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Achillefs Chaldaiakis Plato’s Influences in the Greek Religious Music Theory

Achillefs Chaldaiakis Plato’s Influences in the Greek Religious Music Theory.

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Achillefs Chaldaiakis Plato’s Influences in the Greek Religious Music Theory

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  1. Achillefs ChaldaiakisPlato’s Influences in the Greek Religious Music Theory

  2. “Now the making of the universe took up the whole bulk of each of these four elements. Of all fire and all water and air and earth its framer fashioned it, leaving over no part nor power without. Therein he had this intent […] that it might be a creature perfect to the utmost with all its parts perfect […] And he assigned to it its proper and nature shape. To that which is to comprehend all animals in itself that shape seems proper which comprehends in itself all shapes that are. Wherefore he turned it in a rounded and spherical shape, having its bounding surface in all points at an equal distance from the centre: this being the most perfect and regular shape; for he thought that a regular shape was infinitely fairer than an irregular […] For he assigned it that motion which was proper to its bodily form, of all the seven [: “up and down, forwards and backwards, to right and to left, and finally rotation upon an axis”] that which most belongs to reason and intelligence. Wherefore turning it about uniformly in the same spot on its own axis, he made it to revolve round and round; but all the six motions he took away from it and left it without part in their wanderings” • The Timaeus of Plato, edited with Introduction and Notes by R. D. Archer-Hind, M.A., Felloe of Trinity College, Cambridge, London & New York 1888, pp. 101-103.

  3. Από ελληνικό αλχημικό χειρόγραφο “Ouroboros”; image taken from Greek Alchemy Manuscript http://www.artofwise.gr/html/categories_content/symvola/ourovoros.html

  4. “Ouroboros”; image taken from Greek Alchemy Manuscript (detail)http://el.wikipedia.org/wiki/%CE%9F%CF%85%CF%81%CE%BF%CE%B2%CF%8C%CF%81%CE%BF%CF%82_%CE%8C%CF%86%CE%B9%CF%82

  5. “Ouroboros”; image taken from Codex Marcianus (11th c.) http://www.artofwise.gr/html/categories_content/symvola/ourovoros.html

  6. “The perfect expression and representation of this universal harmony is seen through the use of ratios of the ninenumbers of the decad – a receptacle symbolizing all that exists – and their connection to musical intervals [….] given by the mathematical scale of Theon of Smyrna, a Pythagorean Philosopher. This scale was studied by our medieval ancestors, who as scholars and followers of the old tradition and theory defined, on the basis of this scale, the eight-mode system, also known as the Octoechos, which is divided in four pairs of modes, each pair comprising an authentic mode and a plagal mode”. • Simon Karas, Byzantine Music Genera and Intervals, Athens 1970, pp. 22-23.

  7. The Mathematical Wheel of Theon of Smyrna Simon Karas, Theoreticon, 1st vol., Athens 1982, p. 233.

  8. The Mathematical Wheel of Theon of Smyrna Simon Karas, Byzantine Music Genera and Intervals, ibid., p. 40.

  9. “… number 5 is the mean term of (two numbers whose sum is) the decad, because if, by the addition of any two numbers, one obtains ten, the means of these numbers will be 5 according to arithmetic proportion. Thus, for example, if you add 9 and 1, 8 and 2, 7 and 3, 6 and 4, the sum will always be 10 and the mean term in arithmetic proportion will be 5. This is shown in the diagram in which any addition of two opposite numbers gives 10, the proportional arithmetic mean being 5, which is greater than one of the extremes and less than the other, by the same difference. This number is also the first which embraces the two types of numbers, the odd and the even, that is, 2 and 3, for unity is not a number”. • Mathematics Useful for Understanding Plato, by Theon of Smyrna, Platonic Philosopher, Translated from the 1892 Greek/French edition of J. Dupuis by Robert and Deborah Lawlor and edited and annotated by Christos Toulis and others, with an appendix of notes by Dupuis, a copious glossary, index of works etc., San Diego 1979, p. 67.

