Keresés

Részletes keresés

spiroslyra Creative Commons License 2010.07.05 0 0 994





http://www.archive.org/details/aristoxenouharm00arisgoog
spiroslyra Creative Commons License 2010.07.05 0 0 993

DePauw University, Greencastle, Indiana
in Association with Project Theophrastus

Aristoxenus:
Music, Biography, and Philosophy
in the Early Peripatetic School

Preliminary Program

[To print pdf version]
Aristoxenus: Music, Biography, and Philosophy in the Early Peripatetic School

September 10-12, 2009 - De Pauw University, Greencastle, Indiana. In association with Project Theophrastus

All sessions will be held in the DePauw Memorial Student Union, Room 240 (the boardroom).


Thursday, September 10


Session 1: 9:00 AM- 10:30 AM

Stefan Schorn (Katholieke Universiteit Leuven, Belgium) - Aristoxenus and Peripatetic Biography


10:30-10:45 Break


Session 2: 10:45 AM- 12:15 PM

Carl Huffman (DePauw University, Greencastle, USA) - Aristoxenus' Life of Socrates


Lunch and Break 12:15- 2:15


Session 3: 2:30- 4:00

Andrew Barker (University of Birmingham, England) – Aristoxenus mousikos and the Early Academy


4:00-4:15 Break


Session 4: 15 – 5:45

John Dillon (Trinity College, Dublin, Ireland) – Aristoxenus’ Life of Plato


Dinner 7:00- 9:00 (At Little Mexico in Crawfordsville, IN. Vans leave at 6:30 from the Walden Inn).


Friday, September 11


Session 5: 9:00 AM- 10:30 AM

William W. Fortenbaugh (Rutgers University, New Brunswick, USA) - Apollonius on Theophrastus on Aristoxenus


10:30-10:45 Break


Session 6: 10:45 AM- 12:15 PM

Antonella Provenza (University of Palermo, Italy) - Aristoxenus and Music Therapy: Fr. 26 Wehrli Within the Tradition on Music and katharsis.


Lunch and Break 12:15- 2:15



Session 7: 2:15- 3:45

David Creese (University of British Columbia, Vancouver, Canada) – Instruments and empiricism in Aristoxenus’ Elementa harmonica


3:45- 4:00 Break


Session 8: 4:00-5:30

Eleonora Rocconi (University of Pavia, Italy) - Aristoxenus and the Theory of Musical Ethos


Dinner 7:00- 9:00 (At the house of Carl Huffman and Martha Rainbolt, 707 E. Seminary Street – 5 blocks to the right down the street in front of the hotel)


Saturday, September 12


Session 9: 9:00 AM- 10:30 AM

Stephen White (University of Texas, Austin, USA) – Aristoxenus’ Presentation of Pythagoras


10:30-10:45 Break



Session 10: 10:45 AM- 12:15 PM

Timothy Power (Rutgers University, New Brunswick, USA) – Aristoxenus and the Neoclassicists


Lunch and Break 12:15-2:15



Session 11: 2:15- 3:45

Leonid Zhmud (Russian Academy of Sciences, St. Petersburg, Russia) - Aristoxenus and the Pythagoreans

3:45- 4:00 Break


Session 12: 4:00 – 5:30

Elisabetta Matelli (Università Cattolica del Sacro Cuore, Milan, Italy) – Aristoxenus on Dance


Dinner 7:00- 9:00 (In the Emerald Room (upstairs) at Almost Home on the square in Greencastle).
spiroslyra Creative Commons License 2010.07.05 0 0 992



Greek Writings on Music and
Rhythm
Circa 250 CE

Fragment 2687 of the Oxyrhynchus Papyri, which supplements fragment 9. (View Larger)

The earliest surviving fragments of the writings on music by the fourth century BCE Greek peripatetic philosopher and writer on harmonic theory, music and rhythm, Aristoxenus (Ἀριστόξενος) of Tarentum, are papyri found at Oxyrhynchus.

"Perhaps the most amazing papyrus fragment is a large excerpt from Aristoxenus' Rhythmica, a part of which was first published in 1898 as fragment 9 of the Oxyrhynchus Papyri. In 1968 it was revealed that fragment 2687 of the Oxyrhynchus Papyri completed columns 2-4 by supplying fourteen or fifteen lines at the bottom; this same fragment added substantially to columns 1 and 5. Nearly one hundred lines of the text have now been uncovered in papyrus dating from the third century C.E. But this is not all. Fragments 667 and 3706 of the Oxyrhynchus Papyri preserve in characteristic Aristoxenian language an analysis of conjunct and disjunct scales and of genera. These fragments, too, date from the second or third centuries C.E. and may very well contain parts of the sections of Aristoxenus' Harmonica missing in the manuscript tradition" (Mathiesen, "Hermes or Clio? The transmission of Ancient Greek Music Theory", Palisca, Baker, Hanning [eds.] Musical Humanism and its Legacy. Essays in Honor of Claude Palisca [1992] 5-6).

Filed under: Music , Survival of Information | Bookmark or share this entry »

http://www.historyofscience.com/G2I/timeline/index.php?category=Music+

spiroslyra Creative Commons License 2010.07.03 0 0 991

Aristoxenus "Elements of Rhythm": Text, translation, and commentary with a translation and commentary on POxy 2687
by Marchetti, Christopher C., Ph.D., RUTGERS THE STATE UNIVERSITY OF NEW JERSEY - NEW BRUNSWICK, 2009, 322 pages; 3379159

Abstract:

Aristoxenus of Tarentum makes productive use of Aristotelian concepts and methods in developing his theory of musical rhythm in his treatise Elements of Rhythm . He applies the Aristotelian distinction between form and material and the concept of hypothetical necessity to provide an explanation for why musical rhythm is manifested in the syllables of song, the notes of melody, and the steps of dance. He applies the method of formulating differentiae , as described in Aristotle's Parts of Animals , to codify the formal properties of rhythm.

