{"id":3019,"date":"2025-12-26T18:31:04","date_gmt":"2025-12-26T16:31:04","guid":{"rendered":"https:\/\/www.g-culture.org\/ioannis\/?page_id=3019"},"modified":"2026-03-03T00:25:37","modified_gmt":"2026-03-02T22:25:37","slug":"mathandmusic","status":"publish","type":"page","link":"https:\/\/www.g-culture.org\/ioannis\/mathandmusic\/","title":{"rendered":"Mathematics and Music"},"content":{"rendered":"<p><a name=\"arxaioi\"><\/a>\u0388\u03bd\u03b1 \u03b1\u03c0\u03cc \u03c4\u03b1 \u03b8\u03ad\u03bc\u03b1\u03c4\u03b1 \u03c4\u03b7\u03c2 \u03bc\u03bf\u03c5\u03c3\u03b9\u03ba\u03ae\u03c2, \u03c0\u03bf\u03c5 \u03b1\u03c0\u03b1\u03c3\u03c7\u03cc\u03bb\u03b7\u03c3\u03b5 \u03c4\u03bf\u03c5\u03c2 \u03c0\u03c1\u03ce\u03c4\u03bf\u03c5\u03c2 \u03b8\u03b5\u03c9\u03c1\u03b7\u03c4\u03b9\u03ba\u03bf\u03cd\u03c2 \u03c4\u03b7\u03c2, \u03ae\u03c4\u03b1\u03bd \u03c4\u03b1 \u03bc\u03bf\u03c5\u03c3\u03b9\u03ba\u03ac \u03b4\u03b9\u03b1\u03c3\u03c4\u03ae\u03bc\u03b1\u03c4\u03b1. \u039e\u03b5\u03ba\u03b9\u03bd\u03ce\u03bd\u03c4\u03b1\u03c2 \u03b1\u03c0\u03cc \u03b1\u03c0\u03bb\u03ad\u03c2, \u03b3\u03b9\u03b1 \u03c4\u03b1 \u03c3\u03b7\u03bc\u03b5\u03c1\u03b9\u03bd\u03ac \u03b4\u03b5\u03b4\u03bf\u03bc\u03ad\u03bd\u03b1, \u03c0\u03c1\u03bf\u03c4\u03ac\u03c3\u03b5\u03b9\u03c2, \u03ba\u03ac\u03bd\u03bf\u03bd\u03c4\u03b1\u03c2 &#8220;\u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03b9\u03c3\u03bc\u03bf\u03cd\u03c2&#8221; \u03bc\u03b5 \u03c4\u03b9\u03c2 \u03c4\u03cc\u03c4\u03b5 \u03b3\u03bd\u03c9\u03c3\u03c4\u03ad\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ad\u03c2 \u03b8\u03b5\u03c9\u03c1\u03af\u03b5\u03c2, \u03bf\u03b9 \u03ac\u03bd\u03b8\u03c1\u03c9\u03c0\u03bf\u03b9 \u03b1\u03c5\u03c4\u03bf\u03af \u03bc\u03b1\u03c2 \u03c0\u03b1\u03c1\u03ad\u03b4\u03c9\u03c3\u03b1\u03bd \u03ad\u03bd\u03b1\u03bd \u03b1\u03bd\u03b5\u03ba\u03c4\u03af\u03bc\u03b7\u03c4\u03bf \u03b8\u03b7\u03c3\u03b1\u03c5\u03c1\u03cc \u03b3\u03cd\u03c1\u03c9 \u03b1\u03c0\u03cc \u03c4\u03bf \u03b8\u03ad\u03bc\u03b1 &#8220;\u039c\u03bf\u03c5\u03c3\u03b9\u03ba\u03cc \u03b4\u03b9\u03ac\u03c3\u03c4\u03b7\u03bc\u03b1&#8221;.<\/p>\n<p>\u03a3\u03cd\u03bc\u03c6\u03c9\u03bd\u03b1 \u03bc\u03b5 \u03c4\u03bf\u03c5\u03c2 \u03b1\u03c1\u03c7\u03b1\u03af\u03bf\u03c5\u03c2 \u03b8\u03b5\u03c9\u03c1\u03b7\u03c4\u03b9\u03ba\u03bf\u03cd\u03c2 \u03c4\u03b7\u03c2 \u03bc\u03bf\u03c5\u03c3\u03b9\u03ba\u03ae\u03c2:<\/p>\n<ul>\n<li>&#8220;\u0394\u03b9\u03ac\u03c3\u03c4\u03b7\u03bc\u03b1 \u03b5\u03c3\u03c4\u03af \u03c4\u03bf \u03c5\u03c0\u03cc \u03b4\u03cd\u03bf \u03c6\u03b8\u03cc\u03b3\u03b3\u03c9\u03bd \u03c9\u03c1\u03b9\u03c3\u03bc\u03ad\u03bd\u03bf\u03bd, \u03bc\u03b7 \u03c4\u03b7\u03bd \u03b1\u03c5\u03c4\u03ae\u03bd \u03c4\u03ac\u03c3\u03b9\u03bd \u03b5\u03c7\u03cc\u03bd\u03c4\u03c9\u03bd&#8221;. 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(\u039a\u03bb\u03b5\u03bf\u03bd\u03af\u03b4\u03b7\u03c2. \u03a4\u03bf\u03bd \u03af\u03b4\u03b9\u03bf \u03bf\u03c1\u03b9\u03c3\u03bc\u03cc \u03b4\u03af\u03bd\u03b5\u03b9 \u03ba\u03b1\u03b9 \u03bf \u0392\u03b1\u03ba\u03c7\u03b5\u03af\u03bf\u03c2).<\/li>\n<\/ul>\n<p>\u03a4\u03bf \u03c0\u03bf\u03b9\u03bf \u03b3\u03bd\u03c9\u03c3\u03c4\u03cc \u03bc\u03bf\u03c5\u03c3\u03b9\u03ba\u03cc \u03cc\u03c1\u03b3\u03b1\u03bd\u03bf \u03c0\u03bf\u03c5 \u03c7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03ae\u03b8\u03b7\u03ba\u03b5 \u03b3\u03b9\u03b1 \u03c4\u03bf\u03bd \u03c0\u03c1\u03bf\u03c3\u03b4\u03b9\u03bf\u03c1\u03b9\u03c3\u03bc\u03cc \u03c4\u03c9\u03bd \u03bc\u03bf\u03c5\u03c3\u03b9\u03ba\u03ce\u03bd \u03b4\u03b9\u03b1\u03c3\u03c4\u03b7\u03bc\u03ac\u03c4\u03c9\u03bd \u03ae\u03c4\u03b1\u03bd \u03c4\u03bf \u03bc\u03bf\u03bd\u03cc\u03c7\u03bf\u03c1\u03b4\u03bf. \u038c\u03c0\u03c9\u03c2 \u03c6\u03b1\u03af\u03bd\u03b5\u03c4\u03b1\u03b9 \u03b1\u03c0\u03cc \u03c4\u03bf \u03cc\u03bd\u03bf\u03bc\u03ac \u03c4\u03bf\u03c5, \u03ae\u03c4\u03b1\u03bd \u03ad\u03bd\u03b1 \u03cc\u03c1\u03b3\u03b1\u03bd\u03bf \u03bc\u03b5 \u03bc\u03af\u03b1 \u03c7\u03bf\u03c1\u03b4\u03ae \u03c0\u03bf\u03c5 \u03b1\u03c0\u03cc \u03b1\u03c1\u03ba\u03b5\u03c4\u03bf\u03cd\u03c2 \u03bc\u03b5\u03bb\u03b5\u03c4\u03b7\u03c4\u03ad\u03c2 \u03c4\u03bf\u03c0\u03bf\u03b8\u03b5\u03c4\u03b5\u03af\u03c4\u03b1\u03b9 \u03c3\u03c4\u03b7\u03bd \u03bf\u03b9\u03ba\u03bf\u03b3\u03ad\u03bd\u03b5\u03b9\u03b1 \u03c4\u03bf\u03c5 \u03bb\u03b1\u03bf\u03cd\u03c4\u03bf\u03c5 \u03b4\u03b7\u03bb\u03b1\u03b4\u03ae \u03bc\u03b5 \u03b2\u03c1\u03b1\u03c7\u03af\u03bf\u03bd\u03b1, \u03c7\u03ad\u03c1\u03b9 (Th. Reinach La mus. gr. 127). \u03a4\u03bf \u03bc\u03bf\u03bd\u03cc\u03c7\u03bf\u03c1\u03b4\u03bf \u03c7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03ae\u03b8\u03b7\u03ba\u03b5 \u03b3\u03b9\u03b1 \u03c4\u03bf\u03bd \u03ba\u03b1\u03b8\u03bf\u03c1\u03b9\u03c3\u03bc\u03cc \u03c4\u03c9\u03bd \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ce\u03bd \u03c3\u03c7\u03ad\u03c3\u03b5\u03c9\u03bd \u03c4\u03c9\u03bd \u03bc\u03bf\u03c5\u03c3\u03b9\u03ba\u03ce\u03bd \u03ae\u03c7\u03c9\u03bd. \u039f\u03bd\u03bf\u03bc\u03ac\u03b6\u03bf\u03bd\u03c4\u03b1\u03bd \u03ba\u03b1\u03b9 &#8220;\u03a0\u03c5\u03b8\u03b1\u03b3\u03cc\u03c1\u03b5\u03b9\u03bf\u03c2 \u03ba\u03b1\u03bd\u03ce\u03bd&#8221; \u03b3\u03b9\u03b1\u03c4\u03af \u03b1\u03c0\u03ad\u03b4\u03b9\u03b4\u03b1\u03bd \u03c4\u03b7\u03bd \u03b5\u03c6\u03b5\u03cd\u03c1\u03b5\u03c3\u03ae \u03c4\u03bf\u03c5 \u03c3\u03c4\u03bf\u03bd \u03a0\u03c5\u03b8\u03b1\u03b3\u03cc\u03c1\u03b1. \u03a0\u03bf\u03bb\u03bb\u03bf\u03af 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\u03b4\u03b9\u03b1\u03c4\u03bf\u03bd\u03b9\u03ba\u03cc, \u03c7\u03c1\u03c9\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc \u03ba\u03b1\u03b9 \u03b5\u03bd\u03b1\u03c1\u03bc\u03cc\u03bd\u03b9\u03bf. \u0391\u03bd\u03b1\u03ba\u03ac\u03bb\u03c5\u03c8\u03b5 \u03c4\u03bf \u03bb\u03cc\u03b3\u03bf \u03c4\u03b7\u03c2 \u03bc\u03b5\u03b3\u03ac\u03bb\u03b7\u03c2 \u03c4\u03c1\u03af\u03c4\u03b7\u03c2 \u03c3\u03c4\u03bf \u03b5\u03bd\u03b1\u03c1\u03bc\u03cc\u03bd\u03b9\u03bf \u03b3\u03ad\u03bd\u03bf\u03c2), \u03bf \u0395\u03c1\u03b1\u03c4\u03bf\u03c3\u03b8\u03ad\u03bd\u03b7\u03c2 \u03bf \u0394\u03af\u03b4\u03c5\u03bc\u03bf\u03c2 [\u03c3\u0384 \u03b1\u03c5\u03c4\u03cc\u03bd \u03b1\u03c0\u03bf\u03b4\u03af\u03b4\u03b5\u03c4\u03b1\u03b9 \u03bf \u03ba\u03b1\u03b8\u03bf\u03c1\u03b9\u03c3\u03bc\u03cc\u03c2 \u03c4\u03bf\u03c5 &#8220;\u03ba\u03cc\u03bc\u03bc\u03b1\u03c4\u03bf\u03c2 \u03c4\u03bf\u03c5 \u0394\u03b9\u03b4\u03cd\u03bc\u03bf\u03c5&#8221;, \u03c0\u03bf\u03c5 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7 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\u03a7\u03c1\u03cd\u03c3\u03b1\u03bd\u03b8\u03bf\u03c2. \u03a4\u0384 \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03ad\u03c3\u03bc\u03b1\u03c4\u03b1 \u03c4\u03b7\u03c2 \u03b5\u03c1\u03b3\u03b1\u03c3\u03af\u03b1\u03c2 \u03c4\u03bf\u03c5 \u03c0\u03b5\u03c1\u03b9\u03ad\u03c7\u03bf\u03bd\u03c4\u03b1\u03b9 \u03c3\u03c4\u03bf \u039c\u03ad\u03b3\u03b1 \u0398\u03b5\u03c9\u03c1\u03b7\u03c4\u03b9\u03ba\u03cc\u03bd.<\/p>\n<p>\u03a3\u03cd\u03bc\u03c6\u03c9\u03bd\u03b1 \u03bc\u03b5 \u03c4\u03bf\u03bd \u03a7\u03c1\u03cd\u03c3\u03b1\u03bd\u03b8\u03bf, \u03b7 \u03c3\u03b5\u03b9\u03c1\u03ac \u03c4\u03c9\u03bd \u03bf\u03ba\u03c4\u03ce \u03c6\u03b8\u03cc\u03b3\u03b3\u03c9\u03bd \u03c4\u03b7\u03c2 \u03b4\u03b9\u03b1\u03c4\u03bf\u03bd\u03b9\u03ba\u03ae\u03c2 \u03ba\u03bb\u03af\u03bc\u03b1\u03ba\u03b1\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7 \u03c0\u03b1\u03c1\u03b1\u03ba\u03ac\u03c4\u03c9:<\/p>\n<p>\u03a0\u03b1 &#8211; \u0392\u03bf\u03c5 &#8211; \u0393\u03b1 &#8211; \u0394\u03b9 &#8211; \u039a\u03b5 &#8211; \u0396\u03c9 &#8211; \u039d\u03b7 &#8211; \u03a0\u03b1&#8217;,<\/p>\n<p>\u03b4\u03b9\u03b1\u03ba\u03c1\u03af\u03bd\u03bf\u03c5\u03bd \u03bf\u03b9 \u03bc\u03bf\u03c5\u03c3\u03b9\u03ba\u03bf\u03af \u03b5\u03c0\u03c4\u03ac \u03b4\u03b9\u03b1\u03c3\u03c4\u03ae\u03bc\u03b1\u03c4\u03b1. \u03a0\u03b1 &#8211; \u0392\u03bf\u03c5, \u0392\u03bf\u03c5 &#8211; \u0393\u03b1, \u0393\u03b1 &#8211; \u0394\u03b9, \u0394\u03b9 &#8211; \u039a\u03b5, \u039a\u03b5 &#8211; \u0396\u03c9, \u0396\u03c9 &#8211; \u039d\u03b7, \u039d\u03b7 &#8211; \u03a0\u03b1&#8217;. \u0391\u03c5\u03c4\u03ac \u03c4\u03b1 \u03b4\u03b9\u03b1\u03c3\u03c4\u03ae\u03bc\u03b1\u03c4\u03b1 \u03c4\u03b1 \u03bf\u03bd\u03bf\u03bc\u03ac\u03b6\u03bf\u03c5\u03bc\u03b5 \u03cc\u03bb\u03b1 \u03c4\u03cc\u03bd\u03bf\u03c5\u03c2. \u039a\u03b1\u03c4\u03ac \u03b4\u03b5 \u03c4\u03bf\u03c5\u03c2 \u03b1\u03c1\u03c7\u03b1\u03af\u03bf\u03c5\u03c2 \u0388\u03bb\u03bb\u03b7\u03bd\u03b5\u03c2 \u03c4\u03b1 \u03bc\u03b5\u03bd \u03c0\u03ad\u03bd\u03c4\u03b5 \u03bf\u03bd\u03bf\u03bc\u03ac\u03b6\u03bf\u03bd\u03c4\u03b1\u03b9 \u03c4\u03cc\u03bd\u03bf\u03b9, \u03c4\u03b1 \u03b4\u03b5 \u03b4\u03cd\u03bf \u0396\u03c9 &#8211; \u039d\u03b7 \u03ba\u03b1\u03b9 \u0392\u03bf\u03c5 &#8211; \u0393\u03b1 \u03bf\u03bd\u03bf\u03bc\u03ac\u03b6\u03bf\u03bd\u03c4\u03b1\u03b9 \u03bb\u03b5\u03af\u03bc\u03bc\u03b1\u03c4\u03b1. \u039a\u03b1\u03c4\u03ac \u03b4\u03b5 \u03c4\u03bf\u03c5\u03c2 \u03b5\u03c5\u03c1\u03c9\u03c0\u03b1\u03af\u03bf\u03c5\u03c2 \u039a\u03b5 &#8211; \u0396\u03c9, \u0392\u03bf\u03c5 &#8211; \u0393\u03b1 \u03bf\u03bd\u03bf\u03bc\u03ac\u03b6\u03bf\u03bd\u03c4\u03b1\u03b9 \u03b7\u03bc\u03af\u03c4\u03bf\u03bd\u03b1 \u03c4\u03b1 \u03b4\u03b5 \u03bb\u03bf\u03b9\u03c0\u03ac \u03c0\u03ad\u03bd\u03c4\u03b5 \u03c4\u03cc\u03bd\u03bf\u03b9.<\/p>\n<p>\u0395\u03b4\u03ce \u03c0\u03c1\u03ad\u03c0\u03b5\u03b9 \u03bd\u03b1 \u03c3\u03b7\u03bc\u03b5\u03b9\u03c9\u03b8\u03b5\u03af \u03cc\u03c4\u03b9 \u03c4\u03b7\u03bd &#8220;\u0395\u03c5\u03c1\u03c9\u03c0\u03b1\u03ca\u03ba\u03ae \u03b4\u03b9\u03ac\u03c3\u03c4\u03b1\u03c3\u03b7&#8221; \u03c4\u03b7\u03c2 \u03ba\u03bb\u03af\u03bc\u03b1\u03ba\u03b1\u03c2 \u03c0\u03bf\u03c5 \u03c0\u03b5\u03c1\u03b9\u03b3\u03c1\u03ac\u03c6\u03b5\u03b9 \u03bf \u03a7\u03c1\u03cd\u03c3\u03b1\u03bd\u03b8\u03bf\u03c2, \u03c4\u03b7 \u03b4\u03af\u03bd\u03b5\u03b9 \u03c3\u03c9\u03c3\u03c4\u03ac \u03bf \u039d\u03b9\u03ba\u03cc\u03bb\u03b1\u03bf\u03c2 \u03a0\u03b1\u03b3\u03b1\u03bd\u03ac\u03c2 \u03c3\u03c4\u03b7\u03bd \u03ba\u03bb\u03af\u03bc\u03b1\u03ba\u03b1 \u03c0\u03bf\u03c5 \u03c0\u03b1\u03c1\u03b1\u03c4\u03af\u03b8\u03b5\u03c4\u03b1\u03b9 \u03c3\u03c4\u03bf\u03bd <a href=\"http:\/\/www.g-culture.org\/ioannis\/2013\/05\/02\/%CE%AE%CF%87%CE%BF%CF%82-%CF%80%CF%81%CF%8E%CF%84%CE%BF%CF%82\/\">\u03a0\u03c1\u03ce\u03c4\u03bf \u03ae\u03c7\u03bf.