  10. Diagrams of the Mathematical Scale of Theon of Smyrna • TheonisSmyrnaei, PhilosophiPlatonici, Expositio Rerum Mathematicarum adLegendumPlatoneumUtilium, RecensuitEduardus Hiller, Lipsiae, In Aedibus B. G. Teubneri, MDCCCLXXVIII [1878], p. 102.

  11. Diagram of the Mathematical Scale of Theon of Smyrna • Mathematics Useful for Understanding Plato, by Theon of Smyrna, Platonic Philosopher […], ibid.

  12. The Wheel of Eight Modes of the Greek Religious Music The Mathematical Wheel of Theon of Smyrna

  13. Diagrams of the Mathematical Scale of Theon of Smyrna • TheonisSmyrnaei, PhilosophiPlatonici, Expositio Rerum Mathematicarum adLegendumPlatoneumUtilium, RecensuitEduardus Hiller, Lipsiae, In Aedibus B. G. Teubneri, MDCCCLXXVIII [1878], p. 102.

  14. The Wheel of Eight Modes of the Greek Religious Music The Mathematical Wheel of Theon of Smyrna

  15. The Wheel of Eight Modes of the Greek Religious Music The Mathematical Wheel of Theon of Smyrna

  16. “The above, I suppose, must be enough to demonstrate the marvelous kinship of the Modes. However, if somebody makes an even more accurate scrutiny of these matters, he will find thousands of features which prove the kinship…”.Ibid., p. 59, § 55. “Their names have already been written, both their proper names and those which indicate their order. As far as concerns the Modes, however, it must be born in mind that we do not name the quantity of sounds, but the quality […] Thus, the designations of the Modes are not made for counting purposes but to represent the sound quality of the Melos” • Jorgen Raasted, “The Hagiopolites. A Βyzantine Treatise on Musical Theory (preliminary edition)”, Cahiers de l’ Institut du Moyen-Age Grec et Latin 45, Copenhague 1983,pp. 37-38, § 30.

  17. Great Theory of Music by Chrysanthos of Madytos, translated by Katy Romanou, New York 2010 (The Axion Estin Foundation, New Rochelle), pp. 56-60§§66-76

  18. Wheel of Chromatic Modes of the Greek Religious MusicPublished by George Konstantinou, Theory and Practice of Ecclesiastical Music, Mount Athos Monastery of Vatopedi 20136, p. 334

  19. Chrysanthos, in his Great Theory of Music [ibid., pp. 123-125§§246-252], points out that a relevant full (ascending and descending) chromatic scale could also be sung as follow:

  20. “The ecclesiastical musicians represented these four interval, in ascend with the following four words annanes, neanes, nana, agia; in descent, with the following, which are similar, aanes, necheanes, aneanes, neagie. Those eight notes are called the notes of trochos […] The annanes derives from ana anes, that is anax afes [king let]; the neanes, from ne anes [do, let]; the nana from ana ana [king, king]; and the agia from agie [saint]; the entire, anax afes, ne afes anax anax agie being a wish addressed to God [God forgive me, please, forgive me, God God, you, the holy one]. Constantinos Porphyrogennetos says that the nana means Thee Thee [God God] and the agia, soson di [do save]. He also makes up a word composed from those two, nanaia”. • Great Theory of Music by Chrysanthos of Madytos, ibid., p. 56§66, note 11

  21. 1. Ascending & Descending Diatonic Tetrachord:

  22. 2. Ascending & Descending Full Chromatic Scale (Octachord):

  23. Diagrams of the Mathematical Scale of Theon of Smyrna • TheonisSmyrnaei, PhilosophiPlatonici, Expositio Rerum Mathematicarum adLegendumPlatoneumUtilium, RecensuitEduardus Hiller, Lipsiae, In Aedibus B. G. Teubneri, MDCCCLXXVIII [1878], p. 102.

  24. The Mathematical Square of Theon of Smyrna The Square of Eight Modes of the Greek Religious Music

  25. The Square of Eight Modes of the Greek Religious Music

  26. Codex No. 35/188a of K. Psachos’ Collection (A.D. 1781), f. 114r[“Κanonion” made by the Protonotarios of Cyprus Archdiocese Matthew Tzigalas]

  27. “The more someone knows, the more one understands, the more one realizes that everything revolves around a circle”…

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