Aristoxenus' description of the rhythmic foot presents several interpretive challenges. Our text is fragmentary, and we lack Aristoxenus' definitions of several key terms. This study seeks to establish the meanings of these terms on the basis of a close examination of the structure of Aristoxenus' argument. Parallel passages in Aristides Quintilianus' On Music are considered in detail for their consistency or lack thereof with Aristoxenian usage. Parallel passages in POxy 2687 are cited as illustrations for several rhythmic constructions and principles Aristoxenus mentions; because these involve original interpretations of some points in POxy 2687, they are supported by a thorough presentation of POxy 2687 in a separate chapter.

One central conclusion of this study is that Aristoxenus viewed rhythmic feet as musical functions, analogous to the theory of melodic functions he had presented in his Elements of Harmony . Only limited conclusions about the applicability of Aristoxenus' theory to the history of ancient Greek music can be justified. While some of the extant remains of Greek music are in accord with Aristoxenian theory, others contradict it. Much of ancient poetry is more rhythmically complex than what is presented in our text of E.R. , but regular poetic forms such as the anapestic dimeter and the stately rhythms of religious hymns may have provided the original starting points for subsequent rhythmic developments Aristoxenus seeks to explain.


Advisor: Figueira, Thomas
School: RUTGERS THE STATE UNIVERSITY OF NEW JERSEY - NEW BRUNSWICK
Source: DAI-A 70/11, p. , May 2010
Source Type: Ph.D.
Subjects: Classical studies; Music
Publication Number: 3379159

http://gradworks.umi.com/33/79/3379159.html


Aristoxenus' Elements of Rhythm: Text, Translation, and Commentary with a Translation and Commentary on POxy 2687. By Christopher C. Marchetti ...
mss3.libraries.rutgers.edu/dlr/TMP/rutgers-lib_25847-PDF-1.pdf
spiroslyra Creative Commons License 2008.08.31 0 0 990

Aristoxenus Mus. : Elementa harmonica : Page 9, line 5

Εἶτ' ἀποδοτέον τὰς τῶν γενῶν διαφορὰς αὐτὰς τὰς ἐν
τοῖς κινουμένοις τῶν φθόγγων, ἀποδοτέον δὲ καὶ τοὺς τόπους
ἐν οἷς κινοῦνται. τούτων δ' οὐδεὶς περὶ οὐδενὸς πώποτ' ἔσχη-

~~~~~~

Aristoxenus Mus. : Elementa harmonica : Page 13, line 18

συνεχῶς—λέγω δὲ συνεχῶς κατὰ τὸν χρόνον—ὑπερ-
βαίνουσα μὲν τοὺς περιεχομένους ὑπὸ τῶν τάσεων τό-
πους, ἱσταμένη δ' ἐπ' αὐτῶν τῶν τάσεων καὶ φθεγγομένη
ταύτας μόνον αὐτὰς μελῳδεῖν λέγεται καὶ κινεῖσθαι δια-
spiroslyra Creative Commons License 2008.08.31 0 0 989

Aristoxenus Mus. : Elementa harmonica : Page 12, line 5

ἂν εἴη τῷ τὴν εἰρημένην μεταχειριζομένῳ πραγματείαν
περὶ τοῦ τῆς φωνῆς τόπου καθόλου καὶ κατὰ μέρος εἰ-
πεῖν ἐφ' ὅσον ἐστὶ δίκαιον· ἐστὶ δ' ἐπὶ τοσοῦτον ἐφ' ὅσον

~~~~~~

Aristoxenus Mus. : Elementa harmonica : Page 15, line 14

τητος πρὸς δὲ τούτοις τάσεως. ἡ μὲν οὖν ἐπίτασίς ἐστι
κίνησις τῆς φωνῆς συνεχὴς ἐκ βαρυτέρου τόπου εἰς ὀξύτε-
ρον, ἡ δ' ἄνεσις ἐξ ὀξυτέρου τόπου εἰς βαρύτερον· ὀξύτης
δὲ τὸ γενόμενον διὰ τῆς ἐπιτάσεως, βαρύτης δὲ τὸ γενό-

~~~~~~~~

Aristoxenus Mus. : Elementa harmonica : Page 34, line 4

γὰρ ἀπείρους τὸν ἀριθμὸν τὰς λιχανούς· οὗ γὰρ ἂν
στήσῃς τὴν φωνὴν τοῦ ἀποδεδειγμένου λιχανῷ τόπου
λιχανὸς ἔσται, διάκενον δ' οὐδέν ἐστιν τοῦ λιχανοειδοῦς τό-
που οὐδὲ τοιοῦτον οἷον μὴ δέχεσθαι λιχανόν. ὥστ' εἶναι
μὴ περὶ μικροῦ τὴν ἀμφισβήτησιν· οἱ μὲν γὰρ ἄλλοι δια-