<\/a><\/p>\n<p>\u039a\u03b1\u03b9 \u03bf \u03c3\u03c5\u03b3\u03b3\u03c1\u03b1\u03c6\u03ad\u03b1\u03c2 \u03c4\u03bf\u03c5 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\u03c4\u03b1 12. \u03a0\u03c1\u03bf\u03c2 \u03b4\u03b5 \u03c4\u03bf\u03bd \u03b5\u03bb\u03ac\u03c7\u03b9\u03c3\u03c4\u03bf\u03bd 9 \u03c0\u03c1\u03bf\u03c2 7. \u0395\u03c0\u03bf\u03bc\u03ad\u03bd\u03c9\u03c2 \u03ba\u03b1\u03b9 \u03bf \u03b5\u03bb\u03ac\u03c7\u03b9\u03c3\u03c4\u03bf\u03c2 \u03c4\u03cc\u03bd\u03bf\u03c2 \u03ad\u03c7\u03b5\u03b9 \u03bb\u03cc\u03b3\u03bf \u03c0\u03c1\u03bf\u03c2 \u03bc\u03b5\u03bd \u03c4\u03bf\u03bd \u03bc\u03b5\u03af\u03b6\u03bf\u03bd\u03b1 \u03c4\u03cc\u03bd\u03bf 7 \u03c0\u03c1\u03bf\u03c212, \u03c0\u03c1\u03bf\u03c2 \u03b4\u03b5 \u03c4\u03bf\u03bd \u03b5\u03bb\u03ac\u03c3\u03c3\u03bf\u03bd\u03b1 7 \u03c0\u03c1\u03bf\u03c2 \u03c4\u03b1 9. \u038f\u03c3\u03c4\u03b5 \u03b1\u03bd \u03c5\u03c0\u03bf\u03c4\u03b5\u03b8\u03b5\u03af \u03cc\u03c4\u03b9 \u03c4\u03bf \u03b4\u03b9\u03ac\u03c3\u03c4\u03b7\u03bc\u03b1 \u03c4\u03bf\u03c5 \u03bc\u03b5\u03af\u03b6\u03bf\u03bd\u03bf\u03c2 \u03c4\u03cc\u03bd\u03bf\u03c5 \u03b5\u03af\u03bd\u03b1\u03b9 \u03af\u03c3\u03bf 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\u03b3\u03b9\u03b1 \u03c4\u03bf\u03bd \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03b9\u03c3\u03bc\u03cc \u03c4\u03c9\u03bd \u03bc\u03bf\u03c5\u03c3\u03b9\u03ba\u03ce\u03bd \u03b4\u03b9\u03b1\u03c3\u03c4\u03b7\u03bc\u03ac\u03c4\u03c9\u03bd \u03c3\u03c4\u03b7\u03bd \u03c0\u03b1\u03bd\u03b4\u03bf\u03c5\u03c1\u03af\u03b4\u03b1 \u03b5\u03be\u03ad\u03c6\u03c1\u03b1\u03c3\u03b1\u03bd \u03c4\u03b1 \u03bc\u03ad\u03bb\u03b7 \u03c4\u03b7\u03c2 \u039c\u03bf\u03c5\u03c3\u03b9\u03ba\u03ae\u03c2 \u03a0\u03b1\u03c4\u03c1\u03b9\u03b1\u03c1\u03c7\u03b9\u03ba\u03ae\u03c2 \u0395\u03c0\u03b9\u03c4\u03c1\u03bf\u03c0\u03ae\u03c2. \u0397 \u03b5\u03bd \u03bb\u03cc\u03b3\u03c9 \u03b5\u03c0\u03b9\u03c4\u03c1\u03bf\u03c0\u03ae \u03c3\u03c5\u03c3\u03c4\u03ac\u03b8\u03b7\u03ba\u03b5 \u03c4\u03bf 1881 \u03ba\u03b1\u03b9 \u03c4\u03b7\u03bd \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03bf\u03cd\u03c3\u03b1\u03bd: \u03bf \u0391\u03c1\u03c7. \u0393\u03b5\u03c1\u03bc\u03b1\u03bd\u03cc\u03c2 \u0391\u03c6\u03b8\u03bf\u03bd\u03af\u03b4\u03b7\u03c2, \u03bf \u03a0\u03c1\u03c9\u03c4\u03bf\u03c8\u03ac\u03bb\u03c4\u03b7\u03c2 \u0393\u03b5\u03ce\u03c1\u03b3\u03b9\u03bf\u03c2 \u0392\u03b9\u03bf\u03bb\u03ac\u03ba\u03b7\u03c2, \u03bf \u0395\u03c5\u03c3\u03c4\u03c1\u03ac\u03c4\u03b9\u03bf\u03c2 \u03a0\u03b1\u03c0\u03b1\u03b4\u03cc\u03c0\u03bf\u03c5\u03bb\u03bf\u03c2, \u03bf \u0399\u03c9\u03ac\u03c3\u03b1\u03c6 \u03bc\u03bf\u03bd\u03b1\u03c7\u03cc\u03c2, \u03bf \u03a0\u03b1\u03bd\u03b1\u03b3\u03b9\u03ce\u03c4\u03b7\u03c2 \u039a\u03b7\u03bb\u03c4\u03b6\u03b1\u03bd\u03af\u03b4\u03b7\u03c2, \u03bf \u0391\u03bd\u03b4\u03c1\u03ad\u03b1\u03c2 \u03a3\u03c0\u03b1\u03b8\u03ac\u03c1\u03b7\u03c2 \u03ba\u03b1\u03b9 \u03bf \u0393\u03b5\u03ce\u03c1\u03b3\u03b9\u03bf\u03c2 \u03a0\u03c1\u03c9\u03b3\u03ac\u03ba\u03b7\u03c2. \u0397 \u03b5\u03c0\u03b9\u03c4\u03c1\u03bf\u03c0\u03ae \u03b2\u03b5\u03bb\u03c4\u03af\u03c9\u03c3\u03b5 \u03bf\u03c5\u03c3\u03b9\u03b1\u03c3\u03c4\u03b9\u03ba\u03ac \u03bf\u03c1\u03b9\u03c3\u03bc\u03ad\u03bd\u03b1 \u03c3\u03b7\u03bc\u03b5\u03af\u03b1 \u03c4\u03bf\u03c5 \u03b8\u03b5\u03c9\u03c1\u03b7\u03c4\u03b9\u03ba\u03bf\u03cd \u03ad\u03c1\u03b3\u03bf\u03c5 \u03c4\u03bf\u03c5 \u03a7\u03c1\u03c5\u03c3\u03ac\u03bd\u03b8\u03bf\u03c5.<\/p>\n<p>\u0397 \u039c\u03bf\u03c5\u03c3\u03b9\u03ba\u03ae \u0395\u03c0\u03b9\u03c4\u03c1\u03bf\u03c0\u03ae \u03b5\u03c1\u03b3\u03ac\u03c3\u03b8\u03b7\u03ba\u03b5 \u03c3\u03c4\u03bf \u03a6\u03b1\u03bd\u03ac\u03c1\u03b9 \u03c9\u03c2 \u03b5\u03be\u03ae\u03c2: \u03c3\u03cd\u03bc\u03c6\u03c9\u03bd\u03b1 \u03bc\u03b5 \u03c4\u03b9\u03c2 \u03bf\u03b4\u03b7\u03b3\u03af\u03b5\u03c2 \u03c0\u03bf\u03c5 \u03c0\u03b1\u03c1\u03ad\u03c7\u03b5\u03b9 \u03c4\u03bf \u039c\u03ad\u03b3\u03b1 \u0398\u03b5\u03c9\u03c1\u03b7\u03c4\u03b9\u03ba\u03cc, \u03cc\u03c1\u03b9\u03c3\u03b5 \u03c4\u03bf\u03c5\u03c2 \u03b4\u03b5\u03c3\u03bc\u03bf\u03cd\u03c2 \u03c3\u03b5 \u03c7\u03bf\u03c1\u03b4\u03ae \u03c0\u03c1\u03bf\u03c2 \u03c0\u03b1\u03c1\u03b1\u03b3\u03c9\u03b3\u03ae \u03c4\u03bf\u03c5 \u03c4\u03b5\u03c4\u03c1\u03b1\u03c7\u03cc\u03c1\u03b4\u03bf\u03c5 \u0394\u03b9 &#8211; \u039d\u03b7, \u03bb\u03b1\u03bc\u03b2\u03ac\u03bd\u03bf\u03bd\u03c4\u03b1\u03c2<\/p>\n<ul>\n<li>\u03b3\u03b9\u03b1 \u03c4\u03bf\u03bd \u0394\u03b9 \u03c4\u03bf \u03bc\u03ae\u03ba\u03bf\u03c2 \u03c4\u03b7\u03c2 \u03c7\u03bf\u03c1\u03b4\u03ae\u03c2 1<\/li>\n<li>\u03b3\u03b9\u03b1 \u03c4\u03bf\u03bd \u039a\u03b5 \u03c4\u03bf \u03bc\u03ae\u03ba\u03bf\u03c2 \u03c4\u03b7\u03c2 \u03c7\u03bf\u03c1\u03b4\u03ae\u03c2 \u03c4\u03b1 8\/9<\/li>\n<li>\u03b3\u03b9\u03b1 \u03c4\u03bf\u03bd \u0396\u03c9 \u03c4\u03bf \u03bc\u03ae\u03ba\u03bf\u03c2 \u03c4\u03b7\u03c2 \u03c7\u03bf\u03c1\u03b4\u03ae\u03c2 \u03c4\u03b1 22\/27<\/li>\n<li>\u03b3\u03b9\u03b1 \u03c4\u03bf\u03bd \u039d\u03b7 \u03c4\u03bf \u03bc\u03ae\u03ba\u03bf\u03c2 \u03c4\u03b7\u03c2 \u03c7\u03bf\u03c1\u03b4\u03ae\u03c2 \u03c4\u03b1 3\/4<\/li>\n<\/ul>\n<p>\u03a3\u03c4\u03b9\u03c2 \u03b8\u03ad\u03c3\u03b5\u03b9\u03c2 \u03b1\u03c5\u03c4\u03ad\u03c2 \u03ba\u03b1\u03b9 \u03c3\u03c4\u03bf \u03bc\u03ac\u03bd\u03b9\u03ba\u03bf \u03b5\u03b3\u03c7\u03cc\u03c1\u03b4\u03bf\u03c5 \u03bf\u03c1\u03b3\u03ac\u03bd\u03bf\u03c5 \u03c4\u03bf\u03c0\u03bf\u03b8\u03b5\u03c4\u03ae\u03b8\u03b7\u03ba\u03b1\u03bd \u03ba\u03b9\u03bd\u03bf\u03cd\u03bc\u03b5\u03bd\u03b1 \u03c4\u03ac\u03c3\u03c4\u03b1. \u03a0\u03b1\u03c1\u0384 \u03cc\u03bb\u03b1 \u03b1\u03c5\u03c4\u03ac \u03cc\u03bc\u03c9\u03c2 \u03c5\u03c0\u03ae\u03c1\u03c7\u03b1\u03bd \u03c0\u03c1\u03bf\u03b2\u03bb\u03ae\u03bc\u03b1\u03c4\u03b1: &#8220;\u03b5\u03bd\u03c4\u03b5\u03cd\u03b8\u03b5\u03bd \u03c6\u03b1\u03af\u03bd\u03b5\u03c4\u03b1\u03b9 \u03cc\u03c4\u03b9 \u03b2\u03b1\u03c3\u03b9\u03bb\u03b5\u03cd\u03b5\u03b9 \u03c3\u03cd\u03b3\u03c7\u03b9\u03c3\u03b9\u03c2 \u03c0\u03b5\u03c1\u03af \u03c4\u03b7\u03bd \u03b2\u03ac\u03c3\u03b9\u03bd \u03b1\u03c5\u03c4\u03ae\u03c2 \u03c4\u03b7\u03c2 \u03b5\u03c1\u03b3\u03b1\u03c3\u03af\u03b1\u03c2. \u0391\u03bb\u03bb\u03ac \u03b5\u03ba\u03c4\u03cc\u03c2 \u03c4\u03b7\u03c2 \u03c3\u03c5\u03b3\u03c7\u03af\u03c3\u03b5\u03c9\u03c2 \u03c4\u03b1\u03cd\u03c4\u03b7\u03c2 \u03b1\u03bc\u03c6\u03cc\u03c4\u03b5\u03c1\u03b1\u03b9 \u03b1\u03b9 \u03b1\u03bd\u03b1\u03bb\u03bf\u03b3\u03af\u03b1\u03b9 \u03b1\u03c5\u03c4\u03b1\u03af \u03bf\u03c5\u03b4\u03ad\u03bd \u03c3\u03b7\u03bc\u03b1\u03af\u03bd\u03bf\u03c5\u03c3\u03b9\u03bd \u03b1\u03ba\u03bf\u03c5\u03c3\u03c4\u03b9\u03ba\u03ce\u03c2. \u039f\u03b9 \u03b4\u03b5 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03af 12, 8, 7 \u03ae 88, 66, 63 \u03b4\u03cd\u03bd\u03b1\u03bd\u03c4\u03b1\u03b9 \u03c4\u03bf \u03c0\u03bf\u03bb\u03cd \u03bd\u03b1 \u03ad\u03c7\u03c9\u03c3\u03b9\u03bd \u03b5\u03b9\u03ba\u03bf\u03bd\u03b9\u03ba\u03ae\u03bd \u03c3\u03b7\u03bc\u03b1\u03c3\u03af\u03b1\u03bd &#8230;. \u0395\u03bd \u03c4\u03b7 \u03c0\u03b1\u03c1\u03b1\u03b4\u03cc\u03c3\u03b5\u03b9 \u03bb\u03bf\u03b9\u03c0\u03cc\u03bd \u03bc\u03cc\u03bd\u03b7 \u03bd\u03bf\u03bc\u03af\u03b6\u03b5\u03b9 \u03b7 \u0395\u03c0\u03b9\u03c4\u03c1\u03bf\u03c0\u03ae \u03cc\u03c4\u03b9 \u03ad\u03b3\u03ba\u03b5\u03b9\u03c4\u03b1\u03b9 \u03b7 \u03b8\u03b5\u03c1\u03b1\u03c0\u03b5\u03af\u03b1 \u03c4\u03bf\u03c5 \u03ba\u03b1\u03ba\u03bf\u03cd&#8221;. \u0393\u03b9\u0384 \u03b1\u03c5\u03c4\u03cc \u03bb\u03bf\u03b9\u03c0\u03cc\u03bd \u03c4\u03bf \u03c3\u03ba\u03bf\u03c0\u03cc \u03ba\u03bb\u03af\u03b8\u03b7\u03ba\u03b1\u03bd \u03bf\u03b9 \u03b4\u03ac\u03c3\u03ba\u03b1\u03bb\u03bf\u03b9 \u03c4\u03b7\u03c2 \u03b5\u03c0\u03bf\u03c7\u03ae\u03c2 \u03bf\u03b9 \u03bf\u03c0\u03bf\u03af\u03bf\u03b9 \u03b1\u03ba\u03bf\u03cd\u03b3\u03bf\u03bd\u03c4\u03b1\u03c2 \u03c4\u03b1 \u03b4\u03b9\u03b1\u03c3\u03c4\u03ae\u03bc\u03b1\u03c4\u03b1 \u03c4\u03b1 \u03c0\u03c1\u03bf\u03c4\u03b5\u03b9\u03bd\u03cc\u03bc\u03b5\u03bd\u03b1 \u03b1\u03c0\u03cc \u03c4\u03b7\u03bd \u0395\u03c0\u03b9\u03c4\u03c1\u03bf\u03c0\u03ae, &#8220;\u03b5\u03be\u03ad\u03c6\u03c1\u03b1\u03b6\u03bf\u03bd \u03c4\u03b7\u03bd \u03b5\u03b1\u03c5\u03c4\u03ce\u03bd \u03b3\u03bd\u03ce\u03bc\u03b7\u03bd. \u039a\u03b1\u03b9 \u03b5\u03ac\u03bd \u03bc\u03b5\u03bd \u03b7 \u03b1\u03c0\u03cc\u03b4\u03bf\u03c3\u03b9\u03c2 \u03b5\u03bc\u03b1\u03c1\u03c4\u03c5\u03c1\u03b5\u03af\u03c4\u03bf \u03c0\u03b9\u03c3\u03c4\u03ae \u03ba\u03b1\u03b9 \u03b3\u03bd\u03b7\u03c3\u03af\u03b1, \u03c3\u03c5\u03bd\u03b5\u03ba\u03c1\u03af\u03bd\u03bf\u03bd\u03c4\u03bf \u03bf\u03b9 \u03c6\u03b8\u03cc\u03b3\u03b3\u03bf\u03b9 \u03c4\u03bf\u03c5 \u03c5\u03c0\u0384 \u03cc\u03c8\u03b9\u03bd \u03bf\u03c1\u03b3\u03ac\u03bd\u03bf\u03c5 (\u03c4\u03bf\u03c5 \u03c8\u03b1\u03bb\u03c4\u03b7\u03c1\u03af\u03bf\u03c5) \u03b4\u03b9 \u03bf\u03bc\u03bf\u03c6\u03c9\u03bd\u03af\u03b1\u03c2 \u03c0\u03c1\u03bf\u03c2 \u03c4\u03bf\u03c5\u03c2 \u03c6\u03b8\u03cc\u03b3\u03b3\u03bf\u03c5\u03c2 \u03c4\u03bf\u03c5 \u03bc\u03bf\u03bd\u03bf\u03c7\u03cc\u03c1\u03b4\u03bf\u03c5 \u03ba\u03b1\u03b9 \u03b5\u03c3\u03b7\u03bc\u03b5\u03b9\u03bf\u03cd\u03bd\u03c4\u03bf \u03c4\u03b1 \u03b1\u03bd\u03c4\u03af\u03c3\u03c4\u03bf\u03b9\u03c7\u03b1 \u03bc\u03ae\u03ba\u03b7 \u03c4\u03b7\u03c2 \u03b1\u03c5\u03c4\u03ae\u03c2 \u03c7\u03bf\u03c1\u03b4\u03ae\u03c2 \u03b5\u03c0\u03af \u03c4\u03b1\u03c2 \u03c5\u03c0\u03cc \u03c4\u03b7\u03bd \u03b2\u03ac\u03c3\u03b1\u03bd\u03bf\u03bd \u03b4\u03b9\u03b1\u03b9\u03c1\u03ad\u03c3\u03b5\u03b9\u03c2. \u0395\u03b9 \u03b4\u03b5 \u03bc\u03b7, \u03b1\u03c0\u03b5\u03c1\u03c1\u03af\u03c0\u03c4\u03bf\u03bd\u03c4\u03bf \u03b1\u03c5\u03c4\u03b1\u03af \u03c9\u03c2 \u03b5\u03c3\u03c6\u03b1\u03bb\u03bc\u03ad\u03bd\u03bf\u03b9 \u03ba\u03b1\u03b9 \u03bd\u03cc\u03b8\u03bf\u03b9&#8221;. \u0391\u03c0\u03cc \u03c4\u03b9\u03c2 \u03c0\u03b1\u03c1\u03b1\u03c0\u03ac\u03bd\u03c9 \u03b8\u03ad\u03c3\u03b5\u03b9\u03c2 \u03ba\u03b1\u03b8\u03b9\u03b5\u03c1\u03ce\u03b8\u03b7\u03ba\u03b1\u03bd \u03c4\u03b1 \u03bc\u03ae\u03ba\u03b7 \u03c7\u03bf\u03c1\u03b4\u03ce\u03bd<\/p>\n<p>&nbsp;<\/p>\n<table border=\"1\" width=\"100%\">\n<tbody>\n<tr>\n<td align=\"center\" width=\"12%\">\u039d\u03b7<sub>1<\/sub><\/td>\n<td