Fig. 8 Division of the monochord after Giovanni Maria Lafranco, Scintille di musica, Brescia, 1533. C-d2 9/8; C-E 81/64; C-F 4/3; C-G 3/2; C-A 27/16; C-B 243/128; C-c 2/1
Fig. 6 Harmonical proportions according to Pythagoras and Aristoxenus. Pythagoras divides the string length into 9 parts, in order to calculate an harmonical proportions shown in the figure. Aristoxenus, to achieve the same result, divides it into 15 parts.
Fig. 7 Division of a monochord puris numeris from Ludovico Foliano, Mvsica Theorica, Venezia 1529. C-d1 - 10/9; C- d2 - 9/8; C-E - 5/4; C-F 4/3; C-G 3/2; C-A 5/3; C-Bb1 16/9; C-Bb2 9/5; C-B 15/8; C-c 2/1
It is an ancient term and it needs an ancient definition, because the ancient idea of Beauty, Unity and Harmony are the bones and flesh of the renaissance and baroque art. Musical instrument making was the part of that art.
Harmony is beauteous because it is a spiritual form, which consciously sets order and unity among plentiful of divers voices into a unique and perfect concords[7].
The above expression is consonant with Palladios idea of Beauty, yet there is a subtle but important difference. There is a variety of rational and irrational proportions found in the Nature, however, some of them were preferred to others, and it is essential to understand why.
The story starts some time in the 6th century BC with Pythagoras, discovering numerical ratios between musical intervals. In Pythagorean vision, the Universe governed by a divine Number. His postulate all is a Number fed human thought for two millenniums and a half, and constituted the basis for the medieval and renaissance cosmology, Pythagorean philosophy and �thetics.
The laws of Harmony, according to Vitruvius, were systematized by the follower of the early Pythagorean doctrine Aristoxenus[8]. Vitruvius dedicated a whole chapter to harmonics. Chapters on Greek theater and acoustics (famous for its acoustic characteristics!) explain how to achieve excellent acoustics using the laws of harmonics, and how to diagnose acoustic related problems. Vitruvius gives us yet another crucial bit of information:
These natural laws[9] are followed by the skilled workmen who fashion musical instruments, in bringing them to the perfection of their proper concords[10].
Not only ecclesiastic minds and philosophers, but also renaissance and early baroque artists believed:
The solids of the Universe, to all appearances and in all probability, are ideally proportional[12].
Artists therefore took these cosmic proportions as ideal: if numerical harmony was spread in the Universe[13] and God used them to create the human and the Universe, they must be pretty good. These harmonical proportions, the most influential in whole European art, follow in the fig.6:
Ancient Greece recognized as consonants only a unison, a fourth, a fifth, an octave, an octave and a fourth, an octave and a fifth, and the double octave.
Intervals such as seconds, thirds and sixths are missing because they were not considered as consonants until the Renaissance.
More divisions of an octave shown in the figures 7, 8 and 9.[14]
[7] Leon Ebreo, fl. ca.1461 ca.1521, Dialogues about Love; in V.Shestakov, Renaissance Esthetics, p.355.
[8] Aristoxenus, fl. ca.364 BC - ca.304 BC, Greek peripatetic philosopher, studied in Athens under Aristotle and Theophrastus. He is the first authority for classical musical theory, the author of Elements of Harmony. Apart from his musical treatises, fragments remain of his reconstruction of the old Pythagorean ethics. His theory that the soul is related to the body as harmony is to the parts of a musical instrument seems to follow early Pythagorean doctrine (Britannica).
[9] The laws of harmonics D.B.
[10]M.Vitruvius, Ten books on Architecture, translated by M.H.Morgan, Dover, 1965
[11] From Robert Fludd, Utrisque Cosmi, Oppenheim, 1617-21; inMarco Tiella, Officina di Orfeo.
[12] Vicenzo Danti, fl. 1530 1576; Primo libro sulle perfette proporzione da imitazzi da nel disegno, 1567; V.Shestakov, p.451.
[13] Leonardo da Vinci, Book of Painting; in V.Shestakov, Renaissance Esthetics, p.355.
