Phonons

>}>>Gary, this is not correct. E = H nu applies to all energy quanta, whether
>in
>}>>the form of light, sound, or whatever. The quantum of light is the photon;
>}>>the quantum of sound is the phonon.
>
>} If by this you mean that sound is conveyed by phonons in the same sense
>}that light is conveyed by photons, then the more I think about it, the less
>}I buy it.
>
>I'm not surprised. As a young one I read stacks of Scientific Americans from
>the '70s. Seeing articles about phonons led me to feel much as you do now.
>Although I did not specifically study phonons in quantum mechanics, I have
>learned the fundamentals well enough so that my skepticism has been abated.
>That is, the truly astonishing things about quantum mechanics reside at a
>much deeper level and force us to throw away our customary "pictures" of
>physical phenomena, which rely on philosophical assumptions such as
>Einstein's reality principle, which has been shown experimentally to be false
>(via Bell's theorem). If one finds a way of accepting the crazy axioms of
>quantum mechanics, or just takes them for granted, one can construct the most
>verifiably accurate physical theory known to mankind (general relativity has
>been verified slightly more accurately in some contexts).
>
}Now there's normally no realistic value in studying sound at the
}sub/atomic level, because everything about sound can be modeled many
orders
}of magnitude more simply at the macroscopic level of mechanics. But
still,
}down at the level of fundamental forces, air-pressure is manifested by
}collisions of air molecules, and any form of collision is carried out
by
}repulsion between the electrons in the outer shells of those molecules.
}Electron repulsion is in turn carried out by photons.

Classically, two spherically symmetric neutral atoms would experience no
electrostatic forces even if separated by a very small distance.
Electron repulsion would be exactly balanced by attraction to the other
atom's nucleus. Quantum mechanically, this is not quite the case, and
you get the so-called Van der Walls forces which vary as the sixth or
twelfth power of the distance.

But it is the Pauli exclusion principle, not electrostatic or
electromagnetic interactions at all, which is responsible for collision
forces. Let's consider crystals, however, where it is not collisions
that transmit sound energy.
>
>}So sound is, at this otherwise not very interesting sub/atomic level,
>}ultimately conveyed by photons. The invention of a new particle, the
>}phonon, seems to be no more than a pointless complication that side-steps
>}well-accepted physical models for no apparent reason.
>
>The concept of the phonon had proved very useful in the study of crystalline
>lattices and semiconductors. It does not side-step quantum mechanics (the
>most well-accepted model), and your classical way of viewing things is only
>valid at the macroscopic level, where it emerges as an approximation.
>Electron-phonon scattering is very real, just like electron-photon
>scattering, even though the photon is "only" a wave propogating through the
>electromagnetic field. Just as the equations of the electromagnetic field,
>describing how an electric field is produced by a changing magnetic field and
>vice versa, give rise to wave solutions, so do the equations of a crystal
>lattice, with bodies vibrating around their equilibrium positions and
>interacting with one another according to Van der Walls-type forces or, in
>the case of an ionic crystal, electrostatic repulsion and/or attraction.
>There are transverse as well as longitudinal wave solutions to these
>acoustical equations. The quantum-mechanical duality between energy waves and
>particles is universal. Even you are a wave, capable of interference,
>diffraction, and all -- it's just that your wavelength is so short that these
>effects are undetectable.
>
}When I think about the classic experiments for illustrating the
}particle-wave duality of light, it's difficult for me to see any way to
}apply them to sound. I can't imagine any way for example, that you
could
}get a particle-like distribution from the famous "two-slit" experiment
if
}conducted with sound rather than light. But presumably that just means
}that I'm conducting an unrevealing experiment.

Single quanta of sound are extremely difficult to isolate in the
laboratory. By the formula E=H nu, you can see that the energy of a
phonon is astronomically smaller than the energy of a photon, which is
already so small that light energy was thought to come in continuous
quantities until this century.

I think that's enough physics for this list. E-mail me in person, or
better yet, go study quantum mechanics!


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From: "Paul H. Erlich"
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I've noticed that melodies and harmonies don't necessarily have to share
the same scales. When I studied with Ben Johnston, it was an assumption
that all pitches needed for harmony and melody would be part of the same
set. I now questions that.

As an example, let us take the tune "Amazing Grace" which is itself
pentatonic. it came be harmonized by confining oneself to the pentatonic
pitches (anything pretty much goes), or by using other scales. For
example, in most hymnbooks, it is harmonized in diatonic harmony, which
requires the 4th and 7th scale degrees. In Ben's variations, he goes
further along, harmonizing it with 7th partial relationships (and 11th, if
I recall correctly.) The piece works, I think!

I see no reason why the pitches used for melodic material need to be the
same as those used for harmony. Actually, for anyone who has played with
scales in just intonation, it is obvious that the second scale degree
(let's call it 'Re') which is a perfect fifth above 'Soh' is not the same
note as the one that is a minor third below 'Fa.' And it is also true
that there are two 'Fa's: the one that is a perfect fifth below 'Doh', and
the one that is a minor seventh above 'Soh.'

Of course, in equal temperament, we just sort of average out the
differences, but if we really want to play in tune, then we need more
notes than are in a diatonic scale.

Joe Downing,
in Syracuse


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>I've noticed that melodies and harmonies don't necessarily have to share
>the same scales. When I studied with Ben Johnston, it was an assumption
>that all pitches needed for harmony and melody would be part of the same
>set. I now questions that.

I'm inclined to agree, based upon the small and large ensemble
performance on imprecise-pitched instruments I've done over the years. For
example, in some comparatively homophonic contexts wherein the "chord"
parts have a fairly slow harmonic rhythm, I have heard many cases where
melodies are rendered closer to equal, and harmonies closer to JI. But I
don't mean that to suggest that that's a general pattern; just one type of
scenario I've noticed before.

Along similar lines, I have also noticed in duet-playing on woodwinds, a
tendency for the harmony part to come closer to JI relative to the melody
part's approximately ET pitch.


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From: mr88cet@texas.net (Gary Morrison)
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