The Earliest Musical Notation Author(s): David Wulstan Source: Music & Letters, Vol. 52, No. 4 (Oct., 1971), pp. 365-382 Published by: Oxford University Press Stable URL: http://www.jstor.org/stable/734711 Accessed: 24-08-2016 14:58 UTC

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This content downloaded from 194.81.230.99 on Wed, 24 Aug 2016 14:58:27 UTC All use subject to http://about.jstor.org/terms THE EARLIEST MUSICAL NOTATION

BY DAVID WULSTAN

THERE is something particularly fascinating about the discovery and decipherment of ancient scripts that rarely fails to stir even the popular imagination; and in musicians the quest for early notations often arouses a glint of fervour in the eye. This may be because, in some obscure way, we feel a mysteriously close contact with a people whose music we can listen to or perform. The law of supply and demand operates here as elsewhere, and accordingly ancient notations are from time to time identified in the most unlikely sources and duly deciphered. The most famous illusory notation of recent times has been that of Sachs and Galpin. Although it has been shown repeatedly by Assyriologists that what Galpin and Sachs regarded as notation was no more music than a laundry list is, speculation along these lines does not appear to have abated. A recent article' has pushed imagination to its furthest absurdity, purporting to find notation in hieroglyphic texts and constructing a whimsical, Tolkien-like fantasy out of the most unpromising material. In reality, as our understanding of ancient music increases, our certainty of knowledge decreases. In the field of classical Greek music, for example, some writers (notably R. P. Winnington-Ingram and the late Isobel Henderson) have repeatedly stressed the tenuous nature of the connection between theory and real music, and that the few genuine fragments of Alypian notation (fewer than is commonly supposed) cannot be read, after all, with complete accuracy. Yet awareness of these facts seems rather less than general in writings about Greek music, the volume of which shows no significant decrease. Although the Alypian -notation tells us little or nothing about Greek music, and is in any case very late (c.25o B.C.) it is of interest that the earlier version of the notation was founded on a consonantal alphabet of the Phoenician type (it was later revised using largely Greek symbols). A notation from the Near East would not, therefore, be entirely unexpected. Interest in Babylonian music has recently been revitalized by the identification of musical terms in a series of tablets. The tablets so far known are like a chain in which each forms a link to the interpretation of the next. At the end of this chain is the possibility of by far the earliest notation known, dating from C. I 300 B.C.

1 Maureen M. Barwise, 'Hearing the Music of Ancient Egypt', The Consort, 25

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This content downloaded from 194.81.230.99 on Wed, 24 Aug 2016 14:58:27 UTC All use subject to http://about.jstor.org/terms The names of intervals It was Mrs. Draffkorn Kilmer who first published the tablet that provides the beginning of the chain. Nabnitu XXXII, col. i (= U.30I i) names the strings of an instrument, and it can thus be recognized that another tablet (CBS IO996, col. i) gives a list of names of intervals. The texts of the two tablets are based on the transcriptions of Mrs. Draffkorn Kilmer, though corrections due to the later tablets are incorporated :2

CBS IO996, col. i Line I I. SA qud-mu-uz uz SA 5-su I-V SA nis GAB.RI I2. SA 3 uh-ri u SA Su VII-V SA rse-e-ruml I3. SA sva-GE, U SA 4 uh-ri II-VI SA i-sar-tum ('normal') I4. SA qud-mu-uz uz SA 4 uh-ri I-VI SA sal-s'a-tum ('third') 15. SA 3-su SIG U SA 3-su uh-ri III-VII SA em-bu-bu ('pipe') I6. SA sa-GE, U SA 3-su uh-ri II-VII SA 4-tu ('fourth') I7. SA d-a DU Uz SA qud-mu-u IV-I SA SUB! MURUB4 (=nid qabli!) I8. SA qud-mu-u u SA 3-su SIG I-III SA GIS. SUB!BA I9. SA 5-su u SA id-GE, V-II SA MURUB4-tU (- qablitu, ('middle') 20. SA sa'-GE, Uz d-a-D U II-IV SA rtiturl MURUB4-tU ('bridge, middle') 2I. SA 4 uh-ri u SA 3-su SIG VI-III S[A kit-mu] ('cover') 22. SA 3-Su SIG U SA Su III-V SA ti-tur i-svar-tum] ('bridge, normal') 23. SA 3-su uh-ri u' [SA d.9-a-DU' VII-IV SA Pi-tum] 24. SA dE-a-DU [U' SA 4 uh-ri IV-VI SA z/$ir-du] (Remainder of col. i destroyed.)

