Elementos de Armonía - Aristóxeno de Tarento [m-a-000274-f2] ()

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re Kal •qpe/j.lav (ptovrjs [Kal] 0 eKeivoi K(vr)<rtv. TaCra fxev

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1.13 A P I 2 T 0 S E N 0 T

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106

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1.22 API2T0EEN0T

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APM0NIKX2N ST0IXEli2N a I.25

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bnrXa<r(<i). TOVTO be iarlv eKTrjjiopiov, eXarrov bt,a<rrr)fia

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20 tdrr] bidrovos Trjs (3apvrdTT)s biaTovov Secret £CTTL O-VVTOVO>-

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30 KOIVOS TOV r e biaTovov Kal TOV xP^Ma T o y> ° 8' eTepos Ibws

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b' aiTiov TO KOtvas etvai r a s itapvnaWas T&V yevStv, yCyverai

10 yap e/itjoteA.es TtTp&yopbov eK irapv\Tr&Tris r e XPC 0 / ' t a n K ' ? s ( r ^ s )

Kal biaTovov \i)(avov Trjs crwrovcorttrT/s. 'O be

1 xPa>/iaTllch • • • naffd Ian restituit Marquard 4 TAS] TOUS sedsupra o ras. in qua o fuisse vid. Ma: robs V S , B (sed ov in ras. eta suprascr.) ov ex ov Me : ov V S TOV ajroSeSnyfiAvov T6TTUAiX">'w ^ a> sec^ a supra TOV, to supra cwroSeSery/teVou et ou supra Aixwaiadd. Me : T6TTU \txdpa> V S : T TTOU (a suprascr.) \ixavov B 5 5']•yetp H 8 fiivov H 9 SWov6s Meibom : Siarop6s codd.avTjjs post /110s add. R 15 ra add. Mx 16 io-rl] en B :iar\ B in marg. 18 T& plv . . . •saf\ni,Ti\s om. R 20 TO]r y S T $ AixayoB om. R 21 a/iforepas Marquard: a/Mporepoiscodd, 23 Tijj ftapuTdrris conieci: irapwdrris codd. (R et Bin marg.): fiapvTtpas nvbs T^I fi/itTovtaias ante irapinrdTris add.Marquard

APMONIK&N 2TOIXEII2N a' I.27

rfjs •mzpuTrdrrjs TOTTOS (pavepos icrri e/c TS>V epirpoaOev,biaipeOeis re /cat avvTeOels ovos iorCv. |

i

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5 fyatvertu be Toiavrq r ts <f>vo-i.s eivaL TOV o~vvexpvs ev TTJ(obiq ota KCU iv rfj Ae'|fei irept rr\v TQ>V ypap.fi&To>v cruv- 20deaiv Kal yap ev raj biaXeyecrOat. (f>vcret. rj (/KOI'TJ Kafl' IK^OTTJVTWI" 0"uAAa/3i3i' irp&rov TI /cat bevrepov rav ypamiAraw r(9r)o-iKal TpCrov /cat reraprov Kal Kara | rovs \onrovs apidixoiis 25

10 axraOTcoy, ov TTCLV ixera -nav, dAA.' ecrrt rotatJiTj r ts c/>v(rt/cr)av£r]o~is rrjs ovv9eo~eoos. irapairA.?j(7tcos 8e /cat ev T 5 /xeA.- •oifieii' lot/cey ^ C OJI'TJ TiOevai Kara avve\eiav | rd re 8taoT7j- 30fiara Kal roiis (pdoyyovs <\>WIKT\V Tiva o~vvdeo~iv biacpvXdr-Tov<ra, ov ttav \xera irav biao-rqixa fj.eX.a>bovo~a OVT' icrov OVT'

15 Svio-ov. Zr)Tr)Te'ov be TO avvexes oi\ cos ot ap\\ixoviKol ev 28rats raw biaypamxaWoiv KaTairvKViio-ecrw airobibovai -ncip&v-rat, rovrous a/nocpaCvovTes TG>V <p66yyo)v k£rjs dAA.7)A.a)vKelcrdai, oh (rvjj.\l3e^r]Ke TO e\a\i<TTOV biao-rqiia bieyeiv a<p' 5avr&v. ov yap o n [ 77] bwarbv biecreis OKTCO /cat eiKoo-iv

2 0 e^ijs ju,eA.a)8^crat rrj (pcovfj eorCv, d\A.a Tt)v rpirqv Stecrti'•navTa -noiovaa ov\ ola | re' ecrrt -npoa-TtBevai, dAA' eirl ixev 10TO 6£v eX&xicrTov pieAcpfiei ro Xonrbv TOV bia rea-crdpaw,—•rd 8' e\&TT(i) TravTa e^aSwareT—roCro 8' ecrrti' ^frot OKTO-TrAdcrtoi; r^s eAaxtcrr?)s SieVeajs rj p-t/cpai rwt | TravreAcos /cal 15

2 <nn>Tf8eU M V B S : avvnfch R : ivrtOeh Marquard 4 wirooij-Helvat S 7 ^] ?) B c wcjj B Ka8fKa(TT7j H 8 «] T«B R 9 \omovs om. H 10 dA\' ia-n . . . avviiatws om. M,in marg. Me (01 in Toiairi) in ras.): Vb in marg. sed TOIOUTT) et TIS om.TOIOUTT; TIS] TU aBnj S TIJ om. B 16 ypapudTuv S 17 4{^sex { ^s Me: { ^s V: < <:{7js H o\A. A.wy post (ceifffloi ponit H19 oil yhp p.6vov rh /ify SvvacrBai S. 6. K. i. 4. ^cXifSatrBai TTJS 0tu»^s (TTfvMarquard Sri conieci: rov codd. /»^ seclusi Swarb^ conieci:Bwarrflai codd. Sie'cris B ao /ueA S crat conieci: /neAijiSeTirflaecodd. 24 Sie'crcMs] Si in ras. Mb

119

1.28 API2T0HEN0T

^ro) eXarrov, em be TO /3apv raw bvo 8iecreaw Toviaiov

eXarrov ov Swarat fxeXabelv. Ov brj upocre/creW el TO

20 o~vve)(e$ ore fxev e£ tcra)z> ore 8' e£ dviacov yiyverai, | dXXa

irpbs TT]V Trjs jxeXwbCas <pvo-iv Treipariov pXeireiv KaTavoeZv

re irpo6vfj.ovfxevov TC juera TL irecpvKev r) (fxavr) bi6.arqfj.a5

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25 bwaTov eyyvre'pcio /xeXuibrjaaL <p66yyov fxeo-qs, avTi] b\v etrj

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e/c TQ>V elpr]i>.ev(ov ~n5>s be ylyverai Kal TC fiera TL

2 9 TCOeraC re Kal ov rCdeTai, ev TOIS 11 o-TOixeCoi

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15 acrvij.<pG£>v6s io-Tiv. 'TiroKefo-flco 8e Kal | rerrtipajj' yiyvo-

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20 bia I TreWe TOV bia Tecro-dpuiv v-nepexei, evavrCws Tl6ea-0ai 25

1 &/i.e\(t>S-!)Ta>] i\ in ras. Mb EAOTTOC Meibom : iKdrrovt M V S R :i\A.TTuvi B Tovtalov Meibom : roviaiwv M V R : roviaiov B S2 eKa-rroy supra lin. Mx. om. Va, add. in marg. Vb Svvarbv HS^] 5£ H el conieci: e/s codd. 7 Svvarhv om. B : SOCOTJ) S, Vb(sed i) in ras.) 9 TOV restituit Marquard 12 T( om. H13 /itcT'ek conieci: fi\v codd. rb tiurvKvov ex rbv itvKvbv (ut vid.) Mb14 fiAi TlBeaiaC] ftcraTiSeaSat M 15 XimroiUvav H 18 rottrirpaffi del. Meibom 19 rots trims del. Meibom ao elvcuom. H robs ofs] TOATOIS R 24 \oiiron4vov H ^ ex ^ Mb :^ S r i ex TOO Ma (?) S : rb Vb cum ras. post & 25 ^Meibom: {mep4")(Giv codd.

120

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acrvvOeTa irdvTa fxeyedrj. 'Aya>yq b' ^orco 77 bia T&V e£fjs

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121

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i 2TOIXEIHN AETTEPON

I o BeArtov forces eort TO irpo5t [eA.tfeti' TOP Tpoirov rqs itpa-yixarelas rls TTOT' ZOTLV, Xva irpoyiyv<&<rKOVTes &(nrep obbv if

fiabuTTeov pabiov iropevooixeda eibores re Kara rC ixepos ecrixev 5

15 avrrjs I Kal p.ri \6.6mixev ^juas avroiis •napvnoXanfiavovTe's TO

irpayp.a. K-aOAirep ' Apio-roTeXrjs ael birjyeiTo TOVS irAetorous1

T&V CLKOvaAvrwv irapa YIX&TCOVOS TTJV -rrepl Tayadov aKpoacriv

20 -naOtiv. | TrpocrUvat. pxv yap eKao-rov virokaix^dvovTa A.77-

\jreo-$aC TL T&V vo/xi^oixivoiv TOVTCOV avOpoiirivaiV ayad&v otov 10

TTXOVTOV vyUiav la\vv TO O\OV evbainoviav Tiva davfiacrTrjv

25 ore be | <j>aveCr]<rav ol \6yoi irepl ixadrju&Twv Kal apiOjx&v

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3 1 eo-Tiv ev, TtavTeX&s o?/xat ira/)a8o||^oV TL i<paiveTO a v r o t y

fffi ol p.ev viTOKaTecppovovv TOV irp6.yy.aTos ot be /care- 15

Ixe/xcpovTo. Tl ovv TO OXTIOV; OV irporjbeo-av, dXA' &anep

5 ot epto-TiKol I irpos Tovvojia avrb viroKe-^rjvOTes Trpoojjeirav

et 8e ye TIS ot)uai irpoe^eTiOei. TO okov, aireyivcao-Kev av 6

fxeWiav aKoijeiv i) et-rrep fjpecrKev avr& bie)xevev b\v ev Tr\Jo elpr])xevrj inroXri'ij/ei. | IIpoeAeye /xev ovv Kal avroy 'Apio-TO- 20

3 irpoeXSety (Si suprascr.) B 4 rls Marquard: rt codd.6 TrapvTroKa/i.fitu'oi'Tiiiy Ma, sed « supra eov scr. Mb 11 v\ovrov\post 0 ante v ras. M uyeiay M V B S 6u5ai/*oWos Ti/uJ>i' R12 S£ supra lin. add. Mb 17 01' om. lac. 4 syllabb. R 18 irpo-efeT flj; Ma praeter 6i\ quod cum ei superposito ab Mb in ras. qua plusuna littera deleta erat lireyivaxrKzv ex curey. M : iircylvaaKevrell. ig «ol infra lin. ante f/ add. Mb 2Marquard

122

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aKpoacrOai irap' avrov, irepl rivmv T' earlv fj •npayixareia /cat

rCs. BeXriov §e Kal fip.lv | <pa(verai, Kad&irep eluofiev ev 15

apxfj, TO irpoeiblvai. TCyverai yap evCoTe i<p' eK&repa

5 ap.aprCam ol jxev yap p.£ya n VTtoka\if5avovai.v etvai TO

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li.e\oTrou&v eK&crrqv Kal TO okov, rrjs p.ovcriKrjs \ on fj 25

10 p.ev ToiavTT] fiXa-nrei ra ijOr] fj be roiavrr) dxpeX-el, rovro

avrb TrapaKovo-avres, TO b' on KaS1 ocrov JMOVO-IKT) bvvarai

dxpeXelv ovb' aKOvcravres o\a>s'—oi be iraXiv ws ovbev | aW' 30;

77 jiiKpov n Kal fiov\6jj,evoi p,rj etvai Iftireipoi p,r]be TL TTOT'

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15 (ppovrjTov eori Tivi os vovv eyei TO p.a6r\p\,a—brjXov 8' l o r a i

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elvai irpbs iravra, KaO&irep oXovrai rwes . TtoWh yap br] Kal

erepa vtrapyei. [77] KaOa-nep ael kiyerai. T& | IXOVCTIKZ' p.4pos 5

yap e<rnv fj app.oviK7] itpayjxareia Trjs TOV {JLOVO-IKOV H^ews, ;

20 KaQairep rj re pvO/xiKr) Kal 77 ixeTpiKr) Kal f) opyaviKr], AeKTiov

ovv "Kepi avrfjs re Kal TU>V jxepQ>v.\

KadoXov jxev ovv vorjTeov ovcrav fjyxv rr)v Oeonplav irepl 10

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\ II.32 API2T0HEN0T

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124

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25 p.ovo'i.Krjs avayKaiov Kal ev ro t s Trept TO fipp.oo-p.evov <rvve-

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11.34 API2T0EEN0T

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126

APM0NIKI2N ST0IXEI12N /3' II.35

fK\iinravov<ra>v re Kal aOemp-qTuiv buupop&v, Kara TCLVTHJV

ayvorjcroyi.iv | | TOLS ev rots ixe\wbovixevois bia<f>opis. 36

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127

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MACRAN K 129

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ixikos Kal elb4vai TC ecrri TO (ppvyiov p.ekos—brjkov OTL

25 OVK hv eXr\ Tt)s eiprjjj.evr]s \ €Tno-Tr\fx,r\s -nepas i) •napa.o-q- 15

fiavTiKri. "On 8' akrjOfj r a keyoficva Kal eo-riv avayKaiov

T 5 TTapao-r)naivoiJ.ev<j> fxovov TCL ixeyeOr) T&V biao-Tr]ix6.TWV

3° biaiaQavecrOai, dpavepbv yivovr hv | eT!i<TKoiiov\j.evois. 'O

yap Tideixevos arj/nua T&V biacrTr]p,6.T(ov ov KaO' eK&o'Trjv T&V

evvnapypvo-&v airois bia<fiop&v Xbtov TiOerai a-rjixeiov, olov 20

4 0 et TOV bia Teavapcov Tvyx&vovo-iv al bi\\aipi<reis ovo-ai

nkewvs as TTOIOV(TIV al T&V yev&v biacpopai, rj cr^^iaTa

irkeiova Ttoiel f/ rfs T&V acrvvdeTuiv 8(aoTT}jLuira>i> T&£ea>s

5 akkoLOMTis' TOV avTov be koyov | Kal irepl T&V bvv6.fj.eaiv

epovfj.ev as al T&V Terpa)(opba>v dpvo-eis iroLovo~t,, TO yap 25

3 TOV ex TO Mb 4 T V supra lin. add. Mb 7K6TOS B OA?J0CS post yap add. H ou post Sri add. Mar-

quard 9 -ypctyao-flai] 7op a^oirfloi R I I TOV] TJ M V S\ UtTpov . . . lafij}iK6v restituit Marquard 14 Kal &pio-T<l ye

\ ei'SeVoi in marg. Mc(?)R Kol post iim add. H 17 Tip exTCI Mb p.6vcp B 20 vTrapxoviTcoy H : 4vvirapxovo~G)v exivvTapxivTuv Ma avTols supra lin. add. Me 21 ei in ras. MbSick supra lin. add. Me: om. V B in marg. Sia Tetro-dpuv] S' S23 & post TrKeiova add. Marquard rj] i) R avvQerwv E24 Acfycuj/ S

APM0NIKI2N 2TOIXEII2N /3' n.40

vvepftoXaicov Kal VTJT&V Kal fxio-cov Kal inraT&v r<5 OVT& ypd-

(pfTai (Trjixfiui, r a s be T&V bvvdfj.eoov bia(j>opas oi bcopi^ei TO, |

0-rnj.eZa. ( a W e ) /xe'xpi T&V peyeO&v avr&v Kel&dat, iroppwTepeb 10

8e p.rjbiv. " O n 8' ovbev e a r i fiepos Trjs o~vimd<rr\s £vvio~ecos TO

5 biaio-6dveo-6ai T&V fieyeO&v OVT&V, ZXexQrj fxiv irons Kal iv

apxfj, pabwv I 8e ml ZK T&V pr]6r\ao\J.iva>v awiJbeiv OVTS yap 15

TCLS T&V TeTpa)(opbmv ovre r a s T&V <f>06yyaiv bwdfteis ovre TCLS

T&V yev&v bicupopas oire, dirASs elireiv, rr\v TOV vvvOeTov

ml TT\V TOV davv\6iTov bia<popav OVT€ TO CLTTKOVV KO.1 /.tera- 20

10 fioXrjv fxov °vTe TOVS T&V (j.e\oTrou&v Tpoirovs OVT 8.W0

ovbiv, axravTuts zhttiv, bi aw&v T&V fieye6&v yiyveTai

yvdpip-ov. E t iJ.ev ovv 8t' ayvoiav TTJV vir6\\r]^/iv Ta6rr]v 25

eo~x/im<riv 01 m\ov)j,fvoi apjxoviKoi, ro fikv q6os OVK hv etev

axoiroi, TTJV be ayvoiav lo~)(vpdv riva Kal /xeydX.r]v elvai nap

15 OVTOIS avaymiov el be arvvop&VTes, o n OVK [ Ic rn ro irapa- 30

o~qp.aivecr6ai Trepas Trjs elprjfxevqs emo-Trnxris, xapi^6p.evoi 8e

' TOIS i8t<urais Kal ireLpcoixevoi airobibovai. 6<j)6a\iJLoeibes TL

ipyov Tavrqv eKTeOeUao-i TT)V tnr6X.7]\j/tv, neydX-qv |] {av) 41

av^is avr&v aTO-niav TOV Tpo-nov KaTayvo(r]V Trp&Tov fiiv,

20 OTL KpiTi]v olovTai belv mTao~Kevd£eiv T&V emo-TT]iJ.&v TOV

ibidTTfv—aroTros yap av | elr\ TO avTO ixavOdvoov r e Kal 5

Kpivcov 6 avTos—, £itei6' OTI (irepas) roS £vvievai Tidevres

p f i v Kal vtyrtav Kal fiefftoy Kal virarSiy conieci forep-f}oAalcov Kal CTjTtDc] T^r virtpfloXatas H : iirepfiohatas V^TIJS B : inrep-Po\alas Kal virtis R : inep$o\alas rell. (in marg. B) jiiauvKal virwrSiv] fieffTjs Kal VTT6.TT]S codd. 2 Siopifct ra Marquard :SiopiCzrai codd. 3 o-jj/te^ R SHTTC restituit Marquard6 TOV ^Bricroufvov H TO Kara, post yty add. Westphal8 ws ante anKcbs add. H TT)V R : Tcts rell. TOV (TvvQirovMeibom: TWV GvvBiTtav codd. 9 KOI TG>V atxvvBeruiv b~ia<popasH 10 OSTE a corr. suprascr. B neAoiroCiav V : fieXoiroiuvrell. 12 yvapifxav B Si' &yvoiav~\ Siavoiav H 14 8i]Si H 17 ISi^Tats S aTroSoCvai H o<p8a\/iofiSeo'Ti M a :accent, acut. supra e alterum, et T supra a add. Me 18 ^KTeefacurtS i7r<<\cit|(ii/ H tu> restituit Marquard 19 Karayvoiriv] vadd. Mb 21 ISiirnv S aa jre'pos restituit Marquard TOV]T A M V S B : om. R