So let's have a look at the so-called just system of tuning, originally from India and named after a Greek called Aristogenes or Aristoxenos. Instead of relying solely on the fifth (3/2), it introduces thirds, both major (5/4) and minor (6/5) into the picture, forming a web of frequency relationships which I have organised as a honeycomb. Note that however far we extend this honeycomb in any direction, we will never find two notes of exactly the same frequency!
The Indians and Aristoxenos had a comma too, called the syntonic comma, which as a fraction is 81/80; as a percentage: 1.25%; and in cents: 21.51. This comma was considered the smallest nuance distinguishable by the human ear. In Indian music it is the distance between two neighbouring shrutis. Here, each plus or minus represents a difference of one comma.
Aristoxenos versus E.T.
We should take this opportunity to zoom out and see how all the honeycomb frequencies compare to Equal Temperament - the MIDI standard. The E.T. semitone or halftone is divided into 100 cents, which are the same as those displayed on your electronic tuner.
A note sitting on the bold line going down the middle is in tune to E.T. Notes on the left are sharp and those on the right are flat. The pale lines represent cents. If you click on one of the lower rows you will see a dotted line joining two notes only 1.954 cents apart, almost the same value as the Pythagorean schisma (see above). It fulfills a similar function, because being imperceptible to all but the gods, both the Turkish and the Indians (and maybe others) have used it to simplify and limit their tone factory output. You can liken it to a warp or wormhole in tonespace forming a shortcut between two distant points. So I don't know whether to call it the Oriental wormhole, or Turkish Tonewarp.
In this chart I have given the notes names according to the "thirds" rule. You can see by running your mouse over a few names that the same name may represent several widely differing frequencies, while two notes joined by the dotted line will have different spelling. Enharmonic spelling, a legacy of the Pythagorean system, breaks down completely with Just Tuning.
Hagel Stefan
Modulation in altgriechischer Musik. Die Delphischen Paiane und die antike Musiktheorie
Modulation in ancient Greek music. The Delphic paians and ancient music theory
Schlagworte englisch: music; antiquity; ancient Greek music; music theory; modulation; scale systems; Aristoxenos; paian; Delphic paian;
Zusammenfassung deutsch:
Die Musik des zweiten Abschnittes des sogenannten ersten Delphischen Paians, eines Werkes des hellenistischen Musikers Athenaios, hielt man bislang fόr mit der antiken Skalenlehre unvereinbar. Nichtsdestoweniger zeigt gerade eine Interpretation im Rahmen der antiken Musiktheorie die verwendete kunstvolle Modulationstechnik auf. Der musikalische Plan gipfelt im Wechsel zwischen zwei Tonarten, die nur einen Halbton voneinander entfernt sind. Der fόr diese — nach antiker Lehre ‚auίermelodischen‘ — Modulation nφtige Ton wird jedoch όber eine Reihe ‚melodischer‘ Wendungen eingefόhrt. In deutlichem Kontrast zum archaisierenden ersten Abschnitt scheint der zweite Teil damit ein Beispiel fόr den Stil der ‚Neuen Musik‘ zu bieten, die von Seiten Platons und der δlteren Komφdie so viel Ablehnung erfahren hat. Die Deutung der Musik des Paians wirft neues Licht nicht nur auf weniger gut erhaltene Musikfragmente, sondern auch auf manche bisher dunkle Konzepte antiker Theorie. Der eigentlichen Arbeit ist eine kurze Einfόhrung in die antike Skalenlehre vorangestellt. Im Anhang findet sich eine rhythmische Analyse des Paians sowie ein Abriί der Entwicklung von den modalen Skalen des fόnften Jahrhunderts bis zum ‚diagramma polytropon‘ des Aristoxenos, in dem jede Art von Modulation beschrieben werden konnte.