Nabnitu XXXII, col. i (UR 301I)

sa.di qud-mu-u[m] fore (string) sa.us sa-mu-su-um next (string) sa. 3 sa.sig sd-al-4u qa-a[t-nu] third, thin (string)

sa.4.tur a-ba-nu-[z'] ~ 1 j Akk.:Sum: Ea-creator fourth, small 5. sa.di.*5 ha-am-4u fifth (string) sa.4.a.ga.gul ri-bi uh-ri-i[m] fourth of the behind (string) sa.3.a.ga.gul sval-vi uh-ri-im third of the behind (string) rsa.2.a.gal .gul si-ni uzh-ri-im second of the behind (string) [sa.I]. [a].ga.gul.la uzh-ru-um the behind-one (string) I0. 9 .sa.a 9 pi-it-nu nine strings [ ] x (y) pi-is-mu ... [ ] ti-ar-ti normal [ ] [ti]-rt6-,ur i-s'ar-tum bridge, normal [ ] [ki-i]t-mu cover [ ] [x y (z) k]i-it-mu . . . cover

2Note that pointed brackets enclose editorial material, square brackets denote restorations of broken material, and half brackets show that the original is partly legible.

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This content downloaded from 194.81.230.99 on Wed, 24 Aug 2016 14:58:27 UTC All use subject to http://about.jstor.org/terms [ ] [x y]-um [ ] [x y-u]m (Remainder of col. i broken.)

*Asterisks denote departures from the original text, exclamation marks revised readings.

Some of the names of intervals given at the end of each line of CBS I0996, i may also be the names of instruments, but only embubu may be certainly identified in this way. The restorations of lines 20 foll. of the tablet are based upon previous lines, which repeat the whole sequence. The two columns of Nabnitu XXX, i are parallel, the first being in Sumerian, the second in Akkadian. As was pointed out in an article by Mme. Duchesne-Guillemin,3 the epithets 'fore' and 'behind' can be interpreted with reasonable ease, for on many instruments of the lyre-type (for example Queen Pu-'abi's lyre, recently discussed by Dr. Barnett of the British Museum4) there is a figurehead which must have faced outwards in respect of the player. Since the strings to the front of all harps, and perhaps a majority of lyres (though by no means all, as Mme. Duchesne-Guillemin appears to think), are smaller than those at the back, the intervals of the CBS tablet can be taken to be in ascending order. Compared with modern terminology, the Babylonian scheme contains more interval names, thus giving an impression of greater exactness. But, as can be seen from the tablet U 7/80 discussed below, the intervals are not of fixed value, as in modem usage, but express merely the inter-relationship of the two strings. In addition, it is only the modem intervals of the third, fourth, fifth and sixth that appear; no seconds are given. Since the sequence of the CBS tablet starts (the number of missing lines can be cal- culated, and can be assumed to commence as at line i i) with the interval I-V, a fifth, and only indicates fourths when this is neces- sitated by the assumption of seven strings (as opposed to the nine of Nabnitu XXXII), it is obvious that the fourths and sixths are simply the inversions of the fifths and thirds. The tablet U 7/80, shortly to be discussed, confirms this supposition. Like Nabnitu XXXII, it is in terms of nine strings, so two more intervals can be included as fifths. The two extra strings, since they double the two lowest, also confirm the natural assumption of a heptatonic scale to be valid. In a previous article5 I put forward a possible explanation for some of the names of the intervals; but this was extremely hypotheti- cal and is of no importance for the present purposes. A reason for the 'thin string' was also given; I compared it to the red and blue strings used on modem harps as a means of orientation. The desig- nation 'Ea string' remains obscure, although this was a central feature of the theory earlier put forward by Mme. Duchesne-

3 Revue de Musicologie, xlix (I963), pp. 3-17. ' Iraq, xxxi (I969), pp. 96-I03. ' 'The tuning of the Babylonian harp', Iraq, xxx (I968), pp. 215-28.

