The Spondeion Scale

PSEUDO-PLUTARCH DE MUSICA, 1134F-1135B AND 1137B-D. Our information about the early stages of Greek music is so slight that these references of the Pseudo-Plutarch to a scale employed by the legendary figure Olympus take on an immense value for us. The dialogue itself is an unskilful patchwork, but the author’s sources are often good. These particular passages are almost certainly both derived with small alteration from Aris- TWANAGNAaASM,2.2 toxenus, in whose time the traditional music ascribed to Olympus was still in use. For the elucidation of the scale’s history and structure we have three? pieces of evidence to help us. There is the first passage mentioned above, which deals with the discovery of the enharmonic genus by Olympus, which is connected, at first sight obscurely, with the Spondeion scale; and the second passage, which discusses the scalar limitations of the omovSed£wr Tpömos, with especial reference to an elementary polyphony. There are also the ancient scales quoted by Aristides Quintilianus (ed. Meibom, p. 21). Our best starting-point will be Plutarch’s account (1134F) of the origin of the enharmonic, which runs as follows (in Weil and Reinach’s edition, §§ 104-117): (104) "OXvumos dt, bs "Apıoröfevös drow, dürohauBävera vd THY povoiwxdv TOD évappoviov yévous ebper)s yeyevñodar: Sidrova Kai xpwpatixd Hv. yevéo Oar. (106) (105) Ta yap mpo ékeivou mavra ümovoodeı de Tv ebpeoiy Tosaurnv Twa (107) avaatpepopevov tov "OAvumov ev TO dtarovo ral ScaBiBatovra TO pédos moAAdkıs eri THY Biatovov mapumarnv, TOTÈ pèv dmò THS Tapapéons rorè de amo THs péons, Kal mapaßalvovra Tv Sidrovoy Aıyavov, (108) karanadeiv To KuAAos TOU HOous, Kal odrw TÓ Ex THs avadoyias cuverTHKOS ovornua Oavpdcavra Kal àmodeËauevoy, Ev rovrm moueîy émi Tod Awpiov Tövov. (109) obre yap tav Tod Siatovou idiwy ote THY TOD ypéparos ämreoËa, GAN oúde THY TIS dppovias. (110) elvas $' avr rá mpôTa Tv Evappoviwv Toradta * Tibéaor yap ToUTwY mp@Tov TO amovbeiov, ev @ obdeuia Tôv Siatpécewy TO idvov éupaivei, (111) el un Tes eis TOY œuvrov@Tepor amovderacpòv BAérwv avrò roùro dLdrovov elvas árreixaon» ÔAov 8 Ste nal \rebdos ra) éxperès Once 6 Tosodro rubeis- (112) yeddos pev, Ste Biérer EXatroy ¿ori Tovou Tov mepi Tov Tıyenöva rerpévov * (113) éxperes dé, Tu, al ei Tes Ev TH TOD Tovialov Suvaper rein TO TOD œuvrovw- Tepov orovderac pod idiov, cupPaivor Av Bo ¿Ens Tideodaı Sitova, To pèv do vvderov, Tù Se auvderov. ! Or four, if we (114) Ta pèv odv pata TÓv évapuoviwv ToradTa* include the reference of the passage of Aristoxenus, that Aristides Quintilianus (p. 28,-Meibom) to an interval orovderacpds, consisting of a rise of three- Plutarch himself makes use of. quarters of a tone, which are lost to us, and very possibly culled from one of them his list of ancient scales (cf. This must certainly have some connexion with the Spondeion scale. It is, however, possible that Aristides’ only authority vi for it was (115) TO yap Aristides probably was in possession of books of Aristoxenus J. F. Mountford in C.Q., Vol. XVII.).

