Yahoo Tuning Groups Ultimate Backup mills-tuning-list What Einstein believed (Paul E)

From: PAULE

Einstein has been called "the last classical physicist." He pushed a 19th
century viewpoint as far as it could go in explaining the world. He espoused
a "principle of reality" that he thought would govern any physical theory.
After Einstein's death, John Bell showed that quantum mechanics contradicts
Einstein's principle of reality, and countless experiments have settled the
question in favor of quantum mechanics. The two most important attempts at
reconciling realism with physics have been Bohm's theory and the many-worlds
interpretation. These theories leave dicussions of an ether far behind.

Quantum field theory, aside from general relativity the most accurate
scientific theory known, explains forces in terms of exchanges of particles
and fields in terms of virtual particles continually coming into and out of
existence. In some cases, such as the strong nuclear force, the intermediary
particles themselves are subject to the very forces they mediate, making
mathematical understanding very difficult; computer simulations are
currently the best way of understanding the strong nuclear force. The
concept of an ether is again left far behind, even in the most "realist"
ways of discussing the subject matter such as Feynman's.

Any attempt at a new physical theory must deal with all these issues and
explain the phenomena better and more accurately than existing theories.
Although there is nothing wrong with speculation and imagination, especially
for musical inspiration, a critique of modern physical theory cannot begin
without a solid understanding of what we have learned in the last century.
Ray Tomes' discussions are guided by a distinctly 19th century understanding
(I could provide ample evidence but don't want to start a thread here). This
view of the world is eminently comfortable and is held by nearly every
student of physics at one time or another. Upon learning of the discoveries
of modern physics, the student is almost invariably overtaken by feelings of
shock and disbelief, and attempts to distort the evidence to fit the
classical understanding. This was the reaction of most of the scientific
community, including Einstein, in the first few decades of this century.

Physics and mathematics have made such tremendous advances in this century
that the understanding of our political and moral leaders, artistic and
literary figures, and most intellectuals have at best only begun to scratch
the surface of what has been learned. Mostly there is misinformation, and
not a few "scientists" and "science educators" are badly misinformed and
propagate the misinformation. The quality of education has not kept pace
with the advances in physics and mathematics, so most of us are left far
behind. Feeling frustrated at this situation, many rebel; rather than
studying physics so that they can construct better theories, the
reactionaries spout very respectable-sounding 19th century dogma and claim
that the establishment took a wrong turn in this century.

It is an unhappy situation to have acquired such a firm and comprehensive
understanding of the world and then have the rug pulled out from under your
feet. Scientists considered the field of physics to be nearing a close at
the end of the 19th century. But soon a few holes in the dam began to
appear, and not long after the whole structure came toppling down. From the
bricks that remained, Planck's radiation equation, the Lorentz
transformations, etc., a new structure was erected that was bizarre by all
accounts but beautiful nonetheless. The work done remains incomprehensible
to anyone who has not dedicated all their intellectual resources to the
subject for years at a time. The motivations for such dedication have
dwindled tremendously as the short-term value of pure science is
overshadowed by that of applied science, and the social respectability one
obtains by dealing in increasingly abstract disciplines is near the bottom
of the ladder. As a result, there are fewer and fewer capable teachers of
physics and the ignorance of the public increases.

So for now, back to music.

-Paul E.

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🔗Paul Hahn <Paul-Hahn@...>

On Fri, 14 Mar 1997, Atlas Eclipticalis wrote:
> What is the acoustical basis for this chord / unique sonority?
>[the French 6th]

Well, personally I interpret it as the combination of two 4:5:7 triads,
one inverted. In other words:

7/5 <--(4:5)--> 7/4

^ ^ ^
\ / \
(5:7) (4:7) (5:7)
\ / \
v v v

1/1 <--(4:5)--> 5/4

This is analagous to, say, a major seventh chord being made up of two
4:5:6 triads, like so:

3/2 <--(4:5)-->15/8

^ ^ ^
/ \ /
(2:3) (5:6) (2:3)
/ \ /
v v v

1/1 <--(4:5)--> 5/4

--pH http://library.wustl.edu/~manynote
O
/\ "'Jever take'n try to give an ironclad leave to
-\-\-- o yourself from a three-rail billiard shot?"

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🔗Andrew Milne <andymilne@...>

Richard E Barber wrote:

> What is the acoustical basis for this chord / unique sonority? What is
> the tuning implications of using a non-tertian sonority as a dominant or
> penultimate or half-cadence function?

The chord should be tuned as it is written. It is easiest relate this
chord to the root of its tonic (or resolution chord), so C E F# A#
should be analysed relative to B.

In any meantone system, therefore, C should be tuned as the minor second
above the tonic (in J.I. that is 16/15), the E as the perfect fourth
above the tonic (in J.I. that is 4/3), the F# as the perfect fifth above
the tonic (in J.I. that is 3/2) and the A# as the major seventh above
the tonic (in J.I. that is 15/8).

I have expressed elsewhere why I think it is inappropriate, in such a
context, to view any of these intervals as 7-limit ratios (despite their
similarity).