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This content downloaded from 194.81.230.99 on Wed, 24 Aug 2016 14:58:27 UTC All use subject to http://about.jstor.org/terms Guillemin,6 who interpreted the CBS tablet as a tuning-cycle and constructed a scale from the material. I showed the untenability of this theory in the above-mentioned article. It will be noticed that Nabnitu XXXII contains, from line I2 onwards, what looks like a list of some of the CBS intervals, but in a different order, and with possible divergences in terminology. But the cyclic order of the intervals is a noticeable feature, and also the alternation of what I have called 'primary' (fifths) and 'secondary' (thirds) intervals.

Octave species It was due to the encouragement of Professor 0. R. Gurney7 of the Oriental Institute, Oxford, that I had written about the tablets already discussed. But before the article was published a new tablet turned up. Due to the kindness of Dr. E. Sollberger of the British Museum, Professor Gurney was able to publish a transcription,8 and I was therefore able to comment on this new material at the same time. The new tablet, B.M. U 7/80, consists of two columns. The left-hand column contains string and interval names. But because there is no regularity of sequence no sense can be made out of what little remains. For the right-hand column the position is different. Although very fragmentary, a cyclic order prevails which makes reconstruction of the whole possible. Professor Gurney's transliteration of the tablet follows:

LEFT COLUMN RIGHT COLUMN

I. [ . x u]h?-ri?-im [sum-ma gig zA.Mf pi-i-tum-ma] 2. ... . ].-tum I. [e-e]m-b[u-bu-um la za-ku] 3 .*. re-b] u-tum 2. la-al-?[a-am qa-at-na-am te-ni-ma] 4 [** qa'-ab-li-tim 3 . e-em-bu-bu-u[m izlfs-z/s a- . . .] 5 [. ..] i-sar-tim 4. sum-ma gisz[A.Mf e-em-bu-bu-um-ma] 6. [uI] - ru - ur 5. ki-it-mu-um [la za-ku] 7 [**. ] i-s'ar-tum 6. re-bi u'h-ri-im [te-ni-mal 8. ... . ].-tim 7. ki-it-mu-um i[z/s-z/sa- .. 9. . * z/sir-d]i-im 8. sum-ma giszA,Mf k[i-it-mu-um-ma] io. ... . ki-it-m]u-um 9. i-sar-tum la za-[ka-at] II. [.. y .Y] lh-ri-im I o. s'a-mu-s'a-am uz uzh-ri-a-a[m te-ni-ma] 12. I * I. i-sar-tum izls-zlsa-[ ..] 12. NU SU I 3. sum-ma giszA.Mf i-sar-t [um-ma] 14. qd-ab-li-ta-am ta-al-pu-[ut] 15. sa-mu-sa-am z uh-ri-a-am te-[ni-ma] I 6. [giS']zA'.mf ki-it-mu- [um-ma] I 7. [sum]-ma gigzA.Mf ki-it-m[u-um-ma] I 8. [i-s'a] r-ta-am la za-ku-ta-am t [a-al-pu-ut] I 9. [re-bi] uth-ri-im te-n[i]-m[a] 20. [gigzA.Mf e-em-bu-bu-um-ma]

6 Revue de Musicologie, lii (I966), pp. 147-62. A further note appeared in lv (1969), pp. I-I i, which I answered in lvi (I970). 7My debt to him, as mentor and friend, I should like to acknowledge here. 8 Iraq, xxx (I968), pp. 229-33.

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This content downloaded from 194.81.230.99 on Wed, 24 Aug 2016 14:58:27 UTC All use subject to http://about.jstor.org/terms Lines i-i i contain a sequence of four-line formulae, repeated with different interval-names. Lines 8-i i read, for example: "If the ZA.MI is kitmum and the isartum is not clear, you alter the samusum and uhrum strings so that isartum will stand". After the untranslatable signs NU SU the tablet continues in a sequence of four-line formulae representing lines i-ii in reverse. Thus, lines I3-I6 read: "If the ZA.MI is i'artum, and you have played an unclear qablitum, you alter the uhrum and then the zA.Mi is kitmum". The interval 'not clear' is obviously a dissonant tritone. What is being described is the altering of one of the strings (or two when there is also one doubled at the higher octave as in line Io) of the tritone in order to retune to a perfect interval. The effect of this re-tuning is to produce what might be called 'modulations'. It is evident, however, that the interval names are being used in this tablet in two different ways: in addition to describing the distance between two strings, they are also used in the sense of tunings. The sequence of tunings represented by lines 13 foll. can be represented as follows:

Thetic notation Dynamic notation I II III IV V VI VII VIII IX i.e. 'Starting-note' isartwn- LC.'Sta,ti}> noe( tuningE tritone = qablitum-interval

kitmwm- - _ - ( tuning -> A

new tritone =iartum-interval

embubum- I - -f tuning D new tritone = kitmum-interval

ttum-. --JRG -O tuning ;p-# .; -n)..--- -- G new tritone = embubum-interval

nitid A MURUB- __ __'___ C tuning Tj new tritone pitum-interval

nil GABRI- #- * tuning

new tritone = nild MURUB interval

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This content downloaded from 194.81.230.99 on Wed, 24 Aug 2016 14:58:27 UTC All use subject to http://about.jstor.org/terms aLitum g el t W ,. tuning - __- d_ _ __) B new tritone nii GABRI-interval

itartumr - 1 t 11 - "- tuning

The reason for supposing that this order of tunings, rather than that of lines i-i i, is the conventional order may be gathered from the tablet KAR 158, viii printed below, and also from the order of intervals in the latter part of Nabnitu XXXII. The connection between these scales and the Greek 'octave-species', and their possible relation to the Pythagorean 'harmony of the spheres' is discussed elsewhere.9 The precise reason for the designation of these scales by the particular interval-names chosen is obscure.lo It is important, however, not to connect these tunings with the late medieval, and erroneous, conception of 'modes'. As is now known," modes had little connection with scales until the present millennium, and then only in the minds of theorists. Another tablet gives a list of songs classified according to the tuning required by their music. Although this tablet has been known longer than any of the others discussed here, it is only now that its significance can be properly appreciated. The portion quoted below is a summary of a catalogue of songs. It is not implausible, in the light of the tablets to be dealt with under the next heading, that this was a summary of notated lyrics. Here is the text of the relevant part of the tablet:

Line 45. 23 iratu la e-s.ir-te Akkadf KI '23 love songs, of the "normal" (type), Akkadian' 46. I17 iratu la ki-it-me '17 love songs, of the "cover" (type)' 47. 24 iratu la eb-bu-be '24 love songs, of the "pipe" (type)' 48. 4 ziratu sa pi-i-te '4 love songs, of the pitum (type)' 49. iratu sa ni-id MURUB, '... love songs, of the nid qabli (type)' 50. iratu la ni-*is GAB.RI love songs, of the nis GAB.RI (type)' 51. iratu la MURUB4-te love songs, of the "middle" (type)' The isartum, kitmum and pitum may be the names of instruments, though there is no real evidence for this assumption at the present. The embubum, however, is known to have been a pipe. If it turned out

9 Ibid., p. 225. 10 Ibid., p. 222. See, however, the postscript on p. 381. 11 Cf. Wulstan, 'The Origin of the Modes', Studies in Eastern Chant, ii (197 I).

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This content downloaded from 194.81.230.99 on Wed, 24 Aug 2016 14:58:27 UTC All use subject to http://about.jstor.org/terms that the names of the octave-species given above were indeed the names of instruments, it would be possible to suppose that the octave- species were named after the instruments for which they were typical. In Sumerian literature it is not uncommon to find poems with the name of an instrument attached, as though it signified the class of poem. But only one of these terms is certainly to be identified as an instrument: the tigi, which was a type of drum. It therefore seems impossible that these names had any significance other than that such songs should be accompanied by a drum, or sung at a drum- ritual. Any connection between octave-species and instruments, if there were one, would most probably have had a different basis.

Tablets from Ras-as-samra This material is not particularly new, some of it having been published some years ago. Laroche, who first printed transcriptions of the tablets,12 was naturally unaware at the time that they contained musical material. But when Professor Giiterbock of Chicago first saw Ugaritica v, he had just been reading the articles by Professor Gurney and myself in Iraq, so he at once recognized their musical connections and kindly brought them to our notice.13 These tablets differ from those already discussed in several ways. They are of Ugaritic provenance, and contain substantial portions of Hurrian, an imperfectly understood language; but for present purposes they differ principally in that the musical terms discussed earlier appear in a non-cyclic order. The precise form of each term differs to a greater or lesser extent from the Akkadian forms already knowrn; since they were foreign terms, this is hardly surprising. With few exceptions, each term is followed by a numeral. Each tablet in this series is divided horizontally by a double (sometimes single) rule. The musical portion of the text is in all discernible cases below this division, while above are written Hurrian texts which appear to have lyric characteristics. In one or two cases some sense can be made out; such passages point to the hymnodic character of the texts-an impression reinforced by the litany-like repetitions of some of the lyrics. In one (h. 5) there seem to be references to music: ki-in-na-ri (? = Ug. knr Heb. kinnor-'lyre') and 'i-i-ri (twice, ? = Ug. sr Heb. sir-'song') 14 All these features-the non-cyclic appearance of interval names, their position below apparently lyric texts, and the regular inter- vention of numerals-lead to the inescapable conclusion that these tablets represented words and music. Professor Giiterbock had independently come to the same conclusion. Unfortunately, all