PSEUDO-PLUTARCH DE MUSICA, 1134F-1135B AND 1137B-D. Our information about the early stages of Greek music is so slight that these references of the Pseudo-Plutarch to a scale employed by the legendary figure Olympus take on an immense value for us. The dialogue itself is an unskilful patchwork, but the author’s sources are often good. These particular passages are almost certainly both derived with small alteration from Aristoxenus, in whose time the traditional music ascribed to Olympus was still in use. For the elucidation of the scale’s history and structure we have three! pieces of evidence to help us. There is the first passage mentioned above, which deals with the discovery of the enharmonic genus by Olympus, which is connected, at first sight obscurely, with the Spondeion scale; and the second passage, which discusses the scalar limitations of the orovSerdfwv Tpórros, with especial reference to an elementary polyphony. There are also the ancient scales quoted by Aristides Quintilianus (ed. Meibom, p. 21). Our best starting-point will be Plutarch’s account (1134F) of the origin of the enharmonic, which runs as follows (in Weil and Reinach’s edition, §§ 104-117): (104) “OXvyrros dè, ds ’Apıoröfevös brow, dbrodapBaveras dTd THY pouvoir TOD évappoviov yévous eüperijs wyeryevijodart® (105) Ta yap mpd éxelvou mávra Sidtova Kai ypwpatixa Fv. (106) Úmovoodor de Tv eÜpeow Touaÿrmv Twa yeveodaı. (107) dvanrpeböuevov Tov "OAyumov Ev TO Òraróvp Kai GaBuBabovra To pédos moAAarıs ert THY SidtTovey Mapvmarnv, TOTÈ pev aT TŸS Tapapéons YOY 20 Un / \ 7 \ 2 / ‚a Tore Òè amo THs péons, Kal mapaßalvovra Tv Öuárovov Auyavov, (108) karauadeiv A CA 2 A 2 4 \ / [4 TO\ kaAAos Todao”Nous, Kal\ oüTw TO\ ex THs avadoyias ovveornròs avornua Havud\ 2 # 2. / a > \ a # Ja # \ cavra Kai amode&duevov, Ev ToUT@ Troteiv ert Tod Awpiov Tóvov. (10g) oùTe yap A A , 297 # A A 2 ¢ > ’ EEND A a Tv Tov SvaTévou idiwv oùTe TOY TOD YpwmaTos ämreodal, ANN oùë THY THs äppovias. (110) eva Ô aùr® Ta TpaTa TOY évappoviwr TouadTa * Tibéaor yap € # 3 u > A \ A A ? va A LA \ ToÚrwv mp®Toy TO omovdelov, Ev @ ovdepia TaV Siatpécewv TO idioy eudaiver, (III) ei un Tus eis TOY ouvrovwrepov amovdeaouov [BAérwv aùrò TOTO SiaTovoY elvaı dmeındon‘ Shdrov Ô Ste Kai Weddos Kai Ermedès Onoet 6 TowodTo Tubeis: (112) Weddos jèv, te Öuéoer EXaTTOV Eorı TÓvov TOD Tepl TOV iyepóva KELpEévOU * (113) éxperes dè, GT, Kal el Tus Ev TH TOD Tomaiov Övvaneı Tıdein TO TOD ovvTovoTépov orrovdetac pod iStov, cupBaivos Av Òúo EEns Tier Oat Sitova, TO pèv doúvderov, Tò 5é ovvOeTov. (114) TA pev ody TPATA TOV éevappoviwy ToLadTa* (115) TO yap 1 Or four, if we include the reference of Aristides Quintilianus (p. 28, Meibom) to an for it was the passage of Aristoxenus, that Plutarch himself makes use of. Aristides probinterval orovdeacuds, consisting of a riseof threequarters of a tone. This must certainly have ably was in possession of books of Aristoxenus which are lost to us, and very possibly culled some connexion with the Spondeion scale. Itis, however, possible that Aristides’ only authority from one of them his list of ancient scales (cf. J.F. Mountford in C.Q., Vol. XVII.).