K 2 131

11.43 APISTOHENOT

Kivovvrai ot aikol Kal ovbiirod' dxravrcos eypvrnv dA.A' e/caora

15 T5>V av\ovp.iva>v p.eTaJ3d\\.ei | ((cara) ray CLITLCLS d(/>' &v

avXelrai. ^S^ebbv 8?) <pavepov, on 81' oibeptav alriav els

TOVS aiXovs avaKTeov TO p.iXos, ovre yap /3e/3aiciS<rei rt]v

TOV 7jpp.oa-y.ivov TOL^IV [TO elpr]p.evov\ opyavov OVT , et TLS | 5

ao <fr\6r) beiv els opyavov ri iroieio-dai TYJV avaycoyqv, els TOVS

avXovs r\v -novr\Teov, eiteihr] y.akicrTa irXavarai Kal Kara TT\V

avkoisodav KOX Kara TTJV xeipovpyiav Kal Kara TTJV Ibiav

(pvaiv. I

25 *A jxev ovv irpohiiXOoi TIS civ Trepi rfjs app.oviKrjs KaXov- 10

TTpay/xaTeCas a^ebov ecrri ravra- ixeWovras 8' e m -

xrj Trepl ra o ro t^e ra Tr/say/nareia 8et Trpobiavorj6fjvai

30 ra 7"ot|a8e* on OVK ei>8eY^exot xaA(3s airriv bie^ekOeTv JXTI

•RpovTrap£avTO)v rpi&v r&v pr}6r}o-op.ev<i>v upSirov [lev OVTS>V

T&V (paivofievaiv icak&s krj<pdevT(ov, eirevra biopiaOevriav ev 15

4 4 avrois T5>V 11 r e Trporepoov Kal TG>V varepcdv opO&s, rpirov be

TOV oviifialvovTos r e Kal 6p.oX.oyovp.ivov /cara Tpo-rtov avv-

5 0(p6evT0S' 'Eiret be iraa-qs emcrTripL-qs, rj TLS e/c T[pofi\y)\p.6.TU>v

Tt\ei.6vmv o-vvetTTrjKev, apxas TrpocrrJKov e o n kafielv e£ §>v

beixOweTaL Ta H-€Ta Ta$ o.pX"-s> avayKOiov av e%r\ \ap.fiaveiv 20

Trpoo-i)(ovTas bvo rourSe* TtpS>Tov jxev oiroos a\r]6is r e Kal |

io (paivqp.evov ^Kaarov e o r a i r&v apxoeLb&v Trpof$\r}p,6.Tu>v,

eTTfW OTTUIS TOLOVTOV olov ev TrpatTois inrb rfjs alo-6r)o~e(as

crvvopaadai. T&V TTJS app.oviKrjs •npayp.areias p.epQ>v TO yap

15 Trcoy airavrovv cnrobeigiv | OVK ecmv apxoeibis. KaOoXov 25

8' ev r £ apxecrOai -napaTr\prjTeov, OTTOS JU.TJT' els rr\v

inrepopCav ep."nlTXTu>[i.ev a/no TLVOS (poovrjs jf Kivqo~eoos aipos

1 post av\ol unum verbum eras. M 2 nark restituit Meibom3 Si)] Si H 4 /idXos H 5 T 1 tlpy/ievou seclusi ef om.M V B S 6 a 7 o . 7 ^ M V S R H 7 ft/] %v ex fa Mb : VV S B, H (ante cfe robs) 8 /col /caT& T^C x*lPovPv'lav ' n ma rg- Mbi o irpoeAfloi B in marg. 17 rbv ante rp6irov add. M V S Bauvaip&ivTOS H 18 &rei ex &rl Mb ig irpoaixovTa H24 ixerpav H 25 iras S oireTow H 26 T^V om. V S27 timhrTunev] lac. irra/iey R : i/nrlTTonev H $ conieci: ^ codd.

134

APMONIKilN STOIXEIiiN /3' II.44

, ixr\T av KapTtTOVTes ZVTOS irok\\a T&V olneCwv 20

Tpia yevr\ T&V /xeXcoSoujueVow earCv biarovov

5 ap)j,ovia. al fiev ovv biacpopal TOVTMV varTepov pr)Or)(rovrai'

TOVTO 8' OLVTO eKKtivOoo, 6V1 T:CLV | fj,e\os l o r a i ffroi biaTOvov 25

*; Xpuip-arLKOv rj evapjxoviov rj IXLKTOV IK TOVTOIV r\ KOIVOV

TOVTCDV.

AevTepa 8' earl biaipecris T&V biacrrqixdTcov eTvat TO. jxev

10 o"6iJL(pmva TO. | 8e bi6.(poiva. yvcopificaraTai fikv boKovcnv eivat 30

awa i bvo T&V Staorrj/xartKcSy biadx>p&v, 17 re \xeyeBei 8ta-(pipovcriv a.k\rj\wv KOL fj TO. crvix(p(ova T&V biacpdvinv irepie-

\eTai b' f/ vcrTepa prj^eicra 11 biadjopa rrj Trporepa, trnv yap 4 5

crviA(pa>vov -rravTos biacptovov biacptpei neyidei. 'Ewet be T&V

15 crvijupuvoiv Tr\.eiovs elal irpbs aXXrjXa bia<popai, /xia r u TJ

yvcopijAGOTaTT] OVT&V zKKelaOco (jipdrrj)1 OSTT] 8' earlv tj /cara 5 •

jj.iye6os. vE(rr&) 8rj T&V (TVfj.<pcavo)v o/cra) fxeyidrj' e\.d)(itTTOV

fjiev TO bia Teaaapcov—ovpfialvei 8e roSro {aitrfj) rrj TOV

(jxeXovs) (pvcrei eka\icrTov etvai' crrifxeiov be | r o jxektobeiv 10

20 ju.ei; fjixas TTokXa TOV bia recrtrapcov Z\&TTU>, TT&VTO. ixevToi .

biacpoova—>. befoepov be r o bia irevre, 0 TL 8' av TOVTOOV

ava ixeaov y fxeyeOos iiav Icrrat bidcfxavov. Tpirov (8') e/c

T&V elpr\\j.e]v(av avp.(p(ovu>v crvvQeTov TO bia Ttacr&v, TO. be 15

4 Mb in marg. apxh Vb in marg. ir6<ra ydyri peAipSias iariv ins.Mb : om. R 5 apfiovia] vid. fuisse apuovlav M 6 fid\os H^ TOI ex '6 re Ma (b ?) 7 ^c om. M V B R S 9 ^O-T^ postSitHrni/tttrwy ponit H post itrrl una litt. eras., vid. fuisse £<TT\V M12 Sia<pwvuv ex Siatyopwv Ma 13 y ante T^ add. H 14 iravrbsom. et fieyedei ante Siatptivov ponit H 8po HopQvpiov iv T<f ei's'Ap/AO t/cct TOU IlToAe/iafou inrofivfipaTi in marg . H 16 irp&Ti)restituit Marquard, sed ante iKKeiatia ponit 18 (rv/ijSc' KE Si) HauT7j restituit Westphal TTJ om. B TOU B : avrov M V S R :"OUTOC H 19 /i.i\ovs restituit Westphal 20 iroAAi om. R2a oy i ne<Tmv B ^trrai H : eTvai rell. post etvai add. \eyofievMarquard S" restituit Marquard 23 truvreB^i/ H

'35

11.45 APISTOSENOT

ava fxeo-ov bidcpoova earai. Tavra fxev ovv

a irapa TSSV e^itpoo-Otv T!apeikrj^>ap.ev, irepl be TS>V XOITT&V

20 JII&V avTois bkopLareov. | TIp&Tov fjiev ovv XeKTeov, OTI irpos

T<3 bia, iraoS>v nav o~6fi(j)u>vov Trpoo-TiOe/xevov 8taorjj/j.a TO

yiyvofxevov e£ avT&v p.eye6os o~uyt.<$>(i>vov -noiel. Kal CO-TLV 5

35 Ibiov TOVTO TO irados TOV avixcfxavov | TOVTOV, Kal yap e\a,T-

TOVOS Trpoo~TedevTOS Kal iaov Kal ixeiCovos TO yiyv6\t,tvov IK

TTJS o~vv6eo-€(os o-v/xcpaivov yiyvtTai- TOIS be irpdrois

cj)civois oi (rvfj,l3aivei. TOVTO, ovre yap TO tcrov

30 av\T&v avvTeOev TO O\OV o~6)j.(f)(ovov 7roiei ovre TO e£ exa- 10

Tipov avr&v Ka\ TOV bia iracrutv o-vyKeijxevov, dAA' ael

bia<pcovrj(rei TO eK TS>V elpj]p.ivu>v avjx^xavuiv crvyKeifMevov-

4 6 ToVos 8' earlv u TO 81a mure | | TOV bta Tecro-dpoov ixelCov

TO be bia Tecrar&pcav bvo TOVCOV /cat fjixicreos. T&v be rod

TOVOV fiepwv /xeAaiSetrat TO ijfu<rv, a KaAeirat rjfXLTOviov, Kal 15

5 TO Tp'wov y.epos, | o KaXetrat bieais xPa>lJ-a'rLKV

Kal TO TerapTov, b KaAetTat b[eo~L$ evap\xovios

TOVTOV 8' lAarToy ovbev ji/eAa)8etTat bidcmjua. Aei be

io irp&Tov fiev TOVTO airb p.-q ayvo&v, OTI ] TTOAAOI i)bi\ 8177-

HapTov VTToXafiovTes r]y.as keyew OTI 6 TOVOS els {rpta rj) 20

Tecrarapa l<ra biaipovjj.evos /zeA&)8eu"ai. o~vve(ir] 8' avTois

TOVTO -napa TO JXT] KaTavoeiv OTI eTepov eo-Ti TO re kajieiv

15 Tpbrov \i.e\po% TOVOV Kal TO bieXovTa els rpCa TOVOV /neAuSeii'.

eireiTa arnkGis fiev ovdev virokap.^6,vop.ev etvai 8taoT7}jua

25

I hva fiecrav H Sti<j>ava elycu \ey4/iev. Tavra /xhv oiv irapaMarquard (S. e. \ey6fi.eva T. /i. 0. ir. Porphyrius) i<rrai H : elvairell. 3 /ih supra lin. add. Mb 4 Tip] rh S H B in marg.5 7roie?rai H 7 /icyeBovs post fietCovos add. H yiyvSfievovMarquard : \ey6/i(voi> codd. : yfvo/itvov Porphyrius 9 ov supraHn. add. Mb vdSos post TOVTO add. H n Sir Te84vTos postaiT&v add. Meibom &el SiaQurfio-ei] r) 5ia<p<ivT)<Tts M V B S : t)Sia<l><ivi)o-is R 13 TOV] Kal R 14 i/plo-eas B H 17 Kal. . . iXaxio-Tti om. H o R : om. rell. 20 {nroKaftivTes eximo\afi6vTa5 Mb Tpta % restituit Marquard 21 ctuTOir postTOVTO ponit H 24 eireiO' airA&s S

136

APM0NIKI2N 2TOIXEIX2N /3' II.46.

At Se T&V yev&v bia(popal A.a///3d]i>02>rat ev Terpa)(opb(a 20

ro tovru otoV eor t TO cmb \j.eo~t]s ecjS vir6.Tr]v, T&V ixev aKpwv

fxevovToov, T&V be p.io-u>v Kivovixivoov ore /lev an<pOT£pa>v

OTe be Oarepov. 'Ewet 8' avayKoiiov TOV Kivov\\j.evov (j>96y- 25

yov ev Toircp TLVI Kivelo-Oai, Xr\T!Teos hv eir) TOTTOS a>pio~fievos

eKwrepov T&V elprjfxivuiv <p96yyu>v. (f>a[veTai by OVVTOVUI-

Ta.Tr] \xkv eTvai At^avos fj TOVOV airb fxecrris aTre)(OV(Ta, |

Trotet 8' avTrj bidrovov yevos, f3apvT6.Tr] 8' fj birovov, yiyveTai 30

8' avTi) evapfj.6vis*<;' aitrr' elvai (pavepbv he TO^TCOV, OTL

10 roiucuds ecTiv 6 Trjs ki^avov TOTIOS. TO be •napvni.T'qs (jcal

v-naT-qs) 8wio-nj/Lta ZKCLTTOV pev OTL OVK hv yevoiTO 8tecrea)s | |

evapixoviov (pavepov, eireihrj irdvTUiv T&V fxeXwbovfievwv 4 7

eo~Ti b[eo-LS evapfiovios' or t be Kal TOVTO els TO

av£eTai, Karavo-qTeov. orav | yap em TTJV avTr)v 5

15 T&aai cupiKtavTai r\ r e \t\avbs aviefxivr) Kal fi irapviraTr]

eiriTeivofJievri, dp[£eo~0aL 80/cet eKarepas 6 TOTTOS. &CTT' etvai

(pavepov, (OTL OV p.ei^u>v Ste'tretos ekayld-rr]s eorlv 6 Trjs

•napvTraTrjs TOKOS. "H8rj 8^ TLves davixA^ovcri) TT&S ecrri

\i\avbs KLvrjdivTos evbs OTOV | 87]7rore T&V ixea~r]s Kal Xi^avov 10

20 bLao-Trnia.Tu>v 810 TC yap fxe'oTjs p.ev Kal Trapap.io-r)s ev earL

Stciarrj/^a /cat 7rdA.1i' av /xecrrjs r e /cat VTrdTrjs Kal T&V aXXcav

ocrot (p.rj} KL\vovvTaL T&V (f>66yyo>v, TO. be jxeo-ys Kal Xt^avoC 15

iroAAa OeTeov elvaL- Kpelrrov yap T&V (f>06yya>v

2 TOIV supra lin. add. Mb 3 5e supra lin. add. Mb: om. BSh n4<ruv H : /n4<rwv S^ rell. antyoTtpwv ex afuporepov (ut vid.) Mb4 iirel S' hv M : ^reiSai- V B S 5 ATjirreos] Te'os corr. Mb6 kKm-ipov Marquard : tKarepav codd. Sh] | (J |B 8 OSTTJ H :avTij M V B S : aur^ R jSopuTarr) Se T] Si in ras. Mb ^ om. S10 «al ujraTijs restituit Marquard 11 e\arroy Me in marg. B :iKaTTovi. M a V S B 6V1 om. R 12 TOUTCW post iricTwi' add. H15 iA.aiv~\ rd^iv H r) irapvirdTii] virapwdr)] B 16 dpl£etr6aiMarquard : &>pla@ai R : 6pla6ai in marg. B : SpteitrBcu rell. 6 om. H17 8TI . . . 8a.vnd(ov<ri restituit Studemund 19 mviBevros B :reBivTos Marquard 20 trapafieo-qs ex vapa/xecrov Me : trapa/ieaovV S : Trapa juecrov B 21 08 ex auAo! (Aol eras.) Mb Kal UITI£T»JIom. in marg. B 22 ;u}j restituit Meibom KiyoCrroi R : Kivovaiex Keivtniai (ut vid.) Mb : KIKOCO-I rell.

n11.47 API2T0HEN0T

TO, ovojjLaTa KiveTv /XTjxert KaXovvras Xi)(avovs ras Xoiiras,eireibav fj bfoovos (Xi\avbs) KXTJOTJ r) T&V hXXtav /xCa rjns

20 iror' ovv. betv yap | krepovs etvai (j)06yyovs roiis TO erepovfieyeOos opi^ovras' oxravTcos be beiv i\ei,v Kal TO. avn-crTpedjovTa. ra yap icra T&V jxeyed&v rcus aiirois 6v6)j.acn 5

25 TrepiXrj^TTTeov itvai. YIpos bi) ravra TOIOVTOL rives eke^drja-avkoyoi' Trp&rov /xev on TO a£wvv TOVS biadjepovras a\krj\a)v(f>66yyovs Xbwv peyeOos e\eiv Stacrr^/xaros p.eya TL Kivelv

30 ecrriv 6pS>ixev yap | on vqrr] fj.ev Kal /xecrr] irapavqrrjs KalXiX.av°v bia<pepei Kara rqv bvvajxiv Kal TTCLXIV av irapavqrr] 10re Kal kixavbs rpiTrjs re Kal TTapvTrarrjs, oxravTcus be Kal

48 oSroi Trapaneo-qs re /cat XITTAT^S—Kal bia ravTr/v 11 TT/V alriavf, tbia Kelrat ovofxara eK&arois avT&v—•, Stdorrj^a 8' avrois

}, naa-Lv v-noKeirai. ev, TO bia irevre, ScrO' on fj.lv ovx otov r '/ 5 ael rrj T&V cpdoyyaiv bia\<popq TTJV T5>V biao-T-qixanK&v fieye- 15\ 6Q>v biacpopav aKoXovdeiv (pavepov. "On b' oibe rovvavriovI aKokovdeXv dereov, Karavorjaeiev av r i s ex T&V pr\Qr)(ro\t.ivuyv.

