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 On the interpretation of Qreek music. 
 
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ON THE 
 
 INTERPRETATION 
 
 OF 
 
 GREEK MUSIC 
 
 By CECIL TORR, M.A. 
 
 S)S apxaio\oy^<raii/ iiuv koI xaravl'liuv arrh yA^rris ciravras 
 
 LUCIAN 
 
 HENRY FROWDE 
 
 OXFORD UNIVERSITY PRESS WAREHOUSE 
 
 AMEN CORNER, E.G. 
 
 1896 
 
 l/ill rights reserved] 
 
HORACE HART, PRINTER TO THE UNIVERSITY 
 
A YOUTH, PLAYING AN EIGHT-STRINGED LYRE, WITH THE PLECTRUM IN HIS 
 RIGHT HAND AND HIS LEFT HAND ON THE STRINGS. 
 
 From a Greek vase in the Author's collection. 
 
 ON THE INTERPRETATION OF 
 GREEK MUSIC. 
 
 I. 
 
 The ancient notation was arranged for one-and-twenty notes 
 within the octave, each of the seven original notes being 
 followed by two supplementary notes. And as the compass 
 was three octaves and a third, there were seventy notes in all. 
 
 Two letters were assigned to every note, one set of letters 
 being prescribed for instruments and another set for voices. 
 
 A 
 
4 GREEK MUSIC. 
 
 This is the lettering for voices, taking the notes in order of 
 ascent : — 
 
 |D^5|CAj-HgblJip I'l 1/1 WVai-'^ri/FVipV 
 n>|'X<|)TTCPnOZN MAKieHZEArSA 
 UAH ^ JLl O'Z'N' M'A'K'I'e'H'Z'E'AT'B'A' 
 
 U' 
 
 And this is the lettering for instruments :— 
 CiOcTT-iTguogHU HhxriEiu3»- IhTLL 
 K'iviFii.TCoDKi^ )in<^<V>C UZIN/ \ 
 Z ^ \ h V ■/ K'si' )l'T<'A^'<'V'>'c'U'=]'N'/'V 
 
 Z' 
 
 Thus, in the lettering for voices, the common letters of the 
 alphabet are taken in their natural order from A to n. Next 
 beyond the common £1 comes V, a modified A, beginning the 
 alphabet again with every letter modified. And next before 
 the common A comes U, a modified il, finishing the alphabet 
 with another set of modifications. But here the alphabet 
 omits the letters s, p, it, and passes on from 1 to 0', Z', N', &c., 
 for the sixteen highest notes. This departure from the natural 
 order must be connected with the fact that in the lettering for 
 instruments, as well as here, the letters for these sixteen notes 
 are distinguished only by an accent from the letters for the 
 notes an octave lower down. And this all looks as though 
 the sixteen highest notes were added at some later time. 
 
 In the lettering for instruments the modifications are in- 
 troduced in groups of three, the object being to associate each 
 pair of supplementary notes with the original note to which 
 they properly belonged. No doubt, Alypios ^ is mistaken in 
 
 ' Alypios, eisagoge, describes the letters passim ia setting out the scales. Thns, 
 he speaks of A , A, \- , ■/ as ijnia\ipa, either iptaTepSf or Seii6v and /niriv vevov or 
 avca vivov : of H as ^ra 6.ne\rfriicliv KaSeiKKvanivov: of / and \ as d(aa and Papaa : 
 of n, \ and •< as irt KoSeiXmanivov, ^/lideKm KoSaXmaiUvov and inilStXra 
 ■nX&yiav : also of ^ , "1, ^ as ^lu/iv, apurrepdv or Se(i6v or iirriov. , 
 
GREEK MUSIC. 5 
 
 deriving ti and R frona PI instead of H, and also in deriving T 
 from n, as this would naturally be 7, a modification of A 
 that matches the adjacent < and A- And clearly / and \ 
 are modifications of M and N, not accents, as he says. But 
 apparently A and -V must be derived from A, and V and i 
 from V, though the first pair is attached to Z, and the second 
 pair to H, which appears to be derived from H. And these 
 anomalies make one suspect that the notes originally ended 
 here at Z, an octave under Z'. The lettering, moreover, is 
 anomalous in the lowest notes as well, ending there with T, 
 -», -c ,*,-$, C! ,just as the lettering for voices ends with -i, 
 ^5 •"■. *. ^) I3- And that looks as though the notes 
 originally stopped at % , two octaves under Z. But this g 
 and the f and C above coincide with the § and 1 and C in 
 the lettering for voices. So these three letters and the six 
 below may be survivals from a time when both the letterings 
 were alphabetical. But this is all a barren ground for specu- 
 lation, as nothing can be proved. 
 
 The letterings have been transcribed as follows in all the 
 best-known versions of the music found at Delphi and else- 
 where within the last few years : — 
 
 !3-a}-§ b9iiiw-'^7FnnY<i)rcPo 
 >5fcH u nvsiri vpvx T n 
 
 
 ■<s- '^t^ --- 
 Q'o^HgooHUhEuJHirN.i Fu-CuK 
 
 MA I e Z r B U A ^ JL 0' M' A' 1' e' Z' r' B' U' 
 Z N K H E A A X 1 Z'N'K' H' E'A'A' 
 
 
 -g^g^ 
 
 n < < V c N / Z A h V K' T< ' <' V c' N' /' Z' 
 Si )| ^ > U 3 N A y Si' )1' A' >' U' 3' \' 
 
 A 2 
 
6 GREEK MUSIC. 
 
 This system of transcription produces only forty notes in 
 place of seventy, so that thirty of the modern notes are used 
 for two Greek notes apiece. And this gives rise to three 
 objections. 
 
 In the first place, the transcript is ambiguous. Thus, for 
 
 S_^_^"r F=^ may stand for any 
 
 example, the group 
 
 one of sixteen different things, c U Zl Z, > N / \, &c. ^ And 
 this ambiguity does actually lead to blundering. Quite re- 
 cently, in dealing with a piece of ancient music, an excellent 
 
 critic took an 
 
 ^) ^^ ~ i in the transcript to mean an N in the 
 
 original, and proceeded to argue that the piece was written in 
 a certain key; when in reality the original had U, a note 
 belonging to another scale ^. > 
 
 Secondly, in making one modern note do duty for two 
 ancient notes, the transcript is giving the same pitch to notes 
 that were of different pitch. 
 
 In a degenerate form of ancient music there were indeed 
 such things as homotones, or notes of equal pitch. Thus, in 
 setting out a scale of semitones, Gaudentius^ puts ■*>■, ^ , § s 
 b, 9, Ml in the scale with H, jj, M as o/xo'roi/a, while Aristeides* 
 puts ■*'■,-', ) U, 9, H in the scale with J- , b, I'l as (rv^Kpoovlai. 
 But the origin of these homotones is plain. The old notation 
 had provided for a pair of supplementary notes after each of 
 the original notes, putting ^ {y) and H (r) between ^ (^) and 
 3 (s), b (p) and U (t) between % (s) and 9 (0), and so forth. 
 But when the scale was limited to semitones, there was only 
 one supplementary note between (^ and s, only one between 
 s and 0, &c. ; and as these supplementary notes were placed 
 about half-way between, it did not really matter whether they 
 
 ' See the Classical Review for December last, vol. ix. p. 468, and the author's 
 note thgreon in the Athenaum of December 14. 
 