~~~~~~

Aristoxenus Mus. : Elementa harmonica : Page 74, line 14

τοῦ βαρυτέρου συστήματος ὀξυτέρῳ ὅρῳ. κατὰ μὲν οὖν
τὸν πρότερον τῶν τρόπων τόπου τέ τινος κοινωνεῖ τὰ
τῶν ἑξῆς τετραχόρδων συστήματα καὶ ὅμοιά ἐστιν ἐξ ἀνάγ-
spiroslyra Creative Commons License 2008.08.31 0 0 988

Aristoxenus Mus. : Elementa harmonica : Page 19, line 7

δεῖν. ἁπάσης γὰρ φωνῆς ὀργανικῆς τε καὶ ἀνθρωπικῆς
ὡρισμένος ἐστί τις τόπος ὃν διεξέρχεται μελῳδοῦσα ὅ τε
μέγιστος καὶ ὁ ἐλάχιστος. οὔτε γὰρ ἐπὶ τὸ μέγα δύναται

~~~~~~

Aristoxenus Mus. : Elementa harmonica : Page 21, line 1

αὐτὴν τάσιν ἐχόντων. φαίνεται γάρ, ὡς τύπῳ εἰπεῖν, δια-
φορά τις εἶναι τάσεων τὸ διάστημα καὶ τόπος δεκτικὸς
φθόγγων ὀξυτέρων μὲν τῆς βαρυτέρας τῶν ὁριζουσῶν τὸ

~~~~~~

Aristoxenus Mus. : Elementa harmonica : Page 29, line 5

σεις αἴτιαί εἰσι τῆς τῶν γενῶν διαφορᾶς φανερόν. τίς δ' ὁ
τόπος τῆς κινήσεως ἑκατέρου τῶν φθόγγων τούτων λεκ-
τέον. λιχανοῦ μὲν οὖν ἐστι τονιαῖος ὁ σύμπας τόπος ἐν
ᾧ κινεῖται, οὔτε γὰρ ἔλαττον ἀφίσταται μέσης τονιαίου δια-

~~~~~~

Aristoxenus Mus. : Elementa harmonica : Page 30, line 9

τούτων μὲν οὖν ἐπὶ τοσοῦτον ἀρκείτω· ὁ δὴ τῆς λιχανοῦ
τόπος τονιαῖος ὑποκείσθω, ὁ δὲ τῆς παρυπάτης διέσεως
ἐλαχίστης. οὔτε γὰρ ἐγγυτέρω τῆς ὑπάτης προσέρχεται

~~~~~~

Aristoxenus Mus. : Elementa harmonica : Page 35, line 6

τε χρωματικῆς <τῆς> βαρυτάτης καὶ διατόνου λιχανοῦ τῆς
συντονωτάτης. ὁ δὲ τῆς παρυπάτης τόπος φανερός ἐστι
ἐκ τῶν ἔμπροσθεν, διαιρεθείς τε καὶ συντεθεὶς ὅσος ἐστίν.

~~~~~~

Aristoxenus Mus. : Elementa harmonica : Page 57, line 16

δὲ θατέρου. ἐπεὶ δ' ἀναγκαῖον τὸν κινούμενον φθόγγον
ἐν τόπῳ τινὶ κινεῖσθαι, ληπτέος ἂν εἴη τόπος ὡρισμένος
ἑκατέρου τῶν εἰρημένων φθόγγων. φαίνεται δὴ συντονω-

~~~~~~

Aristoxenus Mus. : Elementa harmonica : Page 58, line 1

γίγνεται δ' αὕτη ἐναρμόνιος· ὥστ' εἶναι φανερὸν ἐκ τούτων,
ὅτι τονιαῖός ἐστιν ὁ τῆς λιχανοῦ τόπος. τὸ δὲ παρυπάτης
<καὶ ὑπάτης> διάστημα ἔλαττον μὲν ὅτι οὐκ ἂν γένοιτο

~~~~~~

Aristoxenus Mus. : Elementa harmonica : Page 58, line 7

αὐτὴν τάσιν ἀφίκωνται ἥ τε λιχανὸς ἀνιεμένη καὶ ἡ πα-
ρυπάτη ἐπιτεινομένη, ὡρίσθαι δοκεῖ ἑκατέρας ὁ τόπος,
ὥστ' εἶναι φανερόν, <ὅτι οὐ μείζων διέσεως ἐλαχίστης ἐστὶν
ὁ τῆς παρυπάτης τόπος. ἤδη δέ τινες θαυμάζουσι> πῶς
ἐστι λιχανὸς κινηθέντος ἑνὸς ὅτου δήποτε τῶν μέσης καὶ

~~~~~~

Aristoxenus Mus. : Elementa harmonica : Page 60, line 1

γιγνομένων ἴδια ζητήσομεν ὀνόματα, δῆλον ὅτι ἀπείρων
ὀνομάτων δεησόμεθα, ἐπειδήπερ ὁ τῆς λιχανοῦ τόπος εἰς
ἀπείρους τέμνεται τομάς. ἔπειτα πειρώμενοι παρατηρεῖν
spiroslyra Creative Commons License 2008.08.31 0 0 987