10 Ylp&Tov fxkv ovv el Kal Kad' e/ca|crrjji' av£rjo-iv re /cat eX&r-; TUHTIV TQ>V -nepl TO TTVKVOV yiyvojxeva>v £8ia (flTrjcrofj.ev ovo-

j ^iara, bjjXov OTL aireCpoov 6vop.ar<x>v ber)o-6p.eda, eireibriTTep 6 20

49- 7 TVS h-iXav°v r ° i J T o y *ls cnreipovs reixverai rofids. \\'&$ aXrjd&iyap TIVL av r t s TTpoa0eiTo TS>V ap.(pi<r(ir}TovvTtov -nepl r a s T&V

i 10 yev&v I yjpoas; ov yap br\ Trpbs TTJV avTTjv biaipeo-w /3Xe-

m. >t I Tct add. Mb a ^] ^ codd.: % ri Marquard Sirrovos RKiXavbs addidi: OVTCO Marquard 5JT« renovat Mb accent, add. Me :TJTIS cum ras. supra Hn. V 3 SriV Marquard : StT codd. rb om. S4 5e? H 5 yap Iffa Studemund: irdpicra codd. : 8' Taa Marquard6 rotovTol] OVTOI H iXixBrjaav^ e in ras. Me (?) 9 impavl)Ti)sex Trapavfirriv Mb io 5' post ira\iv add. H II vapvirdrris]iirirns R la vTdrrts] v4)rr\s H 13 avrwv supra lin. add.corr. B 14 iv, rb eonieci: iv r<ji codd. 15 StacrTri/idruv H17 aKo\ov8e?v Sereov eonieci: a/foA.ouflrjTc'ov codd. 18 el Kal] KO!om. H ihaTToatv S 19 fyiThaanev M V S B 20 5eri<r6fi,eda]i\ai in ras. Vb 21 rituierai post TO/I&S ponit H &sa\7i6Sis . • . Buupe<re<oi> legg. in codd. post Sia/nevety in p. 140, 1. 1 :ordinem mutavi 22 irpoa9eiro ex icpoa8ol.ro Me: vpoaBoiro V B Sa/i.<l>i<rfi7]ToiTui> (V suprascr.) B

138

APMONIK&N STOIXEmN 0 II.48

irovres irdvres ovre TO yjiG>\xa ovre TT\V apfioviav

cocrre TL jxaXXov TTJV biTOVov \i)(avbv \SKT4OV TJ TTJU

crvvTovwTepav; ap|ju.ozua jxev yap elvai rrj aio-ftfo-ei /car' 15

afj.<pOTfpas r a s Siaipecrets </>aiz>erat, TO. be ix.eyeQrj T&V biacrTr]-

5 fidrav bijkov OTL ov TavTa sv eKaripq T&V biaipeaeaw. |

eneura iretpco/xezxH Traparripeiv TO T "LVOV KCLL TO OVKTOV airo- 4 8 . 15

/3a\ovfJL€v TTJV TOV ojxoiov r e KOX avofioiov bi6.yv<a(Tt.v, toirre

ixrjbe TTVKVOV KaXeiv e£co evbs neyiOovs, brj\ov b' OTL (XTJS'

apixoviav /J.rjbe xp^l^a> TOiry | yap TWI Ka\ Tavra 8twptcrrat. 20

io ArjXov b' OTi ovbev ToijTonv eo r t irpos TTJV TTJS alo~dr)o-ecm

<f>avTao-iav eKeivq jxiv yap ds oixoioT-qTa evos TLVOS elbovs

fiXe-novaa TO r e XP^a \ ^e 'y e t K a ' TVV apij.ov(av dXX' 25

OVK eiy ei>dy TIVOS 8ta<rr7j/xaros /JLeyeOos, \eya> be TTVKVOV

}xev elbos rt^eicra ecos hv TO. bvo StaarTj/^ara roS evos

15 eAdrrto TOTTOV KaTeyrj—e^aiveTai, yap ev -navi TOLS | TTVK- 30

VOLS irvKvov TWOS (pcovr] KaCirep avCaoov air&v OVTOOV—

XP&IMTOS be etSoy ecos hv TO poifxaTiKov ?J0os e/x(^aforjrat.

Iblav yap br] Kivqa-iv tKaorov T&V yev&v KLveirai irpbs T-qv

ato-6r)(TLv ov 11 /xta ^piifxevov TeTpaxppbov Statpecret aXKa 4 9

20 TroWais. cocrr' etvai (pavepov, OTL KLVovfieviav TG>V fieyeOSiv

crv^aiveL (jxeveLv) TO yevos, ov yap opotoos KLvevrai T&V

\xe\ye65>v KLVov^evcov /xex/" rtuo's, aWa. 8iaju.eVef TOVTOV be 5

2 post Scrre add. oi irdvv paSiov (TvpiSeTv Marquard S'ITOVOV conieci :SI&TOVOV codd. ^] p H 3 ap/xovias sed as postea corr. B4 /J.ey48r] post StaffTtifidrwy ponit H 5 ravra M V B S 8 8TJ\OV5' 8TI om. et jujjO' pro fiyS' scrib. Marquard 8' S : om. rell. n yapom. V S la jSAeirovira in ras. Ma 13 ou/c e»j evbs renov.Mb cis om. B eiVlv &>s R TruKyoC/tei/ B 14 eTSos inmarg. Mb : eiSovs M V S post eiSos add. Srav T\ (pay)) <pavrj ra Sta-(TT'/ifiara OVTU Marquard TcfleTtro M V S B ems conieci : &s codd.(Sta)(TT'iiiJ.ara TOS erat in ras. deinde renov. Mb 15 KaT*xflv

H eV Tra.cn TOTS renov. Mb 16 (icai)Trep aviaaiv renov. Mb17 Sh eitios ecus conieci : 5£ fj 8ie<recos R : Set Sieireas rell. {Sieareas inras. Mb) av rb XP"> ' n r a s - Mb ijj.<palvriTai Marquard : 4p.<palveTaicodd. 18 ISia S Si) icivri<riv] Seixwcriv R (Ktv)eiTai irpbs ri]vin ras. Mb 19 /ua] ^ in ras. Mb Siatpeaei ex Sia/peiriv Mbai /leVeic addidi : rairTby ehat Marquard ov in ras. Mb aa 81a-

V renov. Mb139

11.49 APISTOHENOT

eJ/cos Kat r a s T&V (pOoyyonv bwd/xeis biapeveiv. TO

' 20 yap elbos TOV Terpa)(opbov ra t> | ro , St' o-nep Kal TOVS T&V

|; Staor?7/xara)i> opovs dvayKOiov eiireiv TOVS OVTOVS. KadoXov

ji, 8 ' eiireiv, ecos &v fievp r a T&V irepie^ovTcov oVojuara Kal

)| 25 XeyqTat OVT&V fj /j.ev o£vrepa jue'trrj viraTt] 8 ' ^ | j3apwepa, 5

.'• 8tajitei»€t Kat TO. T&V •nepie\op,ivu>v ovofxara Kal pij^jjcrerat

)'• ' avT&v f) fjiev 6£vTepa Xt)(avbs r) be /3apurepa irapvira.Tr], del

I yap TOVS ju.era£i> jj.io-r\s r e Kat iJmzTTjs Xiyavov r e /cat Trap-

I; . 30 viraTr/v (jj) aL<r6r\\<ns Ti6r\o-iv. To 8' afciovv rj TO. taa bia-

i arr/fjiMTa ro ts ot/rois ovofxaaiv bpi^eaOai rj r a avio-a erepots 10

I1 i*.dxeo-0ai ro t s (paivopevois eort" ro [re] yap •uTrdrTjs /cat

i irapvirdTr/s T& irapvirdrris [irX.eovd.Kis Xcrov fxeXcfbeiTai rj]

0 50 (KOI) Xwavov 11 ueAcoSetrat wore Itrov irore Sviaov on 8'

)j OHK e2 /8e^6 ra i 8KO biao~Tt]yi.aTu>v k£r}s K€i[ieva>v TOXS avTois

/,;. 5 ov6fj.ao-iv eKaTepov air&v irepieyeo-Oai (pavepov, | eiirep ^ 1 5

i] fiiXXoi 6 peaos bvo e£eiv ovofiaTa. ArjXov be Kal e m T&V

jj avCo-uiv TO liToirov ov yap bwarbv biaixevovTos TOV erepov

:' T&V ovofidTOiv TO erepov KiveiaOai, irpbs aXXrjXa yap XeXe-

i 10 Kraf I [aScnrep yap 6 r e r ap ros dwo r ^ s /xearj? virdTr] irpbs

Aeyerat, OVTCDS 6 eyojxevos TTJS y.eo~qs Xiyavbs irpbs 20

Ae'yerat.] IIpbs pev {pvv TavTrjv) TT)V biairopiav

Too-avra elprjcrdw. |

s y&p conieci: 8' codd. sTSos ex oI8os Ma 4 yueVei S H5 ^.tyTjTat] yivt\Tai H vir6.Tt\ 8* 7] fiapvTtpa] inriiry) in ras. Mb 8esupra lin. add. Me T\ om. M 8 '^om. V S B ^ Se 0apvrepa(omissis umtrij 8e) R, in marg. B 6 SiafieveT Marquard : Sta/ityeicodd. 7 Aix a ^ s Marquard : fiiat\ codd. •RapvTt&n\\ inrdrTjsed Trap ante u eras. M : iird-nj rell. 9 T\ restituit Marquard atoBi)-ffiv S 10 TOTS ante eTepois add. H 11 /to^etrfiai] ffvj>ex*tr8&1 Reori ante roTr tpaivo/xepots ponit H re seclusi 12 TrAFoyiiKis. . . 4} del. Meibom 13 /cal restituit Meibom TTOTE ^eAaiSeiToi(J3 supra TOTE, et a supra /iEAcoSeiVai scr.) Ma TOTE piy laov irore Seixtaou H 14 OUTOIS supra lin. add. corr. B 17 TO posteaadd. Ma (ut vid.) 18 \eyerai H 19 faenrep . . . Ki^avis irphsfUffriv Aeyercu seclusit Marquard imdrqs H : (mh-q sed v post t) eras.M: {mdrriv V B sed iirdrri in marg. B 20 AeyeTeu in ras. Mb: deinde4 litt. eras, quarum extremae TOI fuisse videntur ante irphs fiiariv add.(col Me 21 0S1/ TOIJTIJV restituit Marquard 22 TOO-OCTO] TOUTO H

140

APMONIK&N 2TOIXEIX2N /3' II.50

UVKVOV be \eyeo~9ai fJ-expi TOVTOV eats av ev Terpaxppba 15

bia T€<rcrapa>v o-vp.(poovovvTa)v T&V aKpoov ra bvo bvao-rrjfiaTa

avvTeOivra rov evbs eAcirrco TOVOV Kare^r). Terpayppbov

be elcri bi\aipecreis e^aiperoC re Kal yvatpifwi aSra t at elo~iv 20

5 els yva>pt.na biaipov^evai ^.eyeOrf 8iaor?7/xara)i>. M i a \iev ofliv

(jovroiv) TS>V biaipeo-edv ecrriv evap\j.6vios ev 77 TO p:ev TTVKVOV

fjfjuToviov ecrTi TO | 8e XOITTOV biTovov. rpels 8e )(poifj.aTiKal, 25 »

17 r e rod jxaXaKov xP<*>lxaT0S K a ' V T°v fiiuo\(ov nal TJ rov

roviaiov \xa\aKov fiev ovv xpco/naros ecrn biatpecris ev r/ TO

IO fj,ev iivKvbv €K bvo xpod\iAariK.S>v bie<recov eAax/oraw a~uy- 30.

Keaai, TO be \oiirbv bvo fierpois ixerpeiraL, fiiUTOvta fiev

rpis, xp<"Ma r t K^ Se Stecret tiira£, &o-re iierpeta-dai rpicrlv

rjfXLrov(ois Kal rovov r p i r u jxepei aTra^1 eari be raiv xpcop.a-

TIK&V TTVKVWV eX&xioTov KOI \i)(avbs atfrj] /3apv7"drrj rod 11

15 yevovs TOVTOV. rjp.ioX.iov be XP^M01"05 biaipeffls eo-riv ev 51

rf TO r e ITUKVOV r)ixwki6v eo r t rod [r'] evap/xoviov Kal TG>V

(eKarepa) eicarepas T&V evappovCwv o n 8' earl |

TO f/pLLoXiov iwKvbv TOV ixakaKOV, pabiov o~vvibeTv, 5

rb ijiev yap evapp:oviov bieo-ecos \eiirei TOVOS etvai TO be

20 xpayfiaTiKTJs. roviaiov be \pd>p^aTos biatpeo~is eo~Tiv ev jf

TO jxev TTVKvbv e£ r)ni\Toviu>v bvo cruyKeircu TO be Xonrbv 10

eoTLV. Me^pi p.ev ovv ravrrjs TTJS biaipeo-eois

1 &>/ om. R 3 Karext e x Karexel Mb : K x pxpK.T.A.] in marg."Opa TlToAefiaiov iii'Ap/j.ovtKo?s H 4 ante i^alperoiuna litt. eras. M oV! «ol R 5 el yvdpifid 4<rri rei Sicupoi/tevafieysBrj TUP SiaffTTifiaTup H Siaipovfieva M V S 6 Toiniav addidiTwvom.H Staipeirtav post eVri ponit H irvKvbv in ras. Mb: fwcphv R7 5/TOJW] post 1 litt. a eras. M 8 r) rod rovialov] r\ TOV supra lin.add. Mb: TI/IITOVIOV R 9 oiv om. R 10 /col ante HUtrewvadd. R 12 Tp«s H 8e add. Me : om. V B S iiiaei] ti inras. Mb : SieVis Va aira| (SScrre iierpiiadtu om. M V B S H S(rre. . . aira£ om. R rpiffiv TjfiiTovlois Kal T6VOV rpiroa tepet in marg. Mb14 irvKvtav R : irvKvbv rell. \txctvbs~\ os in ras. Mb 16 T*del. Marquard ivap/Mviov] in add. Mb 17 liearepa restituitMarquard (lac. 2 syllab. R) 19 T<(J>OS post efyoj ponit H 20 Sio(-

1 vvHvdpeo-is~\ alp add. Mx in marg. Mb (?) Vc < ivap/ioy. fiakaK. ri/uo\.

( T i) #141

II. 5i APISTOSENOT

djucpo'repot Ktvowrat ol <p66yyoi, p.eTa raCra 8' T) p.ev irap-

j 15 vir6.Tr] pevei, bieXrjXvde yap TOV avTrjs TOTTOV, r) be \ Xiyavos

• Kiveirai bieo-iv evap\i6viov Kal y tyvera t TO Xvyavov Kal

/) viraT-qs Sidcrrrj/xa Xcrov T& Xi)(avov Kal p.eo-r)s, coore jUTjKe'ri

jj yiyveaOai TTVKVOV ev ravrrj TTJ Statpecret. o-vpiftaCvei 8' a/xa 5

•*/ 20 7rai5eo"0ai TO im^Kvbv o~vvio-Ta.ii.evov ev TTJ T&V rerpaxopSa)!)

jj 8tatpecret Kal apxecrOai yiyvo^evov TO bi&Tovov yevos. Wicrl

be biuo biaTovov biaipiaeis, r) r e TOV p-aXaKov Kal r) TOV

25 (TVVTOVOV. paXaKov p-ev ovv ecrrt Starovou 8tat|pecrtj ev fj

TO fxev vit6.Tr)s Kat irapviraTrjs r)p.LTovlaiov eo r t , TO be trap- 10

Mi DTrdrrjs Ka t Xiyavov Tpi&v biA(re(x>v evapp.ovt(ov, r o be ,

/)! Kal jxe(rr\s irivTe biecrewv (TVVTOVOV be ev f\ TO p.ev

fj 30 Kat ira\pim6.Tr]S fjixiToviaiov, T&V be Xon&v Toviaiov eKarepov

J\ eo-Tiv. Kiyavol pkv ovv el(rlv e£, \x(a evapp.6vws, Tpeis

j'j; 52 xPC 0M a r t ' c a ' K a^ ^^° Sidrovot, oaai irep at | | T&V rerpa^dpScoi; 15

)'| biaipeo~eis, irapuTrdrat be bvo eXaTTOvs, TTJ yap r\p.iToviaia.(-} '• yjp(j>p.e6a irpos re r a s 8tarwous Kat irpoy TT)V TOV Toviaiov

h1.- 5 xpco/xaros bialpe\o-w rerrdptoy 8' ova-&v irapviraT&v r) p.ev

u evapp-ovios t8ta ecrrt TTJS apfiovias, at be rpeis Koival TOV

j ' re SiarovoD Kat TOV xpco/j,aros. Tcoy 8 ev rto Terpa)(opb<p 20

j ':. 10 8tacrrrj]u,(ira)i; ro /xey wdrr j s | Kat TrapDirdrjjs rw irapviraTrjs

Kat Xtx.ai>oi; ?j tcroi' /xeXuSeirat ?) eXarrov, \xel(fiv 8' ovSe-

1 wore, ort fxev oSi> ^croy {(pavepbv eK TTJS evapp.ov(ov 8tat-

/, , pe'trecos Kai T&V \pcap.aTiK&v, ort 8' eXarrov eK pev T&V

I biaTovwv) cpavepov, IK 8e T&V \p(op.aTLK&v OVTCDS av TLS 25

{ '. 15 KaraiiOTjcreiei;, et TrapuTrdrr/i; | p.ev Ad/3ot r ^ TO

2 auTrjs Marquard: aiiTijs codd. 8 Siaipetris SianicouH 9 o?>» om. R 10 ante yfiUToviaiov 5 fere litt. eras,(vid. x p ^ o fuisse) M l(rn om. R ia KO.\ in marg. Me: om.rell. 13 TOVLOLOV ex TjfiiTovtalaiv Ma ToviaT(ii' post eKarepovponit H 14 e£. . . rhrapes in marg. Mb: om. R 15 tiaaiex Hffa Ma 16 iropuTrciToi S rtrrapes seclusit Marquard irapu-iraTijs B : iropuiro (T ' suprascr.) S 5ue?v M: Suoii' V S 19 JS(oH : ISios rell. 21 T $ iropwriT7)y om. R 23 tpavepov . . .Siorrfyav restituit Westphal

APM0NIK12N 2TOIXEIi2N /3' II,52

yj)d>\xarosy Xiyavhv be Trjv (JOV) Toviatov Kal yap al Toiavrai

biaipeo-eis T&V ITVKV&V ejxp.eke'is (paivovrai. TO 8' eK/xekes

y&voiT av eK Trjs evavTias kfjtyeons, et | TIS TTapvTrdrrjv fiev 20,

k&fioi Trjv rjiiLTovtaiav, kiyavbv be Trjv TOV rjixiokiov XP^~

5 ixaTos, rj TrapvTTaTrfv pev Trjv TOV fjiuokiov, kixavov be Trjv

TOV ixakaKov xpcojuaros1 avapfxoo-Toi yap | (paCvovTai al 25

ToiavTai biaipeo-eis. T o 8e TrapviraT-qs Kal \i\avov (rfi

XiXavov) Kal fiea-qs Kal iaov /oteXwSetTat (cat avicov afupo-

Tepms' icrov /J.ev ev T 5 crvvTovcoTepco biarovca, eka.T\Tov 8' 30

10 ev Ttao-i TOIS XOLTTO'LS, ixei(ov 8' OTOV (TLS) kuxav& /xev Trj

o-WTovcoTCLTri T&V biaTovoiv, TrapuTTCLTrj be TSIV fiapvTepiav

Tivl Trjs rjiXLTOviaLas \pr]o-r]Tai.