év Tals uéoais évappovioy muKvòv, @ viv KpÔvrar, où Soxet rod motnTod eivar. padıov & éorl cuvideiv, dav Tus dpyarks Tivos adrovvTOS akovan* doúvderov yap Bovnretat eivaı Kal To &v Taîs péoas muurovov* (116) Dorepov Ôè To murôvio SunpéOn Ev Te roîs Audlous Kai Ev roîs Dpuyios. (117) patverart 8 "OAvumos ad£noas povotkny TÔ ayévntov Tt Kal ayvootpevoy dd TÔv Eumpocdev eloaryayetr, Kal apynyos yéver Oar Tis “EXAnvirijs Kal Karts mouais. The text of this passage is fairly sound, and, although we may have doubts about the exact order of the sentences, the meaning is fairly clear. On the grounds of the last sentence Aristoxenus or Plutarch has been accused of muddle-headedness. This is quite unfair. It is true that Olympus according to this account did not introduce the quarter-tones of the enharmonic genus, but it is equally true that these quarter-tones were not the only characteristic of the enharmonic; the omission (hypothetical) of the G and the resulting Sitovos Avyavos were an essential preliminary to the splitting of the semitone, which may originally have been in the nature of an ornament. We need not, of course, believe any actual musician to have omitted a note in the diatonic series. Olympus, as we have seen, was a legendary figure; the enharmonic was no accidental discovery. The tradition amounts to this—that Greeks at some point before accurate musical history begins came in contact with a type of music which used the öirovos doúvderos, and adopted it and the quarter-tones, which were an elaboration of it. Plutarch calls it ‘ Hellenic and beautiful.’ On any theory it is curious that music, regarded as the invention of Olympus and subsequent to the diatonic, should be called ‘ Hellenic.’ It is accounted for by the later popularity of this style, and particularly by Aristoxenus’ glorification of it. The gapped scale, then, which the enharmonic implies, was a real contrast to a completer series of diatonic notes which we can assume to have been pre-existent in Greece, and ‘Olympus’ really did enrich Greek music with a new element. The legend of the manner of his discovery is a picturesque fiction emphasizing that contrast; we need not pursue its details so far as to ask in what exact scale, mode, or key Olympus was playing when he made his great ‘discovery.’ We are told, however, that he constructed a Dorian scale ex ríjs dvadoyias. This can only mean that the later Greeks were aware of an old scale of this sort: EF ABC (E). ‘Such,’ continues our author, ‘ was the character of the first enharmonic compositions of Olympus, for they count as the first of them the Spondeion, in which none of the (tetrachordal) divisions manifests its peculiarities.’ The omovdeiov, then, bore some relation, possibly of identity, to the earliest enharmonic music. Further, it contained no notes characteristic of any of the genera—that is, it had neither the diatonic lichanos and dirovos oúvberos, nor, at least as yet, the ruxvor. Weil and Reinach ($ 110, n.) quote a number of passages to prove that it was a Dorian scale. This seems very probable, in which case it must have been very similar to the scale written out a few lines 1 Probably it was the name given to the Dorian varieties of the early enharmonic, otherwiseknownasrà Aúpia. We know that Phrygian and Lydian varieties also existed. See p. go n.

above. Further information, however, is given about it in the Plutarch text. There was, he says, in it an element that might be described as diatonic— namely, ‘the higher spondeiasmus’; this, however, was an erroneous way of looking at it, and implied an unmelodious succession of intervals—a ditone (aúvderov) followed by a ditone (davvOerov). This is of course impossible according to the principles of Aristoxenus; and it is carefully explained that the omovöeıacuös interval is not a tone, but three-quarters of a tone, smaller, that is, than the disjunctive tone which precedes it. We get, then, a scale of this sort:! EF AB C* The look of it not being liked by editors, it is suggested that Aristoxenus, who can almost certainly be accounted the actual author of the sentences in question (the argument proceeds according to the canons laid down in his Harmonics, Bk. III.), has made a mistake, interpreting an old crovêeacuos of three semitones (the Pythagorean Oéeous, see Philolaus, ap. Nic. 9; Adrastus, ap. Theo., p. 55, Hiller) as though it were of three modern véoeus, or quarter-tones.” When it was seen that this alteration gave a scale EF AB D(E) not only closely resembling the rporos omovdeafov of the later passage in the dialogue, as usually interpreted, but also the supposed defective heptachords of Terpander and Philolaus, belief in this hypothesis was much strengthened. We shall see that there is no more reason to believe in the one than in the other. Apart from that, however, we should not accuse Aristoxenus of so grave a mistake without good reason. This theory leads us to assume either that the interval known as omovòeracpós changed from a tone and a half to three-quarters of a tone concurrently with the change of usage of the word öiecıs, which is absurd ; or that there never was an interval orrovöeracgós in the orovdetor scale, but merely one of three semitones, which Aristoxenus mistook by a verbal mistake for the later omordeaouôs that he knew, which is also absurd; or else that the only omrovòevacpós there ever was was of three Pythagorean Géces, and that Aristides (p. 28, Meibom) merely perpetuated the mistake of Aristoxenus and described a never existing interval, which is just possible, but unlikely. Aristoxenus in the Plutarch passage is describing, surely, a scale he knew, not one he had laboriously reconstructed from a purely verbal tradition. We must then believe in the scale as given by Plutarch in default of some valid reason for rejecting it. We come next to the tpdzros orrovòeudtwv. Various notes of this scale are mentioned (Plut., § 172, etc.) in an attempt to prove that the ancients had limited their art by omitting from their scales notes they might have employed. It is a curious way of putting it, but not so erroneous as is sometimes suggested if we believe that the complete diatonic series was known comparatively early, and used concurrently with less complete scales of possibly non-Hellenic origin. Three notes in particular, according to this passage, were not employed in the rpórros orovdeadfov—namely, rpirn, vnrn, and ‘rpérn ouvnuuevov. (The 1 The symbol * aftera note here indicates that it is raised by a quarter of a tone. ? Greif also (Rév. des Et. G., 1910) makes the same assumptions to produce the scale (D) EF ABD CED. But he assumes, further, that Aristoxenus was completely misinformed about the scale, and imported the disjunctive tone into his account.