 ° Gaudentins, eisagoge, 22. 
 
 ' Aristeides, de musica, i. 11. The reader may be cautioned against the version 
 of this passage in Jahn's edition of Aristeides, p. 17. It is printed there virith 
 Bellermann's emendations ; and he ' emended ' the reading of the MSS. to make it 
 suit a theory of his own. 
 
GREEK MUSIC. 7 
 
 were known as v or r, as p or tr, &c. Gaudentius, however, has 
 selected the letters that come first, v after <j), p after s, ^ after 
 o, &c., while Aristeides has selected the letters that come 
 second, t, it, v, &c. 
 
 That is exactly what has happened to the sharps and flats 
 in the modern scale of equal temperament. There is only 
 one supplementary note there between F and G, only one 
 between G and A, &c. ; and as these supplementary notes are 
 placed half-way between, they are known indifferently as 
 F sharp or G flat, as G sharp or A flatj &c. In some keys, 
 however, the modern musician follows Gaudentius in taking 
 the first term in each pair, and speaks of all the supplementary 
 notes as sharps ; whereas in other keys he follows Aristeides, 
 takes the second term, and calls them flats. 
 
 But this method of transcribing does not make homotones 
 of the notes that actually were such. It attaches n (t) to % (s) 
 in place of f- (u), U (ir) to 9 (o) in place of b (p), and so forth. 
 In fact, it follows the system of the tempered scale in giving 
 the same pitch to F double sharp and G natural, to G double 
 sharp and A natural, &c. And there is not any precedent 
 for that. 
 
 The lettering for instruments does indeed suggest the use 
 of sharps and double sharps in place of sharps and flats, as 
 the modified letters are both placed after the original, letter 
 in every group. For example, the letters F, u., ■q, C, u, D, 
 K, Si, )l, n seem to answer better to Gi G sharp, G double 
 sharp, A, A sharp, A double sharp, B, B sharp, B double 
 sharp, C, than to G, G sharp, A flat, A, A sharp, B flat, B, 
 B sharp, C flat, C. And there is no harm in speaking of the 
 supplementary notes as sharps and double sharps. But when 
 the transcript gives the same pitch to 1 and C, to 3 and K , 
 to Si and H, &c., it is assuming that the same pitch may be 
 given to G double sharp and A, to A double sharp and B, to 
 B sharp and C, &c. — a thing that is impossible without the 
 tempered scale. 
 
 And that provokes the third objection to this system of 
 transcription, to wit, that it involves the modern scale of equal 
 temperament. 
 
8 GREEK MUSIC. 
 
 There are some passages in Aristoxenos which look as 
 though he was acquainted with a tempered scale ; but when 
 these passages are taken with their context, that notion is 
 dispelled. 
 
 He defines a Fourth as the smallest of the intervals that 
 make a concord, and a Fifth as the next smallest of those 
 intervals ; so that his Fourth is clearly a true Fourth, and his 
 Fifth a true Fifth. Having made these definitions, he states 
 that a Tone is the amount by which a Fifth exceeds a Fourth, 
 and elsewhere he defines a Tone as the difference between the 
 two smallest of those intervals that make a concord ; so that 
 his Tone can only be a major Tone ^. And thus, when he 
 proceeds to say that a Fourth contains two Tones and a half, 
 he must be using ' a half quite roughly, to indicate a quantity 
 that was not really more than "443475. 
 
 Several of the ancient writers call attention to the fact that 
 what was termed a Semi-Tone was not exactly half a Tone. 
 And they explained the fact by saying that the term was not 
 to be compared with terms like Semi-Cubit, which meant 
 a measurement of half a Cubit, but only with such terms as 
 Semi- Vowel, which meant a letter not unlike a Vowel \ No 
 doubt this explanation may be incorrect ; but the fact itself 
 is incontestable. 
 
 In face of those definitions of a Tone and Fourth, it is 
 absurd to argue that Aristoxenos must be speaking of a mean 
 Tone and a tempered Fourth, when he says that a Fourth 
 contains two Tones and a half, or when he uses language to 
 
 ' Aristoxenos, p. 45, ed. Meibom, earw Sfj rSiv aviupiivaiv iierSi /leyiSij. i\axt- 
 arov lUv, rb 8id naaifmi . . . Stirtpov Si, to Sia irivre . . . r6vos S' ioTiv, § ri 5<A 
 TivTi Tov SicL Tiaa&ptav /ioCov. Cf. p. 2i, effri 8^ t6vos ^ rSiv irpin-aiv avfupiivaiv 
 KCTOL itiycBos 8ia^o/»i. 
 
 ' Gaudentius, eisagoge, 13, to Si fiiuT6viov KaKoi/uvov ovk tanv dK/jijSSs 
 ^HirSviotf. Proclos, in Timsenm, p. 191 D, E, tA Key&iuvov ■liiur6viov, ov Rvplois 
 ■^IMt6viov. Theon, de musica, 8, ri iUvtoi ijiurSviov ovx iis ^luav rSvov Kiyereu, 
 K.T.\. Censorinus, de die natali, io, abusive hemitanion appellat. Macrobius in 
 somnium Scipionis, ii. i, non ita accipiendum est {semitonium) ut dimidius tonus 
 putetur. Boetins, de musioa, ii. 27, videntur enim semitonia nuncufata, non quod 
 vere tonorum sunt medietahs, Sfc. Theon and Macrobius proceed to a comparison 
 with the ■^lufavov or semivocale. 
 
GREEK MUSIC. 9 
 
 the same effect in other passages. And outside his writings, 
 and those of his disciples, there is nothing to imply that any 
 tempered scale was known in ancient times. 
 
 The third objection to this system of transcribing is there- 
 fore very serious. Not only are the notes within the octave 
 reduced from twenty-one to twelve by making nine of them 
 of equal pitch with others, but the remaining twelve are 
 forced into the tempered scale ; the result being that, which- 
 ever of the twenty-one is selected as a tonic, the other twenty 
 must all be more or less inaccurate in pitch. 
 
 These errors would be avoided by transcribing the ancient 
 letters into modern letters in the following way : — 
 
 jo 5. x-a }-H§bU9hlHWVi^-'^ri7FvnP V 
 
 C!<*TT-{Tgoo§HBRhXHEiu3l-lHrL t 
 
 nVX*YTCPnOZNMA K I e H ZEATB A 
 ffxhgSxSi aa^aib byb^ c Cy c^ d d^ 4 e e^ e^ f f^ f^ 
 ^i.v1Fll.^CuDKii)|^<^<V>cU:3N/\ 
 
 UAXe JLl O'Z'N'M'A'K' I' G'H' Z'E'AT' B' A' 
 
 SS\S^ « «i «2 ^ ?i ^2 f fii f!^ ^ ^ ^2 f fi f2 / /i fj. 
 
