

Not 432 Hertz per se but the overall behavior of vibration/oscillation in its natural state - uninterferred with. In this natural and dynamical state A=432 occurs but not A=440 unless as a participant in obtuse or unnatural tuning arrangements. It's (A=432 et al) correlation is with consciousness in its quiescent state; i.e., meditative Whole Mind state. Whereas A=440 is more in line with consciousness in its 'excited' state of thinking, worrying, fear, guilt, etc. Hence the use of this tuning in our times as it facilitates these states and subsequently the "necessary" social commands and controls to "check" such (mis)behaviors.

It is therefore theorized that if the tuning to A=432 were more prevalent (truly ubiquitous) society would settle down as individuals settled down into a closer approximation of who and what they are: Love (Peace, etc.) [See Chord of Life Windchime]

The dynaspheres (and windchimes) are exemplifications of this theory, applied. People (not all!) feel a sense of deep Love, Peace and Joy when close to these devices. So in a way, as much as we've been enabled to date, we are demonstrating this theory in practice.

You also elude to a few of the problems in tuning the various types of instruments whether string, horn or keyboard. Mark was asking about accented notes. It was in addressing these and other difficulties and conundrums that led me to relentlessly dig after whatever underlying principles of tuning, harmonic generation/suppression, etc., etc. that could be discerned. What struck me in the face after working hard on music theory and vibration physics for seventeen years and misbelieving I was a dunce or something because I wasn't making sense of it all was that I was working with a hodge-podge of more or less bogus material. It wasn't me!!! It was the material. The music theories we have extant today are inherited kludges and mish-mash assemblies patched and stitched together over centuries. In short music theory is a "friggin' mess".

Some years ago I developed a program to compute limited harmonic series and summation tones. During my combating the Devil of Confusion over certain musical principles I managed to well scramble that original code as I attempted this or that matrix/algorithm. Some day when I'm not so caught up in more essential things like finding groceries and gas money I'll debug that code and expand upon it to include substractive (sub) harmonics. I will most likely do this new programming in Mathematica should I ever be able to afford a copy and master its esoteric programming. Until then I yield the floor on this topic to whoever wants it. It is likely this may become a group project before its done and completed...

And there is the so-called spiritual side of music that mathematics cannot quantify.

440
"In 1910 Deagan persuaded the American Federation of Musicians, at its annual convention, to adopt A-440 as the standard universal pitch for orchestras and bands, thus settling a question which had long agitated musical circles. It was also accepted by the United States government and generally throughout the world." http://www.deaganresource.com/

Howard Boase
"I can unequivocally say without any reserve whatsoever that the reason why the A440 Frequency came into effect which was actually instigated by a German musician was for the simple fact that it would disallow many sections of people and cultures from being able to sing in tune or a particular key and this I have actually tried out on a person who is no longer in the land of the living when she was alive of course and asked her to sing her favorite song by Louis Armstrong and of course she said I will sing completely out of tune and after she sang to her favorite song she said to me that she thought she'd sang completely out of tune but in reality she had sang every single note perfectly in tune and we were using the A432 Frequency as it happens and she has never ever sung a note in key for part whole entire life you using the A440 frequency.
It is interesting to note that the New York Symphony Orchestra and the Boston Symphony Orchestra actually use A442 and the Russian Symphony Orchestra uses A443. I have actually tuned pianos to both of these unusual frequencies and was bold over by The Incredible vibrancy of the piano's when tuned to these particular frequencies.
As a footnote to this it is also interesting to note that during the second World War German officers forced Jewish people to play using the A440 Frequency as well which was very much against their natural A 432 frequency which they had been using and musicians all over the world have been using up until a particular point in historical music time." [Howard Boase]

See Also

04 - On the Pitch of Musical Sounds
05 - The Melodic Relations of the sounds of the Common Scale
528
concert pitch
Concordant Chords of Sympathy
Etheric Vibratory Scale
Figure 10.01 - Tuning Forks in Sympathy
Figure 8.5 - Summation Tones
Figure 8.14 - Some Basic Waveforms and their constituent Aliquot Parts
GRADUATION OF MACHINES
GRADUATION OF SYMPATHETIC MACHINERY
Graduation
Music
Overtone Series
Positive graduating Chladna
Scale of the Forces in Octaves
Scale
sympathetic graduation
Table 11.03 - Roots Powers of Two and Indig Numbers
tuning fork
Tuning Forks Sympathy
Tuning
MUSICAL CULT CONTROL: THE ROCKEFELLER FOUNDATION'S WAR ON CONSCIOUSNESS THROUGH THE IMPOSITION OF A=44OHZ STANDARD TUNING
1.23 - Power of Harmonics through Summation Tones