erroneous text of Weil and Reinach will provide a convenient starting-point for our argument.) However, though they were not employed in the melody, they were employed in the accompaniment in the following manner: rpirn consonantly with wapumarn; vir dissonantly with mapavÿrn and consonantly with péon and rapapéon; tpitn ovvnupévov dissonantly with mapavjrn and Avxavos (again adopting for the moment the readings of Weil and Reinach). According to their interpretation we now have a scale with the following scheme: HÉXos - EFGAB D } Kpovots - - BC E This is naturally brought into relation with the supposed defective scale of Philolaus, with its tpunusroviov doúvderov, and with the orovdetor of the earlier Plutarch passage, emended to correct the supposed mistake of Aristoxenus and endowed with a diatonic lichanos. (For the moment we can disregard the notes of the accompaniment; the rest of the scale existed before they were employed, which cannot have been earlier than the time of Archilochus.) We have seen that there is no good reason to believe in this ‘howler’ of Aristoxenus. There is no more reason for supposing that the omwovdeiov ever had a diatonic lichanos. In the earlier passage we are told that the orovôetor of Olympus was an enharmonic of the early type which had no quarter-tones— such were the first enharmonics; later the semitone was divided. implication. This is the It is, then, natural to suppose that the osrovdetov remained enharmonic, and that Aristoxenus (if Aristoxenus it is) in referring to its notes refers to the notes of the enharmonic genus, not the diatonic. This is the natural assumption in the absence of specific instructions to the contrary. The notes of the melody then become EE*F ABC; those of the accompaniment, B* and E (‘ rpirn ovvnuuevov ’ shall be left for separate and later consideration). This interpretation, besides being logical, has certain striking advantages and confirmations. In the first place, the scale it gives corresponds very closely with the scale of Olympus’ enharmonic, as deduced from the Plutarch account, differing from it only in the split semitone of the lower tetrachord. It also corresponds with the early omwovdeiov discussed in the same passage, except that there is no suggestion that the B-C interval was widened to a three-quarter tone. But above all it simplifies the account here given of the polyphony of the omroverdfwv rpomos. Let us take the three accompanying notes one by one. First, we are told (172) that the ancients abstained from the note rpirn, the omission of which contributed to the characteristic effect of the style. In the accompaniment, however, it was used consonantly with mapurärn. Of course, the tpirn in any genus would always form the consonance of the fifth with the rapurärn. There is no need here to mark a lacuna with Weil and Reinach, as there is no reason why Plutarch should necessarily have given more than one example; further, on our interpretation there is no other note

with which the pgeoómvkvov, tpitn, would form a likely interval, consonant or dissonant. Apart from the question of polyphony, the absence of the splitting of the semitone becomes most interesting when we turn to $ 115. There we are told that the splitting of the semitone in the tetrachord péowy was not the work of Olympus, implying that this was the first step; further, that the old-fashioned style of flute-playing in the day of Aristoxenus (presumably) tended to leave even the semitone in the tetrachord méowv undivided— a fortiori, that in the tetrachord Sefevyuevwv. Here in section 172 we have implied a Spondeion scale,! in which only the lower tetrachord has its semitone divided ! Sections 175-177 deal with vry. All accounts agree that this note did not form part of the early melodic compass, and most of them ascribe its addition to Terpander. It is not surprising, therefore, to find that it was not used in the Spondeion melodies, when even the diatonic scale had not attained to it. When the ‘ Dorian vyrn ’? was added, it was not inserted ruthlessly in this well-established style of music, but used when polyphony came into practice in two ways—dissonantly with wapavyrn, consonantly with péon. If we interpret wapavyrn as the enharmonic srapavijry (=C) we abolish that discordant D-E interval, which has always made the orthodox theory of polyphony, if not slightly ridiculous, at least incomprehensible, and substitute for it an interval, the major third, just such as we should have expected the Greeks to employ if once they had wandered beyond those they recognized as consonant. The concordant use with méon (E-A) needs no comment. It is unnecessary to add with Weil and Reinach «al mpös mapauéonv from 