Aristoxenus Mus. : Elementa harmonica : Page 7, line 10

ριστέον τῷ μέλλοντι πραγματεύεσθαι περὶ μέλους αὐτὴν
τὴν κατὰ τόπον. οὐ γὰρ εἷς τρόπος αὐτῆς ὢν τυγχάνει·
κινεῖται μὲν γὰρ καὶ διαλεγομένων ἡμῶν καὶ μελῳδούντων
τὴν εἰρημένην κίνησιν—ὀξὺ γὰρ καὶ βαρὺ δῆλον ὡς ἐν
ἀμφοτέροις τούτοις ἔνεστιν, αὕτη δ' ἐστὶν ἡ κατὰ τόπον
καθ' ἣν ὀξύ τε καὶ βαρὺ γίγνεται—ἀλλ' οὐ ταὐτὸν εἶδος

~~~~~~

Aristoxenus Mus. : Elementa harmonica : Page 13, line 6

αὐτῶν, περὶ δὲ τῆς πρώτης νῦν πειρατέον διελθεῖν.
Πρῶτον μὲν οὖν ἁπάντων αὐτῆς τῆς κατὰ τόπον κι-
νήσεως τὰς διαφορὰς θεωρῆσαι τίνες εἰσὶ πειρατέον. πάσης

~~~~~~~~~~

Aristoxenus Mus. : Elementa harmonica : Page 13, line 10

δύο τινές εἰσιν ἰδέαι κινήσεως, ἥ τε συνεχὴς καὶ ἡ διαστη-
ματική. κατὰ μὲν οὖν τὴν συνεχῆ τόπον τινὰ διεξιέναι
φαίνεται ἡ φωνὴ τῇ αἰσθήσει οὕτως ὡς ἂν μηδαμοῦ ἱστα-

~~~~

Aristoxenus Mus. : Elementa harmonica : Page 14, line 8

τὴν κίνησιν· ὅταν δὲ στῆναί που δόξασα εἶτα πάλιν δια-
βαίνειν τίνα τόπον φανῇ καὶ τοῦτο ποιήσασα πάλιν ἐφ' ἑ-
τέρας τάσεως στῆναι δόξῃ καὶ τοῦτο ἐναλλὰξ ποιεῖν φαι-

~~~~~~~~

Aristoxenus Mus. : Elementa harmonica : Page 14, line 12

κίνησιν λέγομεν. τὴν μὲν οὖν συνεχῆ λογικὴν εἶναί φαμεν,
διαλεγομένων γὰρ ἡμῶν οὕτως ἡ φωνὴ κινεῖται κατὰ τόπον
ὥστε μηδαμοῦ δοκεῖν ἵστασθαι. κατὰ δὲ τὴν ἑτέραν ἣν

~~~~~~

Aristoxenus Mus. : Elementa harmonica : Page 15, line 3

τὸ μέλος ἀκριβέστερον. ὅτι μὲν οὖν δύο κινήσεων οὐσῶν
κατὰ τόπον τῆς φωνῆς ἡ μὲν συνεχὴς λογική τίς ἐστιν ἡ
δὲ διαστηματικὴ μελῳδική, σχεδὸν δῆλον ἐκ τῶν εἰρημένων.

~~~~~~

Aristoxenus Mus. : Elementa harmonica : Page 15, line 8

τάσεις αὐτὰς φθεγγομένην φανερὰς καθιστάναι, —ἐπειδὴ
τὸν μὲν τοῦ διαστήματος τόπον ὃν διεξέρχεται ὁτὲ μὲν ἀνιε-
μένη ὁτὲ δ' ἐπιτεινομένη λανθάνειν αὐτὴν δεῖ διεξιοῦσαν, τοὺς

~~~~~~

Aristoxenus Mus. : Elementa harmonica : Page 16, line 13

μούσης ἤδη καὶ ἑστηκυίας. ταὐτὰ δὲ ἐροῦμεν καὶ περὶ τῆς
ἀνέσεώς τε καὶ βαρύτητος πλὴν ἐπὶ τὸν ἐναντίον τόπον.
δῆλον δὲ διὰ τῶν εἰρημένων, ὅτι ἥ τ' ἄνεσις τῆς βαρύ-

~~~~~~~~~~

Aristoxenus Mus. : Elementa harmonica : Page 60, line 11

μέγεθος· λέγω δὲ πυκνοῦ μὲν εἶδος τιθεῖσα ἕως ἂν τὰ δύο
διαστήματα τοῦ ἑνὸς ἐλάττω τόπον κατέχῃ—ἐμφαίνεται
γὰρ ἐν πᾶσι τοῖς πυκνοῖς πυκνοῦ τινος φωνὴ καίπερ ἀνίσων

~~~~~~

Aristoxenus Mus. : Elementa harmonica : Page 62, line 15

χόρδῳ διὰ τεσσάρων συμφωνούντων τῶν ἄκρων τὰ δύο
διαστήματα συντεθέντα τοῦ ἑνὸς ἐλάττω τόπον κατέχῃ.
τετραχόρδου δέ εἰσι διαιρέσεις ἐξαίρετοί τε καὶ γνώριμοι αὗ-

~~~~~~

Aristoxenus Mus. : Elementa harmonica : Page 63, line 17

ἀμφότεροι κινοῦνται οἱ φθόγγοι, μετὰ ταῦτα δ' ἡ μὲν
παρυπάτη μένει, διελήλυθε γὰρ τὸν αὑτῆς τόπον, ἡ δὲ
λιχανὸς κινεῖται δίεσιν ἐναρμόνιον καὶ γίγνεται τὸ λιχανοῦ

~~~~~~~~

Aristoxenus Mus. : Elementa harmonica : Page 68, line 4

καθ' ἣν δήποτε τῶν συμφωνιῶν, <ἢ> πρὸς τὸ αὐτὸ συμ-
φωνεῖν μὴ ἐπὶ τὸν αὐτὸν τόπον συνεχῆ ὄντα ᾧ συμφωνεῖ
ἑκάτερον αὐτῶν. ἔστι δ' οὐδὲ τοῦτο αὔταρκες πρὸς τὸ