 U' 
 
 r 
 
 The notes that are transcribed as a, b, c, d, e, / g have 
 enough in common with the modern notes A, B, C, D, E, F, G 
 to make these letters useful as a guide to memory. A sufEx 
 1 or 2 distinguishes the first and second supplementary notes, 
 while the punctuation . and .. and ... distinguishes the octaves. 
 So this modern lettering gives all the information that is 
 given by the ancient lettering, and gives it in a simpler form. 
 
lO GREEK MUSIC. 
 
 II. 
 
 When a musical note is produced by the vibration of 
 a string, its pitch depends upon the rate at which the string 
 vibrates. And the rate of this vibration varies inversely with 
 the length of the string, so long as the tension and the 
 thickness of the string remain the same. 
 
 Thus, an Octave is produced by strings whose lengths are 
 in the ratio of i to a, a Fifth by those which have the ratio 
 of a to 3, and a Fourth by those which have the ratio of 
 3 to 4. Suppose, then, that four strings are taken with 
 a length of 6 inches, 8 inches, 9 inches, and la inches respec- 
 tively; Then the 6-inch and the la-inch strings will give an 
 Octave, since the lengths are in the ratio of i to a. Ths 
 6-inch and the 9-inch strings will give a Fifth, and so also 
 will the 8-inch and la-inch strings, the ratio being a to 3 in 
 both these cases. The 6-iiich and the 8-inch strings, and 
 again the 9-inch and the la-inch strings, will give a Fourth, 
 the ratio being 3 to 4. And the 8-inch and the 9-inch strings 
 will give a Tone, with the ratio of 8 to 9, since a Tone is 
 represented by the difference between a Fourth and Fifth ^. 
 
 These simple ratios of i to a and a to 3 and 3 to 4 were 
 used to fix the four chief notes of every octave, two near the 
 middle and one at either end. And generally the ratio of 
 8 to 9, which is involved in those of 3 to 3 and 3 to 4, was 
 used to fix the four remaining notes. 
 
 Between the two notes near the middle and the two at 
 either end there were two intervals in which the ratio was 
 3 to 4. Now 3 to 3 1 and 3I to 3! J each had the ratio 
 of 8 to 9 ; or if these figures were multiplied by 64 in order 
 to eliminate the fractions, 19a to 216 and ai6 to 243 each 
 had the ratio of 8 to 9, while 19a to 356 was in the ratio of 
 3 to 4. And thus the introduction of two intervals that had 
 
 ' This is all demonstrated in dne form by Enclid, sectio canonis, propositions 6, 
 8, 12 and 13: also by Plutarch, de musica, 22, 23, and others. 
 
GREEK MUSIC. II 
 
 the ratio of 8 to 9 into an interval that had the ratio of 
 3 to 4 produced an interval that had the ratio of 243 to 356. 
 In other words, the introduction of two Tones into a Fourth 
 produced the interval that technically was called a Diesis or 
 Leimma and vulgarly a Semi-Tone. 
 
 Plato seems to have styled the interval a Leimma, though 
 the word itself does not occur in any of his extant writings^ ; 
 and this name lived on beside the name of Semi-Tone, which 
 probably was introduced by Aristoxenos^- The earlier 
 Pythagoreans had used the name of Diesis^. 
 
 When the first four notes of any octave were given by strings 
 whose lengths were 192 and 216 and 243 and 256, the fifth 
 note and the eighth note were given by strings whose lengths 
 were 288 and 384 respectively ; since 192 to 384 was in the 
 ratio of i to 2, while 192 to 288 and 256 to 384 were in the 
 ratio of 2 to 3, and 288 to 384 was in the ratio of 3 to 4. 
 And as this interval was treated like that other interval in 
 which the ratio was 3 to 4) the sixth and seventh notes were 
 given by strings whose lengths were 334 and 364^ ; since 
 288 to 324 and 324 to 364^ each had the ratio of 8 to 9, while 
 3644 to 384 was in the ratio of 243 to 256. These figures 
 being multiplied by 2 in order to eliminate the fraction, the 
 eight notes of the octave were given by strings whose lengths 
 were 384 and 432 and 486 and 512 and 576 and 648 and 729 
 and 768 respectively. 
 
 If these eight notes were taken in order of descent, the 
 pitch decreasing as the length increased from 384 to 768, 
 the intervals were Totte, Tone, Leimma ; Tone ; Tone, Tone, 
 
 ' Plato, Timseus; p. 36 A, B, ijiuoKiav Si huun&aem' not ImTplTuai ual iiroy36oiv 
 yevoftivotv l« to^tojv tSiv Sefffiuv iv rats •np6o9ev SicufTdffeffi, ry rod ktroySdov 
 Siaffr^fMTt rd iirirpna irivra, ffvvetrKTjpovTOj Kei-najv airr&v kK^arov fidptoVf Tijs rod 
 ftopiov Ta^Tjs dtatTTOiffeajs keupBeiffrjs dpiOfiov irpds apiOfj^v exoiffTjs roiis 6povs (TVS* 
 irpbs a/f/. This use of A-efoiw and \iup9(iaris seems to involve the use of Xaiipa. 
 cf. Macrobius, in somnium Scipionis, ii. 1, Plato semitonium Kaptiia vodtavit. 
 
 ' See above, page 8 and note 2. 
 
 ' Nicomachos, encheiridion, 9, 12, Stobaeos, eclogs, i. 21. 7, and Boetius, de 
 musica, iii. 8, quote sayings of Philolaos in which this interval is styled a 5^E<rif ; 
 and Theon, de musica, 12, and Macrobius, in somnium Scipionis, ii. i, remark 
 this usage of the term among his followers. 
 
 A 3 
 
12. GREpK MUSIC. 
 
 Leimma — there being a ratio of 8 to 9 for every Tone and 
 243 to 356 for every Leimma. But in the scales the Hypo- 
 Lydian group put e a Fourth above b and a Fifth above «, 
 and the Hypo-Phrygian group put d a Fourth above a and 
 a Fifth above ^, while the Hypo-Dorian group put c a Fourth 
 above ^ and a Fifth above /^ And thus, as a Tone was the 
 difference between a Fourth and a Fifth and a Leimma was 
 the difference between two Tones and a Fourth, the eight 
 notes e, d, c, b, a, g, f, e were separated by the intervals of 
 Tone, Tone, Leimma ; Tone ; Tone, Tone, Leimma. So 
 these eight notes, or their equivalents in the octaves up 
 above, were given by strings whcise lengths were in the ratios 
 just described. 
 
 A supplementary note was placed in every Tone by reckon- 
 ing the ratio for the Tone as 16 to 18 in place of 8 to 9, and 
 thereby bringing in the ratios of 16 to 17 and 17 to 18 ^- And 
 commonly the name of Semi-Tone was given to both the 
 intervals that were created in this way, although the first 
 of them was rather more than half a Tone and the second 
 was rather less. But technically the first was known as an 
 Apotome and the second as a Leimma^. 
 
