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Thread: European Race-Culture and Pythagoras' Musical Ratio

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    Post European Race-Culture and Pythagoras' Musical Ratio

    MAGNA EUROPA EST PATRIA NOSTRA?
    By: David J. Stennett (in consultation with "Ursus Major")


    I've been asked by fellow students to explain how we Euro-Americans (and Euros everywhere) manifest a unique Unity. Certainly it's not in pigmentation. Just looking around campus, one can see that none of the so-called "Whites" are white: milk is white, snow is white, but "White" students - meaning Euros - range from the very fair to quite swarthy. They also exhibit a wide range of physical characteristics: long-headed Nordics, round-headed Alpines, Mediterranean attributes, Hungarians and Finns with almost Oriental bone-structures. Can these really comprise an existential Unity?

    No, the foundation of this Unity is not fundamentally physical. Our Culture-Distorting defamers are quick to point out that Semites, Hindus, and Ethiopians also have markedly similar underlying bone-structure, and this is true. They also relish in the fact that many Euro languages - Finnish, Basque, Hungarian, etc. - have nothing to do with the "Aryan" shibboleth: also true. Religion is no criterion. Few Euros practice the old ways, but Mexico has gone from steeped in massive cannibal rites to being (nominally) totally Catholic; yet very few Mexicans are true Euros.

    I do my best to delineate the concept of Race-Culture: that which transcends the purely physical, incorporating Race-Memory and a common Weltanschauung, or perception of reality. (This is, alas, usually 'way above the heads of those indoctrinated in Mongrolian "Goodthink.") I try to explain the concept of a " Euro-Soul," which clearly shows we are a diverse aggrigate of peoples possessing the same Inner Spirituality. (Nota Bene: Spirituality, not Religion!) At this point, my fellow students think I've been spending too much time looking into crystals.

    Those who are willing to hear me out will cast a wary eye and respond, "Yeah? Well how can you prove this?" (Funny those who are quite willing to believe that a renegade Egyptian climbed up a mountain, where "God" gave him The Law - and showed him His rump! - and that virgins can produce children demand proof - but then that's written down and has to be True ... because it is written down [?]!) Still, they are in the right: I'm postulating something as fact, and so The Burden of Proof lies on me, in so far as it can be proven ... and I believe it can!

    First of all, we must go back in time - historical time and a series of events which can be Proven - beginning at about 530 b.c. (a century before Plato). It was then that, on the Island of Samos, there was born a mystic and mathematician by the name of Pythagoras. Everyone's heard of Pythagoras, because of the geometrical theorem named after him: that in a right-triangle, the square of the hypotenuse is equal to the sum of the square of the sides: if a and b are the sides of a right-triangle, and c is the line connecting a to b, then a^2 + b^2 = c^2. (Yeah, yeah, you know that. Anyone who's been through high school geometry ends up having to recreate the proof. What you probably don't know is that it is a very minor element in the overall contribution of Pythagoras, that it wrought havoc with Greek mathematics - and that 2,000 years later became the motive force that transformed the famous philosopher Hobbes into an agnostic!)

    The theorem results in something the Greek mind could not cope with: the irrational number. What if each side equals 1? Then the length of the hypotenuse = sq./rt. of 2. The square-root of 2 is an irrational number: there are no p & q, such that p/q = sq./rt. of 2. The Ancients believed that the very existence of the Universe depended upon Divine Law: Logos (in Greek), Torah (in Hebrew): nothing that was irrational could exist.

    If the irrational existed, then the whole Order of the Universe would collapse and revert to Chaos. There had to be that "p&q": they were just hard to find. Whole lifetimes were spent looking for them and a rational value for PI (3.1416). The Greeks could - and did - measure the circumference of the Earth (coming within 50 miles of the current estimate), but they couldn't find p&q, nor a square whose area equaled that of a circle. Irrational numbers do exist, and between any two rational numbers - no matter how close they are - there are an infinite number of irrational numbers. (Now, perhaps, you understand why priests and rabbis rarely discuss mathematics.)