12 Palais Royale d'Ugarit, iii (1958), pp. 327-35 and Ugaritica, v (I968), pp. 462-96. Numbers in bold type identify tablets by the numbers given there. 13 Though this article went to press before the appearance of the contribution of Prof. Guterbock in Revue d'Assyriologie, 64, I have been able to take advantage of some of his readings, as will be evident. 14 Although according to R.S. 20.I23, SIR ('song') = halmi (Akk. zammarum).

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This content downloaded from 194.81.230.99 on Wed, 24 Aug 2016 14:58:27 UTC All use subject to http://about.jstor.org/terms of the tablets are fragmentary, and few represent anything like the complete text. The most continuous excerpt is printed here, following Laroche: Recto-verso i (a) [x-x] ha-nu ?-ta ni-ya-sa zi-uz-e s4[i?]-nu-te zu-tu-ri-ya u-.pu-x-ra [x-x-x] (b) -ur-ni ta-sa-al ki-il-[l] a [z] i ?-li si-i [p ?-x] hu-ma-ru-ha-at u'-wa-ri 2 (a) ku-ma-ru-ha-at u-wa-ri wa-an-da-[n] i-ta u'?-ku-ri ku-ur-ku-ur-ta i-Sa-al-la (b) uz-la-li kab-gi a [l]-li-x-gi Vsi-ri-it? x-[x]-nu-svu-w9-sv(-a1 ta-ti-ib ti-svi-a 3 (a) wa-sa-al ta-ti-ib ti4-i-a u'-nu-[g]a? kap-si-li- u-nu-ga?-at ak-li Sa-am-sa-am-me- x - (b)-li-il uk-la-al tu-nu-ni-ta-x [x-x]-ka ka-li-ta-ni-il ni-ka-la 4 (a) ka-li-ta-ni-il ni-ka-la ni-h [u?-r]a?-sa-a1 ha-na ha-nu-te-ti at-ta-ya-as-al? (b) a-tar-ri hu-e-ti ia-nu-ka[ a]s-sa-a-ti we-e-wm ha-nu-ku

Ro 5. kab-li-te 3 ir-bu-te I kab-li-te 2? x-x-x [ti]-ti-mi-4ar-te io ul-ta-ma-a-ri 6. ti-ti-mi-sar-te 2 zi-ir-te I sa-[a]h-ri 2 x-x-te 2 ir-bu-te 2 7. tup-pu-nu I sa-aS-Sa-te 2 ir-bu-te x [f]a-[as-s]a-t[e] x ti-tar-kab-li I ti-ti-mi-?ar-te 4 8. zi-ir-te I sa-ah-ri 2 Sa-a?-Aa-t[e] 4 ir-bu-te I na-at-kab-li I .a-ah-ri [I] 9. sa-as-sa-te 4 sa-ah-ri I sa-as-' [a-t] e 2 sa-ah-ri I sva-as-sa-te 2 ir-[b] u-[te] 2 IO. ki-it-me 2 kab-li-te 3 ki-it-[me] I kab-li-te 4 ki-it-me I kab-li-te 5 ?

I I. [an-nu]-u'-za-am-ma-as'-sa ni-it-kib-li za-[lu-zi x'su m Am-mu-ra-bi

It will be noticed that below the 'music' is a rule under which a colophon appears. Besides containing the name of the scribe, this line contains the phrase zamassa nit kibli. Guterbock has now pro- posed that in line II, za-am-ma-ru ! sa should be read instead of Laroche's za-am-ma-as-ss. Gurney tells me he finds this alteration convincing. The line is then in Akkadian and means "This [is] a song [in the] nitkibli [i.e. the nid qabli tuning], a zaluzi . . . written down by Ammurabi".15 Only five tablets are extant on which the tuning indication survives. They all designate nid qabli tuning. It may well have been the most common tuning in use, for there is elsewhere rather curious reference to the voice of Adad thundering "like a pitnum, [that is to say] a pitnum of the nid qabli (tuning)".16 Although the colophon uses a musical term in the sense of 'tuning' the 'music' portion of the tablets can hardly use the interval names in the same way; here the symbols must represent melodic fragments after the manner of the neume. If, however, the interval names are to be regarded as neumes, several questions must be asked. First, are there more intervals than we already know-for example, symbols