Zusammenfassung englisch:
The music of the Delphic Paian by Athenaios, a Hellenistic score of which the initial three parts have been preserved, the second of which has always startled modern scholars, reveals a delicate scenario of modulation of tone (metabolι kata tσnon), if interpreted under the point of view of ancient music theory. The musical setting includes a harsh modulation between two scales but a semitone apart, which was judged non-melodic (ekmelιs) by theorists, but it introduces the special tone needed for this modulation by a serious of melodic (emmelιs), if sometimes surprising, movements. Thus, in contrast to the archaizing first section, the second part of the Paian seems to be characteristic for the ‚New Music‘, which Plato and the comedy disapproved so much. Its music may shed new light not only upon the interpretation of other scores, less well preserved, but also upon some theoretical concepts, hitherto badly understood. The thesis begins with a brief introduction on the concepts of ancient music theory. The appendix contains a rhythmical analysis of the Paian as well as an outline of the development of the ancient scale-system from fifth-century modal scales to the ‘diagramma polytropon’ by Aristoxenos, which allowed for any kind of modulation.
Availability: Universitaetsbibliothek der Universitaet Wien,
Dr. Karl Lueger-Ring 1, A-1010 Wien, Austria
"Ever since his own age a great controversy has raged about the teachings of Aristoxenus. Instead of using ratios, he divided the tetrachord into 30 parts, of which, in his diatonic syntonon, each tone has 12 parts, each semitone 6. . . ." [J. Murray Barbour, Tuning and Temperament, a Historical Survey, Da Capo Press, New York, 1972, p22.]
Perfect Immutable System
Aristoxenus, The Harmonics of Aristoxenus, translated by Henry S. Macran, M.A., Oxford At The Clarendon Press, Henry Frowde, M.A., Publisher to the University of Oxford, New York, 1902, p249
Ancient Greek Music
Iliad (a page from SORGLL Society for the Oral Reading of Greek and Latin Literature)
Schlesinger
HERACLEITUS
Friends of Classics
John Curtis Franklin - Ancient Greek Music Homepage
Ancient Greek Music at the Austrian Academy of Sciences (Stefan Hagel)
Music Library of Greece (Lilian Voudouri)
In lieu of a dirth of metrical analysis, syllable by syllable, of ancient Greek poetry, I offer my initial steps towards analyzing the Iliad.
Iliad Stanza 1
. . . The school of Aristoxenes in the fourth century divided the tone into four "rigorously equal" quarter tones, but in reality this division was not considered as exact because Aristoxenes did admit in practice a certain "freedom of variation of the intervals," a certain "latitude" for each note. (d'Erlanger, Baron Rodolphe, La musique arabe. 3 vols. Paris: Paul Geuthner, 1930) in [Daniélou, Alain, Music and The Power of Sound, Inner Traditions, Rochester, Vermont, 1995, p81
. . . The . . . Fourth . . . its apparent value . . . consists of two and a half tones. [Aristoxenus, The Harmonics of Aristoxenus, translated by Henry S. Macran, M.A., Oxford At The Clarendon Press, Henry Frowde, M.A., Publisher to the University of Oxford, New York, 1902, p182]
. . . there is a problem about what exactly is meant by a 'tone'. The Greek writers define it as the interval by which a fifth is greater than a fourth. Strictly speaking, that is the interval given by the ratio 9 : 8, or 204 cents. But Aristoxenus regards it as being at the same time a unit of which a fourth (properly 498 cents) contains exactly two and a half. In effect he is operating with a tempered tone of 200 cents and a tempered fourth of 500 cents. . . . [West, M.L., Ancient Greek Music, Clarendon Press, Oxford, 1994, p167]
Az okori zenet kutato korunk gorog tagozata uj talalkozohelyet lelt a vasarnapi beszelgetesek melle. Szombatonkent matol kezdve alkalmunk van oszejonni a Gorog Technikai Intezet konyvtaraban, ahol az igazgatono segitokeszen rendelkezesunkre bocsat egy 'zugot'. Tervezzuk, hogy a helyhez illoen, meghivjuk ide a zene irant erdeklodo, de technikai ismeretekkel is rendelkezo szakerto baratainkat, hogy tanacsaikkal segitsenek elsajatitani a szamitogepes "trukkoket" a zenei kutatasban. Erre nagy szukseg van, mert mint latjatok, Arisztoxenosz olvasasa kozben, a 'lagyabb' bevezeto, torteneti resz utan a'surubb' teoriai kerdesekhez ertunk, ahol peldaul igen nehez szavakkal korulirni a lychanos vagy a parhypate topost, grafikus, szemlelteto abra nelkul. De magam is szegyenlem, ha csip-csup kerdeseimmel zaklatlak benneteket, itt az ido megtanulnunk a gep kezeleset, marcsak azert is, mert a szamitogep segit athidalni koztunk a tavolsagot, es mint remelem, jo elokeszuleti lehetoseget ad a talalkozohoz, Szentjakabon.