    As a young man, Pythagoras spent much time traveling "in the East." We don't know how far "East" we went; however, there are strong indications he made it to India. Why? Because his doctrine affirmed the transmigration of souls. That is a Hindu/Buddhist belief. Another aspect of his teachings was that everything consisted of numbers: numbers were the sole reality. This is much akin to the concept that everything material is merely illusion (and, if one thinks about it, not far removed from Einstein's famous e=mc^2).

    If everything is but numbers, then music too must be "numbers." It devolved to Pythagoras to find the fundamental relationship of music - not just Greek music, but Euro-Music: that commonality which is Unique to the Euro peoples and proves the Existential Identity: one musical schema for all Euros!

    Pythagoras discovered that all Greek music (the only Euro-Music extant at the time) was built upon one fundamental basis: the Tetrachord. "Tetra" means "four," and "chord" means "tone." The Tetrachord - three whole steps and a half-step at the end: C, D, E & F on a keyboard - ended on the 4th (F). Pythagoras discovered that the ratio of the octave (the only interval the same in all musical systems) is 2:1, that of the 4th (the last tone in the tetrachord) 4:3, and of the 5th (the first note of the second tetrachord superimposed upon the original to complete the octave) of 3:2.

    (In our keyboard example, with C as the root [Do], 3x the frequency of F [the 4th: Fa] = 4xC; while 2x G [1st note of 2nd tetrachord: So] = 3x C.

    This C to C' ("the white keys") is the major (Ionian) mode. The other retained mode is the minor (Aeolian), going from A to A'.

    Pythagoras had found the basis for the diatonic scale: the indigenous Euro-scale. The Greeks, being the first Euros of history, were the first to deploy it. They devised modes by starting and ending their octaves on any one of the seven tones of the doubled Tetrachord. While there might have been seven modes, they all used the same seven tones, all that differed was on which of the seven in the scale - called diatonic, as it went though ("dia" equals "through") all seven - it started. Much, much later (after the seven modes had been simplified to two), each of the notes was assigned a higher and lower (sharp/flat) to "color" it. (These sharps and flats were not thought of as separate notes but "colorations," allowing for the use of either mode beginning on any tone. This scale was named chromatic, as "chroma" is Greek for "color.")

    Why are the Ionian and Aeolian modes, the two which endured, the principal modes of Euro-music? Because of the extreme import these modes give to the 4th, 5th, and octave. Pythagoras portended they infused the soul with "cosmic energy," giving a vitality to the musical-poet (for all poetry was sung in ancient times: it was all bardic poetry; the drama too was sung - as odes and choruses - never merely spoken) that drew upon the heavens themselves. Just another one of Pythagoras' quirks (like eschewing beans)?

    One might think so, until in the late 18th century, the Titus-Bode Law of planetary distances was put forth. The Titus-Bode Law involves only three constants: 2, 3, and 4. What is the ratio of the octave? - 2:1; of the 4th? - 4:3; of the 5th? - 3:2. Even before that, Johannes Kepler had published his findings of the observations of Tycho Brahe under the title Harmonia Mundi: "The Harmony of the World." (With Kepler, astrophysics was born: both Newton and Einstein were directly dependent on the discoveries of the one-time Court Astrologer, Johannes Kepler.)

    Kepler found that the square of the time (t^2) is proportional to the cube of the planetary distance (d^3) in revolution; and that the principal of the elements is ½ the major axis (a); therefore, orbit-size is proportional (a^4): Harmonia Mundi - the fundamental constants in the diatonic scale, present in planetary movement and distances.

    While other Race-Cultures (most dramatically the Hindu, with its myriad of modes and ragas), rely upon pentatonic (primarily) scales, with an endless assortment of quarter-tones (if indeed there is any melodic sound; some "music" is simply drum-beating), Euro music is everywhere based upon these modes, with their ratios which - most curiously - reflect ratios in planetary rotation and distances from the sun. (Do we have any reason to assume that the Titus-Bode Law would not hold true, wherever planets are formed?)