M e r a be Tavra beiKTeov Trepl TOV e£fjs

irp&Tov avTov TOV |[ TpoiTov Ka6' ov a^iwTeov TO e£i}s acp- 5 3

15 opi^etv. 'ATTX.U>S fJ.ev ovv elirelv Kara Trjv TOV pekovs (pvo-iv

(j]Tr]Teov TO e ^ s Kal oi)( £is ol els Tr)v KaTairvKva>\o~iv /3A.e- 5

TTOVTCS elddaaiv cmobibovai TO crwexes. eKetvoi ixev yap

okiycopeiv cpaivovTai Trjs TOV fxekovs ayutyfjs' (pavepbv 8' e/c:

TOV TTXJIOOVS TG>V e£fjs riOefievcav bieo~ea)V, [ov yap bia

20 ToaovToov I bvvrjOeCrj TIS &V] p.e\pi yap Tpi&v fj (pwvr) bvvaTai 10

o~vvelpeiv &(TT etvai (pavepbv OTI TO e£rjs OVT' ev ro ts

OVT ev rots d^tcots OVT1 ev (rots) tcrots ael

v, akk' a.Kokov\6r]Teov Trj <pvo~ei. Tbv 15

1 TO5 restituit Marquard 2 e'lU/teAeTs] ^K/j.e\e7s H / ]li<ne\t?s B : 1/j.fieAes (K supra prius /i scr.) H 4 ri/i.io\lov]fi/iio\lov M sed post Tiixi una litt. eras., \i in ras. in qua rovial fuissevid. Me : rj^iToviaiov V S B H 5 ^ . . . xpcfrfiaros om. H 8£add. Me Vb 7 T$ \ixavov restituit Meibom 8 yueApScrraipost &[upoT€pais ponit H 10 TIS addidi II fiapvTfpuv npY\(iapvTovwv Tra.pvTra.Tti Si T&V (iapvTivtav TIV\ B : fjapurepav in marg. B1 2 XP1^0'77Tai e x XP^ f f e T c t I ^ a I 4 wpoplfcirOai H 16 Kal ovxSis ol EI'S Tb in ras. Mb 17 $ib~6vai H 19 oh . . . tai seclusiut glossema : ov yap supra lin. add. Mb 20 ta> om, codd. praeterR rpiuv\ Tivuv B 21 o"vveipetv ex ffvyJipetv Ma (?) O&T' 4V -ex oi/Te Mb 22 rots restituit Marquard 23 iutoAovdeoy H

M3

n.53 API2T0EEN0T

fxev ovv aKpijifj Xoyov TOV e£fjs ovTroo pabiov airobovvai, eoos

av at o-vvOeaeis raw 8taor?j^(ira)i; a-noboOGxnv OTI 8' ecrri

30 r i e,£ijs ical r £ iravTeX&s aireCpui (pavepbv ysvoiT* civ | 8ia

Totatr8^ ru>os eTraycuyrjs. Hidavbv yap TO fjLrjbev elvai

bt6.0Tqfj,a b neXabovvres els aiteipa Tijj.vojj.ev, a.XX' eu>ai 5

riva fieyurTOV apidfibv els bv SiaipeTrat TG>V biao~Tr}n,a.Tu>v

25 eKaaTov VTTO | 7"?js jueAcoSias1. E i 8e TOVTO d^ap.ev ijroi

•niQavbv r\ KCLL avaytcaiov etvai, brj\ov OTI 01 {TOV} TTpoeiprj-

Hevov apiOfiov fJ.ept] irepiexpvTes djdoyyoi e£fjs aXKriXoiv

expvTai. boKovo~i 8' elvai (TOLOVTCOV) TO>V (j>66yycov nal | 10

30 ovToi oh Tvyxa.voiJ.ev en iraXaiov xpa>ij.evoi olov fj vqnfj

(/cat) fj TTapavr/Tr] nal 01 TOVTOLS avvexe'is.

'Fi\6fj.evov 8' hv eXrj TO a<popl,crai TO irp&rov KO.\ avayKai-

5 4 OTorov T5>V o-vvTeiv6v\\T(ov -npbs ray e ^ e A e i ? o-vv6eo~ei,s TG>V

biaffTr]jx6.TUiv. 'Ev iravrl be yevei airb -iravTos (pOoyyov bia 15

5 TO>V e^qs TO p.e\os ayofj-evov Kai eirl TO fiapv Kal eiii TO | O£V

•r) T6V TiTapTOv T&V e$fjs bia Te<r<rapcov rj TOV t:k\x.TSTOv 8ta

Trevre o~6jx<paivov Xa/^/3av^ra), <S 8' av fj/qberepa TOVTWV cruju.-

/3awjj, eKixeXr/s lorco OVTOS irpbs airavTas ols o~vp.fiefir)Kev |

10 a.o-vp.<p<i)V(o elvai Kara TOVS elpr\jj.evovs apiOp-ovs. Oi bet 20

8' ayvoeiv, OTI OVK eariv avrapKes TO elprjfxevov irpbs TO

eju/xeA.<3s o~vyKelo~6ai r a o-vo-Tr\}j.aTa !K TGIV biao~Trj)j,&T(i>v'

15 oibev yap KonXijei o-vjj,<pa>\vovvT<i>v T&V (pOoyyonv Kara, TOVS

dprj/J-evovs apiO/iovs in^eXus TO. (rD(rr?j/j,ara avveo-T&vai,

3 T$ add. Mb : om. R <pavepbv~\ avepov S 5 Tefivcofiev H6 bv] i S 8 irv8avbv H TOC restituit Marquard irpoeiprnu.evovapiBfiov Marquard : irpotipniiivoi (Trpoeipri in ras. Mb) apiB/iol M V S B :(oT)ye elprindvoi api6/io\ R 10 TOWVTUV restituit Marquard 11 riv{\Tti Westphal : ^ H H : ^ rell. 12 Kal add. Marquard ^irafav4)Tr] H (coni. Marquard): rjj irapav^Tri rell. 01 TOUTOIS ffuyex^sR : ii rovrois avvt-)(j\s rell. 16 T£I/] rby H 17 T2U> . . . rbv\rb • . . TO H TW Marquard: rip codd. 18 trv/upovov SActjuflafETco conieci: Aa/xflaveTai codd. /iriBerepov Meibom <ru t-6a(yci H 19 &c/«A^s (^K in ras.) Mb: 4/i/ie\^s in marg. B OSTUSH ofj H : & aits rell. 20 havn<pd>voi.s H 5ei H : om. rell.22 (ruyKerirflai] KweTirSai R 23 KWAVOI S avp.ip(ivav Avrwv H34 £/c/ieAcDs(&inras.) Mb: ^jueAoisR o'wecTTai'ai H : awiarivairell.

144

APM0NIKI2N ST0IXEI12N ]$'\ \';':\'': ;A%i

aXXa TOVTOV jir) vir&p)(0VT0$ oibev I n yiyverai T&V Xom&v

o<peXos. Oereov ovv TOVTO irp&rov els [ ap)(T]s T&£IV ov 20

p.r) irn&pypvTos avaipeirai TO r}pfj.o<rixevov. "Opoiov 8' ecrrt

TOVTV Tpo-nov riva KCLI (JO) irepl ras TS>V TfTpa\6ph<M> irpbs

5 aAAjjAa Bevels' Set yap TOIS TOV avrov avoTrijiaros | rerpa- 25

Xophois eo-0/j.ivois bvoiv Qarepov vitctpxeiv, r) yap ovixdpuivelv

TTpbs a\Xr]\a, aicrd' ^Kacrov tKacrTO) o~inj.<pu>vov etvai KCLO'

rjv br/iroTe r&v o-vp.(pu)ViS>v, (rj) TT/JOJ TO OVTO (rv/xcpcove'LV ju.?)

eiii TOV I avTov TOTIOV avveyj\ ovra w av^cnvel eK&Tepov 30

10 avrcav. "Ean 8' ovbe TOVTO avTapnes TTpos TO elvai TOV

avrov o~vcTTrJiJ.aTos TO. r e r p ^ o p S a , TrpocrbelTai yip TIVCOV KOI

eTeputv iiepi <av ev TOIS eirevra pr\ \ | Grjo-erai, a\X' &vev ye 55

TOVTOV navTa ylyveTai ra Xoiira

' E i m be TS>V biaaTrjixaTLK&v jxeyeOSiv TO. fxev T&V o-vfj.<j)(a-

15 vcov T]TOL oXois OVK I ex.€tv Soxet TOTTOV aXJC evl fxeye6ei 5

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TTOXXG) rJTTOv TOVTO veirovQe Kal bia TavTas ras ahlas TTOXV

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77 ro ts T&V biacpdvoov a.KpifieoTa.Tr] 8' hv etr] bia<p<avov

20 8tao-TT7/xaroy Xij\jns r) bia avp.(paivias. 'Eav fiev ovv TT/JOCT-

vaxOfj irpbs T& boOivTi <p66yya> Xajielv eirl TO fiapv TO |

biacpwvov olov bfoovov rj aXXo TL T&V bvvaT&v Xi](p9rjvai 15

8ta o-vjupaivias, eiri TO 6£V airb TOV bodevTos cpOoyyov Xrj-

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MACRAN L 145

tei1..

,^5, : • : ; , ; APISTOEENOT

irreov TO bia Teo-cdpcov; e ir ' eirl TO /3apv TO bia irivre, etra

20 irdkiv eirl TO | d£i) TO bia Teo-o-dpoov, e ir ' eirl TO fiapv TO

bia irevre. Kal owrtos Icrrai TO birovov airb TOV kr]<p8evTos

(pOoyyov elkrjfxpivov rb eirl TO /3apv. eav 8' eirl Tovvavriov

25 TT/jooTax^r) kafietv TO btd<pw\vovj evavriws irofqreov rr\v TS>V 5

krj^jnvi TCyverat be Kal eav airb o-vpcpaivov

TO bid<p(tivov a<paipe6ii hia oi)p.(pa)vias Kal TO

30 konrbv bia o~vp.<pcov(as elkrujLfxevov a<paipeto-9a> | yap TO

btTOVov airb TOV bia Tevcrdpwv (bia) o-vp\<poovtas' bfjkov br)

on ol TT)V virepoyj]v irepie\ovTes 77 TO bta feo-crdpwv virepey^et 10

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5 6 jJievoi' virdp\\)(,ovo-i p.ev yap ol TOV bia reo-crdpcov opoi O-6JX-

(fxovoi' curb be TOV o^vrepov avT&v kapfidveTai (f>66yyos

o-vij.(p(ovos eirl TO 6£V bia Teo-o-dp<nv, curb be TOV k>i\<p6evTos

5 erepos enl TO fiapv bia irevTej- (e t ra irdktv eirl fb d^ii bia 15

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10 (TIJV) virepo^riv 6pi£6vr<ovi war' elvai <pa\vepov, oTt, eav dirb

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TO konrbv bta ovp.(pa>vias elkr\ji.fxivovi 20

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15 bio Tovaav Kal fjp:(\o-eos, Kara rovbe TOV rpoirov e^eTaaeiev

&v Tis a.Kpij3io-TaTa' elkrjcpdai yap TO bia reo-o-dpcav /cat irpbs

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20 8rj OTi dvayKatov r ay | virepoxas t<ras etvat, eireibtfirep /cat 25

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146

APM0NIKI2N 2TOIXEIX2N 0 JI.56

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5 on irpbs enaTepa r<ov opifflvToiv TO yeyovbs 0-vorqiJ.a bvo

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10 bfj\ov on OVK etrrai TO bia Tecro-dpwv t>vo TO\\V<X>V ml ^/xtcreos, Si

ei be o-vjj.<puivrj<rovcn 8ta -nevre [recrcrapa,] bijX-ov OTI bvo

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oTjjxcpcovov r S TO fiapioTepov biTovov eirl TO o£i> bpifyvri,

15 TOV 8' o^vraTov TS>V ei\rip^j.ivuiv (p86yya>v bia irevTe O-VJX-

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L 2 147

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5 8 (jiOoyycav fiei^co [lev 11 ffvp-^xaviav rrjs bia Teo-adpav

be TTJS 8 ta iraa&v, avaytcaiov OVTOVS bia itevre o-u

TOVTO yip e o n fwvov fUyeOos avficfKovov f«ra£i i TOV bia | 10

5 Tfo-o-dpav Kal TOV bia

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148

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2TOIXEIHN I*

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5 <rxJ]iAa TOVOS TJ dva fiicrov. " O r t 8' dz>ay/catoi> trepov irorepov

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15 an<p6repa TOUT' eor tv k£fjs rd r e <ruvr}ii.yiiva Kal TO. 8ie-

£evyfjieva. Upbs 8?) ravra TOIOVTOC Tares ekeyovro \6yoL'

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2-4 Hrav . . . Srav Suo"] erat '6 rt, r tw supra lin. add., re corr. in Svo,et TC inscr., reliqua in marg. Me : om. V B, R (sed 'postea alieno locointerponuntur' v. Herwerden) 2-5 2re pro Srav Sio leg., e£rjs. . . ffXVf1^ o m . S 5 irirepov om. H 7 Teraproi B : 8 rell.tru/Mpdvav &vres H 9 S« Meibom : rl codd. 12 T(£5e postc£rjs add. H 14 piyor Me (supra lin.), R H : ipov M B S T/Jiixov]tpiv e eorr. V Karci om. H S1 c! Marquard : 8^ codd.16 8J) H ; 5i rell. TOWVT&V B 17 ovffTJj/iBTa exMb

149

III. 59 APISTOHENOT

15 el<rlv 7] I eiraXXaTTOvcrtv. TOV 8' If/ys bvo Tpoiroi el(r(, Kal

6 /xev (/ca0' OV TZ TOV o^vrepov atxTTrifiaTOS j3apvrep(a op<o

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8' erepos, Ka6' bv 6 TOV d£vripov o-varrmaTos fiapijTepos opos

e£rjs icrTL T 5 TOV /Hapvreppv oTJOTTj/xarps d^vrepo) opa>. Kara 5

20 JAW OVV TOV I TTpOTipOV T&V TpOTTWV TOTtOV TI TWOS KOWWVfl

TCL TG>V e^rjs TeTpa)(op§(tiv crucmj/xara Kal O\J.OI6, ICTTIV ef

avdyKrjs, Kara 8e TOV erepov Ke^ttSptorat air' aWr/Xoov Kal

25 fyioia 8 w a r a i yi\yveo-6ai TO. eihr) TG>V TtTpayppbtov TOVTO be

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opoia Taiavra av^aivnv e£rjs aXXriXaiv etvat

30 cSv fjTot TOVOS ava | iiiq-ov tarlv rj 01 Spot tiraWaTTOvo-iv.

tSore TO. effjs rerpti^opSa Sfioia ovra r) avvquniva avayKaiov

elvat, rj SieCevyiiiva. <$>afiev 8e beiv TS>V k£qs Terpa)(opba>v

6 0 fjToi airkfas jfirjSei/ eT||i»ai d m jxecrov TtTpayophov r) y.r) 15

avofAoiov. TG>V iiev pvv 6\xoiuiv /car' e?8os T€Tpa\opha>v ov

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5 iJ.ev I 1 ^ 9 8' oibev Tidea-Qai bvvaTov ava pea-ov TtTphyppbov.

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10 'AtruvOeTov 8' eurl S^dcrrTj/iia r 6 •UTTO T&V efrjs

irepLexpixevov^ el yap e£rjs ot irepiexovTes, oibelp eKKipTtavei,

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15 pr)o~ei, b be fj.r] biaipecriv ej^et ovbe avvOeo'i.v | e£ei' TTOLV yap 25

I cla\v in ras. Ma : om. V B S iiraWaTTovatv ex sTreXarTOvaw Mb(ut vid.) 2 «afl'.. . Hpos restituit Meibom 3 o^irepov B4 ofvrepou om. B 6 rp6in>y Marquard : 6pG>v B : 'ipau rell.KoivwvoviXiv H 7 Sfjioiii Meibom : a^/zom codd. 4ffTiv om. H11 ante Sfioia a litt. eras. M TOIOSTO Marquard: TaSnt codd.trvuPaivei B 13 •()] IJTOI H 15 1) yttj) Meibom : <•( /t^ e{ ^ B :el fi.ii rell. 16 &v6/ioiov Meibom : fytoiop codd. 17 riBetrBai Hfa/oitnmi Meibom : S^oiov codd. 17 T&V 5' . . . rerp&xopBovom. R 18 rWeo-flai ex riBerai Me : riderat rell. 19 S£] SJ) H2a Staa'T'finara R 25 5iatpe<ni> ex Siaipriatv vel vice versa M

150

APM0NIKJ2N 2TO1XEII2N / III.6o

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r post KOX ras. M 2 aSiaiperov V S Si Marquard : S^ codd.4 irdnrore H atrivBer ov Ma, sed ov supra 8er et ace. et spir. add.Me S y' conieci: om. V S B : ov rell. 5 irZs post iroTueponit H iraKtv] iv ras. in Me : ira\oi V S 6 iarlv post Svvwrovponit H Sh Marquard : 8^ S : Be 8^ rell. 12 6p((ov<ri B13 post o-ivBerov in unc. quad. aXA' 4v TO?J irepiexouiri <p86ryyois S17 TJ S' . . . ianv seclusi 19 dicitMarquard 'post h una lift,eras, quae v fuisse vid. M' : sed ego quidem ye fuisse suspicor.Quod si legitur, turn certe verborum translatione nulla opus es t :neque, si omittitur, ordinem librorum mutare velim verba ft . . .rtTpaxo'pSov post ^pfioaftivov ponit Meibom 20 T&V rov 81ft addiditWestphal 21 fiivov H aaw84rwv seclusi 23 ix*iMeibom: <?x°' codd. irapit TOUTO] Trapa post ravra eras, et supralin. add. Me TOCTO iropi V B S T& supra lin. add. Mb (?)

III.6I API2T0HEN0T

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5 ^eAo)8etrat 17 ev bia£ev£ei, KaO&itep | epvirpoo-Qev etp?jrai.

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yev&v evbexeTai Kara /iiav xpo'av ka^avojxevov eK -nkeioviav

15 aa~uv6iTa>v o-uvTe\6rjvai T&V ev T& bia nevre OVTCHV, [brjkov

2 rots om. V B S 3 TOV restituit Marquard 4 T6VUVB R 5 Trepiex&VTwv post fjapvrepov ponit H ifiolws 5' et «a!seclusit, et 5' addidit Westphal 7 TOV restituit MarquardjSopi/Tcpos . . . ntpiex&vrav ' n niarg. Me: om. V B : T6VOV ir^piex^vTavTO TO fiapirepov btfrrepov T&v 4v TTJ S. S 8 irepiexovTavpost rb o£vrfpov ponit H 6£irepov ex fiapvrepov Mb : ftapirepov B10-13 SOT' . . . elpnfievats SiaipopaTs om. R 10 STI supra lin. add.Me: om. V B S 12 AfforoiT1] cXnorr' R KWCITCU B 14 raaddidi 16 f/nrpocrBev om., et irpSrepov post tipjjTtti add. H18 /j.6vav Meibom : /i6vii codd. ly irpoo~Ti6e7o-a conieci: iimpoaBevreBeiffa codd.: irpotrTiOeiaa Marquard 22 Kafifidvofiev B inmarg. 23 iv r& ex e/c T&V M : 4K T&V V S B SrjKov Sri seclusitMarquard

152

APM0NIKX2N ST0IXEH2N / III.6a

OTI] ev exaoTO) yevei Tocravra eforat ra •nke'tara ouruvdeTa Sera

ev T& bio. nevTe.