 As there were five Tones in every Octave, these ratios of 
 16 to 17 and 1 7' to 18 introduced five supplementary notes. 
 And as the Tones were e to d,d to c, b to a, a to ^ and ^ to/, 
 
 these supplementary notes belonged to d, c, a, g and f. But 
 the scales all show that d^, c^^ a^, g^ and f^ were the only 
 supplementary notes that had to stand a Fourth or Fifth 
 away from one or other of the original notes : so these must 
 represent the supplementary notes that were inserted in the 
 middle of each Tone. 
 
 • The scales are all given by Alypios, eisagoge. See below, page i8. 
 
 ' Plutarch, de animffi procreatione, i8. Aristeides, de mnsica, ili. i. Ptolemy, 
 harmonica, i. lo. Boetius, de mnsica, i. i6, iii. i. Proclos, in Timaenm, p. 195 A. 
 
 ' A Kainjia and dTroTO^^ together made a Tone, and the d7roro/in( was larger than 
 the XtT/tfia — see Gandentius, eisagoge, 14 ; Boetius, de musica, ii. 39 ; Proclos, in 
 Timseum, p. 195 D — so that, if the Kdiijia took the ratio of I'j to 18, the itroroiiti 
 would get the ratio of 16 to 17. And' this was probably the genuine Ktimia, the 
 interval of ratio 243 to 256 being properly a Utats. Thus in Theon, de musica, 36, 
 the interval of ratio 243 to 256 is distinguished as rd Sieiriaiai' \dniM. 
 
GREEK MUSIC. 13 
 
 Two more supplementary notes might then have been 
 inserted in each Tone by doubling the ratios of 16 to 17 and 
 17 to 18, and bringing in the ratios of 33 to 33 and ^^ to 34 
 within the ratio of 3a to 34 and the ratios of 34 to 35 and 35 
 to 36 within the ratio of 34 to ^6^. But the notation shows 
 that only one more supplementary note was placed in every 
 Tone ; and as d^ came between d^ and d, c^ between c^ and c, 
 a^ between a^ and a, g^ between g^ and g, and /^ between f^ 
 and /, the ratios of 34 to '^^ and ^^ to ^6 were those that 
 fixed the five notes d^, c^, a-^,g-^^ and/^. 
 
 The interval that had the ratio of jiS to 3^ was smaller 
 than the interval that had the ratio of 34 to 35 ; and the 
 whole interval of ratio 34 to 36 was smaller than the interval 
 of ratio 3a to 34 that was required to complete the Tone. 
 So these little intervals were far from being a quarter of 
 a Tone apiece, although they generally were reckoned as 
 such^ The usual name for them was Diesis, but originally 
 they bore the name of Diaschisma *. 
 
 If similar methods were employed in dealing with the* 
 intervals in which the ratio was 243 to 356, one supplementary 
 note was inserted there by doubling this ratio and bringing 
 in the ratios of 486 to 499 and 499 to 51a, and then another 
 was inserted by doubling the latter ratio and bringing in the 
 ratios of 998 to loii and loii to 1034. And zs c b axidfe 
 were the intervals in which the ratio was 243 to 256, the first 
 of these supplementary notes was b^ or e^ and the second was 
 ^1 or e^. 
 
 The eight original notes being given by strings whose 
 lengths were 384 and 43a and 486 and 51a and 576 and ^m/- 
 and 7a9 and 768 respectively, the following list will show the 
 lengths required for all the supplementary notes, the figures 
 being multiplied by 4 in order to get rid of fractions : — 
 
 ' Aristeides, de musica, iii. i. 
 
 ^ Thus, for example, Baccheios, eisagoge, 8, and Vitnivius, de architectura, v. 4, 
 make a Sictrts a quarter of a Tone. Aristeides, de musica, iii. i, and Proclos, in 
 Timaeum, p. 191 E, remark the error. 
 
 ' Boetius, de mnsica, iii. 8, quoting Fhilolaos, diaschisma {est) dimidium diestos. 
 Cf. note 3 on page 1 1 for diesis in Fhilolaos. 
 
14 
 
 
 GREEK 
 
 MUSIC. 
 
 
 1536, f. 
 
 i7a8,<^. 
 1632,^2- 
 
 1944, c. 
 1890, <:j. 
 1836, <:2- 
 
 ao48, ^. 
 aoaa, 3i. 
 1996,32- 
 
 3304, a. 
 aa4o, «;. 
 ai 76, a2. 
 
 »59a, ^• 
 2520, ^1- 
 ^448, ^2- 
 
 2916,/ 
 
 a835./i. 
 
 a754,/2- 
 
 307a, ^. 
 
 3033.^1- 
 
 2994,^2 
 
 Having some doubts about the working of a scale con- 
 structed in this way, the author requested Messrs. Broadwood 
 to procure for him a series of ten tuning-forks to represent 
 the notes from e to b. The length of the strings was enough 
 
 to fix the relative pitch of all the notes, but there was nothing^ 
 to fix the absolute pitch of any one of them. For con- 
 venience, however, the author reckoned the pitch of e at 324 
 
 double vibrations per second, and thus obtained the following 
 pitch for the remaiping notes, the rate of vibration varying 
 inversely as the length of string : — 
 
 ^,324 d, a§8 c, 356 b, 343 
 
 di, 296-3% Ci,!i63i^ hi'^A^NxT 
 
 ^2,3°4if <^2, 271x7 ^2.249111 
 Or, putting the fractions into decimals, 
 
 </i, 396-33 fj, 363-31 ^1, 246.13 
 
 d2,3°4-94 ^2. 371-06 b^, 2,49-33 
 
 The tuning-forks were made at Sheffield by Messrs. 
 Valantine and Carr, and were tested by the makers on 
 a Tonometer of their own. After they were delivered to 
 Messrs. Broadwood, they were tested again by Mr. Hipkins 
 on the late Mr. Ellis's copy of the Scheibler Tonometer, 
 now in the Science Department of the South Kensington 
 Museum ^ And these were the results : — 
 
 f, 323-43 d, 387-20 c, 255-64 b, 242-24 
 di, 2,95-33 '^i, 262-45 ^1,245-37 
 ^2. 304-45 ^2, 270-35 *2, 248-52 
 
 ' The author is greatly indebted to Messrs. Broadwood, and especially to 
 Mr. Hipkins, for taking such trouble in the matter. 
 
GREEK MUSIC. 15 
 
 In every instance the rate of the vibrations is rather less 
 than was demanded. But the error is never more than -90 and 
 never less than -^6 ; and being always in the same direction, it 
 has scarcely any effect upon the relative position of the notes. 
 
 Excepting the group of 3, ^j, ^g) the notes all come out 
 clearly at intervals that can easily be recognized; and the 
 sequence is exceedingly melodious. But when 6 or b^ or b^ 
 is sounded by itself, there is some difficulty in saying which of 
 them it is ; although the difference is obvious enough when 
 they are sounded in succession. 
 
 Now, the length of the strings for 6^ and b^ was settled on 
 the supposition that the intervals of ratio 243 to 256 were 
 treated like the intervals of ratio 8 to 9. As the lengths 
 8^ and 8| were taken between 8 and 9, the lengths 2494 and 
 252! were taken between 243 and 256 ; and as these figures 
 were raised to 34 and 35 between 33 and ^6 in the first case, 
 they were raised to 998 and loii between 973 and 1034 in 
 the second case, in order to eliminate the fractions. Suppose, 
 however, that the fraction was eliminated from 252! by the 
 simpler process of ignoring the f altogether, and treating the 
 length as 252. Some very curious results will follow. 
 