Ehoume anangi gia tis ergasies, gia na katanoisume kalitera ton Aristoxeno, kai genika tin archea elliniki mousiki, na shediasoume diagrammata, pinakes, dimiurgisume ikones. Avto sto skopo milisa me tin Katerina Toraki,-(toraki@tee.gr tel:210 3245180, 210 3291714)- dievtintria to bibliotiki Techniko Epimeletirio tis Elladas, zitontas simbouli. Itan poli tethiki i apandisi, kathe savato mas exasfalizi ena grafio, pou boroume na sizitisoume, malista kai na kaloume enan 'idiko', filo mas, opos a kurios Kaligeropoulos. Eine mathematikos, gliptis kai endiaferete to archeo elliniki mousiki, grafi kai technika biblia, gia to archeo theatro, pou anaferi kai to organa. Etsi me hara anakinoso, pos dipla to kiriakatiko aristoxeniko kiklo, ehoume sabatjatika proini sinandisi, pou mathenoume pos boroume na ekmetalevsoume to upologisti gia mousikologiki erevna. Episis antistiho "steki" dimiurgite kai sto Elliniko Kentro Erevnon, pou borite na me vrite kathimerina, na epikinonisoume metaxi mas, allazondas apopsis, plirofories, einai kalo an enas boitai ton allon! :) Idi ehoume 'diktioti' gia prosvasi, anihnevsi gia graptes ka ikastikes martiries. Tis leptomeries tha leme apo konda.
Szabad kerdezni, zenevel foglalkozol? Az inteligencia teszt rovatban mintha erre tennel utalast, de lehet, hogy tevedek.Megbocsass a kivancsiskodasert, de orulunk annak, ha a zenesz cehbol Magyarorszagrol is sikerul kis tarsasagunkat boviteni, mely lassan, csendesen munkalkodik, a gorog temak utan erdeklodoknek probalva forumot teremteni,ahol ki-ki szandeka szerint segitseget, tamaszt talalhat a kerdeseihez. Persze, mint mondod, idod nem nagyon engedi, hogy elmelyedj a temaban, de ha mint "latogato" erkezel, akkor is keszsegesen rendelkezesedre allunk...:) Ismered veletlenul, tudsz valamit Pap Janosrol? A syrinxrol irt egy erdekes tanulmanyt, keresem a cimet, ha sikerul, meghivnank nyari Szentjakabi talalkozonkra.