~~~~~~

Aristoxenus Mus. : Elementa harmonica : Page 68, line 10

Ἐπεὶ δὲ τῶν διαστηματικῶν μεγεθῶν τὰ μὲν τῶν
συμφώνων ἤτοι ὅλως οὐκ ἔχειν δοκεῖ τόπον ἀλλ' ἑνὶ με-
γέθει ὡρίσθαι, ἢ παντελῶς ἀκαριαῖόν τινα, τὰ δὲ τῶν
spiroslyra Creative Commons License 2008.08.31 0 0 986

Aristoxenus Mus. : Elementa harmonica : Page 33, line 16

βαρυτάτης διατόνου διέσει ἐστὶ συντονωτέρα. ἐκ τούτων
δὴ φανεροὶ γίγνονται οἱ τόποι τῶν λιχανῶν ἑκάστης·
ἥ τε γὰρ βαρυτέρα τῆς <βαρυτάτης> χρωματικῆς πᾶσά

~~~~~~

Aristoxenus Mus. : Elementa harmonica : Page 34, line 13

ἀριθμόν. τὰ μὲν οὖν περὶ τῶν λιχανῶν οὕτως ἀφωρίσθω.
παρυπάτης δὲ δύο εἰσὶ τόποι—ὁ μὲν κοινὸς τοῦ τε δια-
τόνου καὶ τοῦ χρώματος, ὁ δ' ἕτερος ἴδιος τῆς ἁρμονίας—

~~~~~~~~

Aristoxenus Mus. : Elementa harmonica : Page 44, line 20

μήτε συνειθίσθαι περὶ τὰς τοιαύτας διαφορὰς ἀκριβολογεῖ-
σθαι· οὔτ' αὐτό πως τοῦτο κατέμαθον ὅτι τόποι τινὲς ἦσαν
τῶν κινουμένων φθόγγων ἐν ταῖς τῶν γενῶν διαφοραῖς.
spiroslyra Creative Commons License 2008.08.31 0 0 985

Aristoxenus Mus. : Elementa harmonica : Page 30, line 17

διέσεως οὔτε πλεῖον ἀφίσταται ἡμίσεος τόνου. οὐ γὰρ ἐπαλ-
λάττουσιν οἱ τόποι, ἀλλ' ἔστιν αὐτῶν πέρας ἡ συναφή,
ὅταν γὰρ ἐπὶ τὴν αὐτὴν τάσιν ἀφίκωνται ἥ τε παρυπάτη
καὶ ἡ λιχανός, ἡ μὲν ἐπιτεινομένη ἡ δ' ἀνιεμένη, πέρας ἔχου-
σιν οἱ τόποι· καὶ ἔστιν ὁ μὲν ἐπὶ τὸ βαρὺ παρυπάτης, ὁ
δ' ἐπὶ τὸ ὀξὺ λιχανοῦ. περὶ μὲν οὖν τῶν ὅλων τόπων
spiroslyra Creative Commons License 2008.08.31 0 0 984

topos , ho (fem. by attraction

A. topon tan kaleimenan Damatreian IG 9(1).32.80 (Stiris, ii B.C.)), place, region, first in A. (v. infr.), afterwds. freq. in all writers; periphr., chthonos pas t., i.e. the whole earth, A. Eu.249; es ton Hellênôn t. Id.Pers.790 ; en Hellados topois in Greece, ib.796; en Aulidost. Id.Ag.191 (lyr.); Pelopos ent. Id.Eu.703 , cf. 292; pros hesperous t. towards the West, Id.Pr.350; prosthe Salaminos topôn before Salamis, Id.Pers.447; Thrêikês ek topôn E.Alc.67 ; Dirkaiôn ek t. Id.Ph.1027 (lyr.): so in Prose, district, ho t. ho Hellênikos Isoc. 5.107 , cf. Ep.1.8; ho peri Thraikên t. D.20.59 ; ho epi Thraikês t. Aeschin. 2.9 , 3.73; ho t. houtos, en toutois tois t., X.An.4.4.4, Cyr.2.4.20; holos t. a whole region, D.19.230; kata topous kai kômas Pl.Criti. 119a ; hoi tês chôras t. the places of a country, Id.Lg.760c, etc. (but ho t. tês chôras the geographical position, D.4.31; region, Pl.Lg.705c); ho hagiost., of Jerusalem, LXX 2 Ma.2.18 (cf. infr. 5); the universe divided into three topoi, Arist.IA706b3, Cael.312a8 (contrast PA666a15, etc.); hoi koinoi t. public sites or buildings, IG42(1).65.8 (Epid.); asulos t. BGU1053 ii 9 (i B. C.), PTeb.5.83 (pl., ii B. C.); oikiai kai topoi houses and sites, ib.281.12 (ii B.C.); so psiloi t. sites not built upon, OGI52.2 (Ptolemais, iii/ii B. C.).