"TapArreiv 8' etaOev eviovs KM. ev row&> T& Trpoj3\tffiaTi

•n&s TO. TrXficrra | •Kpoa-riOerai KCL\ bia rC ofy a.Tt\&s beUvvrai, 20

5 on en Toaovrcov aavvOeTuiv enaorov T&V yev&v o-vveo-rr\Kev

otra earlv ev rai bia Trivre. Upbs ovs ravra Keyerai, OTI

e£ ekajTovoov aavvdirmv l a r a t TTO6' ena\o-Tov T&V yevSiv 25

trvyKeifxevov £K irXeiovmv 8' oibeTrore. A i a ravrrp b\ rrjv

alrCav TOVTO avrb irp&rov airobelKvvrai, OTI OVK evbexeraL €/c

10 TT\€L6V<OV affwOiran) avvreOrjvat T&V ye\vu>v £KCLO~TOV r} ocra kv 3°

T& bia itivTe Tvyyjkvti oVTa. o n 8e nal e f ekarrovoiv wore

o~WTe6rio~eraL t-KcurTov OVT&V, ev rot? eirevra beiKvvrai.

TJvKvbv be irpbs TTVKVZ OV /xeA.&)8ei||Tai ovS1 oKov ovre 6 3

ixipos avTov. 2v/x/3?j(rei-at yap ixijre TOVS TeT&provs TG> bib.

15 Teo~o-&poov <ruij.(puiveiv fj-rire robs TT^TTTOVS r £ 8ta irevre' ol

be OVTO) KeCjxevoi | T&V (pOoyycov eKfieX.eis rjaav. T&V be TO 5

8i7oz>oz> TTepiexpvTdov 6 nev fiapvTepos ogijTaTos eori TTOKVOV

6 8' 6£vTepos fiapvTaTOS' avayKaiov yap ev TTJ o~vva<pr} T&V

•nvKV&v bia Tea~<rapa>v <rvix\<pa>vovvTU)v ava \xe<rov avr&v 10

20 Keio-Oai TO bbrovov, iio-wuTuts be KOL T&V SITOVCOD bia

Teacrapu>v a-v/xcpaivovvTcov avayKaiov ev fxetTto K.el(r9ai TO

1 <rvv9era R Zaa iv T(Jj om. R 3 eiadev] v postea add. M4 irws in marg. Mb 5 avyKelfiev6p ia-rai ante %KO.<TTOV add., etffWitrrriKeu om. H 7 tarai iro0' om. R : effTcu irod* %KauTOV om. Vi(rr\ post yeyav add. R,Mc (supra lin.) post ysvuiv add. avvtaTtiiibsoaa 4<rrlv 4v T<( 5(a TrepTe. irpbj 06s Ae7eiro ' <'T' ^j iXarrivav ourvvBeTwv •rail/ ysvwv S B V b in marg., nisi quod awetXTr\K6s om. Vb, TOV yevebvom. Vb, TOV om. S 10 ^ eras. M : om. V S B H 14 rerdprovsMarquard : 8' in marg. Me, S : om. Va : TfViropay rell. T $ ] rb H :post TB litt. v eras. M : T&V V B 15 ire^irrovsMarquard: ir^yrecodd. -rlf add. Me: om. V S 01 Si \ ouS' H 16 postOUTOI litt. o- eras. M ^K/icXeh ex f jueAcis Me: in/ttkeis V B S17 fiapirtpos Marquard: Papiraros codd. i^iraros . . . fiaptirarosom. R 18 Papvrepos B, sed in marg. fjapiraros 20 Keiatuom., et iivai post Sirovoy add. H ThJi-byVS Si om. S postKal add. y rp <ruya >7i in marg. Me, rfj <ruva<()j) R T^ ante Sick rtaaipwvadd. H 21 post rb litt. v eras. M : Tbv V S B

III. 63 API2T0HEN0T

i

I

15 TTVKVOV TOVTOOV 8' ovTQis e\6vTu>v avayKoiov | eva\ka£ TO re

TTVKVOV /cat TO blrovov Keio-dai, Stare brj\ov o n 6 /«i> /3apv-

repos T&V TrepieyovTuiv TO birovov 6£VTO.TOS earai TOS ewt r o

20 /3a/w Keifxevov TTVKVOV, 6 b' o^vrepos TOV e m TO o£i) | Kety-evov

TTVKVOV fiapvTaTos' ol be TOV TOVOV TrepiixpvTes ajKpoTepoi s

etcri TTVKVOV ftapvTaToi, rffleTat, yap 6 TOVOS ev rrj

p.eTa£v TOLOVTCOV TtTpayppbaiv h oi Trepte^oiTes ft

25 elcri I ITVKVOV' VTTO TOVTOOV be /cat 6 TOVOS i7epte'xerai. o /xez>

yap fiapvTepos T&V (TOV) TOVOV -nepLeyovroov a£vTepos eo-Ti T&V

TO (3apvTepov T&V TeTpaxppbcov irepiexovTOiv, 6 be 6£vTepos 10

30 T&V (TOV) TOVOV TrepiexovTwv /3a\pvrepos eari T&V TO 6£vTepov

T&V TeTpaxopboiv irepie)(6vT0)v, COOT' etvai bfjXov OTI ol TOV

TOVOV TrepieyovTes ftapvTaToi e&ovTai TTVKVOV.

6 4 Avo be birova e£i]s ov Tedrja-eTcu. Ti6e\\o-0a> yap' d/co-

KovOrjcrei br] T& fxev otjvTepip bvrovw TTVKVOV eiii TO j3apv, 15

6£vTaTOs yap 771; TTVKVOV 6 eirl TO /3apv opifav TO btrovov

5 T& be /3api)repa) dt|ToVij) em TO 6£ii aKoKovO-qo-ei TTVKVOV,

PapvraTos yap yv TTVKVOV 6 eirl TO 6£V 6pl(jt»v TO bOrovov.

ToiJTov be o-viu.j3aivovTos bvo TTVKVO. e£i}$ r e ^ c r e r a f TOVTOV

10 he eKy.e\ovs OVTOS ex/xeAes l o r a t | /cat TO. bvo bCrova e£ijs 20

Tideo-Oai.

Ev apfiovCa be /cat \p<ifj,aTi bvo Toviala e£i}s ov TeOrjo'eTai.

TiQeo~9(a yap e m r o o£v irp&Tov avayKaiov by eiirep

£] ace. add. et postea 2 litt. eras. Me : iva\\d£ai V B S (sedin marg. B) 2 fiapirepos Marquard : frapira.TOs codd.

4 rod &rl rb ofu Keifxevov trvKPov in marg. Me : om. V S B 5 irvKvovom. R fSapfa-aTos Marquard: fjapvrepos codd. 01] i B7 roioSrov B & Ma, sed &v suprascr. Me : coy R irepiexocTfsex irepiaxAvTts Me 9 ftapirepos Marquard: fiapiraros codd.rhv restituit Marquard rivwv R irepiex^VTav ota. R 10 rbsupra lin. add. B : om. S ffapirepov Marquard : ffapirarou codd.T&V T€rpax6pSav] TWV supra lin. add. Mx: om. V S 11 rbvrestituit Marquard (legit H) v 12 r&v T«T.] T&V supra lin. add.Mx : om. Va S 14 Shova] post i litt. a eras. M : Sidrova V B S18 Sioptfav R 20 &cjteAe<rflai supra e ace. eras., r suprascr. etin marg. iicftekh iarai add. Me: iicfi.e\h iarai (is tar e corr.) VbKcd om. H Siirova M V S 22 ivapjiivia S 23 8^] hi V S B

APM0NIKX2N STOIXEIfiN / III.64:

6 TOV TTpocrTeOivTa TOVOV | opitjav <p96yyos em TO 15

6£v o-vfj-cfxaveiv 7JTOI T 5 TeT&pTO) rStv e^jjs bw. Te<ro~apO)v rj

r& irifxTTTU) bia. -nivTe' pvqbeTepov (8e) TOVTWV OVTW o-vpi-

/3aivovTO$ avayKaTov eKp.e\.T) etvai. on b' ov (ry/x|/3?7a"erai 20

5 (pavepov tvapp.6vi.os p.ev yap ovca fj \i\avbs reo-o-apas

TOVOVS a-nb TOV irpocr\ri<p6{vTos a<pe£ei <f>66yyos TSTapTos &v,

XpcojuartKTJ 8' e ire /xa\a/<o{i yjxipMTos e%6' ^ I O X I O V nei\£ov 25

a(p4£ei, 8ic£aT7jjua TOV bia irevTe, Tovialov be yevo/xivrj 8ia

irevre (ru/x^cowfo-ei r £ -npoa-Xrj^QivTi <p66yyu>. OVK eSei 8e

jo ye, aWa TJTOI, TOV Teraprov Sia Teo~o-ap<ov o~vfj.(pG)veiv r) TOV

iteymTov bia -nev\Te. TOVTUIV 8' oiberepov yiyverai, &o~T€ 30

(pavepov, OTL eKjxeXrjs e o r a t 6 TOV TTpoa-Xri^Oevra TOVOV 6p[£a>v

(pOoyyos eiri TO O£V. ' E T C 8e TO /3apv Ti6e\xevov TO bevrepov

Toviaiov biaWovov irovf}(rei TO 11 yevos, wore bfjXov OTL ev 6 5

15 apfiovia Kal xptojuan ov TeOrjaeTai hvo Toviaui etfis. 'Ev

8iarovo) be Tpia ToviaXa k£rjs Te9rf<reTai, irXeuo b' ov' 6 yap •

TO TeTaprov \ TOVLOLOV 6piQx>v <p86yyos ovTe r S rercipra) but 5

Teo-<r6.p(&v ovTe rai itipvjiTU) bia irivTe o-vp.<pa>v^o-ei.

' E v rfi a i r u be yevei TOVTUI bvo rip.iTovi.aia e£fjs ov Te-

20 6r)a-eTai. TiQeaOan yap | vpaiTov e m TO j3apv TOV vir6.p)(ov- id

TOS flfJLLTOvCoV TO •KpOOTeOeV fjp.LTOVLOV (TDjUl/3aiVei br] TOV

6pC(ovTa (pOoyyov TO irpoareOev rjp.iToviov fxr\Te T<3 rerct/)T&)

8ta Teo~o-6.pa>v avfKpoiveiv pvqTe T S 7re/x|Tn"&> 8ta irevre. OVTOO 15

p f i e x iK/ie\iis M e : ^ K , u e \ ^ r V S , B ( s e d i n m a r g . / p ) )3 T £ V a n t e 5 i A i r e W c a d d . R (U)75' crepes TOVTO ex ytirjS' krepa roiraM : ,10)8* erepcf) roirtf V S B Si restituit Marquard auT-uv exabrif Me awry post av/if3a(i>ovTOS ponit H 6 £<pi£et B (sedo4>e|fl in marg.) 10 o\A.' V 0 ' e x aAAo TOI deinde 2 litt. eras. Me :a\\& TOIOVTO V B S : a\Ao rhv in marg. B TeVapToj/] 8' S 11 Siin marg. Me : om. VB S 13 eVl rb b£v M rb o|u (cum punctissub &rl T!) O£II altero) B . SfuTepor rovtmov Ma, sed 0 supra Scurfpovet a supra TOVICUOV add. Me 17 T2> om. H 19 ^MtrofiaTa]ToviaTa V S B et Ma, sed TIIU supra lin. add. Me riOtrcu in marg.B, R 21 ri^iTovialov B SJ) H : 8i rell. as rbsupra lin. add. Me : om. V B S 23 av/j.<pavuv post 81^ ITCVTCponit H

155

HI. 65 API2T0HEN0T

1 1'

I

[iev ovv e/c^eA.j)y ecrrai TOV rjfj.iToviaiov r) Oecris. eav 8' kmTO o£i> TeOrj TOV inrapxpvTos, x/)<S/<ia e 'Tai , diore bijKov onkv StaroVft) 8vo f/fUToviaia ov TeOrja-erai etpjs.—ITota fiev |

20 oZv T&V acrvvOirun) bvvarat, lira e£ijs Ti0e<r6ai /cat wocro TOapi6/j.6v Kal Troia rovvavriov ireTtovdev cnr\&s ov hvv&fieva 5Ti9fo-6ai lo-a ovra e ^ s , bebeurar Kepi 8e TOIV avi<ra>v vvvKeicreov. |

25 YlvKvbv fiev ovv npbs 8LTOV<O KO.1 e m rb fiapv Kal em. TO6£v rCBerai. AeSei/crat yap ev rrj avvcupfj ivaWa£ TiOiy-evaTavra TO. diao-rqiiaTa, &are brj\ov OTI eicaTepov eKarepov 10

39 Kal eirl rb fiapv Kal | ivl TO 6£b TedrjcreTai.Tovos 8e irpbs bnov<a iirl TO O£V fxovov riOerai. Ti-

6e<r0a> yap eirl TO fiapv- o-vufirjo-erai bq TF[TTT€IV eirl TYJV»66 avTTjv r&ariv d£i;rai|roz> r e TIVKVOV Kal fiapvTaTov, 6 fxev yap

TO blrovov em to fiapv 6p(£a>v o^vraTos rjv TTVKVOV, 6 be TOV 155 TOVOV eirl TO o£ii fiapvraros. TOVTOOV be Tiiirrovrmv | eirl

TTJV avTrjv TCKTIV avayKalov bvo HVKVO. rlOecrOai. TOVTOV 8'

eKiJ.eX.ovs ovros avayKalov Kal TOVOV em TO fiapv biroviaioveic/ieA.?; eivai.

10 Tovos be irpbs VUKVS) em TO fiapv | \u6vov TiOerai. T t - 206e<r6a> yap em rovvavriov arvufirjcreTai by TO avrb iraXivabvvarov, kirl yap TTJV OVTTJV T6XTIV O^VTOTOS re TTVKVOV

•7fe<reiTai Kal fiapvraros, &o-re bvo TrvKva rideadai e£rjs.

15 TOV\TOV 5' ovros iK/j.e\ovs avayKalov Kal TTJV TOVOV deo~u>

Ttjv iirl TO o£v TOV TtVKVov eKfj.eX.rj eivai. 25

nJ TOV rj/xiToyialov post 7) ponit H 5 Svvd/ieyaM H : Svvdfie$a rell. 6 Si om. R 8 rb fSapb] rb supra lin.add. Me (?): om. S Kal iirl rb 0apb post teal eVi rb o£b ponit Hio STI H: om. rell. 12 rif ante 5ir6vtp add. R 13 rb om. B<ru/i/3 (TfToi] f}fi<rerai in ras. Ma 15 ipifa S 17 OUT^C supralin. add. B iciKvh, B 18 rivav Meibom : rovrov codd.JSirovialou 4K/ieh.rj ex Siroviatov /c/teA r Me: SiroviaTov iK/te\i)S V S B31 irl supra lin. add. B rb avrb post iroAiv ponit H 22 airi/yin marg. add. B Trepetrat post fiapvraros ponit H 24 rivovMeibom: roirov codd.

156

APMONIK&N STOIXEIilN / HI.66

'Ev biaTovti) be TOVOV ecp' eKaTepa r)p,iToviov ov /xeA.&>8eirat.

r a i yap | /wjre TOVS reT&provs rS>v e£i]S bia Tecrcrapcov 20

<rv\J.<\>a>veiv firfTe TOVS TsefiTTTOVs bia irevre. Avo be r o W ,

rj Tpi&v fiiALTOviov e<\> en&Tfpa peAfflSetrar crvix<pa>vrio-ovo-i

5 yap 7] 01 TerapTOi bia Teo-ar<5.\pa>v 77 o\ -jreiiirroi bia TtevTe. 25

['Ai7o fiixiToviov p-ev em TO 6£ii bvo obol Kal eirl ro (3apv

bvo,} airb be TOV bvrovov bvo ixev enl TO 6£V, \iia 8' eiil TO

/3a/)v. AebeiKTai yap eiri fjiev r o | 6£v TTVKVOV TeOeip-evov 30.

Kal TOVOS, -nXeiovs be TOVTMV OVK eo-ovTai obol cmb TOV

10 elp-qp.e'vov biao-rr\jxaTos eirl TO 6£V% [eitl be TO j3apv TTVKVOV

^IOI'OZ',] XefaeTai /J.ev yap TO>V a<rvv8eTu>v TO bCrovov ixovov 11

bvo be bOrova e£r)s ovKe'ri TiOeTai. tSore bfjkov o n bvo fwvai 6 7

0801 Icroi'rat cnrb TOV bvrovov em ro 6£v- em be TO /3apv fila-

bebeiKTal yap, or t o w e 8tTOi>oz> | irpbs burdva Tedr/o-eTai ovTe 5

15 TOVOS em TO fiapv biTovov, a iore XeCireTat TO TTVKVOV. (pavepbv

br) or t cmb biTovov em p.ev TO 6£V bvo 6bo(, fj p.ev eirt TOV TOVOV

•fj 8' em TO TTVKVOV, em be TO [3apv jxla, fj eirt | r o TTVKVOV. 10

'ATTO TTVKVOV 8' evavTicos em pev TO ftapi) bvo oboC, km*

be TO 6£b fiia. Ae'8ei/crat yap CLTTO TTVKVOV em* TO (3apv bi-

20 TOVOV Te6eip.evov Kal TOVOS' rpirrj 8' OVK | l o r a t 68oy, 15

XeCireTai fjiev yap TS>V aavvOiTUiv r o TTVKVOV, bvo be TTVKva

e£rjs ov TiOeTai, &are bfjXov or t p.6vai bvo obol eo-ovrai CLTTO .

1 Siar6vov M V B S TrfyouMeibom: r6vtp codd. a /Marquard : <rv/iirt(re7Tcu codd. 3 av/xfyooveiv in marg. add. B TWVel-rjs post Tre/XTTTous add. H 5 prius ^ ] tjroi H Sii r&raapuv exSth rerdprov Me: 810 Terdprov V S B 6 'Airb . . . 5iSo seclusinhv~\ oil ixkv S Svo dSol ex Svo 8' 01 Me : Svo S' ol V S B Kal inmarg. Me Kal £irl Tb fiapv . . . /ila S' om. V S B 7 curb Si TOVO~IT6VOV . . . iirl rb $apv in marg. Me 8 Sib ante StSeiKrai add.Vb S B yap add. Me : om. V S B TeOeijueVoe] Tc'flijToi R :riBe/xevov H 10 iirl . . . fiivov supra lin. in marg. superior!add. Me: om. V B S 11 SITOVOV (post ( litt. a eras.) M : Sia-TOVOV V B S 13 at ante iSol add. H 14 in o6ri\ SrtovSev H : STI ou8e M V B S 15 <pavtpbv Si) Marquard : eZpovSe codd. 17 jutei- M V B S 19 irvKvov ex o{ii Me : o|{> V B S20 Tide/xevop H 22 ov riSerat . . . $api. e'lrl om. R ' Siio post6S0I ponit S 68o! post iaovrai ponit H

157

III. 67 APISTOEENOT

TTVKVOV ewt TO jSapi;. ewt 8e TO d£ii \xia (jj) eirt TO bCrovov

to OVTS yap | TTVKVOV irpbs TTVKVQI rttferai owe TOVOS em TO

. 6£v TTVKVOV, (Sore A.etTrerat ro biTOVov. <$>avepbv 877 o n airb

TTVKVOV em ixev TO fiapii bvo 6S01, rj r e em (TOV) T6VOV KO1

35 fj em TO bCrovov, e-nl he TO 6£V p-Ca, | 17 em TO birovov.