    Can one assume that a Ukrainian barge-man, pulling his load along the Volga was aware of the 8th root of 2, upon which diatonic intervals are based? Or the Irish peasant, treated scarcely better than cattle by his English overlord? Yet, "The Song of the Volga Boatman" and the Irish folksong, converted into "When Johnny Comes Marching Home" are identical in modal sequence - one can segué from one into the other, and then into the opening of Beethoven's 9th Symphony, without the slightest discord or modal variance. Whether emerging from the soul of a Race-Culture as diverse as the Ukraine or Ireland, or the creation of a consummate genius, it is prima facie evidence of an existential Unity, for nothing is more revealing of a Cultural Essence than the music of that Race-Culture.

    How long has it been going on? Since as long as Euro-man has possessed the ability to notate his music. Pindar (518-438 b.c.) was the greatest of the Greek choral-lyrists. Unfortunately, only one of his odes, that to the Pythoness (the oracle of Apollo at Delphi) survived. It was saved from the destruction of Constantinople, when it fell to the Turks in 1453.

    A monk placed it in the library of a monastery in Messina. A Jesuit (of Greek origin) published it in modern notation in 1655. (Alas the original perished, when a Saracen raid destroyed the monastery, about 1680.) We still have the copy. Like all Greek odes, there is a prologue ("before the words"), the ode (sung), and an epilogue ("after the words"). In Pindar's case, the principal instrument was an aulos: a sort of "double oboe": one tube produced a melody, the other a drone. (The Romans affixed a bladder to it, which could be filled with air. This is the origin of the bagpipe, to which the legions marched in that perfect Roman pace - and, like so many other things the Scots copied.)

    The aulos-player was given a melodic line and expected to improvise little embellishments over it. As the only remaining copy was published in 1655, the embellishments sound somewhat baroque, and could almost pass as "Scottish" music; however, they are only embellishments. When the poet-composer began to sing his ode, the aulos-player simply reinforced the melodic line. This is Euro bardic poetry at its best - from 2,500 years ago. It is the Euro Soul which comes through: Multae Gentes, Una Stirpes, many peoples but One Race-Culture, then and now!


    [AFTERWORD BY "URSUS MAJOR": Writing in Archeologia Musicalis ("Ancient Harmony": 1988), Robert Fink claims the diatonic scale existed in ancient Ugarit, a one-time major city in Syria, near the Mediterranean; and not found until 1929 by French archaeologists. This conclusion is extremely conjectural, based upon cuniform impressions which "mean" what the individual - in this case Prof. Anne Draffkorn Kilmer, an Assyriologist at UCB - say they mean. Who is there to contradict her?

    She maintains they record a song in the Ionian (major: Do, re, mi) mode, with harmony curiously akin to that found in Europe - during the era of Mozart and Haydn[?]! Mr. Fink goes on to state that there is a "natural basis" for the diatonic scale: something which Pythagoras also stated, but was not proven until the advent of celestial mechanics. The whole problem with this canard - and the authors believe it to be a canard! - is if the diatonic scale, founded on natural ratios, existed a millenium before Pythagoras, why was it totally abandoned; why was it replaced by a horde of diverse pentatonic scales riddled with quarter-tones, that sound more like howling wolves than anything by Haydn or Mozart?

    That's where the House of Cards collapses! One can explore every nook of Syria - and the whole Levant, for that matter - but the only diatonic music with Western harmonies will turn out to be music from the West! Well, competition in Academe is stiff, and as Mama Rose told Gypsy, "Ya gotta have a gimick!"]


    Source: This article was originally published by the Euro-American Student Union and is reprinted with the founder's permission

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    Post Re: How we Euros are related: Magna Evropa Est Patria Nostra!