179, as we shall see when we examine the following sections. Before proceeding to the last of the accompanying notes, however, we must digress to discuss shortly the defective scales ascribed to Terpander and Philolaus, which can be closely related to the Spondeion. We will deal with Philolaus first. Nicomachus, in the ninth chapter of his Encheiridion (Musici Scriptores Graeci, Teubner), quotes from him to illustrate the old Pythagorean terminology. He is describing the well-known harmonic framework (dppovia), which can be represented by the notes E-A-B-E. Only he calls the note B, not mapagéon, but rpirn. Howis this? Nicomachus is at pains to explain, but gets himself into a terrible muddle in doing so. He has to imagine an original heptachord EFGAB DE, different from that he assumes in Chapter XI., and that the disjunctive tone (rod d:afevyvivros Tóvov) was inserted between mapavyrn (D) and rpirn (B)! Tpirn thereupon suffered a change of name to mapaueon. Except for the last statement this is pure invention to account for the terminology of Philolaus, and took this form because Nicomachus imagined Philolaus was dealing with a normal diatonic scale. We in our turn now have to account for the Pythagorean’s use of rpirn. It is true it can only apply to a scale in which a single note separated it from v#rn. Is the series more likely 1 Strictly the term ‘Spondeion’ should be reserved for the scale without quarter-tones. This is its development, the orovded{wy rpéros. 2 Section 270,

to have been B-D-E or B-C-E? In view of what we have seen of the old style (the dpya:xol Tpómot of Aristoxenus, p. 23), we can have no doubt that Philolaus was using the nomenclature of a scale in which v#rn (E) had been added to the old Spondeion without the division of the semitone B-C. B-C-E is not the tetrachord of later music, but the trichord of the archaic style (cf. Plutarch, § 171). We may now turn to the Aristotelian problems for an account of the work of Terpander. Four problems of the nineteenth book deal with the heptachord, the octachord, and the position of ueon in them. Problem 47 takes what we may describe as the orthodox view—that the heptachord was merely the octachord without the disjunctive tone, and that its wéon was the lowest note of its upper tetrachord. Problem 44 implies the same point of view. Problems 7 and 32, however, in answering their respective questions, refer to an omission of the note rpirn, and the second of them associates this definitely with Terpander. Gevaert‘ was probably right in regarding these references as interpolations ; he was entirely wrong, however, in ascribing them to followers of Nicomachus and interpreting them diatonically. They must have been written by someone who knew the old Spondeion scale, and that in it the note tpitn, the peoórrvevov, was not regularly employed, who knew also the tradition that Terpander had added the vyrn. He therefore conceived that the innovator, finding a scale EE* F ABB*C (a kind of heptachord), had suppressed the rpirn (B*) in order to add the vyrn (E). As an historical procedure this is of course improbable. It was not the addition of vijrn that caused the omission of rpirn; but the Plutarch passage is borne out in an interesting manner, and we can even believe that vyrn came to be used with the old Spondeion before the splitting of the upper semitone. Gevaert objected that the scale in question must be diatonic, not enharmonic, because otherwise the hypothetical omission of vijrn would leave a scale bounded not by a seventh, but by a sixth. But it is just such a scale that the interpolator contemplates, similar in compass to the old Spondeion and to the Syntonolydian of Aristides Quintilianus. Nor need we be distressed by the variation in the use of rpirn between Philolaus and the Problems. Before the semitone was divided and the pycnon came into being, the nomenclature preserved by Philolaus may well have been used; the introduction of the weoómvrvov obviously renders a change necessary. Nicomachus was thus right on at least one point. We can now return to a consideration of the polyphony of the omrovòerdfov tpotos. A third suppressed note is there dealt with. The MSS. are unanimous in reading ouvmuuéver vijr (or some minor variant). Weil and Reinach, thanks to their interpretation of the nomenclature as diatonic, felt themselves compelled to emend vir to Tpirn, thus landing themselves in hopeless difficulties. On their theory, of course, vntn cvrvnupévor is the same note as the mapavrn, already mentioned as a melodic note; also, it is not dissonant with the lichanos (D-G), as by § 179 it should be. But what is the tpitn avvnunevwv 1 Problèmes Musicaux d’Aristote, Gevaert et Vollgraf.