The origin of this chord is as a chromatic alteration of the second
inversion of F# dominant 7th. It should not be treated as a strange
xenharmonic consonant entity introduced entirely out of context with the
rest of the tonality.

Andrew Milne
Islington
London

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🔗Brian Belet <BBELET@...>

Actually, the various Aug. 6th chords don't need any acoustical
foundation (if one exists, that's fine, but not overly important).

These "chords" are the by-product of very nice chromatic voice-leading.
I.E., they are linear structures, not vertical sonorities. Our
traditional "music theory" courses (I prefer to call them "music systems"
courses, for they examine past, well-established practices, and really
do not address 'theory' at all) get too carried away with Harmony as the
primary structure, while linear melodic connections are actually the most
important area of construction.

While isolated as chords, these Aug. 6th creatures are really chromatic
approaches to the region of the dominant (usually, or initially), and are
thus alternate pre-dominant strucutures. Once this linear principle is
established (aurally and systematically) it is a small step to extend this
connection to areas other than the dominant (e.g., tonic).

-- Brian Belet

***********************************************************
* Brian Belet, D.M.A. bbelet@sjsuvm1.sjsu.edu *
* Music Systems Coordinator VOX: (1)-408-924-4632 *
* School of Music & Dance FAX: (1)-408-924-4773 *
* San Jose State University *
* One Washington Square, San Jose, CA 95192-0095, USA *
*---------------------------------------------------------*
* http://www.music.sjsu.edu/Comp/belet.html *
***********************************************************

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🔗Gary Morrison <MorriSonics@...>

🔗alves@Orion.AC.HMC.Edu (Bill Alves)

>Actually, the various Aug. 6th chords don't need any acoustical
>foundation (if one exists, that's fine, but not overly important).
>
>These "chords" are the by-product of very nice chromatic voice-leading.
>I.E., they are linear structures, not vertical sonorities. Our
>traditional "music theory" courses (I prefer to call them "music systems"
>courses, for they examine past, well-established practices, and really
>do not address 'theory' at all) get too carried away with Harmony as the
>primary structure, while linear melodic connections are actually the most
>important area of construction.
>
>While isolated as chords, these Aug. 6th creatures are really chromatic
>approaches to the region of the dominant (usually, or initially), and are
>thus alternate pre-dominant strucutures. Once this linear principle is
>established (aurally and systematically) it is a small step to extend this
>connection to areas other than the dominant (e.g., tonic).
>
> -- Brian Belet
>
>***********************************************************
>* Brian Belet, D.M.A. bbelet@sjsuvm1.sjsu.edu *
>* Music Systems Coordinator VOX: (1)-408-924-4632 *
>* School of Music & Dance FAX: (1)-408-924-4773 *
>* San Jose State University *
>* One Washington Square, San Jose, CA 95192-0095, USA *
>*---------------------------------------------------------*
>* http://www.music.sjsu.edu/Comp/belet.html *
>***********************************************************

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^ Bill Alves email: alves@hmc.edu ^
^ Harvey Mudd College URL: http://www2.hmc.edu/~alves/ ^
^ 301 E. Twelfth St. (909)607-4170 (office) ^
^ Claremont CA 91711 USA (909)621-8360 (fax) ^
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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🔗alves@Orion.AC.HMC.Edu (Bill Alves)

>These "chords" are the by-product of very nice chromatic voice-leading.
>I.E., they are linear structures, not vertical sonorities. Our
>traditional "music theory" courses (I prefer to call them "music systems"
>courses, for they examine past, well-established practices, and really
>do not address 'theory' at all) get too carried away with Harmony as the
>primary structure, while linear melodic connections are actually the most
>important area of construction.

That's interesting. I think our traditional "counterpoint" courses get too
carried away with linear melodic connections as the primary structure,
ignoring harmony. Seriously, I think that one of traditional music theory's
biggest mistakes is to teach that, for European music from at least the
16th to 19th centuries, it is possible to separate the "linear" from the
"vertical" and judge their relative "importance" separately. A parallel
development of theory and pedagogy in the two areas led to the odd state of
affairs where we now have separate "harmony" and "counterpoint" classes.

Certainly the augmented sixth chords developed through linear processes, as
did sevenths, but the fact that they have an effect on the listener as
sonorities as well cannot be denied. (Schoenberg took this reasoning even
further, saying, "Non-harmonic tones form chords, hence they are not
non-harmonic; the musical phenomena they help to create are harmonies, as
is everything that sounds simultaneously.")

There are plenty of possible "interim" chords formed by voice leadings, but
only certain ones found a common place in common-practice theory. It seems
to me that the use of the German augmented sixth as a pivot chord,
equalling the dominant seventh in another key shows that, for the
classical/romantic composers who used this technique at least, the German
augmented sixth was no less a "passing" sonority than a dominant seventh.