15 Loc. cit., p. 5I. 16 Cf. Draffkorn Kilmer in Assyriological Studies, I6, Chicago (I965), p. 263: (Adad rigimSiu) GIM pi-it-ni SUB / / pi-it-nu 9a x MURUB4.

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This content downloaded from 194.81.230.99 on Wed, 24 Aug 2016 14:58:27 UTC All use subject to http://about.jstor.org/terms denoting the distance between two adjacent strings, hitherto un- known? If not, how were seconds written? In any case, are the neumes to be read as conjunct or disjunct intervals, ascending or descending? It is necessary to give prior consideration to the first question, for on the answer the whole of the discussion must turn. To start with, the symbols must be compared with the interval names known in Akkadian, for in some cases the equation is not immediately obvious. In the left-hand column the names as given in the Hurrian tablets'7 are given opposite those of the right-hand column which may be supposed to be the Akkadian equivalents (standardized to -um forms; the numbers correspond with the lines of the CBS tablet): I I . elis'gi ? ni's GAB.R1 I12. svahri serum I 3. (isarte) isartum 14. sa Rate salsatum I5. [ebbu] be/i embuibum i 6. irbute ributum I 7. nat kabli nid qabli i 8. tuppunu tilpanum I 9. kablite qablitum 20. titar kabli titur qablitum 21 . kitme kitmum 22. titim is'arte titur isartum 23. pitum 24. zirte slzirdum Comments i I. The placing of isgi here, instead of at 23, is conjectural. 12. As Guiterbock observed, ?ahri confirms the reading se-e-ru for CBS Io996, line I12. I3. isarte occurs only in the compound (22). The lack of the simple form is probably merely a coincidence. I5. The occurrence in three places of the final syllable of what might be ebbubeli makes this conjecture reasonable. I 8. According to Guterbock the phrase in CBS I o996, line i 8 should read GIS. SUB.BA rather than GIS. NIM.MA the interpretation of whichl8 I therefore withdraw. The reading of GIS. SUB.BA which most nearly corresponds to the new tablets is tilpanum (throwstick) .19 Unfortunately GIS. SUB.BA can also be read isqu (lot) which might be represented by i/esgi. I think this is sufficiently less likely to merit rejection. 24. Formerly read mus"-du, the first sign is now seen to be slzir- (Guiterbock). Meaning unknown, although zirte - s/zirtum can mean 'olive'.

Almost all the interval names formerly known can thus be

17 Since Laroche gives (Ugaritica, v, pp. 484-5) a concordance to all the terms, I have not given references to the tablets in which they occur; nor have minor differences of spelling been taken into account. 18 Iraq, xxx, p. 228. 19 It is a slight possibility that tilpanum may also be the name of a musical instrument. For loss of I cf. lalJatum > Ilate, for a > u cf. amamIammu > sumisumi (sesame - see Laroche: Ugaritica, v, p. 458). Confusion with tuppe (tablet) may also have helped to produce the form tuppunu. See also p. 374.