doing in this scale at all? The Aeolian used it and perhaps the Mixolydian, but not the Dorian, to which this scale is related. Secondly, it is made to act as accompaniment to a note (rapavñrn) higher than itself in contravention of what must have been a universal law (Ar. Prob. 19, 12). Thirdly, it is argued in the text that the early knowledge of this note was proved by the Phrygian melodies (ra Ppúyia). Now what possible part can the note rpirn cuvnuuévov have had in a Phrygian scale? Weil and Reinach’s suggestion of a modulation into the Aeolian is very weak. Yet it is this very mention of the Phrygian that gives us the clue and bids us restore the MS. reading. If we turn to the Phrygian of Aristides we see immediately that it gives us the Dorian, with the substitution of D for E; purged of quarter-tones, it is DEF ABCD. It is this upper D (called here vijrn cuvnupévwv because the term zrapavúrn is already occupied by the enharmonic note of that description) which was used at a later stage in the accompaniment of the old omovöeior. It was so used, to follow the MSS., against mrapavijTn and srapauéon and Asxavös dissonantly. Weil and Reinach wish to transfer «ai mpos wapapéonv to § 176, as on their theory it makes a hideous discord. On ours, however, it is needless ; vijrn cvvnupévov makes the interval of a minor third (D-B) with mapapéon, and this is as probable and reasonable as the major third between vntn and mapavyrn (§ 176). Acyavés also provides the interval of a major sixth (D-F); again perfectly reasonable, and the type of interval which might have been expected. Ilapauéon is not so obliging; D-C is a tone, which is just the interval which has been so fortunately eliminated from the discussion of the vijrn Ötefevyuevov. It is perhaps a little arbitrary to reject the mpos mapavnrnv altogether, and as we have fortunately been able to confirm the manuscript reading in the rest of the passage it is a pity to abandon it here. It is however conceivable that the srapaméonv originally stood alone, then became accidentally duplicated, and one of the two was altered to zrapavijrnv by an ignorant copyist. This emendation has no ingenuity to commend it. Ifit is not accepted it will leave us precisely where we were before as far as the polyphony is concerned. It will only be accepted if it is considered worth while to eliminate the discord of the second. Probably no one would hesitate to do so if he were not already accustomed to the idea of its employment. Still unexplained is the three-quarter tone interval in the old Spondeion scale. No hint is given in the second Plutarch passage that abnormal intervals were employed; but the first passage is explicit enough, and implies that the interval between mapauéon and mrapavijr (enharmonic) was a three-quarter tone. If the lower tetrachord had a normal semitonal mukvóv (E-F), this would mean dissonance between F and C. Stranger phenomena are known in the history of scales, but this does not seem very like Greek music. Surely we have here the explanation of the debated expression 6 cuvrovwrepos orovèeaopôs. The three-quarter tone interval occurred in both parts of the scale. Of course it was only the upper interval which, from its vicinity to the

disjunctive tone, could create an illusion of the diatonic.! The misconception arose as follows. If F-E is three-quarters of a tone (47), then the interval A-F is 4, which is almost identical with the interval 24, made up by the disjunctive tone and the upper omrovòevacuós, differing in fact only by ys. The uninstructed, assuming A-F to be a ditone, assumed further that C*-A was the same. Light is thrown upon the subject from two other sources. In the first place there is to be compared the hemiolic chromatic of Aristoxenus, the small intervals of which together make a three-quarter tone. This shows that he recognised a mvkvóv slightly larger than the enharmonic semitone, but smaller than the (minor) tone of the normal chromatic. The fact that he calls it chromatic, whereas the Spondeion was regarded as enharmonic, need not trouble us. Aristoxenus was always anxious to preserve the purity of the lowest type of enharmonic thanks to his connexion with virtuoso flute-playing. In any case, such a distinction as this was arbitrary and academic. Still more interesting is the ögaAov diatonic of Ptolemy (Harm. I. 16), of which the lowest interval is 4?