    There is something in this argument; Western Classical music is certainly a unique creation.

    Its relying on 'ratios' a la Pythagoras is no doubt characteristic.

    Although it isn't until the Baroque and the universalisation of Equal Temperament that we get the uniquely European sound.

    In this we find that harmony becomes all important with modulations used for expression.

    But that may have been a compensation for the loss of melodic flexibility with our strict chromatic scale.

    Listening to the music of the Indian 'Ragas' [which means 'feeling'] one hears in the fractal melodies something that was lost in Western music.
    Why are there beings at all, & why not rather nothing?
    [Leibniz/Heidegger]

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    Post Re: How we Euros are related: Magna Evropa Est Patria Nostra! [music]

    just an off-topic observation: the quote Magna Evropa Est Patria Nostra, is not wrong, but it is less correct than Magna Evropa Patria Nostra Est.

    I learned that when i had some latin lessons.

    .

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    Post Re: How we Euros are related: Magna Evropa Est Patria Nostra! [music]

    It's not just a matter of Appearance. It's the shared History and Culture. That makes all Euro-Americans related.

    But of course their are Lines that can be drawn. And those Lines aren't just Arbitrary.

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    Senior Member Moody's Avatar
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    Post Re: How we Euros are related: Magna Evropa Est Patria Nostra! [music]

    Quote Originally Posted by Northern_Paladin
    It's not just a matter of Appearance. It's the shared History and Culture. That makes all Euro-Americans related.

    But of course their are Lines that can be drawn. And those Lines aren't just Arbitrary.
    On that point, and staying within the topic of music; it is obvious that America has had recent non-European influence on its musical forms; from the Amerindians and from the African slaves, of course.

    These recent non-European influences on American music have had global impact due to the USA's world dominance as a hyper-power in the information-age.
    Why are there beings at all, & why not rather nothing?
    [Leibniz/Heidegger]

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    Post Re: How we Euros are related: Magna Evropa Est Patria Nostra! [music]


    On that point, and staying within the topic of music; it is obvious that America has had recent non-European influence on its musical forms; from the Amerindians and from the African slaves, of course.

    These recent non-European influences on American music have had global impact due to the USA's world dominance as a hyper-power in the information-age.
    Yes it's a shame. Especially in Sweden,UK. You can see Wiggers Everywhere in Urban Areas.

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    Post Re: How we Euros are related: Magna Evropa Est Patria Nostra! [music]

    Quote Originally Posted by Northern_Paladin
    Yes it's a shame. Especially in Sweden,UK. You can see Wiggers Everywhere in Urban Areas.
    Actually, the Negro has had a pervasive influence on American music, in things like Gospel music, Jazz, rock 'n roll etc.,

    Indeed, the whole Negroid body-language has influenced American music, so even supposedly 'white' genres have some Negro 'blood'.
    Why are there beings at all, & why not rather nothing?
    [Leibniz/Heidegger]

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    Re: How we Euros are related: Magna Evropa Est Patria Nostra! [music]

    Quote Originally Posted by Moody Lawless
    Actually, the Negro has had a pervasive influence on American music, in things like Gospel music, Jazz, rock 'n roll etc.,

    Indeed, the whole Negroid body-language has influenced American music, so even supposedly 'white' genres have some Negro 'blood'.
    But those styles were made with instruments invented by White people - guitar, trumpet, saxophone, piano, bass, ect.

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    Re: How we Euros are related: Magna Evropa Est Patria Nostra!

    Quote Originally Posted by Moody Lawless
    Listening to the music of the Indian 'Ragas' [which means 'feeling'] one hears in the fractal melodies something that was lost in Western music.
    One can still hear it in the later compositions of Anton Webern and his followers.
    Last edited by Siegmund; Tuesday, May 9th, 2006 at 12:38 PM.

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    Re: How we Euros are related [music]

    Humans are oppertunistic animals and will listen to what they are fed and they are fed rap and r&b drivel.

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