 The intervals b b^ and e e^ will then be determined by the 
 ratio of 252 to 256, or 63 to 64. The intervals dd^, cc^, aa^, 
 gg^ and //i are determined by the ratio of ^^ to 36. And an 
 interval of ratio 35 to 36 becomes an interval of ratio 6^ to 64 
 on subtraction of the well-known interval of ratio 80 to 81. 
 
 Taking 3016 in place of 2032 and 3024 in place of 3033 as 
 the lengths for b^ and e^, and then examining the seven 
 original notes and the seven with suffix j, there is the ratio of 
 I to 3 in ee,e^ei,ff, &c., the ratio of 2 to 3 in eb, e^b^tfc, 
 &c., the ratio of 3 to 4 in ^ a, gc, g^ c^, &c., the ratio of 4 to 5 in 
 g^bi and c^e^^, the ratio of 5 to 6 in e-^g^ and b^d^, the ratio of 
 6 to 7 in e^g and b^d, the ratio of 7 to 8 in abj^ and dgj^, the 
 ratio of 8 to 9 in /£; fi£^i, g a, &c., the ratio of 9 to 10 
 in a^bi and d^^i, the ratio of 15 to 16 in e^/i and b^c^, 
 the ratio of 27 to 28 in ^^/and b^c, the ratio of 27 to 32 in 
 eg, ac, c^c^, &c., the ratio of ^^ to 36 in //i, gg-^, aa^. 
 
l6 GREEK MUSIC. 
 
 &c., and the ratio of 343 to 2^6 in ef and b c. Hence, with b^ 
 and e-^ in those positions, these fourteen notes involve the 
 fourteen most important ratios that Ptolemy employs in his 
 arrangement of the scales ^ But seven of these fourteen 
 ratios depend on ^^ and e^^. 
 
 The four original notes b, c, d, e axe separated by intervals 
 
 of ratio 243 to 256, 8 to 9 and 8 to 9, and thus produce the 
 ordinary Tetrachord of the Pythagoreans, which Ptolemy 
 called the Diatonic Tetrachord of Eratosthenes, and retained 
 in his own system as the Double-Tone Diatonic ^. The four 
 supplementary notes bi,c-y,di, e^ are separated by intervals of 
 ratio 15 to 16, 8 to 9 and 9 to 10, and thus produce the 
 Tetrachord that Ptolemy described as the Severe Diatonic ^ 
 But the four notes b^, c, c^,ei are separated by intervals of ratio 
 37 to 38, 35 to 36 and 4 to 5, and thus produce what Ptolemy 
 called the Enharmonic Tetrachord of Archytas. ' And such 
 coincidences make it fairly certain that b^ and e^ have now been 
 put into their proper places. 
 
 Setting aside the Tetrachords that Ptolemy ciscribes to 
 Aristoxenos — their structure being questionable — there are 
 sixteen other ratios employed in his arrangement of the scales. 
 But all these ratios may be derived from those already quoted. 
 Thus the ratio of 9 to 10 gives rise to those of 18 to 19 and 19 
 to 30, and to those of 38 to 39 and 39 to 40. The ratio of 5 
 to 6 gives rise to those of 10 to it and 11 to 13, and to those 
 of 30 to 31 and 21 to 22. The ratio of 15 to 16 gives rise to 
 those of 30 to 31 and 31 to 33 ; and this ratio of 15 to 16 with 
 that of 14 to 16, or 7 to 8, produces the ratio of 14 to 15. 
 Again, the ratio of 343 to 356 with that of 334 to 356, or 7 to 
 8, produces the ratio of 334 to 243. The ratio of 15 to 19 
 would come from those of 19 to 20 and 15 to 20, or 3 to 4. 
 And the ratios of 45 to 46, 33 to 34 and 24 to 35, or 46 to 
 48 and 48 to 50, might be obtained from that of 45 to 50, or 
 9 to 10. 
 
 As an adjustnient oib^ and e^ brought in seven 6f Ptolemy's 
 
 ' Ptolemy, harmonica, ii. 14. ' ^i&rovov Snovuuov. 
 
 ' AiiTovov aivTOVov. 
 
GREEK MUSIC. 17 
 
 ratios in addition to the seven that already were involved in 
 the original notes and those with suffix j, the probabilities are 
 that some of the remaining ratios could be obtained by a proper 
 adjustment of b^ and e^ and the introduction of the other notes 
 with suffix 2. But the author has not been fortunate enough 
 to find a likely place for b^ or e^ 
 
 The length of 253 was obtained for b^ and e-^ by ignoring 
 the f in 35a| ; and this suggests that the \ in 349^ might be 
 ignored in dealing with b^ and e^. Again, the ratio for b b^ 
 and eei has been converted into 356 to 353, or 64 to 63 ; and 
 this suggests that the ratio for bj^ b^ and e^ e^ may possibly be 
 353 to 348, or 69, to 63. But neither 349 nor 348, nor any 
 other number in that neighbourhood, seems to give a 
 satisfactory result. 
 
 If the ratio of 348 to 356, or 31 to 33, is used provisionally 
 for determining the intervals b b^ and e e^, the lengths of string 
 will have to be reduced from 1996 and 3994 to 1984 and 3976 
 for ^2 and e^- And the lengths for b^ and e^ have already been 
 reduced from 3oa3 and 3033 to 3016 and 3034. 
 
 Then, supposing that an octave of twelve mean Semi-Tones 
 is reckoned as 1300, the intervals ee^^ and b b^ may be reckoned 
 as 37 apiece, ^^ e^ and b^ b^ as a8 apiece, and e^f and b^ c as 35 
 apiece; //i, gg^, aa^, cc^ and dd^ as 49 apiece, /i/^, g^g^, 
 Oia^, Ci c^ and d^ d^ as 50 apiece, anAf^g, g^ a, a^b,c^d and d^ e 
 as 105 apiece ^. And then the ancient notes may be arranged 
 as follows : — 
 
 o,i?. 304,^. 408, f. 498,^. 70a, fl. 906,^. mo,/. 1300,^. 
 ^SSi'k- 359. '^i- 471. *i- 653. «i- 857,^1. io6i,/i. 1173,^1. 
 