align=\"center\" width=\"12%\">\u03a0\u03b1<sub>1<\/sub><\/td>\n<td align=\"center\" width=\"12%\">\u0392\u03bf\u03c5<sub>1<\/sub><\/td>\n<td align=\"center\" width=\"12%\">\u0393\u03b1<sub>1<\/sub><\/td>\n<td align=\"center\" width=\"13%\">\u0394\u03b9<sub>1<\/sub><\/td>\n<td align=\"center\" width=\"13%\">\u039a\u03b5<sub>1<\/sub><\/td>\n<td align=\"center\" width=\"13%\">\u0396\u03c9<sub>1<\/sub><\/td>\n<td align=\"center\" width=\"13%\">\u039d\u03b7<sub>2<\/sub><\/td>\n<\/tr>\n<tr>\n<td align=\"center\" width=\"12%\">1<\/td>\n<td align=\"center\" width=\"12%\">8\/9<\/td>\n<td align=\"center\" width=\"12%\">81\/100<\/td>\n<td align=\"center\" width=\"12%\">3\/4<\/td>\n<td align=\"center\" width=\"13%\">2\/3<\/td>\n<td align=\"center\" width=\"13%\">16\/27<\/td>\n<td align=\"center\" width=\"13%\">27\/50<\/td>\n<td align=\"center\" width=\"13%\">1\/2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<table border=\"1\" width=\"100%\">\n<tbody>\n<tr>\n<td align=\"center\" width=\"12%\">\u039d\u03b7<sub>2<\/sub><\/td>\n<td align=\"center\" width=\"12%\">\u03a0\u03b1<sub>2<\/sub><\/td>\n<td align=\"center\" width=\"12%\">\u0392\u03bf\u03c5<sub>2<\/sub><\/td>\n<td align=\"center\" width=\"12%\">\u0393\u03b1<sub>2<\/sub><\/td>\n<td align=\"center\" width=\"13%\">\u0394\u03b9<sub>2<\/sub><\/td>\n<td align=\"center\" width=\"13%\">\u039a\u03b5<sub>2<\/sub><\/td>\n<td align=\"center\" width=\"13%\">\u0396\u03c9<sub>2<\/sub><\/td>\n<td align=\"center\" width=\"13%\">\u039d\u03b7<sub>3<\/sub><\/td>\n<\/tr>\n<tr>\n<td align=\"center\" width=\"12%\">1\/2<\/td>\n<td align=\"center\" width=\"12%\">4\/9<\/td>\n<td align=\"center\" width=\"12%\">81\/200<\/td>\n<td align=\"center\" width=\"12%\">3\/8<\/td>\n<td align=\"center\" width=\"13%\">1\/3<\/td>\n<td align=\"center\" width=\"13%\">8\/27<\/td>\n<td align=\"center\" width=\"13%\">27\/100<\/td>\n<td align=\"center\" width=\"13%\">1\/4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u0391\u03c0\u03cc \u03c4\u03b7 \u03c6\u03c5\u03c3\u03b9\u03ba\u03ae \u03b3\u03bd\u03c9\u03c1\u03af\u03b6\u03bf\u03c5\u03bc\u03b5 \u03cc\u03c4\u03b9 \u03b7 \u03c3\u03c5\u03c7\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1 \u03b5\u03bd\u03cc\u03c2 \u03ae\u03c7\u03bf\u03c5 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b1\u03bd\u03c4\u03b9\u03c3\u03c4\u03c1\u03cc\u03c6\u03c9\u03c2 \u03b1\u03bd\u03ac\u03bb\u03bf\u03b3\u03b7 \u03c4\u03bf\u03c5 \u03bc\u03ae\u03ba\u03bf\u03c5\u03c2 \u03c7\u03bf\u03c1\u03b4\u03ae\u03c2. \u039c\u0384 \u03b1\u03c5\u03c4\u03cc\u03bd \u03c4\u03bf\u03bd \u03c4\u03c1\u03cc\u03c0\u03bf \u03c0\u03c1\u03bf\u03ba\u03cd\u03c0\u03c4\u03bf\u03c5\u03bd \u03bf\u03b9 \u03c0\u03b1\u03c1\u03b1\u03ba\u03ac\u03c4\u03c9 \u03c3\u03c7\u03ad\u03c3\u03b5\u03b9\u03c2 \u03c3\u03c5\u03c7\u03bd\u03bf\u03c4\u03ae\u03c4\u03c9\u03bd \u03bc\u03b5 \u03b1\u03bd\u03b1\u03c6\u03bf\u03c1\u03ac \u03c4\u03bf \u03c6\u03b8\u03cc\u03b3\u03b3\u03bf \u039d\u03b7<sub>1<\/sub><\/p>\n<p>&nbsp;<\/p>\n<table border=\"1\" width=\"100%\">\n<tbody>\n<tr>\n<td align=\"center\" width=\"12%\">\u039d\u03b7<sub>1<\/sub><\/td>\n<td align=\"center\" width=\"12%\">\u03a0\u03b1<sub>1<\/sub><\/td>\n<td align=\"center\" width=\"12%\">\u0392\u03bf\u03c5<sub>1<\/sub><\/td>\n<td align=\"center\" width=\"12%\">\u0393\u03b1<sub>1<\/sub><\/td>\n<td align=\"center\" width=\"13%\">\u0394\u03b9<sub>1<\/sub><\/td>\n<td align=\"center\" width=\"13%\">\u039a\u03b5<sub>1<\/sub><\/td>\n<td align=\"center\" width=\"13%\">\u0396\u03c9<sub>1<\/sub><\/td>\n<td align=\"center\" width=\"13%\">\u039d\u03b7<sub>2<\/sub><\/td>\n<\/tr>\n<tr>\n<td align=\"center\" width=\"12%\">1<\/td>\n<td align=\"center\" width=\"12%\">9\/8<\/td>\n<td align=\"center\" width=\"12%\">100\/81<\/td>\n<td align=\"center\" width=\"12%\">4\/3<\/td>\n<td align=\"center\" width=\"13%\">3\/2<\/td>\n<td align=\"center\" width=\"13%\">27\/16<\/td>\n<td align=\"center\" width=\"13%\">50\/27<\/td>\n<td align=\"center\" width=\"13%\">2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<table border=\"1\" width=\"100%\">\n<tbody>\n<tr>\n<td align=\"center\" width=\"12%\">\u039d\u03b7<sub>2<\/sub><\/td>\n<td align=\"center\" width=\"12%\">\u03a0\u03b1<sub>2<\/sub><\/td>\n<td align=\"center\" width=\"12%\">\u0392\u03bf\u03c5<sub>2<\/sub><\/td>\n<td align=\"center\" width=\"12%\">\u0393\u03b1<sub>2<\/sub><\/td>\n<td align=\"center\" width=\"13%\">\u0394\u03b9<sub>2<\/sub><\/td>\n<td align=\"center\" width=\"13%\">\u039a\u03b5<sub>2<\/sub><\/td>\n<td align=\"center\" width=\"13%\">\u0396\u03c9<sub>2<\/sub><\/td>\n<td align=\"center\" width=\"13%\">\u039d\u03b7<sub>3<\/sub><\/td>\n<\/tr>\n<tr>\n<td align=\"center\" width=\"12%\">2<\/td>\n<td align=\"center\" width=\"12%\">9\/4<\/td>\n<td align=\"center\" width=\"12%\">200\/81<\/td>\n<td align=\"center\" width=\"12%\">8\/3<\/td>\n<td align=\"center\" width=\"13%\">3\/1<\/td>\n<td align=\"center\" width=\"13%\">27\/8<\/td>\n<td align=\"center\" width=\"13%\">100\/27<\/td>\n<td align=\"center\" width=\"13%\">4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p><a name=\"today\"><\/a>\u03a3\u03c4\u03b7 \u03c3\u03b7\u03bc\u03b5\u03c1\u03b9\u03bd\u03ae \u03c0\u03c1\u03b1\u03b3\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc\u03c4\u03b7\u03c4\u03b1, \u03c4\u03cc\u03c3\u03bf \u03b7 \u03bc\u03bf\u03c5\u03c3\u03b9\u03ba\u03ae \u03b8\u03b5\u03c9\u03c1\u03af\u03b1, \u03cc\u03c3\u03bf \u03ba\u03b1\u03b9 \u03b7 \u03bc\u03bf\u03c5\u03c3\u03b9\u03ba\u03ae \u03c0\u03c1\u03ac\u03be\u03b7, \u03b5\u03c1\u03bc\u03b7\u03bd\u03b5\u03cd\u03bf\u03bd\u03c4\u03b1\u03b9 \u03bc\u03b5 \u03c6\u03c5\u03c3\u03b9\u03ba\u03bf\u03cd\u03c2 \u03bd\u03cc\u03bc\u03bf\u03c5\u03c2, \u03c0\u03bf\u03c5 \u03bc\u03b5 \u03c4\u03b7 \u03c3\u03b5\u03b9\u03c1\u03ac \u03c4\u03bf\u03c5\u03c2 \u03b4\u03b9\u03b1\u03c4\u03c5\u03c0\u03ce\u03bd\u03bf\u03bd\u03c4\u03b1\u03b9 \u03bc\u03b5 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ad\u03c2 \u03c3\u03c7\u03ad\u03c3\u03b5\u03b9\u03c2.<\/p>\n<p>\u03a3\u03c4\u03b7\u03bd \u03b1\u03ba\u03bf\u03c5\u03c3\u03c4\u03b9\u03ba\u03ae (\u03c3\u03c4\u03bf\u03bd \u03b9\u03b4\u03b9\u03b1\u03af\u03c4\u03b5\u03c1\u03bf \u03ba\u03bb\u03ac\u03b4\u03bf \u03c4\u03b7\u03c2 \u03c6\u03c5\u03c3\u03b9\u03ba\u03ae\u03c2 \u03c0\u03bf\u03c5 \u03ad\u03c7\u03b5\u03b9 \u03c9\u03c2 \u03b1\u03bd\u03c4\u03b9\u03ba\u03b5\u03af\u03bc\u03b5\u03bd\u03bf \u03c4\u03bf\u03bd \u03ae\u03c7\u03bf \u03ba\u03b1\u03b9 \u03c4\u03b9\u03c2 \u03b9\u03b4\u03b9\u03cc\u03c4\u03b7\u03c4\u03ad\u03c2 \u03c4\u03bf\u03c5) \u03ad\u03bd\u03b1 \u03bc\u03bf\u03c5\u03c3\u03b9\u03ba\u03cc \u03b4\u03b9\u03ac\u03c3\u03c4\u03b7\u03bc\u03b1 \u03b5\u03ba\u03c6\u03c1\u03ac\u03b6\u03b5\u03c4\u03b1\u03b9 \u03c3\u03b1\u03bd \u03bf \u03bb\u03cc\u03b3\u03bf\u03c2 \u03b4\u03cd\u03bf \u03c3\u03c5\u03c7\u03bd\u03bf\u03c4\u03ae\u03c4\u03c9\u03bd. \u03a3\u03b5 \u03bf\u03c1\u03b9\u03c3\u03bc\u03ad\u03bd\u03b5\u03c2 \u03c0\u03b5\u03c1\u03b9\u03c0\u03c4\u03ce\u03c3\u03b5\u03b9\u03c2 \u03bf \u03bb\u03cc\u03b3\u03bf\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b1\u03c0\u03bb\u03ae\u03c2 \u03bc\u03bf\u03c1\u03c6\u03ae\u03c2 \u03cc\u03c0\u03c9\u03c2 \u03b3\u03b9\u03b1 \u03c0\u03b1\u03c1\u03ac\u03b4\u03b5\u03b9\u03b3\u03bc\u03b1 \u03bf\u03b9 \u03b3\u03bd\u03c9\u03c3\u03c4\u03bf\u03af \u03bc\u03b1\u03c2 \u03bb\u03cc\u03b3\u03bf\u03b9 \u03c4\u03b7\u03c2 \u03ba\u03b1\u03b8\u03b1\u03c1\u03ae\u03c2 \u03c0\u03ad\u03bc\u03c0\u03c4\u03b7\u03c2 (3\/2), \u03c4\u03b7\u03c2 \u03ba\u03b1\u03b8\u03b1\u03c1\u03ae\u03c2 \u03c4\u03b5\u03c4\u03ac\u03c1\u03c4\u03b7\u03c2 (4\/3), \u03c4\u03b7\u03c2 \u03bf\u03ba\u03c4\u03ac\u03b2\u03b1\u03c2 (2\/1) \u03ba.\u03bb.\u03c0. \u03a3\u03b5 \u03ac\u03bb\u03bb\u03b5\u03c2 \u03c0\u03b5\u03c1\u03b9\u03c0\u03c4\u03ce\u03c3\u03b5\u03b9\u03c2, \u03b5\u03bb\u03bb\u03b5\u03af\u03c8\u03b5\u03b9 \u03bc\u03b5\u03b3\u03af\u03c3\u03c4\u03bf\u03c5 \u03ba\u03bf\u03b9\u03bd\u03bf\u03cd \u03b4\u03b9\u03b1\u03b9\u03c1\u03ad\u03c4\u03b7, \u03bf\u03b9 \u03cc\u03c1\u03bf\u03b9 \u03c4\u03bf\u03c5 \u03bb\u03cc\u03b3\u03bf\u03c5 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bc\u03b5\u03b3\u03ac\u03bb\u03bf\u03b9 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03af \u03cc\u03c0\u03c9\u03c2 \u03c3\u03c4\u03bf \u03b4\u03b9\u03ac\u03c3\u03c7\u03b9\u03c3\u03bc\u03b1 (2048\/2025). \u03a0\u03c1\u03bf\u03ba\u03cd\u03c0\u03c4\u03b5\u03b9 \u03bb\u03bf\u03b9\u03c0\u03cc\u03bd \u03c4\u03bf \u03c3\u03c5\u03bc\u03c0\u03ad\u03c1\u03b1\u03c3\u03bc\u03b1 \u03cc\u03c4\u03b9 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b4\u03cd\u03c3\u03ba\u03bf\u03bb\u03b7, \u03b1\u03bd \u03cc\u03c7\u03b9 \u03b1\u03b4\u03cd\u03bd\u03b1\u03c4\u03b7, \u03b7 \u03c3\u03cd\u03b3\u03ba\u03c1\u03b9\u03c3\u03b7 \u03b4\u03cd\u03bf \u03bc\u03bf\u03c5\u03c3\u03b9\u03ba\u03ce\u03bd \u03b4\u03b9\u03b1\u03c3\u03c4\u03b7\u03bc\u03ac\u03c4\u03c9\u03bd.<\/p>\n<p>\u0397 \u03b1\u03c0\u03bb\u03bf\u03cd\u03c3\u03c4\u03b5\u03c5\u03c3\u03b7 \u03c3\u03c4\u03b7\u03bd \u03c0\u03b1\u03c1\u03ac\u03c3\u03c4\u03b1\u03c3\u03b7 \u03c4\u03c9\u03bd \u03bc\u03bf\u03c5\u03c3\u03b9\u03ba\u03ce\u03bd \u03b4\u03b9\u03b1\u03c3\u03c4\u03b7\u03bc\u03ac\u03c4\u03c9\u03bd \u03b5\u03c0\u03ae\u03bb\u03b8\u03b5 \u03bc\u03b5 \u03c4\u03b7 \u03b2\u03bf\u03ae\u03b8\u03b5\u03b9\u03b1 \u03c4\u03b7\u03c2 \u03bb\u03bf\u03b3\u03b1\u03c1\u03b9\u03b8\u03bc\u03b9\u03ba\u03ae\u03c2 \u03c3\u03c7\u03ad\u03c3\u03b7\u03c2<\/p>\n<p align=\"center\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <b>\u03bc\u03ad\u03b3\u03b5\u03b8\u03bf\u03c2 \u03bc\u03bf\u03c5\u03c3\u03b9\u03ba\u03bf\u03cd \u03b4\u03b9\u03b1\u03c3\u03c4\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2 = k * log(f<sub>2<\/sub>\/f<sub>1<\/sub>)\/log2<\/b><\/p>\n<p align=\"left\">\u03c3\u03c4\u03b7\u03bd \u03c0\u03b1\u03c1\u03b1\u03c0\u03ac\u03bd\u03c9 \u03c3\u03c7\u03ad\u03c3\u03b7, \u03cc\u03c0\u03bf\u03c5 f<sub>1<\/sub>, f<sub>2<\/sub> \u03bf\u03b9 \u03c3\u03c5\u03c7\u03bd\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2 \u03c4\u03c9\u03bd \u03c6\u03b8\u03cc\u03b3\u03b3\u03c9\u03bd \u03c4\u03bf\u03c5 \u03bc\u03bf\u03c5\u03c3\u03b9\u03ba\u03bf\u03cd \u03b4\u03b9\u03b1\u03c3\u03c4\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2 \u03ba\u03b1\u03b9 f<sub>2<\/sub>&gt;f<sub>1. <\/sub>\u03a4\u03bf k \u03b5\u03af\u03bd\u03b1\u03b9 \u03bc\u03b9\u03b1 \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03ac \u03b7 \u03c4\u03b9\u03bc\u03ae \u03c4\u03b7\u03c2 \u03bf\u03c0\u03bf\u03af\u03b1\u03c2 \u03ba\u03b1\u03b8\u03bf\u03c1\u03af\u03b6\u03b5\u03b9 \u03ba\u03b1\u03b9 \u03ad\u03bd\u03b1 \u03c3\u03cd\u03c3\u03c4\u03b7\u03bc\u03b1 \u03bc\u03bf\u03bd\u03ac\u03b4\u03c9\u03bd \u03bc\u03bf\u03c5\u03c3\u03b9\u03ba\u03ce\u03bd \u03b4\u03b9\u03b1\u03c3\u03c4\u03b7\u03bc\u03ac\u03c4\u03c9\u03bd.