'ATTO be TOVOV ju.ia e^>' e/carepa obos, em ixev TO j3apv

em TO bOrovov em be TO 6£i) em TO TTVKVOV, 'ETTI y.ev

30 TO fiapii bebeiKTai STL ovTe TOVOS rWerai | ovre TTVKVOV,

uxrTe XeCirerai TO bCrovov em be ro o£v bebeiKTai o n ovTe

TOVOS TiOeTai OVTS SLTOVOV, &O-T€ Xelirerai TO TTVKVOV. <£>ave- 10

pbv br\ or t cmb TOVOV fxia e(j)' eKarepa bhos, eitl [lev TO (3apv

6 8 eTrl TO biTovov, | | eiri 8e TO O£U em TO TTVKVOV.

'OfjLOioos 8' e£ei /cat em T&V xpco/xtircoz; TTXTIV TO ye neo-qs

5 /cat Xtyavov bidarrma fxeTaXaixj^dveTaL avrl bwovov TO | yi-

yvopevov KO.6' l/cdarrji' yjtoav Kara TO TOV TTVKVOV /xiye6os. 15

'O/JMICOS 8' e£ei /cal CTTI riSi; 8tarova)y' airb yap TOV KOLVOV

TOVOV T5>V yevwv [tio, l a r a t ecj)' e/carepa 680s, em [Mev TO

10 j3apv em TO neo-qs Kal Atxa^oS | bidaTrjixa o r t av TTOTe

Tvyxavfl ov KaO' eKao~T7]v xpoav T&V biaTovoiv, em be TO o£i>

em TO Tiapaixeo-qs /cal TpiTrjs. 20V H 8 J J 8e rtert Kat TOVTO TO 7rpo/3Ar;/xa Trapeo-^e irkavrfv

15 6avfj.6.£ovo-i yap | 7r£s oii^.' Tovvavriov o-Vjj.j3a(veL' &Treipoi

yap Tives avrois (paivovTai. etvai obol e<p' eKarepa TOV TOVOV,

eTTeihr)Trep TOV re /iecrjs /cat At^avoB 8tao-r?j/xaros airetpa

1 TJ> O$J] TOV o{i S i) restituit Westphal St ante rh Strovovadd. R , a STC TIJVOS in marg. B 3 Sij Marquard : Se codd.4-6 TvKirov . . . awb Se om. H 4 riy restituit Marquard 5 ^om. B 4TTI Si SITOVOV R M Se . . . UTOVOV in marg. add. Me Vb(nisi quod ^ om. Me) T\ om. R 6 airb Se T VOU /i/o add.in marg. McVb: om. V S 7-12 M fiev . . . VVKV6V om. H8 tniKviv] Slrovoy R 10 TIBSTCU om. R post rlBerai 10 litt. eras.M \e\eiirrat R 11 S^SEMVSB 14 SITSVOV'] ShT6VOV R 15 KOTA R : KOI rell. 18 rb supra lin. add. Me:om. V S B pious /tol om. R KOI supra lin. add. Me: om.V B S 19 Tvyxdvei B S inivuv B 20 didon/ipa postrpirns add. H 24 TC om. S

158

APM0NIKI2N STOIXEIilN / 111.68

cpaivovrai elvai TOV r e TTVKVOV | axrawcoy. YIpbs 8rj 20

Tavra TTp&Tov fj.ev TOVT' eAe'x^Tj, o n ovbev /xaAAor enl TOV-

TOV TOV Ttpo[&\r)\w.Tos kTTij3Xe\jf€Lev 6.V TIS TOVTO 77 eirl TS>V

TrpoTepuiV. brjkov yap or t Kat T&V airb TOV TTUKVOV TTJV

5 ere|pai> T&V ob&v aireipa \j.eyi6r\ 0"Uju./3?iVerai \.a\x^aveiv Kal 25

T£>V airb TOV biTovov [8'] axrawrtos [ais]* TO r e yap rotoCrov

bido-T-qixa olov TO fxicrqs /cat \i\avov aireipa Xaix^ava ixeyedr]

TO r e rotoCrov otov | r o TTVKVOV TOVTO irda^ei TT&OOS r<5 39

eiATrpoo-0(v elprj/xevcf biacrtrnxaTi., dXA.' o/xtoj oiSev "?^rroy aTro

10 r e ro£i TTVKVOV brio ytyvovrai 6801 eirl TO /3apv Kal a-nb TOV

b~vrovov eirl TO 6£V, waavToas 8e Kat airb TOV TOVOV \J.ia

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161

APM0NIKI2N STOIXEIiiN / III.72

rfjs avTrjs rdaecos eixixek&s KOivuivr)aovai' rpeis yap avayKoiovTi\6ea6ai bieaeis e£ijs, edv re fiapvTaros edv r ' d£i/raros 25T<a fjLecra rfjs avTrjs /wra(rx?7 rdcrecos.

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M 2 163

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l o r cu p.eye0r] e£ 3>v ret elpr\p.iva yivr) ovvearTriKoTa e i m u ,

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164

THE ELEMENTS OF HARMONYBY ARISTOXENUS

BOOK I 1

THE branch of study which bears the name of Harmonic i. nis to be regarded as one of the several divisions or specialsciences embraced by the general science that concernsitself with Melody. Among these special sciences Harmonic •occupies a primary and fundamental position; its subjectmatter consists of the fundamental principles — all thatrelates to the theory of scales and keys; and this oncemastered, our knowledge of the science fulfils every justrequirement, because it is in such a mastery that its aimconsists. In advancing to the profounder speculations 2which confront us when scales and keys are enlisted in theservice of poetry, we pass from the study under considerationto the all-embracing science of music, of which Harmonicis but one part among many. The possession of this greaterscience constitutes the musician.

The early students of Harmonic contented themselves, asa matter of fact, with being students of Harmonic in theliteral sense of the term; for they investigated the enhar-monic scale alone, without devoting any consideration to theother genera. This may be inferred from the fact that thetables of scales presented by them are always of enharmonicscales, never in one solitary instance of diatonic or chromatic;and that too, although these very tables in which they con-

1 The references throughout the translation are to Meibom's edition.165

ARISTOXENUS

fined themselves to the enumeration of enharmonic octavescales nevertheless exhibited the complete system ofmusical intervals. Nor is this the sole mark of their im-perfect treatment. In addition to ignoring diatonic andchromatic scales they did not even attempt to observe thevarious magnitudes and figures in the enharmonic as well asin the other genera. Confining themselves to what is butthe third part of that complete system, they selected forexclusive treatment a single magnitude in that third part,namely, the Octave. Again, their mode of treating evenbranches of the study to which they did apply themselveswas imperfect. This has been clearly illustrated in a formerwork in which we examined the views put forward by the

• students of Harmonic; but it will be brought into a stillclearer light by an enumeration of the various subdivisionsof this science, and a description of the sphere of each. We

3 shall find that they have been in part ignored, in part in-adequately treated; and while substantiating our accusationswe shall at the same time acquire a general conception ofthe nature of our subject.

The preliminary step towards a scientific investigation ofmusic is to adjust our different notions of change of voice,meaning thereby change in the position of the voice. Ofthis change there are more forms than one, as it is foundboth in speaking and in singing; for in each of these thereis a high and low, and a change that results in the contrastof high and low is a change of position. Yet although thismovement between high and low of the voice in speakingdiffers specifically from the same movement in singing, noauthority has hitherto supplied a careful determination ofthe difference, and that despite the fact that without sucha determination the definition of a note becomes a task verydifficult of accomplishment. Yet we are bound to accomplishit with some degree of accuracy, if we wish to avoid the

166

THE ELEMENTS OF HARMONY

blunder of Lasus and some of the school of Epigonus, whoattribute breadth to notes. A careful definition will ensureus increased correctness in discussing many of the problemswhich will afterwards encounter us. Furthermore, it isessential to a clear comprehension of these points that wedifferentiate distinctly between tension and relaxation, heightand depth, and pitch—conceptions not as yet adequatelydiscussed, but either ignored or confused. This done, weshall then be confronted by the question whether distance on 4the line of pitch can be indefinitely extended or diminished,and if so, from what point of view. Our next task will bea discussion of intervals in general, followed by a classifica-tion of them according to every principle of division of whichthey admit; after which our attention will be engaged bya consideration of the scale in general, and a presentationof the various natural classes of scales. We must thenindicate in outline the nature of musical melody—musical,because of melody there are several kinds, and tunefulmelody—that which is emplo> 1 in musical expression—isonly one class among many. And as the method by whichone is led to a true conception of this latter involves thedifferentiation of it from the other kinds of melody, it willscarcely be possible to avoid touching on these other kinds,to some extent at least. When we have thus defined musicalmelody as far as it can be done by a general outline beforethe consideration of details, we must divide the general class,breaking it up into as many species as it may appear tocontain. After this division we must consider the natureand origin of continuity or consecution in scales. Ournext point will be to set forth the differences of the musicalgenera which manifest themselves in the variable notes,as well as to give an account of the loci of variation ofthese variable notes. Hitherto these questions have beenabsolutely ignored, and in dealing with them we shall be

167

ARISTOXENUS

compelled to break new ground, as there is in existence noprevious treatment of them worth mentioning.

5 Intervals, first simple and then compound, will nextoccupy our attention. In dealing with compound intervals,which as a matter of fact are in a sense scales as well, weshall find it necessary to make some remarks on the synthesisof simple intervals. Most students of Harmonic, as weperceived in a previous work, have failed even to noticethat a treatment of this subject was required. Eratoclesand his school have contented themselves with remarkingthat there are two possible melodic progressions startingfrom the interval of the Fourth, both upwards and down-wards./ They do not definitely state whether the law holdsgood 'from whatever interval of the Fourth the melodystarts; 'they assign no reason for their law; they do notinquire how other intervals are synthesized—whether thereis a fixed principle that determines the synthesis of anygiven interval with any other, and under what circumstancesscales do and do not arise from the syntheses, or whetherthis matter is incapable of determination. On these pointswe find no statements made by any writer, with or withoutdemonstration; the result being that although as a matterof fact there is a marvellous orderliness in the constitution ofmelody, music has yet been condemned, through the faultof those who have meddled with the subject, as falling intothe opposite defect. The truth is that of all the objects towhich the five senses apply not one other is characterizedby an orderliness so extensive and so perfect. Abundantevidence for this statement will be forthcoming throughoutour investigation of our subject, to the enumeration of theparts of which we must now return.

6 Our presentation of the various methods in which simpleintervals may be collocated will be followed by a discussionof the resulting scales (including the Perfect Scale) in which

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we will deduce the number and character of the scales fromthe intervals, and will exhibit the several magnitudes of scalesas well as the different figures, collocations, and positions pos-sible in each magnitude; our aim being that no principle ofconcrete melody, whether magnitude, or figure, or colloca-tion, or position shall lack demonstration. This part of ourstudy has been left untouched by all our predecessors with theexception of Eratocles, who attempted a partial enumerationwithout demonstration. How worthless his statements are,and how completely he failed even in perception of the facts,we have already dwelt upon, when this very subject was thematter of our inquiry. As we then observed all the scaleswith the exception of one have been completely passed over;and of that one scale Eratocles merely endeavoured toenumerate the figures of one magnitude, namely the octave,empirically determining their number, without any attemptat demonstration, by the recurrence of the intervals. Hefailed to observe that unless there be previous demonstrationof the figures of the Fifth and Fourth, as well as of the lawsof their melodious collocation, such an empirical processwill give us not seven figures, but many multiples of seven.Further discussion here is rendered unnecessary by ourprevious demonstration of these facts; and we may now 7resume our sketch of the divisions of our subject.

When the scales in each genus have been enumerated inaccordance with the several variations just mentioned, wemust blend the scales and repeat the process of enumera-tion. The necessity for this investigation has escaped moststudents ; nay, they have not so much as mastered the trueconception of' blending.'

Notes form the next subject for inquiry, inasmuch asintervals do not suffice for their determination.

Again, every scale when sung or played is located ina certain region of the voice; and although this location

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ARISTOXENUS

induces no difference in the scale regarded in itself, it im-parts to the melody employing that scale no common—nayrather perhaps its most striking characteristic. Hence hewho would deal with the science before us must treat of the' region of the voice' in general and in detail so far as isreasonable; in other words so far as the nature of the scalesthemselves prescribes. And in dealing with the affinitybetween scales and regions of the voice, and with keys, wemust not follow the Harmonists in their endeavour at com-pression, but aim rather at the intermodulation of scales, byconsidering in what keys the various scales must be set soas to admit of intermodulation. We have shown in a previouswork that, though as a matter of fact some of the Harmonistshave touched on this branch of our subject in a purelyaccidental way, in connexion with their endeavour to exhibita close-packed scheme of scales, yet there has been nogeneral treatment of it by a single writer belonging to this

8 school. This position of our subject may broadly bedescribed as the part of the science of modulation con-cerned with melody.

We have now set forth the nature and number of theparts of Harmonic. Any investigations that would carry usfurther must, as we remarked at the outset, be regardedas belonging to a more advanced science. Postponingaccordingly to the proper occasion the consideration ofthese, their number, and their several natures, it nowdevolves upon us to give an account of the primary scienceitself.

Our first problem consists in ascertaining the variousj species of motion. Every voice is capable of change of

, position, and this change may be either continuous or byintervals. In continuous change of position the voice

|f . seems to the senses to traverse a certain space in such a\i manner that it does not become stationary at any point, not

^ 170

1 • • • . . • « * *

t 1

V

THE ELEMENTS OF HARMONY

even at the extremities of its progress—such at least is theevidence of our sense-perception—but passes on intosilence with unbroken continuity. In the other specieswhich we designate motion by intervals, the process seemsto be of exactly the opposite nature: the voice in itsprogress stations itself at a certain pitch, and then again atanother, pursuing this process continuously—continuously,that is, in time. As it leaps the distances containedbetween the successive points of pitch, while it is stationaryat, and produces sounds upon, the points themselves, itis said to sing only the latter, and to move by intervals.Both these descriptions must of course be regarded in the 9light of sensuous cognition. Whether voice can reallymove or not, and whether it can become stationary ata given point of pitch, are questions beyond the scope ofthe present inquiry, which does not demand the raisingof this problem. For whatever the answer may be, it doesnot affect the distinction between the melodious motionof the voice and its other motions. Disregarding all suchdifficulties, we describe the motion of the voice as con-tinuous when it moves in such a way as to seem to theear not to become stationary at any point of pitch; butwhen the reverse is the case—when the voice seems to theear first to come to a standstill on a point of pitch, then toleap over a certain space, and, having done so, to come to astandstill on a second point, and to repeat this alternatingprocess continuously—the motion of the voice under thesecircumstances we describe as motion by intervals. Con-tinuous motion we call the motion of speech, as in speakingthe voice moves without ever seeming to come to a stand-still. The reverse is the case with the other motion, whichwe designate motion by intervals: in that the voice doesseem to become stationary, and when employing thismotion one is always said not to speak but to sing. Hence

171

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ARISTOXENUS

in ordinary conversation we avoid bringing the voice to astandstill, unless occasionally forced by strong feeling to

11 resort to such a motion; whereas in singing we act in11 JO precisely the opposite way, avoiding continuous motion and!j making the voice become, as far as possible, absolutely11 stationary. The more we succeed in rendering each of our

voice-utterances one, stationary, and identical, the morecorrect does the singing appear to the ear. To conclude,enough has been said to show that there are two species ofthe voice's motion, and that one is continuous and employedin speaking, while one proceeds by intervals and isemployed in singing.

It is evident that the voice must in singing produce thetensions and relaxations inaudibly, and that the points ofpitch alone must be audibly enunciated. This is clear fromthe fact that the voice must pass imperceptibly through thecompass of the interval which it traverses in ascending ordescending, while the notes that bound the intervals mustbe audible and stationary. Hence it is needful to discusstension and relaxation, and in addition height and depth ofpitch, and finally pitch in general.

Tension is the continuous transition of the voice from alower position to a higher, relaxation, that from a higher toa lower. Height of pitch is the result of tension, depththe result of relaxation. On a superficial consideration ofthese questions it might appear surprising that we distinguishfour phenomena here instead of two, and in fact it is usualto identify height of pitch with tension, and depth of pitch

II with relaxation. Hence we may perhaps with advantage| observe that the usual view implies a confusion of thought.I In doing so we must endeavour to understand, by observingj the phenomenon itself, what precisely takes place when inI tuning we tighten a string or relax it. All who possess even( - a slight acquaintance with instruments are aware that in

17a

THE ELEMENTS OF HARMONY

producing tension we raise the string to a higher pitch, andthat in relaxing it we lower its pitch. Now, while we arethus raising the pitch of the string, it is obvious that theheight of pitch which is to result from the process cannotyet be in existence. Height of pitch will only result whenthe string becomes stationary and ceases to change, afterhaving been brought by the process of tension to the pointof pitch required; in other words, when the tension hasceased and no longer exists. For it is impossible thai: astring should be at the same moment in motion and at rest;and as we have seen, tension takes place when the stringis in motion, height of pitch when it is quiescent andstationary. The same remarks will apply to relaxation anddepth of pitch, except that these are concerned with changein the opposite direction and its result. It is evident, then,that relaxation and depth of pitch, tension and height ofpitch, must not be identified, but stand to one another inthe relation of cause and effect. It remains to show thatthe term pitch also connotes a quite distinct conception.