 105, <^2. 309. <^2- 443. *2- 603, fl2- 807,^2- I0"»/2- "455^2- 
 
 According to Alypios, the scales were formed of eighteen 
 notes apiece ; and there were five-and-forty scales in all, or 
 fifteen scales of three types each — diatonic, chromatic, and 
 enharmonic. But in the chromatic and enharmonic types the 
 notes were just the same ; and in the diatonic type the only 
 
 » The formula HJ x (log. ;c - log. y) x 40 gives the number of mean Semi-Tones 
 in an interval of ratio x toy. 
 
l8 GREEK MUSIC. 
 
 variation was in notes 4, 7, 10, 14 and 17. Putting the dia- 
 tonic notes for 4 and 7 and 10 in brackets, and omitting the 
 notes from la to 18, as these are only a repetition of the 
 notes from a to 8 an octave higher up, the entire system 
 is reducible to this : — 
 
 I a 3 4 (4) 5 6 7 (7) 8 9 10 (10) II 
 
 Hypo-Dorian / g gigz K) ^ ^1*^2 (4)//i/2 ^"2) «2 
 
 Hypo-Iastian f%g^aa^{b) c^d d^ie) f^g gi («) b 
 
 Hypo-Phrygian g a a^a^ {c) d d^d^{f) g g^g^, K) c 
 
 Hypo-^OLIAN g^ a^b b^ (cg) d^ e e^ {f^) g^a a^ {b) c^ 
 
 Hypo-Lydian a b b^b^ {d) e e-^ e^ [g) a a^ a^ {c) d 
 
 Dorian a^ c c^c^ {d^f Ah (fa) ^2^ h (fa) fa 
 
 lASTiAN b c^dd^{e) Ag g^ (a) b b-^b^ (d) e 
 
 Phrygian c d d^d^ (/) g g^g^ {a^ c c^ c^ {d^ f 
 ^OLIAN C2 d^e e^ {f^giU «2 {b) ^^d d^ {e) f^ 
 
 LYDian d e e^e^ (g) a a-^a^ {c) d d^d^ (/) g 
 
 Hyper-Dorian d^ff^fi (f2)«2^ ^2 (f2) die e^ {f^) g^ 
 Hyper-IastIan e f^g g^ {a) b b^b^ (d) e e^e^ (g) a 
 Hyper-Phrygian/ g g^g^ (a^) c c^ c^ {d^fAA (fa) «2 
 
 HYPER-iEOLIAN /2faf fa (f) f 2 -f f 2 (f) fiS gn. («) * 
 Hyper-Lydian g a a^a^ {c) d d^d, {/) g g^g^ (a^) c 
 I 2 3 4 (4) 5 6 7 (7) 8 9 10 (10) II 
 
 Of course, these scales all differ in pitch, like the modern 
 scales of different keys. But they do not differ, like the 
 modern scales of different modes, in the order of the inters 
 vals alone. The difference here involves the nature of the 
 intervals as well. 
 
GREEK MUSIC. ig 
 
 For example, in the Phrygian scale of c the only supple- 
 mentary notes with suffix j are d^ and g^ and c^, with d^ and g^ 
 in the octave up above ; and these are all determined by the 
 ratios of the Tone. But the Lydian scale of d has ^^and ^j, 
 which are determined by the ratios of the Leimma, as well as 
 «i and rfi and a^, which come from Tones. And thus the 
 Lydian scale admits the well-known intervals of 331, or ratio 
 7 to 8, in de-^ and de^,oi 367, or ratio 6 to 7, in e^g and e-^g, 
 and finally of i8a, or ratio 9 to 10, in d^e-^^, which is thus 
 
 a minor Tone. And in the Phrygian scale these intervals are 
 not to be obtained. 
 
 Thus, in passing from the Phrygian to the Lydian scale 
 there was a change of mode as well as key ; and a change of 
 mode had more effect in ancient than in modern music, since 
 it varied the selection of the intervals. 
 
 No doubt the Lydian music differed from the Phrygian 
 in many things besides this raising of the pitch from cc to dd 
 
 and the admission of these intervals of ratio 6 to 7 and 7 to 8 
 and 9 to 10 ; for the Phrygian was accounted fit for warriors 
 on the field of battle, while the Lydian was consigned to lazy 
 banquetting ^. But presumably the change of mode and key 
 together helped to make these different types of music arouse 
 such different emotions. 
 
 In several of these scales some curious intervals are formed 
 by the connexion of the Leimma with the segments of the 
 Tone, such as that of 195, or ratio 243 to %']%, in a,^c at the 
 beginning of the Dorian scale. As a rule, the scales began 
 with major Tones of 204, or ratio 8 to 9. But in a scheme of 
 Ptolemy's for seven scales to suit the seven notes within an 
 octave, the seven intervals of ratio 7 to 8, 8 to 9, 9 to 10, &c., 
 are taken in turn for the beginning of the scales* : so this rule 
 was not imperative. And there is really no justification for 
 altering the place of a^ to make a^c 2. major Tone, or for 
 tampering with the other notes that incidentally produce 
 abnormal intervals. 
 
 • Plato, politeia, pp. 398 E, 399 A. ' Ptolemy, hannonica,'ii. 11. 
 
20 GREEK MUSIC. 
 
 A couple of examples will suffice to show the nature of the 
 music that was extracted from the ancient notes. 
 
 In the first of the Hymns from Delphi the passage about 
 KkvTa. jiieyaXo'woXts 'A^a^s has the notes /, ^, ^j, £-, c^,c^,c,b ^ 
 Here the voice ascends ao4, ascends 49, descends 49, descends 
 603, descends 50, descends 49, descends 90. The transcript 
 gives F, G, A flat, G, D, D flat, C, B, And there the voice 
 ascends aoo, ascends 100, descends 100, descends 500, descends 
 100, descends 100, descends 100. 
 
 ' Again, in the second of these Hymns the words 8ef(ii«eros 
 aj[x/3/ooVoz/ have the notes d, b, b^ d, e, 6-^^,0^. Here the voice 
 descends 394, ascends 37, ascends 367, ascends 304, ascends 
 37, descends 37. The transcript gives D, B, C, D, E, F, E. 
 And thpre the voice descends 300, ascends 100, ascends 300, 
 ascends aoo, ascends 100, descends 100. 
 
 In fact, the charm of ancient melodies was in the subtle 
 variation of the intervals through which they rose and fell ; 
 and all their icharm is sacrificed when they are forced into 
 a modern scale. 
 
 III. 
 
 The duration of the notes was indicated by the syllables 
 to which they were attached. And thus, if syllables in verse 
 are classed as long and short, and a short is reckoned as half 
 a long, this mode of reckoning must be adopted for the notes 
 as well. 
 
 For example, take the music for the twelfth of the Homeric 
 Hymns'. The notes may not be quite so ancient as the 
 words ; but they can scarcely be condemned as spurious, 
 although their pedigree is incomplete. 
 
 • Bulletin de Conespondance Helldniqoe, vol. xvii. plate 21 bis, and vol. rviii. 
 plate 25. 
 
 ' Ibid., vol. xviii. plates 12 bis and 20. 
 
 ' Published in 1724 by Benedetto Marcello in his Farafrasi sopra li primi 
 venticinque Salmi, vol. iii. p. 132. 
 
GREEK MUSIC. 21 
 
 d d de-^ed d b^ b^^e^ g e^ e-^e-^ea 
 
 Arj/xTjrp' y\vKO\i.ov, (Ti[im\v deov, Spxopi' deCbeiv, 
 
 f S' g ^1^1 e-^e-i^e-^ed ddggbj^ 
 
 AvT^p, Koi Koiprjv, irepiKoKkia Ilep(re<j>6veiav. 
 
 bi b^ b^ bi bi bi b^ e^e^ e^e^ e e ee ea 
 
 Xaipe, flea, koI nji/Se o-aai voKw Spj(e 8' doiS^s. 
 