<\/p>\n<h4 align=\"left\">\u03a3\u03c5\u03b3\u03ba\u03b5\u03c1\u03b1\u03c3\u03bc\u03bf\u03af \u03b3\u03b9\u03b1 \u03c4\u03b1 \u03bc\u03bf\u03c5\u03c3\u03b9\u03ba\u03ac \u03b4\u03b9\u03b1\u03c3\u03c4\u03ae\u03bc\u03b1\u03c4\u03b1<\/h4>\n<p align=\"left\">\u0391\u03bd\u03ac\u03bb\u03bf\u03b3\u03b1 \u03bc\u03b5 \u03c4\u03b9\u03c2 \u03c4\u03b9\u03bc\u03ad\u03c2 \u03c4\u03b7\u03c2 \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03ac\u03c2 k (\u03bf\u03b9 \u03bf\u03c0\u03bf\u03af\u03b5\u03c2 \u03b1\u03c6\u03bf\u03c1\u03bf\u03cd\u03bd \u03b4\u03b9\u03b1\u03af\u03c1\u03b5\u03c3\u03b7 \u03c4\u03b7\u03c2 \u03bf\u03ba\u03c4\u03ac\u03b2\u03b1\u03c2 \u03c3\u03b5 \u03c4\u03cc\u03c3\u03b1 \u03c4\u03bc\u03ae\u03bc\u03b1\u03c4\u03b1 \u03cc\u03c3\u03bf \u03b7 \u03b1\u03bd\u03c4\u03af\u03c3\u03c4\u03bf\u03b9\u03c7\u03b7 \u03c4\u03b9\u03bc\u03ae), \u03ad\u03c7\u03bf\u03c5\u03bc\u03b5 \u03ba\u03b9 \u03ad\u03bd\u03b1 \u03c3\u03cd\u03c3\u03c4\u03b7\u03bc\u03b1 \u03bc\u03bf\u03bd\u03ac\u03b4\u03c9\u03bd \u03bc\u03bf\u03c5\u03c3\u03b9\u03ba\u03ce\u03bd \u03b4\u03b9\u03b1\u03c3\u03c4\u03b7\u03bc\u03ac\u03c4\u03c9\u03bd. \u039f\u03b9 \u03c0\u03b9\u03bf \u03b3\u03bd\u03c9\u03c3\u03c4\u03ad\u03c2 \u03ba\u03b1\u03b9 \u03c7\u03b1\u03c1\u03b1\u03ba\u03c4\u03b7\u03c1\u03b9\u03c3\u03c4\u03b9\u03ba\u03ad\u03c2 \u03c4\u03b9\u03bc\u03ad\u03c2 \u03c4\u03b7\u03c2 \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03ac\u03c2 k, \u03b1\u03bd\u03b1\u03c6\u03ad\u03c1\u03bf\u03bd\u03c4\u03b1\u03b9 \u03c3\u03c4\u03b7 \u03c3\u03c5\u03bd\u03ad\u03c7\u03b5\u03b9\u03b1.<\/p>\n<table border=\"1\" width=\"100%\">\n<tbody>\n<tr>\n<td align=\"center\" width=\"50%\"><b>\u03a4\u0399\u039c\u0397 \u03a3\u03a4\u0391\u0398\u0395\u03a1\u0391\u03a3 k<\/b><\/td>\n<td align=\"center\" width=\"50%\"><b>\u039f\u039d\u039f\u039c\u0391\u03a3\u0399\u0391 \u039c\u039f\u039d\u0391\u0394\u0391\u03a3 \u03a4\u03a9\u039d \u039c\u039f\u03a5\u03a3\u0399\u039a\u03a9\u039d \u0394\u0399\u0391\u03a3\u03a4\u0397\u039c\u0391\u03a4\u03a9\u039d<\/b><\/td>\n<\/tr>\n<tr>\n<td align=\"center\" width=\"50%\">12<\/td>\n<td width=\"50%\">\u03a3\u03c5\u03b3\u03ba\u03b5\u03c1\u03b1\u03c3\u03bc\u03ad\u03bd\u03bf \u0395\u03c5\u03c1\u03c9\u03c0\u03b1\u03ca\u03ba\u03cc \u03b7\u03bc\u03b9\u03c4\u03cc\u03bd\u03b9\u03bf<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" width=\"50%\">53<\/td>\n<td width=\"50%\">\u03ba\u03cc\u03bc\u03bc\u03b1 \u03c4\u03bf\u03c5 \u039c\u03b5\u03c1\u03ba\u03ac\u03c4\u03bf\u03c1\u03b1<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" width=\"50%\">68<\/td>\n<td width=\"50%\">\u0391\u03c1\u03b1\u03b2\u03b9\u03ba\u03ae \u03bc\u03bf\u03bd\u03ac\u03b4\u03b1, \u03b2\u03c5\u03b6\u03b1\u03bd\u03c4\u03b9\u03bd\u03cc \u03b7\u03c7\u03bf\u03bc\u03cc\u03c1\u03b9\u03bf<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" width=\"50%\">72<\/td>\n<td width=\"50%\">\u0392\u03c5\u03b6\u03b1\u03bd\u03c4\u03b9\u03bd\u03cc \u03b7\u03c7\u03bf\u03bc\u03cc\u03c1\u03b9\u03bf<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" width=\"50%\">301<\/td>\n<td width=\"50%\">Savart<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" width=\"50%\">665<\/td>\n<td width=\"50%\">Delfi unit<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" width=\"50%\">1024<\/td>\n<td width=\"50%\">\u039c\u03bf\u03bd\u03ac\u03b4\u03b1 \u0397\/\u03a5<\/td>\n<\/tr>\n<tr>\n<td align=\"center\" width=\"50%\">1200<\/td>\n<td width=\"50%\">cent<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: center;\"><span style=\"color: #ff0000;\">\u03a3\u03a7\u0395\u03a4\u0399\u039a\u0391 POST<\/span><\/p>\n<p>Music and Physics<\/p>\n<blockquote class=\"wp-embedded-content\" data-secret=\"tPJMmzTuOC\"><p><a href=\"https:\/\/www.g-culture.org\/ioannis\/musandphys\/\">Music and Physics<\/a><\/p><\/blockquote>\n<p><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; visibility: hidden;\" title=\"&#8220;Music and Physics&#8221; &#8212; Byzantine Music Electroacoustic Music Musicology Education\" src=\"https:\/\/www.g-culture.org\/ioannis\/musandphys\/embed\/#?secret=Z7182Bzfbl#?secret=tPJMmzTuOC\" data-secret=\"tPJMmzTuOC\" width=\"500\" height=\"282\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe><\/p>\n<p>&nbsp;<\/p>\n<p>\u039c\u039f\u03a5\u03a3\u0399\u039a\u0391 \u0394\u0399\u0391\u03a3\u03a4\u0397\u039c\u0391\u03a4\u0391<\/p>\n<blockquote class=\"wp-embedded-content\" data-secret=\"7ciKaejxXo\"><p><a href=\"https:\/\/www.g-culture.org\/ioannis\/musint68\/\">\u039c\u03bf\u03c5\u03c3\u03b9\u03ba\u03ac \u03b4\u03b9\u03b1\u03c3\u03c4\u03ae\u03bc\u03b1\u03c4\u03b1. \u039f\u03ba\u03c4\u03ac\u03b2\u03b1 \u03c3\u03b5 68 \u03ba\u03b1\u03b9 72 \u03c4\u03bc\u03ae\u03bc\u03b1\u03c4\u03b1<\/a><\/p><\/blockquote>\n<p><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; visibility: hidden;\" title=\"&#8220;\u039c\u03bf\u03c5\u03c3\u03b9\u03ba\u03ac \u03b4\u03b9\u03b1\u03c3\u03c4\u03ae\u03bc\u03b1\u03c4\u03b1. \u039f\u03ba\u03c4\u03ac\u03b2\u03b1 \u03c3\u03b5 68 \u03ba\u03b1\u03b9 72 \u03c4\u03bc\u03ae\u03bc\u03b1\u03c4\u03b1&#8221; &#8212; Byzantine Music Electroacoustic Music Musicology Education\" src=\"https:\/\/www.g-culture.org\/ioannis\/musint68\/embed\/#?secret=pHQh8xy91t#?secret=7ciKaejxXo\" data-secret=\"7ciKaejxXo\" width=\"500\" height=\"282\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe><\/p>\n<p>&nbsp;<\/p>\n<p>\u03a4\u03a1\u0399\u03a3\u0391\u0393\u0399\u039f\u039d \u0391\u03a0\u039f\u03a3\u03a4\u039f\u039b\u039f\u03a5<\/p>\n<blockquote class=\"wp-embedded-content\" data-secret=\"bsF4tVhSce\"><p><a href=\"https:\/\/www.g-culture.org\/ioannis\/trisapsynth\/\">\u03a4\u03c1\u03b9\u03c3\u03ac\u03b3\u03b9\u03bf\u03bd \u0391\u03c0\u03bf\u03c3\u03c4\u03cc\u03bb\u03bf\u03c5<\/a><\/p><\/blockquote>\n<p><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; visibility: hidden;\" title=\"&#8220;\u03a4\u03c1\u03b9\u03c3\u03ac\u03b3\u03b9\u03bf\u03bd \u0391\u03c0\u03bf\u03c3\u03c4\u03cc\u03bb\u03bf\u03c5&#8221; &#8212; Byzantine Music Electroacoustic Music Musicology Education\" src=\"https:\/\/www.g-culture.org\/ioannis\/trisapsynth\/embed\/#?secret=idnHeqsZFS#?secret=bsF4tVhSce\" data-secret=\"bsF4tVhSce\" width=\"500\" height=\"282\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe><\/p>\n<blockquote class=\"wp-embedded-content\" data-secret=\"rpiDRo04Sz\"><p><a href=\"https:\/\/www.g-culture.org\/ioannis\/pldefthsc\/\">\u0389\u03c7\u03bf\u03c2 \u03a0\u03bb\u03ac\u03b3\u03b9\u03bf\u03c2 \u03c4\u03bf\u03c5 \u0394\u03b5\u03c5\u03c4\u03ad\u03c1\u03bf\u03c5 \u0398\u03b5\u03c9\u03c1\u03af\u03b1 \u03ba\u03b1\u03b9 \u03ba\u03bb\u03af\u03bc\u03b1\u03ba\u03b5\u03c2<\/a><\/p><\/blockquote>\n<p><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; visibility: hidden;\" title=\"&#8220;\u0389\u03c7\u03bf\u03c2 \u03a0\u03bb\u03ac\u03b3\u03b9\u03bf\u03c2 \u03c4\u03bf\u03c5 \u0394\u03b5\u03c5\u03c4\u03ad\u03c1\u03bf\u03c5 \u0398\u03b5\u03c9\u03c1\u03af\u03b1 \u03ba\u03b1\u03b9 \u03ba\u03bb\u03af\u03bc\u03b1\u03ba\u03b5\u03c2&#8221; &#8212; Byzantine Music Electroacoustic Music Musicology Education\" src=\"https:\/\/www.g-culture.org\/ioannis\/pldefthsc\/embed\/#?secret=lguWYL62a3#?secret=rpiDRo04Sz\" data-secret=\"rpiDRo04Sz\" width=\"500\" height=\"282\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0388\u03bd\u03b1 \u03b1\u03c0\u03cc \u03c4\u03b1 \u03b8\u03ad\u03bc\u03b1\u03c4\u03b1 \u03c4\u03b7\u03c2 \u03bc\u03bf\u03c5\u03c3\u03b9\u03ba\u03ae\u03c2, \u03c0\u03bf\u03c5 \u03b1\u03c0\u03b1\u03c3\u03c7\u03cc\u03bb\u03b7\u03c3\u03b5 \u03c4\u03bf\u03c5\u03c2 \u03c0\u03c1\u03ce\u03c4\u03bf\u03c5\u03c2 \u03b8\u03b5\u03c9\u03c1\u03b7\u03c4\u03b9\u03ba\u03bf\u03cd\u03c2 \u03c4\u03b7\u03c2, \u03ae\u03c4\u03b1\u03bd \u03c4\u03b1 \u03bc\u03bf\u03c5\u03c3\u03b9\u03ba\u03ac \u03b4\u03b9\u03b1\u03c3\u03c4\u03ae\u03bc\u03b1\u03c4\u03b1. \u039e\u03b5\u03ba\u03b9\u03bd\u03ce\u03bd\u03c4\u03b1\u03c2 \u03b1\u03c0\u03cc \u03b1\u03c0\u03bb\u03ad\u03c2, \u03b3\u03b9\u03b1 \u03c4\u03b1 \u03c3\u03b7\u03bc\u03b5\u03c1\u03b9\u03bd\u03ac \u03b4\u03b5\u03b4\u03bf\u03bc\u03ad\u03bd\u03b1, \u03c0\u03c1\u03bf\u03c4\u03ac\u03c3\u03b5\u03b9\u03c2, \u03ba\u03ac\u03bd\u03bf\u03bd\u03c4\u03b1\u03c2 &#8220;\u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03b9\u03c3\u03bc\u03bf\u03cd\u03c2&#8221; \u03bc\u03b5 \u03c4\u03b9\u03c2 \u03c4\u03cc\u03c4\u03b5 \u03b3\u03bd\u03c9\u03c3\u03c4\u03ad\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ad\u03c2 \u03b8\u03b5\u03c9\u03c1\u03af\u03b5\u03c2, \u03bf\u03b9 \u03ac\u03bd\u03b8\u03c1\u03c9\u03c0\u03bf\u03b9 \u03b1\u03c5\u03c4\u03bf\u03af \u03bc\u03b1\u03c2 \u03c0\u03b1\u03c1\u03ad\u03b4\u03c9\u03c3\u03b1\u03bd \u03ad\u03bd\u03b1\u03bd \u03b1\u03bd\u03b5\u03ba\u03c4\u03af\u03bc\u03b7\u03c4\u03bf \u03b8\u03b7\u03c3\u03b1\u03c5\u03c1\u03cc \u03b3\u03cd\u03c1\u03c9 \u03b1\u03c0\u03cc \u03c4\u03bf \u03b8\u03ad\u03bc\u03b1 &#8220;\u039c\u03bf\u03c5\u03c3\u03b9\u03ba\u03cc \u03b4\u03b9\u03ac\u03c3\u03c4\u03b7\u03bc\u03b1&#8221;. \u03a3\u03cd\u03bc\u03c6\u03c9\u03bd\u03b1 \u03bc\u03b5 \u03c4\u03bf\u03c5\u03c2 \u03b1\u03c1\u03c7\u03b1\u03af\u03bf\u03c5\u03c2 \u03b8\u03b5\u03c9\u03c1\u03b7\u03c4\u03b9\u03ba\u03bf\u03cd\u03c2 \u03c4\u03b7\u03c2 \u03bc\u03bf\u03c5\u03c3\u03b9\u03ba\u03ae\u03c2: &#8220;\u0394\u03b9\u03ac\u03c3\u03c4\u03b7\u03bc\u03b1 \u03b5\u03c3\u03c4\u03af [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"nf_dc_page":"","footnotes":""},"class_list":["post-3019","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.4 (Yoast SEO v27.4) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Mathematics and Music | Systematic Musicology<\/title>\n<meta name=\"description\" content=\"A deep exploration of mathematics and music, focusing on frequency ratios, tuning systems, microtonality and Byzantine modal theory.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.g-culture.org\/ioannis\/mathandmusic\/\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta 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