2. place, position, ou ton tropon, alla ton t. monon metallaxai Aeschin.3.78 ; hupolipou t. leave a space (in a document), PCair.Zen.327.83 (iii B.C.); perikêpôi t. katalipein ib.193.8 (iii B.C.); t. echein have a place, D.H.Dem.23, Plu.2.646a; philou t. echein hold the place of . . , Arr.Epict.2.4.5; Merolas ho hairetheis hupatos eis ton tou Kinna t. D.S.38 /39.3; enegraphê eis tên hierôsunên eis ton Aeukiou Domitiou t. teteleutêkotos Nic. Dam.Fr. 127.4J., cf. D.H.2.73; anaplêroun ton t. tou idiôtou 1 Ep.Cor.14.16 ; t. echein also = have room (to grow), Thphr.HP1.7.1; topôi c. gen., in place of, instead of, Hdn.2.14.5; ana topon on the spot, immediately, E.Supp.604 (lyr., dub.l.); so en topôi IG12(7).515.63 (Amorgos); epi topou Plb.4.73.8 ; epi tôn t. PEnteux.55.5 (iii B. C.), UPZ70.16 (ii B.C.), CIL3.567.3 (Delph., ii B. C.), POxy.2106.23 (iv A. D.), etc.; kata ton auton t. S.E.P.3.1 ; para topon at a wrong place, Str.10.2.21, Arr.Epict.3.21.16 (but para t. kai para kairon by virtue of the place and the time, ib.3.21.14).

3. place or part of the body, Hp.Aph. 2.46, Loc.Hom.tit., Sor.2.40, al., Gal. in titles of works, e.g. peri tôn peponthotôn topôn, peri suntheseôs pharmakôn tôn kata topous; esp. ho topos, pudendum muliebre, Arist.HA572b28, 583a15, cf. Sor.2.62 (pl.).

4. place, passage in an author, kata topous tinas tês historias Plb.12.25f .1, cf. Ph.2.63, Ev.Luc.4.17, Sor.2.57,58, etc.; the word is prob. interpolated in X.Mem.2.1.20.

5. burial-place, IG12(7).401 (Amorgos), al., Ev.Marc. 16.6; also in codd. of E.Heracl. 1041 (fort. leg. taphon); later ho hagios t. is freq. of the grave of a martyr, or of a monastery associated with it, PMasp.94.18 (vi A.D.), etc.

6. in Egypt, district, department, a sub-division of the nomos, = toparchia, PMich.Zen.43.8 (iii B. C.), Theb.Ostr.27.2 (ii B. C.): but most freq. in pl., ho epi tôn t. stratêgos, praktôr, etc., PEnteux.27.9 (iii B. C.), PRein.7.17,35 (ii B. C.), etc.; hoi exô t. dub. sens. in PEnteux.87.2 (iii B. C.), BGU1114.6 (i B. C.), etc.

7. a room in a house, topon hena aneu enoikiou ib.896.4 (ii A. D.); duo topous êtoi sumposia POxy. 1129.10 (V A. D.), cf. 502.34 (ii A. D.), 912.13 (iii A. D.).

8. position on the zodiac, Vett.Val.139.13; esp. the twelve regions of 300, Ptol. Tetr.128, Heph.Astr.1.12.

9. autos ho theos kaleitai topos, tôi periechein ta hola Ph.1.630 , cf. Corp.Herm.2.12, Hippol. Haer.6.32.

II. topic, Isoc.5.109, 10.38, Aeschin.3.216, Plb.21.19.2, Phld. Rh.1.119S., etc.

2. common-place or element in Rhetoric, ho tou mallon kai hêtton t. Arist.Rh.1358a14 , cf. 1396b30, 1397a7; to auto legô stoicheion kai t. ib. 1403a18: pl., Phld.Rh.1.226S.

b. = homologoumenou pragmatos auxêsis, Hermog Prog.11; koinos t. ib.6.

c. generally, sphere, ho pragmatikos t. D.H.Comp.1 .

III. metaph., opening, occasion, opportunity, en t. tini aphanei Th.6.54 (but tropôi is prob. cj.); orgêi didonai t. Plu.2.462b ; mê didote t. tôi diabolôi Ep.Eph.4.27 ; dote t. têi orgêi leave room for the wrath (of God), i.e. let God punish, Ep.Rom.12.19; mê kataleipesthai sphisi t. eleous Plb.1.88.2 ; metanoias t. ouch heure Ep.Hebr.12.17 ; oude phugês topon eumoirêsantes Hld.6.13 ; t. didonai tini c. inf., give occasion to . . , LXX Si.4.5.

http://www.perseus.tufts.edu/cgi-bin/ptext?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3D%23104356
spiroslyra Creative Commons License 2008.08.30 0 0 983

Aristides Quintilianus Mus. : De musica : Book 3, section 24, line 72

ταύτης ἐνδεικτικῷ χρῆσθαί τε καὶ κοσμεῖσθαι.
Τῶν δὴ τοῦ ἐκκειμένου διαγράμματος ἀναλογιῶν αἱ
μὲν ἀριθμητικαὶ ταὐτότητι τῶν ὑπεροχῶν θεωρούμεναι τὸ
spiroslyra Creative Commons License 2008.08.30 0 0 982

Aristides Quintilianus Mus. : De musica : Book 3, section 4, line 21

τούτων οὔτε ἐλάττους. σαφηνείας δὲ ἕνεκεν ὑποκείσθω
καὶ τὰ διαγράμματα.
Δύο δὲ εὐθείας εἰλήφαμεν τὴν μὲν ἀριθμὸν πρῶτον
spiroslyra Creative Commons License 2008.08.30 0 0 981

Aristides Quintilianus Mus. : De musica : Book 1, section 11, line 60

καὶ διὰ πέντε καὶ διὰ πασῶν]
[ταῦτα διαγράμματά ἐστι τῶν στοιχείων·
ἐπεὶ καὶ τῶν γενῶν ἕτερά ἐστι καὶ τῶν
spiroslyra Creative Commons License 2008.08.30 0 0 980