By the term pitch, we mean to indicate a certain per-12sistence, as it were, or stationary position of the voice.And let us not be alarmed by the theory which reducesnotes to motions and asserts sound in general to be amotion, as though our definition involved the propositionthat under certain circumstances motion will, instead ofmoving, be stationary and at rest. The definition of pitchas a certain condition of motion—call it ' equability' or' identity,' or by any more enlightening term you can find—will not affect our position. We shall none the less describethe voice as stationary when our senses assure us that it isneither ascending nor descending, simply fixing on thisterm as descriptive of such a state of the voice without anyfurther implications. To proceed, then, the voice appearsto act thus in singing; it moves in making an interval, it is

\ ARISTOXENUS

stationary on the note. Now if we use the term ' motion 'and say ' the voice moves ' in cases where, according to the

!' physical theory, it undergoes a change in the rate of motion;I. and if, again, we use the term ' rest' and say' the voice rests 'I? in cases where this change in the rate of motion has ceased,I, and the motion has become uniform, our musical theory isi'i not thereby affected. For it is plain enough that the term! . ' motion' in the physical sense covers both ' motion' andi; 'rest ' in the sense in which we employ them. Sufficient/; , has been said on this point here; elsewhere it has been.': treated more fully and clearly.(. 13 To resume; it now being clear that pitch is distinct from1 tension or relaxation, the former being, as we say, a rest of!,'• the voice, the latter, as we have seen, motions, our next1 task is to understand that it is distinct from the remaining1 phenomena of height and depth of pitch. Now, our pre-J1 vious observations have shown that the voice is, as a matter' ; of fact, in a state of rest after a transition to height or depth;i yet the following considerations will make it clear that!l pitch, though a rest of the voice, is a phenomenon distinct

V ! from both. We must understand that for the voice to bestationary means its remaining at one pitch; and this willhappen equally whether it becomes stationary at a highpitch or a low. If pitch, then, be met in high notes as wellas low notes—and the voice, as we have shown, must ofnecessity be capable of becoming stationary on both alike—it follows that, inasmuch as height and depth are absolutely

1 incompatible, pitch, which is a phenomenon common to' both, must be distinct from one and the other alike. Enough

has now been said to show that pitch, height and depth of1 pitch, and tension and relaxation of pitch are five con-

ceptions which do not admit of any identification inter se.

j . i I on the line of pitch admits of infinite extension or diminu-The next point for our consideration is whether distance

THE ELEMENTS OF HARMONY

tion. There is no difficulty in seeing that if we refer solely 14to musical sounds, such infinite extension and diminutionare impossible. For every musical instrument and for everyhuman voice there is a maximum compass which theycannot exceed, and a minimum intervals less than whichthey cannot produce. No organ of sound can indefinitelyenlarge its range or indefinitely reduce its intervals : in bothcases it reaches a limit. Each of these limits must bedetermined by a reference to that which produces the soundand to that which discriminates it—the voice, namely, andthe ear. What the voice cannot produce and the earcannot discriminate must be excluded from the availableand practically possible range of musical sound. In the __progress in parvitatem the voice and the ear seem to fail atthe same point. The voice cannot differentiate, nor canthe ear discriminate, any interval smaller than the smallestdiesis, so as to determine what fraction it is of a diesis or ofany other of the known intervals. In the progress inmagnitudinem the power of the ear may perhaps be con-sidered to stretch beyond that of the voice, though to novery great distance. In any case, whether we are to assumethe same limit for voice and ear in both directions, orwhether we are to suppose it to be the same in the progressin parvitatem but different in the progress in magnitudinem,the fact remains that there is a maximum and minimumlimit of distance on the line of pitch, either common to 15voice and ear, or peculiar to each. It is clear, then, thatdistance of high and low on the line of pitch, regarded inrelation to voice and ear, is incapable of infinite extension orinfinitesimal diminution. Whether, regarding the constitutionof melody in the abstract, we are bound to admit such aninfinite progress, is a question demanding a different methodof reasoning not required for our present purpose, and weshall accordingly reserve its discussion for a later occasion.

ARISTOXENUS

The question of distance on the line of pitch beingdisposed of, we shall proceed to define a note. Briefly,it is the incidence of the voice upon one point of pitch.Whenever the voice is heard to remain stationary on onepitch, we have a note qualified to take a place in amelody.

An interval, on the other hand, is the distance boundedby two notes which have not the same pitch. For, roughlyspeaking, an interval is a difference between points of pitch,a space potentially admitting notes higher than the lower ofthe two points of pitch which bound the interval, and lowerthan the higher of them. A difference between points ofpitch depends on degrees of tension.

16 A scale, again, is to be regarded as the compound of twoor more intervals. Here we would ask our hearers toreceive these definitions in the right spirit, not with jealousscrutiny of the degree of their exactness. We would askhim to aid us with his intelligent sympathy, and to considerour definition sufficiently instructive when it puts him inthe way of understanding the thing defined. To supply adefinition which affords an unexceptionable and exhaustiveanalysis is a difficult task in the case of all fundamentalmotions, and by no means least difficult in the case of thenote, the interval, and the scale.

We must now endeavour to classify first intervals andthen scales according to all those principles of division thatare of practical use. The first classification of intervalsdistinguishes them by their compass, the second regardsthem as concordant or discordant, the third as simple orcompound, the fourth divides them according to themusical genus, the fifth as rational or irrational. As allother classifications are of no practical use, let us disregardthem for the present.

17 In scales will be found, with one exception, all the dis-176

THE ELEMENTS OF HARMONY

tinotions which we have met in intervals. It is obviousthat scales may differ both in compass and owing to thefact that the notes bounding that compass may be eitherconcordant or discordant. The third, however, of the dis-tinctions mentioned in the case of intervals cannot existin the case of scales. Evidently we cannot have simpleand compound scales, at least not in the same way as wehad simple and compound intervals. The fourth dis-tinction—that according to genera—must also exist in thecase of scales, some of them being diatonic, some chromatic,and some enharmonic. It is obvious that they also admitthe fifth principle of division: some are bounded by arational, and some by an irrational, interval. To these fourthere must be added three other classifications. First,there is that into the conjunct scales, the disjunct scales,and the scales that are a combination of both; every scale,provided it is of a certain compass, becomes either conjunctor disjunct, or else combines both these qualities—for casesare to be seen where the latter process takes place. Thereis, secondly, the division into transilient and continuous,every scale belonging to one category or the other; andfinally, that into single, double, and multiple, as all without 18exception admit of classification under these heads. Anexplanation of each of these terms will be given in thesequel.

Starting from these definitions and classifications wemust seek to indicate in outline the nature of melody. Wehave already observed that here the motion of the voice 'must be by intervals; herein, then, lies the distinctionbetween the melody of music and of speech—for there isalso a kind of melody in speech which depends upon theaccents of words, as the voice in speaking rises and sinksby a natural law. Again, melody which accords withthe laws of harmony is not constituted by intervals and

MACKAN JJ 177

ARISTOXENUS

notes alone. Collocation upon a definite principle is alsoindispensable, it being obvious that intervals and notes areequally constituents of melody which violates the laws ofharmony. It follows that the most important and signi-ficant factor in the right constitution of melody is theprinciple of collocation in general as well as its speciallaws. We see, then, that musical melody differs from themelody of speech, on the one hand, in employing motionby intervals, and from faulty melody, on the other hand,melody which violates the laws of harmony, by th a different

19 manner in which it collocates the simple intervals. Whatthis manner is will be shown in the sequel; for the presentit will suffice to insist on the fact that, though melody whichaccords with the laws of harmony admits of many variationsin collocating the intervals, there is yet one invariableattribute that can be predicated of every such melody, ofso great importance that with its removal the harmonydisappears. A full explanation will be given in the courseof the treatise. For the present we content ourselves withthis definition of musical melody in contradistinction tothe other species, but it must be understood that we havesupplied a mere outline without as yet reviewing the details.

Our next step will be to enumerate the genera into whichmelody in general may be divided. These are apparentlythree in number. Any melody we take that is harmonizedon one principle is diatonic or chromatic or enharmonic.Of these genera the diatonic must be granted to bethe first and oldest, inasmuch as mankind lights uponit before the others; the chromatic comes next. Theenharmonic is the third and most recondite; and it is onlyat a late stage, and with great labour and difficulty, thatthe ear becomes accustomed to it.

We shall now return to the second of the distinctionsin intervals previously enumerated, and shall proceed to

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examine one of the two classes there contrasted. Theseclasses consist, as was remarked, of concords and discords, 20and it is the former that we shall now take for consideration.We shall endeayour to establish the facts with regard to oneof the many points in which concords differ, namely respectof compass. The nature of melody in the abstract deter-mines which concord has the least compass. Though manysmaller intervals than the Fourth occur in melody, they arewithout exception discords. But while the least concordantinterval is thus determined, we find no similar determination .for the greatest; for as far at any rate as the nature ofmelody in the abstract is concerned, concords seem capableof infinite extension just as much as discords. If we addto an octave any concord, whether greater than, equal to,or less than, an octave, the sum is a concord. From thispoint of view, then, there is no maximum concord. If,however, we regard our practical capacities—in other words,the capacities of the human voice and of instruments—thereis apparently such a maximum, the interval, namely, com-posed of two octaves and a Fifth. The compass of threeoctaves is, as a matter of fact, beyond our reach. We mustof course determine the compass of the maximum concordby the pitch and limits of some one instrument. Fordoubtless we should find an interval greater than the above-mentioned three octaves between the highest note of thesoprano clarinet, and the lowest note of the bass clarinet;and again between the highest note of a clarinet player 21performing with the speaker open, and the lowest note ofa clarinet player performing with the speaker closed. Asimilar relation, too, would be found to exist between thevoices of a child and a man. It is, indeed, from casessuch as these that we come to know the large concords.For it is from voices of different ages, and instruments ofdifferent measurements that we have learned that the interval

N 2 i79

ARISTOXENUS

of three octaves, of four octaves, and even greater intervalsthan these are concordant. Our conclusion then is that,while the smallest concord is given by the nature of abstractmelody, the greatest is only determined by %our capabilities.

That the concordant intervals are eight in number willbe readily admitted. . . .

The determination of the interval of a tone is our nexttask. A tone is the difference in compass between thefirst two concords, and may be divided by three lowestdenominators, as melody admits of half tones, thirds oftones, and quarter-tones, while undeniably rejecting anyinterval less than these. Let us designate the smallest ofthese intervals the smallest enharmonic diesis, the next thesmallest chromatic diesis, and the greatest a semitone.

Let us now set ourselves to consider the origin and22 nature of the differences of the genera. Our attention

' |'| • must be directed to the smallest of the concords, that ofwhich the compass is usually occupied by four notes—whence its ancient name. [Now since in such an interval

r-< • s>, the notes may be arranged in many different orders, whatorder are we to choose for consideration? One in whichthe fixed notes and the notes that change with the variationin genus are equal in number. An example of the orderrequired will be found in the interval between the Meseand the Hypate: here, while the two intermediate notesvary, the two extremes are left unchanged by genus-variation.]Let this then be granted. Further, while there are severalgroups of notes which fill this scheme of the Fourth, eachdistinguished by its own special nomenclature, there is onewhich, as being more familiar than any other to the studentof music, may be selected as that wherein we shall considerhow variation of genus makes its appearance. It consistsof the Mese, Lichanus, Parhypate, and Hypate.

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That variation of genus arises through the raising andlowering of the movable notes is obvious; but the locusof the variation of these notes requires discussion. Thelocus of the variation of the Lichanus is a tone, for thisnote is never nearer the Mese than the interval of a tone,and never further from it than the interval of two tones.The lesser of these extreme intervals is recognized aslegitimate by those who have grasped the principle of theDiatonic Genus, and those who have not yet mastered it 23can be led by particular instances to the same admission.The greater of these extreme intervals, on the other hand,finds no such universal acceptance; but the reason forthis must be postponed to the sequel. That there is a styleof composition which demands a Lichanus at a distance oftwo tones from the Mese, and that far from being con-,temptible it is perhaps the noblest of all styles—this isa truth which is indeed far from patent to most musicalstudents of to-day, though it would become so if they wereled to the apprehension of it by the aid of concreteexamples. But to any one who possesses an adequateacquaintance with the first and second styles of ancientmusic, it is an indisputable truth. Theorists who areonly familiar with the style of composition now in voguenaturally exclude the two-tone Lichanus, the prevailingtendency being to the use of the higher Lichani. Theground of this fashion lies in the perpetual striving aftersweetness, attested by the fact that time and attentionare mostly devoted to chromatic music, and that whenthe enharmonic is introduced, it is approximated to thechromatic, while the ethical character of the music suffersa corresponding deflection. Without carrying this line ofthought any further, we shall assume the locus of theLichanus to be a tone, and that of the Parhypate to bethe smallest diesis, as the latter note is never nearer to the

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ARISTOXENUS

Hypate than a diesis, and never further from it than asemitone. For the loci do not overlap; their point ofcontact serves as a limit to both of them. The pointof pitch upon which the Parhypate in its ascent meets theLichanus in its descent supplies a boundary to the loci,

24 the lower locus being that of the Parhypate, the higher thatof the Lichanus.

Having thus determined the total loci of the Lichanusand Parhypate, we shall now proceed to ascertain their locias qualified by genus and shade. The proper method ofinvestigating whether the Fourth can be expressed in termsof any lower intervals, or whether it is incommensurablewith them all, is given in my chapter on 'Intervals ascer-tained by the principle of Concord/ Here we shall assume

f: that its apparent value is correct, and that it consists of twoand a half tones. Again, we shall apply the term Pycnumx

to the combination of two intervals, the sum of which isI less than the complement that makes up the Fourth. Let

us now, starting from the lower of the two fixed notes,take the least Pycnum: it will consist of the two least

< enharmonic dieses; while a second Pycnum, taken fromthe same note, will consist of two of the least chromaticdieses. This gives the two lowest Lichani of two genera—the enharmonic and the chromatic; the enharmonic Lichanibeing in general, as we saw, the lowest, the chromaticcoming next, and the diatonic being the highest. Again,let a third Pycnum be taken, still from the same note; thena fourth, which is equal to a tone; then fifthly, from thesame note, let there be taken a scale consisting of a toneand a quarter; then a sixth scale consisting of a tone and

\ a half. We have already mentioned the Lichani bounding\ 25 the first and the second Pycna; that bounding the third is

chromatic, and the special chroma to which it belongs is1 i. e. ' close,' ' compressed.'

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THE ELEMENTS OF HARMONY

called the Hemiolic. The Lichanus bounding the fourth.Pycnum is also chromatic, and the special class to which it -belongs is called the Tonic Chromatic. The fifth scale istoo great for a Pycnum, for here the sum of the intervalsbetween the Hypate and Parhypate and between the Par-hypate and the Lichanus is equal to the interval betweenthe Lichanus and the Mese. The Lichanus bounding thisscale is the lowest diatonic. The sixth scale we assumed isbounded by the highest diatonic Lichanus. Thus thelowest chromatic Lichanus is one-sixth of a tone higherthan the lowest enharmonic; since the chromatic diesisis greater than the enharmonic by one-twelfth of a tone—the third of a quantity being one-twelfth greater than thefourth—and similarly the two chromatic dieses exceed thetwo enharmonic by double that quantity, namely one-sixth—an interval smaller than the smallest admitted in melody.Such intervals are not melodic elements, or in other wordscannot take an independent place in a scale. Again, thelowest diatonic Lichanus is seven-twelfths of a tone higherthan the lowest chromatic; for from the former to theLichanus of the hemiolic chroma is half a tone; from thisLichanus to the enharmonic is a diesis; from the enhar-monic Lichanus to the lowest chromatic is one-sixth ofa tone; while from the lowest chromatic to that of thehemiolic chroma is one-twelfth of a tone. But as a quarter 26consists of three-twelfths, it is clear that there is the intervaljust mentioned between the lowest diatonic and the lowestchromatic Lichanus. The highest diatonic Lichanus ishigher than the lowest diatonic by a diesis. These con-siderations show the locus of each of the Lichani. EveryLichanus below the chromatic is enharmonic, every Lichanusbelow the diatonic is chromatic down to the lowest chroma-tic, and every Lichanus lower than the highest diatonic isdiatonic down to the lowest diatonic. For we must regard

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ARISTOXENUS

the Lichani as infinite in number. Let the voice becomestationary at any point in the locus of the Lichanus heredemonstrated, and the result is a Lichanus. In the locusof the Lichanus there is no empty space—no space incapableof admitting a Lichanus. The point we are discussing isone of no little importance.' Other musicians only disputeas to the position of the Lichanus—whether, for instance,the Lichanus in the enharmonic species is two tones re-moved from the Mese or holds a higher position, thus

; T assuming but one enharmonic Lichanus; we, on the other! / hand, not only assert that there is a plurality of Lichani

/ , in each class, but even declare that their number is infinite./ Passing from the Lichani we find but two loci for the

Parhypate, one common to the diatonic and chromaticgenus and one peculiar to the enharmonic. For two of thegenera have the Parhypate in common. Every Parhy-

27 pate lower than the lowest chromatic is enharmojiic; every;, ' other down to this point of limitation is chromatic and\{'' diatonic. As regards the intervals, while that between the

Hypate and Parhypate is either equal to or less than thatbetween the Parhypate and the Lichanus, the latter maybe less than, equal to, or greater than that between theLichanus and the Mese, the reason being that the twogenera have their Parhypate in common. We can havea melodious tetrachord with the lowest chromatic Parhypateand the highest diatonic Lichanus. Enough has now beensaid to show how great is the locus of the Parhypate bothin respect of its subdivisions and when regarded as awhole.

Of continuity and consecution it would be no easy taskto give accurate definitions at the outset, but a few roughindications must be offered. Continuity in melody seemsin its nature to correspond to that continuity in speech which

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THE ELEMENTS OF HARMONY

is observable in the collocation of the letters. In speaking,the voice by a natural law places one letter first in eachsyllable, another second, another third, another fourth, andso on. This is done in no random order: rather, the growthof the whole from the parts follows a natural law. Similarlyin singing, the voice seems to arrange its intervals and noteson a principle of continuity, observing a natural law ofcollocation, and not placing any interval at random afterany other, whether equal or unequal. In inquiring into 28continuity we must avoid the example set by the Harmonistsin their condensed diagrams, where they mark as consecutivenotes those that are separated from one another by the-smallest interval. For so far is the voice from being ableto produce twenty-eight consecutive dieses, that it can byno effort produce three dieses in succession. If ascendingafter two dieses, it can produce nothing less than the com-plement of the Fourth, and that is either eight times thesmallest diesis, or falls short of it only by a minute andunmelodic interval. If descending, it cannot after the twodieses introduce any interval less than a tone. It is not,then, in the mere equality or inequality of successiveintervals that we must seek the clue to the principle ofcontinuity. We must direct our eyes to the natural laws ofmelody and endeavour to discover what intervals the voiceis by nature capable of placing in succession in a melodicseries. For if after the Parhypate and the Lichanus thevoice can produce no note nearer than the Mese, then theMese is the next note to the Lichanus, whether the inteavalbetween them be twice or several times that between theLichanus and the Parhypate. The proper method of in-vestigating continuity is now clear; but how it arises, andwhat intervals do and do not form a succession, are questions 29which will be treated in the Elements.

We shall here assume that, having posited a Pycnum or185

ARISTOXENUS

a scale that is not a Pycnum, the smallest interval that can. succeed in the ascending scale is the complement of thej interval of the Fourth, and that the smallest similarly in thei descending scale is a tone. We shall assume that if a series

of notes be arranged in proper melodic continuity in any\ genus, any note in that series will either form with the fourth( from it in order the concord of the Fourth, or with the fifthi from it in order the concord of the Fifth, while possibly/ forming both. A note that answers to none of these testsI ' cannot belong to the same melodic series as those withI which it makes no concord. Further, we shall assume that; whereas there are four intervals contained in the interval ofj the Fifth, two of which are usually equal, viz. those con-j stituting the Pycnum, and two unequal—one the complement

of the first concord, the other the excess of the interval ofthe Fifth over that of the Fourth, the unequal intervalswhich succeed the equal intervals do so in different orderaccording as we ascend or descend the scale. We shallassume too that notes which form respectively the same

'( , concord with consecutive notes are themselves consecutive ;!• that in each genus a simple melodic interval is one which

the voice cannot divide in a melodic progression ; that notall the magnitudes into which a concord can be dividedare simple; that a sequence is a progression by consecutivenotes, each of which, between the first and last, is pre-ceded and succeeded by a simple interval; and that adirect sequence is one that maintains the same directionthroughout.