Meta tauta triton eiliftho puknon pros to auto, to ex imitoniou kai imioliou diastimatos sunestikos sustima eiliftho* ekton de to ex imitoniou kai tonou. Ai men oun ta duo ta prota lifthenta pukna orizousai lihanoi eirintai* i de to triton puknon orizousa lihanos hromatiki men estin, kaleitai de to hroma en o estin imiolion. I de to tetarton puknon orizousa lihanos hromatiki men estin, kaleitai de to hroma en en o esti tonieon. i de to pempton lifthen sustima orizousa lihanos, o meizon idi piknou in, epeidiper isa esti ta duo to eni, barutati diatonos estin. i de to ekton lifthen sustima orizousa lihanos suntonotati diatonos estin, I men oun baritati hromatiko lihanos tis enarmonion baritatis ekto merei tonou oxitera estin, epidiper i hromatiki diesis tis enarmoniou dieseos dodekatimorio tonou meizon esti. Dei gar to tou autou tritimorion tou tetartou merous dodekatimorio uperehein, ai de duo hromatikai ton duo enarmonion dilon os to diplasio. touto de estin ektimorion, elatton diastima tou elahistou ton melodoumenon. Ta de toiauta amelodita estin, ameloditon gar legomen o mi tattetai kath' eauto en sustimati. I de baritati diatonos tis baritatis hromatikikis imitonioo ka dodekatimorio tonou oxitera estin. epi men gar tin tou imioliou hromatos lihanon imitonion in ap autis, apo de tis imioliou epi tin enarmonion diesis, apo de tis enarmoniou epi tin barutatin hromatikin ektimorion, apo de tis barutatis hromatikis epi tin imiolion dodekatimorion tonon. to de tetartimorion ek trion dodekatimorion sugkeitai, ost' einai faneron, oti to eirimeon disztima estin apo tis baritatis diatonou epi tin barutatin hromatikin. I de suntonotati diatonos tis baritatis diatonou diesei esti suntonotera. Ek touton di faneroi gignintai oi topoi ton lihanon ekastis* i te gar barutera tis hromatikis pasa estin enarmonios lihanos i tis diatonou barutera pasa esti (hromatiki mehri tis barutatis hromatikis i te tis diatonou suntonotatis barutera pasa esti) diatonos mehri tis barutatis diatonou. Noiteon gar apeirous ton arithmon tas lihanous* ou gar an stusis tin fonin tou apodedigmenou lihanou topou lihanos estai, diakenon d' ouden esti tou lihanoeidous topou oude toiouton oion mi dehestai lihanon. Ost' einai mi peri mikrou tin amfisbitisin*
Agapite Spiro,agapiti Karbon,geia chara!
Me megali chara sinantithikame kai pali geia na
melethsoume auton ton yperocho tomea pou kaleitai "Archea
Elliniki Mousiki",prochorontas akomi ligo parakato auton
ton makri dromo pou echoume na dianu=ysoume eos otou
fthasoume ston pothito proorismo mas,diladi ena neo phorum
gemato theories kai mousikes!Sas echome kali ebdomada kai
sto epanidein eos thn epomeni synantisi mas.
[Itt a konyvembol kiragott harom sort a nyomda 'egere'...:( majd kesobb kinezem mashonnan.]
...oi men gar ti nun katehousi melopoia sunitheis monon ontes eikotos tin ditonon lihanon exorizousi* suntonoteras gar hrontai shedon oi pleistoi ton nun. touto d' aition to boulesthai glukainein aei, simeion d' oti toutou stohazontai, malista men gar kai pleiston hronon en to hromati diatribousin, otan d' afikontai pote eis tin armonian, eggus tou hromatos prosagousi sunepispomenou tou ithous. Peri touton men oun epi tosouton arkeito* o di tis lihanou topos toniaios upokeistho, o de tis parupatis dieseos elahistis, ote gar eggutero tis upatis proserhetai dieseos oute pleion afistatai imiseos tonou. Ou gar epallattousin oi topoi, all' estin auton peras i sunafi, otan gar eoi tin autin tasin afikontai i te parupati kai i lihanos, i men epiteinomeni i d' aniemeni, peras ehousin oi topoi* kai estin o men epi to baru parupatis, o d' epi to oxi lihanou. Peri men oun ton olon topon lihanou te kai tas hroas lekteon. To men oun dia tessaron on tropon exetasteon, eite metreitai tini ton elattonon diastimaton eite pasin estin assimmetron, en tois dia sumfonias lambanomenois legetai* os fainomenou d' [ex] ekeinon duo tonon kai imiseos, keistho touto an einai to megethos. Puknon de legestho to ek duo diastimaton sunestikos a sunthethenta elaton diastima periexi tou leipomenou diastimatos en to dia tesaron. Touton d' outos orismenon pros to barutero ton menonton fthoggon eiliftho to elahiston puknon* touto d' esti to ek duo dieseon (enarmonion elahiston* epeita deuteron pros to auto* touto de estai to ek duo dieseon) hromatikon elahiston. esontai de ai duo lihanoi eilimmenai duo genon barutatai, i men armonias i de hromatos. katholou gar barutatai men ai enarmonioi lihanoi isan, ehomenai d' ai hromatikai, suntonotatai d' ai diatonoi.