—i.e. roughly a three-quarter tone—the complete tetrachord being 1?xHx10, Harm. II. 16. himself. It does not occur in the lyre scales he describes in In fact, the account suggests that Ptolemy had invented it It may, however, be a more or less conscious reflection of the Spondeion, which may not have become completely obsolete by then. If so, the original intervals of Olympus’ scale were Et? F A? Bit C. We are told that Olympus in his discovery of the scale made frequent use of the tritone B-F, which probably means that this interval was much in use in this style. It is certainly more likely to have been the undecimal tritone % than the harsher $§ or the strict tritone #22. It is not so easy to deal with the amplification of the scale through polyphony. The splitting of the threequarter tones produced an interval of a fifth between the two geaórrokva; this is clear enough on any showing. Nyry (E) was added, making an interval of a fifth with ueon and of 34 with mapavnrn, less harmonious unfortunately than the major third earlier suggested in this connexion. Nyry ovvnunevov also was added, making dissonant intervals with Asxavös and srapagéon. It is therefore extremely difficult to decide how the interval C-E (st) was divided by the note D. If we take Ptolemy’s tetrachord (1 id Xs), we have a reasonable interval between D-B, i.e. $, a minor third, but an interval of 55 between D-F. If, on the other hand, we make our tetrachord 47 X 3 X 10, with the larger tone in the middle, according to the canon which Ptolemy laid 1 The lower D, the ürepurdrn, was not in use only occurs in this passage and jin the earlier in this scale, as the continuation of the second Plutarch passage informs us in the following passage about the Spondeion. They must only refer to a special type of early melody, and in words: où öl &yvoay drelxovro Er rois Awploıs Toû rerpaxépôou rovrov (ry ümdrwr). Now the sections 183-185 Plutarch is still discussing the rpbmos omovòerd{wv and cognate scales. Indeed Dorian scale of Aristides possesses the note D. But there is no need to suppose that r& Aupıa this must be so, as éreixoyro can have no subject but of mémo, which is made more explicit in necessarily refers to all Dorian melodies. This expression, together with rà Ppvyia and ra Avda, § 181 ("OAëurov re kal rv dkodovOnodvTww ékeivw).

down (and broke), the interval D-F becomes &, but that between D-B is now 33. This problem, however, is not peculiar to the tuning we are investigating. It is a natural law governing scales that a diatonic octave cannot have all its ffths and fourths perfect. Our own diatonic C-C has a false fifth between D-A. The normal Greek tuning has the same false interval, only in the E octave it becomes a false fourth between A-D. If then the Greeks preserved their normal structure of two tetrachords joined by a major tone, it was impossible for all the harmonies deduced from the Plutarch passage to be in tune. We need not here inquire whether they tolerated one harsh interval in their polyphony or in what way they solved this tuning problem.” We have only to admit that the harmonies to which the three-quarter tone amrovòevacpós leads us are rather more difficult than those given by the normal diatonic tuning. If we believe them to have been too difficult, we must suppose that the 47 interval disappeared in the accompanied version of the scale, which preserved its original character only in the limitation of its melodic notes. All of which does not affect the main purpose of this paper— to demonstrate the enharmonic character of the orovéerdfwv Tpórmros, and so to vindicate the manuscript readings of the Plutarch passage which describes it. R. P. WINNINGTON-INGRAM. 1 The problem is in point of fact soluble only if we suppose that the disjunctive tone (B-A) was a minor tone (3°), and that the consonance of a fifth between rpirn and rapumdrn was obtained by dividing the two muKvá slightly differently. As this was flute music, and the whole srukvór was produced froma single hole of the pipe, this may not have presented much difficulty.