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BOOK II

I T will be well perhaps to review in anticipation the course 30. 10of our study; thus a foreknowledge of the road that we musttravel will enable us to recognize each stage as we reach it,and so lighten the toil of the journey; nor shall we be.harbouring unknown to ourselves a false conception of oursubject. Such was the condition, as Aristotle used often torelate, of most of the audience that attended Plato's lectureson the Good. They came, he used to say, every one ofthem, in the conviction that they would get from thelectures some one or other of the things that the world callsgood; riches or health, or strength, in fine, some extra-ordinary gift of fortune. But when they found that Plato'sreasonings were of sciences and numbers, and geometry,and astronomy, and of good and unity as predicates of thefinite, methinks their disenchantment was complete. The 31result was that some of them sneered at the thing, whileothers vilified it. Now to what was all this trouble due ?To the fact that they had not waited to inform themselvesof the nature of the subject, but after the manner of the sectof word-catchers had flocked round open-mouthed, attractedby the mere title ' good' in itself.

But if a general exposition of the subject had been givenin advance, the intending pupil would either have abandonedhis intention or if he was pleased with the exposition, wouldhave remained in the said conviction to the end. It wasfor these very reasons, as he told us, that Aristotle himselfused to give his intending pupils a preparatory statement of

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ARISTOXENUS

the subject and method of his course of study. And weagree with him in thinking, as we said at the beginning, thatsuch prior information is desirable. For mistakes are oftenmade in both directions. Some consider Harmonic asublime science, and expect a course of it to make themmusicians; nay some even conceive it will exalt their moralnature. This mistake is due to their having run away withsuch phrases in our preamble as ' we aim at the constructionof every style of melody,' and with our general statement' one class of musical art is hurtful to the moral character,another improves i t ' ; while they missed completely ourqualification of this statement, ' in so far as musical art canimprove the moral character.' Then on the other handthere are persons who regard Harmonic as quite a thing ofno importance, and actually prefer to remain totally un-acquainted even with its nature and aim. Neither of theseviews is correct. On the one hand the science is no properobject of contempt to the man of intelligence—this we shall

32 see as the discussion progresses; nor on the other hand'') , has it the quality of all-sufficiency, as some imagine. To

' -—~ be a musician, as we are always insisting, implies muchI : more than a knowledge of Harmonic, which is only one) part of the musician's equipment, on the same level as theli sciences of Rhythm, of Metre, of Instruments.(1 We shall now proceed to the consideration of Harmonic

and its parts. It is to be observed that in general thesubject of our study is the question, In melody of everykind what are the natural laws according to which the voicein ascending or descending places the intervals ? For wehold that the voice follows a natural law in its motion, anddoes not place the intervals at random. And of our answerswe endeavour to supply proofs that will be in agreement withthe phenomena—in this unlike our predecessors. For someof these introduced extraneous reasoning, and rejecting the

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THE ELEMENTS OF HARMONY

senses as inaccurate fabricated rational principles, asserting |that height and depth of pitch consist in certain numericalratios and relative rates of vibration—a theory utterlyextraneous to the subject and quite at variance with thephenomena; while others, dispensing with reason anddemonstration, confined themselves to isolated dogmaticstatements, not being successful either in their enumera-tion of the mere phenomena. It is our endeavour thatthe principles which we assume shall without exceptionbe evident to those who understand music, and that we 33shall advance to our conclusions by strict demonstration.

Our subject-matter then being all melody, whether vocalor instrumental, our method rests in the last resort on anappeal to the two faculties of hearing and intellect. By theformer we judge the magnitudes of the intervals, by thelatter we contemplate the functions of the notes. We musttherefore accustom ourselves to an accurate discriminationof particulars. It is usual in geometrical constructions touse such a phrase as ' Let this be a straight l ine' ; but onemust not be content with such language of assumption inthe case of intervals. The geometrician makes no use ofhis faculty of sense-perception. He does not in any degreetrain his sight to discriminate the straight line, the circle,or any other figure, such training belonging rather to thepractice of the carpenter, the turner, or some other such yhandicraftsman. But for the student of musical scienceaccuracy of sense-perception is a fundamental requirement.For if his sense-perception is deficient, it is impossible forhim to deal successfully with those questions that lie outsidgthe sphere of sense-perception altogether. This will becomeclear in the course of our investigation. And we must bearin mind that musical cognition implies the simultaneouscognition of a permanent and of a changeable element, and,that this applies without limitation or qualification to every

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ARISTOXENUS

branch of music. To begin with, our perception of thedifferences of the genera is dependent on the permanenceof the containing, and the variation of the intermediate,

34 notes. Again, while the magnitude remains constant, wedistinguish the interval between Hypate and Mese from thatbetween Paramese and Nete; here, then, the magnitudeis permanent, while the functions of the notes change;similarly, when there are several figures of the same magni-tude, as of the Fourth, or Fifth, or any other; similarly,when the same interval leads or does not lead to modulation,according to its position. Again, in matters of rhythm wefind many similar examples. Without any change in thecharacteristic proportion constituting any one genus ofrhythm, the lengths of the feet vary in obedience to thegeneral rate of movement; and while the magnitudes areconstant, the quality of the feet undergoes a change; andthe same magnitude serves as a foot, and as a combinationof feet. Plainly, too, unless there was a permanent quantumto deal with there could be no distinctions as to the methods

i\ of dividing it and arranging its parts. And in general,I: while rhythmical composition employs a rich variety ofI. • movements, the movements of the feet by which we note

"; •' . the rhythms are always simple and the same. Such, then,being the nature of music, we must in matters of harmonyalso accustom both ear and intellect to a correct judgementof the permanent and changeable element alike.

These remarks have exhibited the general character ofthe science called Harmonic; and of this science there are,

35 as a fact, seven parts. Of these one and the first is todefine the genera, and to show what are the permanent andwhat are the changeable elements presupposed by thisdistinction. None of our predecessors have drawn this dis-tinction at all; nor is this to be wondered at. For theyconfined their attention to the Enharmonic genus, to the

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THE ELEMENTS OF HARMONY

neglect of the other two. Students of instruments, it istrue, could not fail to distinguish each genus by ear, butnone of them reflected even on the question, At what pointdoes the Enharmonic begin to pass into the Chromatic ?For their ability to discriminate each genus extended not toall the shades, inasmuch as they were not acquainted withall styles of musical composition or trained to exercise anice discrimination in such distinctions ; nor did they evenobserve that there were certain loci of the notes that altertheir position with the change of genus. These reasonssufficiently explain why the genera have not as yet beendefinitely distinguished; but it is evident that we mustsupply this deficiency if we are to follow the differencesthat present, themselves in works of musical composition.

Such is the first branch of Harmonic. In the second weshall deal with intervals, omitting, to the best of our ability,none of the distinctions to be found in them. The majorityof these, one might say, have as yet escaped observation.But we must bear in mind that wherever we come upon adistinction which has been overlooked, and not scientificallyconsidered, we shall there fail to recognize the distinctions 36in works of melodic composition.

Again, since intervals are not in themselves sufficient todistinguish notes—-for every magnitude, without qualifica-tion, that an interval can possess is common to severalmusical functions—the third part of our science will dealwith notes, their number, and the means of recognizingthem; and will consider the question whether they arecertain points of pitch, as is vulgarly supposed, or whetherthey are musical functions, and also what is the meaning ofa musical 'function.' Not one of these questions is clearlyconceived by students of the subject.

The fourth part will consider scales, firstly as to theirnumber and nature, secondly as to the manner of their

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construction from intervals and notes. Our predecessorsi; have not regarded this part of the subject in either of thesejjj respects. On the one hand, no attention has been devotedj \ to the questions whether intervals are collocated in anyl!| order to produce scales, or whether some collocations may]/ not transgress a natural law. On the other hand, the dis-

tinctions in scales have not been completely enumerated byany of them. As to the first point, our forerunners simplyignored the distinction between ' melodious ' and ' un-melodious ' ; as to the second, they either made no attemptat all at enumeration of scale-distinctions, confining theirattention to the seven octave scales which they calledHarmonies ; or if they made the attempt, they fell veryshort of completeness, like the school of Pythagoras of

37 Zacynthus, and Agenor of Mitylene. T h e order that dis-tinguishes the melodious from the unmelodious resemblesthat which we find in the collocation of letters in language.For it is not every collocation but only certain collocationsof any given letters that will produce a syllable.

T h e fifth part of our science deals with the k e y s in whichthe scales are placed for the purposes of melody. No explana-tion has yet been offered of the manner in which those keysare to be found, or of the principle by which one must beguided in enunciating their number. The account of thekeys given by the Harmonists closely resembles the obser-vance of the days according to which, for example, the tenthday of the month at Corinth is the fifth at Athens, and theeighth somewhere else. Just in the same way, some ofthe Harmonists hold that the Hypodorian is the lowestof the keys ; that half a tone above lies the Mixolydian;half a tone higher again the Dor ian ; a tone above theDorian the Phrygian; likewise a tone above the Phrygian theLydian. The number is sometimes increased by the addi-tion of the Hypophrygian clarinet at the bottom of the list.

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Others, again, having regard to the boring of finger-holeson the flutes, assume intervals of three quarter-tones betweenthe three lowest keys, the Hypophrygian, the Hypodorian,and the Dorian; a tone between the Dorian and Phrygian;three quarter-tones again between the Phrygian and Lydian,and the same distance between the Lydian and Mixolydian.But they have not informed us on what principle they have 38persuaded themselves to this location of the keys. Andthat the close packing of small intervals is unmelodious andof no practical value whatsoever will be clear in the courser"of our discussion. -•• • -* "

Again, since some melodies are simple, and others containa modulation, we must treat of modulation, consideringfirst the nature of modulation in the abstract, and how itarises, or in other words, to what modification in the melodicorder it owes its existence; secondly, how many modulationsthere are in all, and at what intervals they occur. On thesequestions we find no statements by our predecessors with*or without proof.

The last section of our science is concerned with theactual construction of melody. For since in the samenotes, indifferent in themselves, we have the choice ofnumerous melodic forms of every character, it is evidentthat here we have the practical question of the employmentof the notes; and this is what we mean by the constructionof melody. The science of harmony having traversed thesaid sections will find its consummation here.

It is plain that the apprehension of a melody consists innoting with both ear and intellect every distinction as itarises in the successive sounds—successive, for melody,like all branches of music, consists in a successive pro-duction. For the apprehension of music depends on these . -two faculties, sense-perception and memory;, for we must-39- •perceive the sound that is present, and remember thatwhich.„ ,

MACRAN O 193

ARISTOXENUS

is past. In no other way can We follow the jAenomena of'music. ""'••"

Now some find the goal of the science called Harmonicin the notation of melodies, declaring this to be the ultimatelimit of the apprehension of any given melody. Othersagain find it in the knowledge of clarinets^ and in the ability

/() ' to tell the manner of production of, and the agencies1 employed in, any piece rendered on the clarinet-

Such views are conclusive evidence of an utter miscon-ception. So far is notation from being the perfection ofHarmonic science that it is not even a part of it, any morethan the marking of ariy particular metre is a part ofmetrical science. As in the latter case one might very wellmark the scheme of the iambic metre without understandingits essencej so it is with melody a lso; if a man notes downthe Phrygian scale it does not follow that he must know theessence of the Phrygian scale. Plainly then notation is notthe ultimate limit of our science;

That the premises of our argument are true, and that thef)i faculty of musical notation argues nothing beyond a dis-

cernment of the size of intervals, will be clear on considera-tion. In the use of signs for the intervals no peculiarmark is employed to denote all their individual distinctions,

40 such as the several methods of dividing the Fourth, which,. . j depend on the differences of genera, or the several figures

of the same interval which result from a variation in thedisposition of the simple intervals. It is the same withthe musical functions proper to the natures of the differenttetrachords; the same notation is employed for the tetra-chords Hyperbolaeon, Neton, Meson, and Hypaton. Thusthe signs fail to distinguish the functional differences, andconsequently indicate the magnitudes of the intervals, andnothing more. But that the mere sense-discrimination ofmagnitudes is n o part of the general comprehension of

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THE ELEMENTS OF HARMONY

music was stated in the introduction, and the followingconsiderations will make it patent. Mere knowledge ofmagnitudes does not enlighten one as to the functions of thetetrachords, or of the notes, or the differences of the genera,or, briefly, the difference of simple and •compound intervals,or the distinction between modulating and non-modulatingscales, or the modes of melodic construction, or indeedanything else of the kind.

Now if the Harmonists, as they are called, have in theirignorance seriously entertained this view, while there isnothing preposterous in their motives, their ignorance mustbe profound and invincible.. But if, being aware thatnotation is not the final goal of Harmonic, they have pro-pounded this view merely through the desire to pleaseamateurs, and to represent as the perfection of the sciencea certain visible activity, their motives deserve condemnation 41as very preposterous indeed. In the first place they wouldconstitute the amateur judge of the sciences—and it ispreposterous that the same person should be learner andjudge of the same thing; in the second place, they reversethe proper order in their fancy of representing a visibleactivity as the consummation of intellectual apprehension;for, as a fact, the ultimate factor in every visible activity isthe intellectual process. For this latter is the presiding anddetermining principle; and as for the hands, voice, mouth,or breath—it is an error to suppose that they are very muchmore than inanimate instruments. And if this intellectualactivity is something hidden deep down in the soul, and isnot palpable or apparent to the ordinary man, as theoperations of the hand and the like are apparent, we mustnot on that account alter our views. We shall be sure tomiss the truth unless we place the supreme and ultimate, notjn the thing determined, but in the activity that determines.

No less preposterous is the above-mentioned theoryo 2 195

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ARISTOXENUS

concerning clarinets. Nay, rather there is no error sofatal and so preposterous as to base the natural laws of

(iji harmony on any instrument. T h e essence and order ofM| harmony depend not upon any of the properties of instru-!'| ments. I t is not because the clarinet has finger-holes and(ijli 42 bores, and the like, nor is it because it submits to certainf' j operations of the hands and of the other parts naturally</ I adapted to raise and lower the pitch, that the Fourth, and1 ! the Fifth, and the Octave are concords, or that each of the, I other intervals possesses, its proper magnitude. For even;j I with all these conditions present, players on the clarinetj j fail for the most part to attain the exact order of me lody ;

and whatever small success at tends them is due to theemployment of agencies external to the instrument, as in

j! the well-known expedients of drawing the two clarinetsapart, and bringing them alongside, and of raising andlowering the pitch by changing the pressure of the breath.Plainly, then, one is as much justified in attributing theirfailures as their success to the essential nature of theclarinet. But this would not have been so if there wasanything gained by basing harmony on the nature of aninstrument. In that case, as an immediate consequence oftracing melody up to its original in the nature of theclarinet, we should have found it there fixed, unerring, andcorrect. But as a fact neither clarinets nor any otherinstrument will supply a foundation for the principles ofharmony. There is a certain marvellous order whichbelongs to the nature of harmony in general; in this orderevery instrument, to the best of its ability, participatesunder the direction of that faculty of sense-perception onwhich they, as well as everything else in music, finally

-...~< depend! To suppose, because one sees day by day thefinger-holes the same and the strings at the same tension^that one will find in these harmony with its permanence

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THE ELEMENTS OF HARMONY

and eternally immutable order—this is sheer folly. For 43as there is no harmony in the strings save that which thecunning of the hand confers upon them, so is there none in ..the finger-holes save what has been introduced by the sameagency. That no instrument is self-tuned, and that theharmonizing of it is the prerogative of the sense-perceptionis obvious, and requires no proof. It is strange that thesupporters of this absurd theory can cling to it in face of thefact that clarinets are perpetually in a state of change; andof course what is played on the instrument varies with thevariation in the agencies employed in its production. It issurely clear then that on no consideration can melody bebased on clarinets; for, firstly, an instrument will not supplya foundation for the order of harmony, and secondly, evenif it were supposed that harmony should be based on someinstrument, the choice should not have fallen on the clarinet,an instrument especially liable to aberrations, resulting fromthe manufacture and manipulation of it, and from its ownpeculiar nature.

This will suffice as an introductory account of Harmonicscience; but as we prepare ourselves to enter upon thestudy of the Elements we must at the outset attend to thefollowing considerations. Our exposition cannot be a suc-cessful one unless three conditions be fulfilled. Firstly,the phenomena themselves must be correctly observed;secondly, what is prior and what is derivative in them must 44be properly discriminated; thirdly, our conclusions andinferences must follow legitimately from the premises. Andas in every science that consists of several propositions theproper course is to find certain principles from which todeduce the dependent truths, we must be guided in ourselection of principles by two considerations. Firstly, everyproposition that is to serve as a principle must be true ande'vident; secondly, it must be such as to be accepted by the

T 9 7 - - " - • - - • •

i'1:1

ARISTOXENUS

sense-perception as one of the primary truths of Harmonicscience. For what requires demonstration cannot stand asa fundamental principle ; and in general we must be watch-ful in determining our highest principles, lest on the onehand we let ourselves: be dragged outside the proper trackof our science by beginning with sound in general regardedas air-vibration, or on the other hand turn short of the flagand abandon much of what truly belongs to Harmonic.

There are three genera of melodies ; Diatonic, Chromatic,and Enharmonic. The differences between them will bestated hereafter; this we may lay down, that every melodymust be Diatonic, or Chromatic, or Enharmonic, or blendedof these kinds, or composed of what they have in common.

/l'l The second classification of intervals is into concords.. and discords. The two most familiar distinctions in

intervals are difference of magnitude, and difference betweenconcords and discords; and the latter of these is embracedby the former, since every concord differs from every discordin magnitude. Now there being many distinctions among

45 concords, let us first treat of the most familiar of them,namely, difference of magnitude. We assume then eightmagnitudes of concords ; the smallest, the Fourth—deter-mined as smallest by the abstract nature of melody; forwhile we can produce several smaller intervals, they are alldiscords ; the next smallest, the Fifth, all intervals betweenthe Fourth and Fifth being discords; the third smallest,the sum of the first two, that is the Octave, all intervalsbetween the Fifth and the Octave being discords. So far wehave been stating what we have learned from our predeces-sors ; henceforth we must arrive at our conclusions unaided.

In the first place then we shall assert that if any concordbe added to the octave the sum is a concord. This propertyis peculiar to the octave. For if to an octave be added anyconcord, whether less than, equal to, or greater than itself,

198