===
~melopoia
~sunitheis
~ditonon
~suntonoteras
~glukainein
~hromati
~armonian,
~hromatos
~ithous
~lihanou
~topos toniaios
~parupatis
~dieseos elahistis
~upatis
~dieseos
~imiseos tonou
~topoi
~peras
~sunafi
~hroas lekteon
~dia tessaron
~elattonon diastimaton
~assimmetron
~dia sumfonias lambanomenois
~duo tonon kai imiseos,
~megethos. p
~puknon
~elahiston puknon touto
~duo dieseon
~enarmonion
~hromatikon elahiston
~armonias
~hromatos
~enarmonioi
~hromatikai
~suntonotatai
~diatonoi.
Arisztoxenost meg keresheted Aristoxenus, Aristoxene, Aristoxeni valtozatban is. Sok sikert a kutakodashoz! Orulnenk, ha ahogy idod enegedi, elmondanad majd nekunk is idorol-idore, mire jutottal a temaban. Mi, ha valamit talalunk, felretesszuk neked.
Udvozol:
S.
Ha jolemlekszem van egy masik konyv is, Duringtol, ami targyalja a temat, valamint ertekes forras Wehrli Arisztoxenosz tanitvanyai cimu antologiajanak Arisztoxenos resze. Erdemes megkeresni a Szabo Ervin konyvtarat, igen jo a filologiaval foglalkozo konyvallomanya.
Mi is mukedvelok vagyunk, de szerencsenkre vannak a kozelunkben hivatasos szakerto baratok, akik segitenek az eligazodasban. Itt a Belis konyv kartyaja:
Aristoxčne de Tarente et Aristote, le Traité d'harmonique /
Annie Bélis
1986
French Book 274 p. : ill. ; 23 cm.
Paris : Klincksieck, ISBN: 2865631206 (pbk.)
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Title: Aristoxčne de Tarente et Aristote, le Traité d'harmonique /
Author(s): Bélis, Annie, 1951-
Publication: Paris : Klincksieck,
Year: 1986
Description: 274 p. : ill. ; 23 cm.
Language: French
Series: Etudes et commentaires ;; 100;
Standard No: ISBN: 2865631206 (pbk.); LCCN: 86-190421
SUBJECT(S)
Descriptor: Music theory -- Early works to 1800.
Music, Greek and Roman -- History and criticism -- Early works to 1800.
Théorie musicale -- Histoire -- Jusqu'ŕ 500.
Musique grecque antique -- Histoire et critique.
Named Person: Aristoxenus. Harmonics.
Aristotle -- Views on music.
Aristoxčne. Éléments harmoniques.
Aristote -- Et la musique.
Note(s): Bibliography: p. 255-260.
Class Descriptors: LC: ML169; Dewey: 781
Responsibility: Annie Bélis.
Document Type: Book
Entry: 19870430
Update: 20030907
Accession No: OCLC: 14943918
Database: WorldCat
Az OCLC keresojet ajanlom szives figyelmedbe. Mindent megtalal. Bar azt hiszem, hogy fizetos, de azt hiszem egy amerikai egyetemi serverrel becserkeszheto. Ha erdekel, megkeresem neked... Ha talalsz minket is erdeklo temakat, megkoszonnenk ha szolnal. Van egy Okori linkek rovatunk is, itt toborzom a Linkek bandajat.