I have always scratched my head over those who claim that, because Bach
used polyphony more commonly and prominently than Beethoven, he was a more
"linear" composer. It suggests that Beethoven didn't care about voice
leading or Bach about harmony, which is ridiculous. All of Bach's
counterpoint results in beautiful triadic harmony, and Beethoven was just
as careful as his predecessor about parallel fifths and proper resolutions
and so on. In this style of music, harmony and counterpoint are part of the
same fabric.

Now, I'm not trying to put all of these arguments into the mouth of Dr.
Belet, but he brought up an interesting topic that is important for tuning
and composition as well. I sympathize with his impatience with traditional
"music systems" instruction and its often one-dimensional perspective.

Bill

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^ Bill Alves email: alves@hmc.edu ^
^ Harvey Mudd College URL: http://www2.hmc.edu/~alves/ ^
^ 301 E. Twelfth St. (909)607-4170 (office) ^
^ Claremont CA 91711 USA (909)621-8360 (fax) ^
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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🔗Daniel Wolf <DJWOLF_MATERIAL@...>

>From recent postings:

<''>These "chords" are the by-product of very nice chromatic voice-leading.
<>I.E., they are linear structures, not vertical sonorities. Our
<>traditional "music theory" courses (I prefer to call them "music systems"
<>courses, for they examine past, well-established practices, and really
<>do not address 'theory' at all) get too carried away with Harmony as the
<>primary structure, while linear melodic connections are actually the most
<>important area of construction.

theory's
<16th to 19th centuries, it is possible to separate the "linear" from the
<"vertical" and judge their relative "importance" separately.''

I think that this is a critical example of how the paper trail of theory
has diverged from practice - and how the theory can feed back upon music
making in a creative misreading (not unlike the literary hermeneutics of
Bloom). From Monteverdi's largely textural division into two practices, and
the solid tradition of counterpoint taught before figured bass, developed
the notion that counterpoint and harmony are independent domains - two
separate courses of study fitting tightly into semester schedules at large
Universities. To be fair, the best teachers and theorists (from Schenker
and Schoenberg to Boulanger) never made things out to be so black and
white, but their attempts to integrate vertical and horizontal viewpoints
rarely survived the journey to the heartlands, and by the mid-1950s, modal
counterpoint was seldom taught at all. A Schenker-inspired countermovement
would move again in the counter-direction, but like the set-theory-based
''new math'' of the 1960's, my impression is that it has been largely
taught in a mechanical way (with the goal of producing identical
'schenkergrams') by teachers not completely comfortable with the
theoretical rationale. I have heard that some schools are now moving in an
algorithmic direction. (Actually, the MacHose text that my Junior High band
director gave me used a statistical approach that could be considered a
prototype of certain trends in this direction).

The most interesting thing is that all of these swings in theoretical
orientation have made real marks on the way that people do make music, both
composing and performing. Ivor Darreg, to take just one curious example
from the microtonal community, learned from his teacher to assemble a
thematic catalog and to outline as many potential harmonizations as
possible. Had his teacher worked from a more contrapuntal basis, I imagine
that Ivor's music would have had a very different character. Partch's
impulse to harmonize on the basis of chords built on ''stacked thirds'' -
as well as the systemic use of inversion - can be heard as a token of a
particular theoretical orientation.

To bring the thread back, Milne criticized my position on the 4-5-6-7
tuning of the dominant by arguing that harmonies with ninths and elevenths
voided my argument. However, I think that the repertoires in which such
extended harmonies are present are already well beyond the tonic-dominant
dynamic, and I am extremely hesitant to speculate about the intonational
content of such repertoires (M. Vogel's book on the ''Tristan'' chord
should be cited in this context). The question is, is 4-5-6-7 an
_acceptable_ (note that I have not said ''authentic'') tuning for the
dominant in a repertoire - say Viennese classical music - where this
dynamic is well established? While practically out of the question for
keyboard instruments, for strings, I find it acceptable - and in some
cases, desirable.

The augmented sixth chord's approximation of 4-5-6-7 in meantone deserves
further comment. As someone has pointed out, this chord was heard in
passing in choral music (which may or may not have been accompanied) and
only with frequency as a sustained chord in repertoire where ET was
established (at least as an ideal). So the question remains, why was this
wonderful chord not used more often in meantone keyboard music? I think
this is an excellent example of how our prejudice towards ''harmony'' - our
bias via training to hearing the vertical consonance - makes us relatively
deaf to the contextual, melodic ''dissonance'' caused by the proximate use
of tones from relatively distant scalar collections. This is, for me, a
wonderful example of how context can make an in-tune chord sound
''dissonant''.

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What Einstein believed (Paul E)

🔗Manuel.Op.de.Coul@ezh.nl (Manuel Op de Coul)

🔗Paul Hahn <Paul-Hahn@...>

🔗Andrew Milne <andymilne@...>

🔗Brian Belet <BBELET@...>

🔗Gary Morrison <MorriSonics@...>

🔗alves@Orion.AC.HMC.Edu (Bill Alves)

🔗alves@Orion.AC.HMC.Edu (Bill Alves)

🔗Daniel Wolf <DJWOLF_MATERIAL@...>