Aristides Quintilianus Mus. : De musica : Book 1, section 13, line 22

ἀμφοῖν ἅμα. μέλος μὲν γὰρ νοεῖται καθ' αὑτὸ μὲν <ἐν> τοῖς
διαγράμμασι καὶ ταῖς ἀτάκτοις μελῳδίαις, μετὰ δὲ ῥυθ-
μοῦ μόνου, ὡς ἐπὶ τῶν κρουμάτων καὶ κώλων, μετὰ δὲ
spiroslyra Creative Commons License 2008.08.30 0 0 979

Aristides Quintilianus Mus. : De musica : Book 3, section 24, line 58

μιᾶς ἀρχῆς καὶ αἰτίας ἐξηρτημένα. σαφηνίσει δὲ καὶ τοῦτο
τὸ διάγραμμα κατὰ τὴν διπλῆν τετρακτὺν πάσας ἀναλογίας
γεωμετρικὰς καὶ μουσικὰς ἐπιδεχόμενον καὶ τοὺς μὲν
spiroslyra Creative Commons License 2008.08.30 0 0 978

Aristides Quintilianus Mus. : De musica : Book 1, section 11, line 40

τῶν ἐν χρήσει γραμμάτων <τὰ> κατὰ τὴν τονικὴν ἔκ-
θεσιν ὑπογεγραμμένα κατατάττοντες. πτέρυγι δὲ τὸ διά-
γραμμα τῶν τρόπων γίνεται παραπλήσιον, τὰς ὑπεροχὰς
ἃς ἔχουσιν οἱ τόνοι πρὸς ἀλλήλους ἀναδιδάσκον· ἐκτέ-
spiroslyra Creative Commons License 2008.08.30 0 0 977

Aristides Quintilianus Mus. : De musica : Book 1, section 9, line 81

καὶ τριημιτόνιον. δίεσιν δὲ νῦν ἐπὶ πάντων ἀκουστέον
τὴν ἐναρμόνιον. σαφηνείας δὲ ἕνεκεν καὶ διάγραμμα
τῶν συστημάτων ὑπογεγράφθω. τούτων δὴ καὶ ὁ θεῖος
spiroslyra Creative Commons License 2008.08.30 0 0 976

Aristoxenus Mus. : Elementa harmonica : Page 42, line 13

δυνάμεις. δεῖ οὖν ἐθισθῆναι ἕκαστα ἀκριβῶς κρίνειν· οὐ
γάρ ἐστιν ὥσπερ ἐπὶ τῶν διαγραμμάτων εἴθισται λέγεσθαι·
ἔστω τοῦτο εὐθεῖα γραμμή, —οὕτω καὶ ἐπὶ τῶν διαστη-
spiroslyra Creative Commons License 2008.08.30 0 0 975

Aristoxenus Mus. : Elementa harmonica : Page 36, line 1

οὔτ' ἴσον οὔτ' ἄνισον. ζητητέον δὲ τὸ συνεχὲς οὐχ ὡς οἱ
ἁρμονικοὶ ἐν ταῖς τῶν διαγραμμάτων καταπυκνώσεσιν
ἀποδιδόναι πειρῶνται, τούτους ἀποφαίνοντες τῶν φθόγγων
spiroslyra Creative Commons License 2008.08.30 0 0 974

Aristoxenus Mus. : Elementa harmonica : Page 6, line 13

λων γενῶν οὐδεμίαν πώποτ' ἔννοιαν εἶχον. σημεῖον δέ· τὰ
γὰρ διαγράμματα αὐτοῖς τῶν ἐναρμονίων ἔκκειται μόνον
συστημάτων, διατόνων δ' ἢ χρωματικῶν οὐδεὶς πώποθ' ἑώ-
ρακεν. καί τοι τὰ διαγράμματά γ' αὐτῶν ἐδήλου τὴν
πᾶσαν τῆς μελῳδίας τάξιν, ἐν οἷς περὶ συστημάτων ὀκτα-
spiroslyra Creative Commons License 2008.08.30 0 0 973

Aristoxenus Mus. : Elementa harmonica : Page 12, line 16

βηκεν εἰρηκέναι κατὰ τύχην, οὐ περὶ τούτου λέγουσιν ἀλλὰ
καταπυκνῶσαι βουλομένοις τὸ διάγραμμα, καθόλου δὲ οὐ-
δενὶ σχεδὸν ἐν τοῖς ἔμπροσθεν φανερὸν γεγένηται τοῦθ' ἡμῖν.
spiroslyra Creative Commons License 2008.08.30 0 0 972

LSJ

diagramma , atos, to,

A. figure marked out by lines, plan, Pl.R.529e: esp. geometrical figure, X.Mem.4.7.3, Pl.Phd.73b, Arist.Cael.280a1, etc.

b. geometrical proposition, Id.EN1112b21, APr.41b14, Ascl.in Metaph.174.9.

2. in Music, scale, Phan.Hist.17; but aph' henos d. hupokrekein on one note, Plu.2.55d, cf. Dem.13.

3. horoscope, nativity, Id.Mar.42.

4. map, Jul.Ep.10.

II. list, register, D. 14.21; inventory, skeuôn Id.47.36 ; register of taxable property, PRev.Laws39.17, al. (iii B. C.), Harp., Suid.