Touton d' outos aforismenon tas ton genon diaforas othen gignontai kai on tropon peirateon katamathein. Dei de noisai ton sumfonn doastomaton (to) elahiston to katehomenon ta ge pleista upo tettaron fthoggon* othen di kai tin prosigorian upo ton palaion eshe... tina di taxin pleionon ouson noiteon; en i isa ta te kinoumena eisi kai ta iremounta en tais ton genon diaforais. Gignetai d' en to toiuto oion to apo mesis ef' upatin* en touto gar duo men oi periehontes fthoggoi akinitoi eisin en tais ton genon diaforais, duo d' oi periehomenoi kinountai. Touto men oun outo keistho. to de sughordion pleionon t' ouson ton tin eirimenin taxin tou dia tessaron katehouson kai onomasin idiois ekastis auton orismenis, mia tis estin i mesisi kai lihanou kai parupatis kai upatis shedon gnorimotati tois aptomenois mousikis en i tas ton genon diaforas anagkaion episkepsasthai tina tropon gignontai. Oti me oun ai ton kinesthai pefikoton fthoggon epitaseis te kai aneseis aitiai eisi tis ton genon diaforas faneron. tis d' o topos tis kiniseos ekaterou ton fthoggon touton lekteon. Lihanou men oun esti toniaios o sumpas topos en o kineitai, oute gar elaton afistatai mesis toniaiou diastimatos oute meizon ditonou. Touton de to men alatton para men ton idi katanenoikoton to diatonon genos ouh omologeitai, para de ton mipo suneorakoton sughoroit' an epahtenton auton* to de meizon oi men sughorousin oi d' ou. de' is de gignetai touto aitian, en tois epeita rithisetai. Oti d' esti tis melopoiia ditonou lihanou deomeni ka oux i faulotati ge alla shedon i kallisti, tois me pollois ton nun aptomenon mousikis ou pani eudilon esti, genoito...
======
Ma az egytememen megkerdeztem Stelios Psaroudakes profeszor urat az alatalad felvetett temarol. Anna Belis Arisztoxenosrol irt konyvet ajanlotta elolvasasra. A tanulmany megvan nekunk is franciaul, baratnenk es tanulotarsunk, Karbon, elvallalta, hogy leforditja. Ezt a tanar ur is szorgalmazzza, mas muveket is javasolva. Igy megprobalunk a tanar ur kore egy forditogarat toborozni. A ma reggeli eloadas,- mit tesz a veletlen!- Arisztoxenosz eletevel kezdodott. Az ogorog zenetortenet tantargy egyik fo figuraja, rajta keresztul ismerjuk meg az ogorog zenet. Hatasa olyan eros volt, hogy mikor a kesobbi korok zeneteoretikusai visszaneztek a zene ostortenetere, az o modszertanat hasznaltak. Igy nemcsak az utanna kovetkezoket befolyasolta, hanem az elotte eloket is az o latasmodja alapjan iteltek meg. Errol az orarol, mivel ma kicsit elfaradtam, holnap szamolok be itt:
http://forum.index.hu/forum.cgi?a=t&t=9103586&uq=23
Mikor a zenetortenetben Arisztoteleszhez erunk, akkor megint ertesitelek. Arisztoxenoszt, fontossaga miatt elsokent targyaljuk, aztan vesszuk, idorendben a tobbieket. Mennyi idod, kedved, energiad van ehhez a temahoz? Mert ha alaposabban erdekel, elvallalhatnad "Lathatatlan szeminariumunkon" a tema gondozasat, kidolgozasat.:) Ehhez minden segitseget, szovegeket, forditast, forrasokat megadnank. Ha gondolod, nyari szentjakabi Lyra-muhely talalkozonkon, vezethetnel a temarol egy kerekasztal beszelgetest. Arisztotelesztol jomagam sajnos csak a Poetikat es a Zenei problemakat olvastam. Te mennyire ismered Arisztoteleszt?
Udvozol:
Spyros
A gorogok is jo par ezer eve itt elnek, toluk raboltak el Europat...:)
... elnezest ha akaratlan erzekenyseget sertek, nem allt szandekomban a bantas, igazan szeretem es tisztelem a magyarokat, amint erombol telik, szeretnem nekik megmutatni, beszelgetni veluk, tanulva egymastol, amivel olvasmanyaim soran talalkozom. Persze eztan jo ha vigyazok, erre int a pelda is - talan nem orrolsz meg erte, ha elmondom... Mikor nalatok jartam, es a Varosligeteben setaltam, hat lepten-nyomon beleleptem a kutyasagokba. Ezt gyanutlanul felpanaszoltam testi-lelki regi jo baratomnak. Ugy meregbe gurult, hogy megijedtem, alaposan oszeszidott, mondvan, hogy 'csusztatok", es hogy elterelem a figyelmet az igazan fontos politikai kerdesekrol. Hasztalan volt a vedekezesem, hogy en csak egyszeruen 'elcsusztam', es nem a politikara, hanem a kutyasagra morgok.
