Chrysippus:

(279-206 BC) a Stoic, regarded pneuma as the vehicle of logos in structuring matter, in animals & the physical world.  In pure form it is difficult to distinguish from logos, the "constructive fire" which drives the cyclical generation & destruction of the cosmos.  When a cycle reaches its end in conflagration, the cosmos becomes pure pneuma from which it regenerates itself.

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and see Chapter I, Introduction, page 33

 

Divine Pneuma:

In Stoic philosophy, pneuma is the concept of the "breath of life," a mixture of the elements air (in motion) and fire (as warmth).  The term originates from Greek medical writers who located human vitality in the breath.  For the Stoic philosophers it was the active, generative principle that organizes the individual & the cosmos.  In its highest form it constitutes the human soul, a fragment of the larger pneuma that is the soul of God (Zeus). As a force it structures matter & exists even in inanimate objects.  In Stoic cosmology everything that exists depends on 2 first principles which can be neither created nor destroyed: matter (passive & inert), and the logos (divine reason- active & organizing).  The cosmos was a whole, single entity, a living thing with a soul of its own, a spherical continuum of matter held together by the orderly power of Zeus through the causality of the pneuma that pervades it.  This divine pneuma is the soul of the cosmos, & supplies the pneuma in its varying grades for everything in the world.

 

Democritus:

(460-370 BC) Greek (Thrace) pre-Socratic philosopher remembered for speculation on atomic structures of the universe; mentioned together with his mentor Leucippus (their exact contributions are often confused).  His theories on atomic structure bears some resemblance to 19th century theory.  Sometimes regarded as "father of modern science", considered more a scientist than many of his peers.  Only fragments of his vast body of work has survived.  Largely ignored in Athens, Plato wished all his books burned but well known to his fellow northern-born philosopher Aristotle.

 

seeing (of Democritus):
Democritus devoted much attention to perception & asserted that sensations are changes produced in the soul by atoms emitted from other objects that impinge on it; the atoms of the soul can be affected only by contact from other atoms.  Sensation, such as sweet & bitter tastes, result from effects caused by the size & shape of the atoms (sweet taste is due to round & not too small atoms).  He was the first to explain colour, which he thought was due to the “position” (which he differentiated from shape) of the constituent atoms. The sensation of white was caused by smooth & flat atoms which cast no shadow; in contrast black was caused by rough, uneven atoms.

 

The State is a body…of all the bodies:

the Greek polis was a political entity ruled by its body of citizens, a religious & political association rather than a territorial identity & while it might control territory & colonies beyond the city, the polis was not simply a geographical area.  In Archaic Greece polis meant "city" but with the development of the governance center in the city it came to signify "state", to include surrounding villages. Finally, with the emergence of citizenship among landowners, it described the entire body of citizens.  The Greeks did not refer to Athens or Sparta or Thebes but rather to the Athenians, Lacedaemonians or Thebans.  The body of citizens came to be the most important meaning of the term polis.

 
law only knows corporeal persons & material: * see Endnote 9
Greek law was primarily about disputes rather than abstract notions of justice or rights.  The general unity of Greek law is reflected in laws of adoption & inheritance, commerce & contract, and in the publicity uniformly given to legal agreements.   There are 2 main sources: the Athenian justice system and the Gortyn code.

 

Classical temple: * see Endnote 10
The Parthenon was famous for its optical refinements: the subtle correspondence between the curvature of the stylobate, the taper of the naos walls & the entasis of the columns. 

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Apollonian physics (material, form, position): * see Endnote  11

Most of Classical Greek physics is derived from Aristotle's work The Physics.

 

Faustian physics (movement force mass): * see Endnote 12

Until the early 20th century Faustian physics was based on Newton's discovery & unification of the laws of motion & universal gravitation.  He developed mathematical models of change providing new methods for solving physical problems.  Faustian physics is not about movement, force or mass as distinct stand-alone concepts but relationships between these concepts, relationships expressed mathematically (in functions). 

 

mass (ratio between force & acceleration): * see Endnote 13

Newton's second law of motion describes a relationship between force & acceleration. They are directly proportional.  If you increase the force applied to an object, the acceleration of that object increases by the same factor.   Force = Mass * acceleration which means  Mass = Force/ acceleration.

 

instrumental music of 18th century masters: * see Endnote 14
The 18th century saw the end of the Baroque (1600-1750) and the emergence of the Classical (1730-1820).    While choral & sacred music, opera & oratorios dominated Baroque, in the new period composers placed greater import on instrumental music.  The new instrumental focus confronted composers with a major problem: how to render a textless composition comprehensible to the listener.  This function, formerly fulfilled by the text, had to be transferred to a purely instrumental movement.  This challenge provided the impetus for new developments.  The need for some kind of unity was ultimately resolved by more formal means, such as melodic similarities and repetitions, and by the emergence of a main theme as agent.  Orchestral music & the symphony became the paradigms which saw music gain ascendance in Western Culture as a whole.

 

Gluck:
see Chapter II, Numbers, page 78

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Beethoven:
see Chapter II, Numbers, page 81

 

Canon of Polycletus:
see Chapter I, Introduction, page 27

 

Lysippus:

see Chapter II, Numbers, page 90

 

Stamitz, strict canon: * see Endnote 15

(1717-1757) Bohemia, Czech composer & violinist; considered founding father of the Mannheim school; his music is transitional, between Baroque & Classical.   His most important compositions are his 58 symphonies & 10 orchestral trios.  The chief innovation in his symphonic works is their 4 movement structure: fast, slow, minuet & trio, Prestissimo finale.  While earlier 4 movement symphonies existed, he was the first to use it consistently.  Over half his symphonies & 9 of his 10 orchestral trios use this pattern.  He also helped develop the sonata form, most often used in symphonic first movements & occasionally in finales.

 

late-Beethoven quartets and symphonies: * see Endnote 16

Works from this period (1815-27) are characterised by their intellectual depth, formal innovations & intense, highly personal expression.  The String Quartet, Op. 131 has 7 linked movements, and the Ninth Symphony adds choral forces to the orchestra in the last movement.  The period is defined by his ambition to write new sounding, more difficult music incorporating more polyphonic styles of music from past composers (Bach, Handel).  Though his output fell compared to earlier periods, this music was his most ambitious &  the most time consuming to write.

 

and see Chapter II, Numbers, page 81

 

Tristan:

see Chapter I, Introduction, page 45

 

Erlosung:
German for salvation