 In the first and last lines the long syllables at the end are 
 sung to two notes each, and must therefore be reckoned as 
 pairs of short syllables in dealing with the music. And thus, 
 with the ordinary signs for long and short, the music is 
 
 d 
 
 d 
 
 d 
 
 i 
 
 e 
 
 d 
 
 d 
 
 h 
 
 ^ 
 
 
 g 
 
 
 w 
 
 fl 
 
 e 
 
 a 
 
 a 
 
 g 
 
 g 
 
 fi 
 
 fi 
 
 
 h 
 
 li 
 
 e 
 
 d 
 
 d 
 
 d 
 
 g 
 
 g 
 
 h 
 
 
 ^1 ^1 ^1 ^1 ^1 ^1 ^1 ^1 ^1 ^1 ^1 ^ s e e e a 
 
 But this is only a succession of long notes with short notes 
 of exactly half their length ; and although a succession of 
 Minims and Crotchets, or Crotchets and Quavers, may be 
 suitable enough in music that has nothing but the Tones and 
 Semi-Tones of equal temperament, some refinement is 
 required here in music that involves the Diesis, Apotome, &c. 
 
 In all probability the duration of the notes was governed 
 by some such rules as those that governed the pitch, for 
 Hexameters were curiously like Octaves ^ Roughly speak- 
 ing, there were six Tones in an Octave, just as there were six 
 Feet in a Hexameter ; a Tone contained a pair of Semi- 
 Tones, or one Semi-Tone and a pair of Quarter-Tones, just 
 as a Foot was either a Spondee of two long syllables or 
 a Dactyl of one long and two short ; and the Fourth and 
 Fifth divided the Octave into two Tones and a half and three 
 and a half, just as the Caesura divided the Hexameter into 
 two Feet and a half and three and a half. But, strictly 
 
 ' The comparison is suggested by Aristeides, de musica, i. 14, 23. 
 
22 GREEK MUSIC. 
 
 speaking, the Octave was divided into two Tones and 
 a Leimma and three and a Leimma in place of two and 
 a half and three and a half, since the whole was rather less 
 than six entire Tones ; and in every Tone the first of the 
 so-called Semi-Tones and Quarter-Tones was rather larger 
 than the second. Hence a Spondee would have made the 
 first note rather longer than the second, while a Dactyl would 
 have made the first note rather longer than the second and 
 third together, and also made the second rather longer than 
 the third. The long note before the Caesura and the long 
 note at the end would each have been abbreviated to repre- 
 sent a Leimma, and likewise the pairs of short notes that 
 occasionally were used in place of them. But obviously the 
 analogy is somewhat strained. 
 
 No doubt the duration of the notes was modified to some 
 extent by their position in the verse ; and the signs for the 
 Caesura and the Foot should perhaps be added to the ordinary 
 signs for long and short, as follows : — 
 
 d d \ d e^ e \ d \\ d \ di 6i e^l g ^i ^i\ ^i ^ <^ 
 
 .f / I f fi 1 .'^1 II .fi fi I fi f "^ I ^ ^ ^ \^ h 
 
 b-i 6i ^1 1 ^i ^1 ^1 ^1 ^1 ^1 ^1 ^1 ^ ^ e \ e e a 
 
 But possibly it would be better to give the words themselves, 
 for this formidable array of signs only touches the duration of 
 the notes so far as that was settled by the rhythm of the 
 verse. 
 
 A system of dots and dashes is employed in two of the 
 surviving bits of ancient music to determine the duration of 
 the notes or their intensity. There is a fragment of papyrus 
 at Vienna^ with a few notes of the music for the Orestes of 
 Euripides. The verses are — 
 
 KO.ToKo^ipo}tx>,\., KaToXo^vgo(mi, 
 fiarepos alfia (ras, o a-' &va^aicxe'6eL ; 
 
 ' Mittheilnngen aus der Sammlung der Papyrus Erzherzog Rainer, vol. v. p. 66. 
 
GREEK MUSIC. 
 
 23 
 
 6 ixiyas oA.j3os ov jiiioz'tj(iios_l/x_ /Sporois* 
 
 ava 6^ \aZ<pos &s 
 rts aK&TQV^ Boas rtva^as baCixoav 
 KariKXva-ev beiv&v •aovutv us irovrov k.t.X} 
 
 In the papyrus the verses are divided by a species of 
 KoptovLs in the shape of Z ; and there is always a dot above 
 this Z and a dot behind the note that follows. Thus there 
 is a Z to divide icoroAo^jJpopiai from fxarepoy, and a P* to give 
 the note for fxa : so also a Z to divide dvajSaKxei^ei from 6 fxiyas, 
 and an I " to give the note for 6 ; and again a Z to divide 
 jSporois from dvd, and an I" to give the note for d. But 
 evidently the scribe was puzzled by the half-verse dva 8e 
 KaL<f)os &s and completed it with rts aKarov Ooas, putting a Z 
 above the line to divide Oaas from Tivd^as and a 0- to give 
 the note for ri, as though this were the beginning of another 
 verse. And having thus lost the guidance of the metre, he 
 makes a long scrawl after KariKkvaev, and tries to start another 
 verse at i)s vovtov by adding Z and I" above the line. 
 
 
 i.-P- C * p 
 
 W PC • ' "^J 
 
 10 5v2>c:^^? 
 
 Apparently there was a dot and dash - to mark the first 
 note of the fourth Foot in every verse. This is distinctly 
 
 > Verses 338-343. 
 
24 GREEK MUSIC. 
 
 visible above the note for ifi in e/x /Sporois at the end bf the 
 third verse, above the note for rov in aKarov doas, which is 
 treated here as the end of the fourth verse, and above the 
 note for a-ev in KareKXva-ev, as though the scribe were trying to 
 make the fifth verse end with KariKkucrev ttovwv in order to 
 begin the sixth with ws ttovtov. There is also a trace of it 
 above the note for (pvp in KaTo\o(i>iponai at the end of the first 
 verse; but nothing can be seen above the note for j3oK/in 
 hva^aKx^iei at the end of the second ^. In this verse, however, 
 the penultimate is long, whereas the other verses make it 
 short ; and possibly the sign was not required here. 
 
 The fragment is not large enough to give the first note of 
 the second or third Foot in any of the verses, except the note 
 for Kar in KariKkvcrev, which must be treated here as the 
 beginning of the third Foot in the fifth verse. But there is 
 not any sign above this note. 
 
 The system is varied in a song inscribed on stone in honour 
 of a man named Seikilos^. His monument was found at 
 Tralles, and is now at Smyrna. 
 
 _ -iv ^ _ . . . _ j.y 
 
 a e e c^de d c^d, edc^ b a bg a 
 
 ocrov fjjs, <}>aLVOV' firjUv Skcos (ru AuwoS" irphs 
 
 . . . _ J.' ... _ -:-/ 
 
 c^e d c^d c^ a bg a c^b d e c^ a a af^ 
 
 6\lyov ecrrl rd 0jv rd r^Aos 6 )(jiovos cmaiTei. 
 