De talan jobb, ha temafelvetesedrol szolunk, ami kulonosen is erdekes. Persze en inkabb az archeomuzsikologia oldalarol kozelitem , de a filozofia es zene sok ponton erinti egymast az ogorogoknel. Jelen pillanatban egy Vasarnapoi olvasokorben, (masneven "Linkek bandaja":) barati tarsasagban lapozgatjuk Arisztoxenost. Mereges-morgos, veszekedos, zsenialis ember lehetett, nem mulaszt el alkalmat, hogy leszedje a keresztvizet szaktarsairol. Azt hiszem, tetszeni fog neked! :) Ket egyetemi orat is latogatunk e temaban, az egyik keddenkent, a masik minden penteken, az ogorog zenerol szol, Arisztoxenosszal a fokuszban. Profeszorunk szerint Arisztoxenosz mesteri modon alkalmazza Arisztotelesz modszertanat. Ha van hozza kedved, olvasd velunk, nezd meg a jegyzeteinket, beszamoloinkat. A kedvedert, es Petyus, valamint mas barataink "udvere" igyekszem magyarra forditani. De egy kis turelem kene hozza, mint ahogy annak idejen maga Arisztoxenosz is ezt kerte hallgatoitol, meltatva az ogorog zenei szisztemat, rendjet, szepseget, mondvan, neki sem konnyu a dolga! Egy piszkozat, vazlat, nyersforditas, mar keszult magyarul Arisztoxenoszrol,baratunk, Petyus kritikus pillantasa, megjegyzesei kiserik, de ez meg pontositasra atdolgozasra szorul, ha "megerik", folveszi Petyus a honlapjarba, a Kabocaba: http://www.terrasoft.hu/kultura/kaboca/ogorog/ Itt sok erdekessget talalsz mar most is. A regebbi levelezesben megleled, ha visszalapozol az Arisztoxenosz disputakat. Milyen nyelven beszelsz? Mert akor kuldok hozza valo irodalmat.
Dr. Craig Cooper
Fig. 9 Harmonical division of an octave by Gioseffo Zarlino, Insitvtioni armoniche, Venezia, 1588. C- d2 - 9/8; C-E - 5/4; C-F 4/3; C-G 3/2; C-A 5/3; C-B 15/8; C-c 2/1
Fig. 8 Division of the monochord after Giovanni Maria Lafranco, Scintille di musica, Brescia, 1533. C-d2 9/8; C-E 81/64; C-F 4/3; C-G 3/2; C-A 27/16; C-B 243/128; C-c 2/1 
Fig. 6 Harmonical proportions according to Pythagoras and Aristoxenus. Pythagoras divides the string length into 9 parts, in order to calculate an harmonical proportions shown in the figure. Aristoxenus, to achieve the same result, divides it into 15 parts.
It is an ancient term and it needs an ancient definition, because the ancient idea of Beauty, Unity and Harmony are the bones and flesh of the renaissance and baroque art. Musical instrument making was the part of that art.
So let's have a look at the so-called just system of tuning, originally from India and named after a Greek called Aristogenes or Aristoxenos. Instead of relying solely on the fifth (3/2), it introduces thirds, both major (5/4) and minor (6/5) into the picture, forming a web of frequency relationships which I have organised as a honeycomb. Note that however far we extend this honeycomb in any direction, we will never find two notes of exactly the same frequency!
"Ever since his own age a great controversy has raged about the teachings of Aristoxenus. Instead of using ratios, he divided the tetrachord into 30 parts, of which, in his diatonic syntonon, each tone has 12 parts, each semitone 6. . . ." [J. Murray Barbour, Tuning and Temperament, a Historical Survey, Da Capo Press, New York, 1972, p22.]