III. ordinance, regulation, GDI5040.64 (Cret.), PEleph.14.27 (iii B. C.), D.S.18.57; to d. tô Antigonô OGI7 (Cyme); = Lat. edictum, Plb.22.10.6, Plu.Marc.24.

http://www.perseus.tufts.edu/cgi-bin/ptext?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3D%2324649
spiroslyra Creative Commons License 2008.08.29 0 0 971
The ancient science of harmonics investigates the arrangements of pitched sounds which form the basis of musical melody, and the principles which govern them. It was the most important branch of Greek musical theory, studied by philosophers, mathematicians, astronomers and others as well as by musical specialists. This book examines its development during the period when all its central ideas and its rival schools of thought were established, laying the foundations for the speculations of later antiquity, the Middle Ages and the Renaissance. It concentrates particularly on the theorists' methods and purposes and the controversies which their various approaches to the subject provoked. It also seeks to locate the discipline within the broader cultural environment of the period; and it investigates, sometimes with surprising results, the ways in which the theorists' work draws on and in some cases influences that of philosophers and other intellectuals,

Περισσότερες λεπτομέρειες
The science of harmonics in Classical Greece
Των Andrew Barker
Εκδόθηκε από Cambridge University Press, 2007
ISBN 0521879515, 9780521879514
494 σελίδες
spiroslyra Creative Commons License 2008.08.29 0 0 970

The science of harmonics in Classical Greece -

Andrew Barker - 2007 - Science - 494 σελίδες
The term katapyknosis is cognate with the expression to pyknon, ... Katapyknosis, of course, also recalls the word pyknoma which we met in the Republic (p.

http://books.google.gr/books?id=xRM9WLpswiEC&pg=PA42&lpg=PA42&dq=katapyknosis&source=web&ots=Vx5KGutlQP&sig=htNAUKZSmsHQ6C6iNS8XvnCGT_I&hl=el&sa=X&oi=book_result&resnum=4&ct=result
spiroslyra Creative Commons License 2008.08.29 0 0 969

JSTOR: Aristides Quintilianus and Constructions in Early Music Theory

The issue will hang on our understanding of a procedure which Aristoxenus ascribes to his predecessors, and which he calls katapyknosis. ...

links.jstor.org/sici?sici=0009-8388(1982)2%3A32%3A1%3C184%3AAQACIE%3E2.0.CO%3B2-V
spiroslyra Creative Commons License 2008.08.29 0 0 968


Aristoxenus's Ghost: An Ancient Metaphysical Mystery Solved: Katapyknosis Diagrams: The Universal Blueprints by Mitzi DeWhitt


* Publisher: Xlibris Corporation
* Pub. Date: September 2004
* ISBN-13: 9781413457889
* 160pp
spiroslyra Creative Commons License 2008.08.29 0 0 967

Nicomaque de Gérase : Manuel d'Harmonique (traduction)

[87] Καταπύκνωσις, littéralement: morcellement; subdivision d’un système décomposé en intervalles minimes, c’est-à-dire en quarts de ton. ...

remacle.org/bloodwolf/erudits/nicomaque/harmonique.htm
spiroslyra Creative Commons License 2008.08.29 0 0 966

LSJ

katapukn-oô ,

A. stud thickly, trêmasi to teichos Plb.8.5.6 ; thuras hêlois D.S.18.71 ; tois aphônois tas sullabas D.H.Comp.16 ; paradeigmatôn plêthei tên polin Plu.Lyc.27 ; tois huperbatois Phld.Rh.1.160 S.:--Pass., of the sky, katapepuknôsthai . . plêthei asterôn Arist.Mete.346a29 ; of a country, elaiais katapepuknôsthai to be thickly planted with . . (v.l. for -pephuteusthai), D.S. 3.44: metaph., bios en thaliais -pepuknômenos Porph.Plot.23 .

II. force into a small compass, compress, condense, Epikouros houtô katepuknou tên hêdonên Damox.2.62 ; talant' egô soi katepuknôsa tettara spent four talents in a lump, ib.4; to illustrate this is cited the dogma of Epicur., Sent.9, ei katepuknouto pasa hêdonê ktl., cf. katapuknôsis; ho Lukourgos tous politas têi siôpêi piezôn sunêge kai katepuknou Plu.2.510f :--Pass., -pepuknôtai hê pragmateia Porph. Plot.14 ; also ei mê -puknoutai soi to apo dogmatôn orthôn hekasta prassein that your habit of acting . . is not consolidated, M.Ant.5.9.

2. in Music, k. to diagramma fill up the intervals in a scale (with smaller intervals), Aristox.Harm.p.7 M.:--Pass., Theo Sm.p.91 H., Nicom. Exc.7.

III. Pass., to be condensed, of complex forms of inference (cf. puknoô v), Arist.APo.79a30.

http://www.perseus.tufts.edu/cgi-bin/ptext?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3D%2354953
spiroslyra Creative Commons License 2008.08.29 0 0 965

LSJ

katapukn-ôsis , eôs, hê,

A. condensation (v. katapuknoô 11 ), tou hêdomenou densification, solidification of pleasure by filling in unoccupied gaps in time and completing the penetration of the organism, Epicur.Fr.432: pl., Dam.Pr.354.

2. in Music, close packing of the intervals in a scale, Aristox.Harm.p.7 M., Nicom.Harm.11.

http://www.perseus.tufts.edu/cgi-bin/ptext?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3D%2354954

Ha kedveled azért, ha nem azért nyomj egy lájkot a Fórumért!