 Excepting the first three words, this can be arranged in 
 verses of one type, as follows : — - 
 
 fxribev o\(os <n) Kvirov' — w w — \j — — 
 
 •npos dklyov eorl to Cv^' yj kj \j w— \j — — 
 rd Tekos 6 \p6vos d'jratreT. oww wwu \j — — 
 
 The sign -' is used here, like the sign Z in the papyrus, 
 as li species of Kopcovls for marking ofif the verses ; and there is 
 always a dash — above the last note of the third Foot, just as 
 
 ' The author has examined the papyrus. 
 
 ' Bulletin de Correspondance HelUnique, vol. xviii. plate 13. 
 
GREEK MUSIC. 25 
 
 the papyrus has a dot and dash -^ above the first note of the 
 fourth Foot. Thus the words oa-ov ^fjs must form a verse 
 apart, as they answer to the endings of these other verses, av 
 kwTov, TL TO ^ijv, aTrairet. And then the word ^alvov will also 
 form a verse apart. There is a dot underneath the Kopoovis at 
 the end of this little verse -v-', and a dash —above the first 
 note in the verse that follows, although no dash or dot is 
 given to the first note in the other verses. And some dots 
 may be observed above the three notes of the second Foot in 
 the longer verses at the end, whereas the papyrus has only 
 a dot behind the first note of each verse. 
 
 There is altogether such a difference between the system in 
 the papyrus and the system on this stone, that no valid rules 
 can be established for the distribution of the dots and dashes. 
 But obviously the system is only meant to show the rhythm 
 of the verses, for the position of all these signs is determined 
 by the metre. In reality no signs were needed for this 
 purpose ; and none were used in the remaining bits of ancient 
 music. Of course, such signs might possibly have been omitted 
 in the copying of pieces that are only known through manu- 
 scripts ; but the Hymns discovered at Delphi are originals on 
 stone, and they have not these dots and dashes. 
 
 While the metre may have varied the duration of the notes 
 that normally were classed as long or short, it must certainly 
 have varied their intensity; for no rhythm can have its full 
 effect unless some stress is laid upon the syllables that come 
 at certain stages of the verse. So this lengthening or shortening 
 of the notes would be attended by an increase or a decrease in 
 their strength. Apart from this, the entire melody might 
 grow louder or softer in successive parts of an elaborate piece, 
 and the time might likewise grow faster or slower ; but there 
 is nothing to indicate such changes. 
 
 Thus it is impossible to fix the absolute, pitch, duration or 
 intensity of any of the ancient notes. The evidence only gops 
 to prove that certain notes were higher or lower, longer or 
 shorter, louder or softer than certain other notes. And in 
 dealing with their relative pitch, duration and intensity, the 
 pitch alone can be determined with precision. 
 
26 
 
 GREEK MUSIC. 
 
 There is consequently a serious fault in much that has been 
 written of late about the music of the ancients. Transcripts 
 have been made upon a plan that necessarily gives the 
 wrong pitch to twenty notes out of every twenty-one and 
 does not necessarily give the right pitch to the twenty-first, 
 while it probably is just as much at fault in the duration of 
 the notes and their intensity. Arguments have been founded 
 on these transcripts, as though all originals had now been 
 superseded ; and the conclusions are astonishing. In fact, 
 some ancient music has actually been compared to works of 
 Beethoven and Wagner, from which it differs fundamentally, 
 But this was perhaps to be expected when so many scholars 
 and musicians have plunged into a higher criticism of ancient 
 music without taking the trouble to make themselves acquainted 
 with the notes. 
 
 A FLUTE-PLAYER, TAKING A DRINK, WITH HER FLUTE-CASE SLUNG OVER HER LEG. 
 
 From a Greek vase in the Author's collection. 
 
BY THE SAME AUTHOR. 
 
 ANCIENT SmPS. Illustrated. Bemy 8wo. 1894. loj. 6^. 
 
 ' Independent research, erudition without pedantry, and a respectable know- 
 ledge of modem seamanship and nautical terminology are conspicuous merits 
 of this treatise.' — Times. 
 
 ' Farla egli delle navi a rami ed a vela, delle loro dimensioni, dei materiali 
 impiegati, degli alberi, delle vele, della pittura, del timone, dei dipinti di 
 prora e di poppa, delle ancore, gomene, bandiere, fanali, scandagli, battelli, 
 ecc, ecc, in una parola, di tutti gli attrerzi e le particolaritJi inerenti alia 
 forma ed armamento marinaresco d' una nave a remi ed a vela, coiroborando 
 le sue speditive affermazioni con un ricco e sovratutto ben scelto e corretto 
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 Simsta MaritHma. 
 
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 Sammlung und Verzeichnung der auf seinen Gegenstand beziiglichen literar- 
 ischen Uberlieferung aus dem Alterthum. Sie reicht von Homer bis auf die 
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 ausfuhrlichsten alteren Werke.' — Literarisehes Centralblatt. 
 
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 sur un solide echafaudage de textes et de monuments, de tout ce qui louche 
 a la structure proprement dite et i I'^quipement des navires antiques : rames, 
 dimensions et tonnage, mat^riaux, coque, ancres, cSbles, gouvemail, mSture, 
 signanx, tons ces sujets sont trait^s successivement avec nne singuli^re maitrise 
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 ' His book contains the results of long, laborious, and careful research. 
 It is a scholarly work, and brings to the surface a vast amount of useful 
 information hitherto scattered on the bottom of the ocean of ancient history.' — 
 New York Times. 
 
 Bonbon: C. J. CLAY and SONS, 
 
 CAMBRIDGE UNIVERSITY PRESS WAREHOUSE, 
 
 AVE MARIA LANE. 
 
 (Bfoegcw : 263 argyle street. 
 
BY THE SAME AUTHOR. 
 
 RHODES IN ANCIENT TIMES. Demy%vo. 1885. ioj.6rf. 
 
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 archaeology in which we English are too poor.' — Guardian. 
 
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 Ausgrabungen zu Tage gekommenen kunstarchaologischen Fundstiicke sowohl 
 wie die massenhaften Inschriften verarbeitet worden sind.' — Berliner Philo- 
 logische Wochenschrift. 
 
 RHODES IN MODERN TIMES. Demy %vo. 1887. 8j. , 
 
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 MEMPHIS AND MYCEN-E, an Examination of Egyptian 
 Chronology and its application to the Early History of 
 Greece. Demy 8vo. 1896. 5^. 
 
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 to contain much useful matter about Egyptian chronology, which the author 
 deals with in a learned, but withal highly businesslike, manner.' — Times^ 
 
 'Egli ha il merito d' aver messo il dito.suUa piaga, e diavere scosso la cieca 
 fede in una cronologia, che oramai minacciava di essere considerata siccome 
 canonica.' — £a Cultura, 
 
 BoniOtt : C. J. CLAY AND .SONS, 
 
 CAMBRIDGE UNIVERSITY PRESS WAREHOUSE, 
 
 AVE MARIA LANE. 
 
 (Bfaegow : 263 argyle street.