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This content downloaded from 194.81.230.99 on Wed, 24 Aug 2016 14:58:27 UTC All use subject to http://about.jstor.org/terms recovered from the new tablets. It remains to be seen what other symbols are contained therein, and whether these represent further intervals. Here some difficulty arises, for unlike the names already tabulated, which occur with some frequency, the remaining words are rarer and most fragmentary. This in itself allows the presumption that none of the remaining names are those of intervals, least of all seconds, which might have been expected to be extremely common. In addition, the forms of these 'residual terms' are conspicuously different, having more the appearance of real Hurrian words rather than of borrowed forms.20 Moreover, at least two of these words are certainly Hurrian a-nd their meanings are known. a'shue V 'high' and tldurie V 'low' occur with comparative frequency, but always in connection with sahri, irbute and (dubiously) zirte. Since these words interrupt the sequence symbol + numeral, it may be inferred that in some way they modify the named interval.21 uOta mari occurs several times (as far as can be gathered) in varying states of preser- vation. It seems regularly to follow, but not precede, a numeral. But because in h. 6 it ends a line this phrase is more likely to modify the previous, rather than the succeeding, symbol, if modification can be assumed. bentamma also has -no following numeral in the three cases it may be identified, but whether a number preceded the phrase or not is not discernible. pugarna, however, appears to take the place of a number, following a known interval symbol (or ashue in h. 4). The basis for discussion of the remaining phrases is scant indeed. They are mostly hapax legomena. Kazae occurs once, preceded by a number; whether one followed cannot be gathered. udga [ ] etama seani(?) hizawesa(?) and pahita (index finger ?22) have, apart from their rarity, one thing in common with the rest of the 'residual terms': so far as can be ascertained, they break the symbol + -numeral sequence which holds good for all the known interval names (except nat kabli in h. 2x, almost certainly an error); the presumption that these terms were not intervals is thus fortified. hapsema is something of an oddity, for it sometimes has a following (possibly also preceding) number, but elsewhere it is intercalated between two other terms. However, it might be maintained (with some reason) that hapsema is cognate with Akk. hamsu 'fifth', and that it might be a synonym for the interval called tilpanum above on the analogy of salsatum, ributum. But this theory would require that there were synonyms for primary intervals. Since all the tablets so far agree in their terminology for primary intervals (allowing that nis GABRI iS of doubt- ful equivalence at present), and probably for the secondaries, this hypothesis appears very doubtful. The same applies to gi-es-sa in h. 4. Even if the meaning of these 'residual terms' is obscure, their

20 For example, the endings -a, -ta, -ae. 21 How they did this is uncertain. In the theory outlined below possible meanings such as sharp/flat/natural or higher/lower octave are not tenable for these particular intervals. 22 A mere guess on the basis of Laroche's partie du corps.

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This content downloaded from 194.81.230.99 on Wed, 24 Aug 2016 14:58:27 UTC All use subject to http://about.jstor.org/terms breaking of the symbol + numeral sequence makes it reasonably certain that their function was to modify the notation in some way. Lack of knowledge of these details does not, however, entirely prevent a decipherment of the notation as will be seen. The problems that remain concern the way in which the interval names were used as neumes. Were they understood as conjunct or disjunct intervals? That is to say, did the interval I-V include the intermediate steps or merely the boundaries? In either case, did the intervals ascend or descend? As is well known, melodic movement is more by conjunct than disjunct steps. This is par- ticularly true of plainsong and other music which Babylonian music might be expected to resemble in some degree. It is therefore reason- able to prefer the theory that the neumes were conjunct in structure. As to the question of upwards or downwards movement, since melodic motion is in both directions, the neumes must have been similarly flexible. But how may ascending, as opposed to descending, neumes be recognized? The CBS tablet furnishes what might be taken to be a clue to this problem. The tablet CBS I0996 presents alternate 'primary' and 'secon- dary' intervals. That these intervals are fifths and thirds, the apparent fourths and sixths being merely inversions, has already been shown. Now the striking feature of the ordering of the intervals in the CBS tablet is that though the fifths commence by upward reckoning (e.g. I-V), the notation for thirds begins in reverse (e.g. VII-V). This situation does not, at first sight, hold good for the succeeding intervals. But when the invertibility of intervals is taken into account, the pattern can be seen in a different light. This will be evident from the following table. On the left is given the CBS string numbers as they stand; on the right the intervals are shown, so that no inversions are necessary, in terms of a hypothetically extended instrument.

CBS line Strings i.e. I I I-V I-V 12 VII-V VII-V 13 II-VI II-VI 14 I-VI VIII-VI 1 5 III-VII III-Vil I6 II-VII IX-VII 1 7 IV-I IV-VIII I 8 I-III III-I I9 V-II V-IX 20 II-IV IV-II 21 VI-III VI-X 22 III-V V-Ill 23 VII-IV vII-xi 24 IV-VI VI-IV

Note how the progression from lines I I-I 7 is effectively the same, as is shown by the right-hand column. At line i8, however, the

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This content downloaded from 194.81.230.99 on Wed, 24 Aug 2016 14:58:27 UTC All use subject to http://about.jstor.org/terms symmetry of the right-hand column is interrupted. A glance at the left-hand column shows why this might be so: since the primary intervals are now having to be shown in inversion, as fourths rather than fifths, the scribe seems to have decided to show the opposite direction of the secondary intervals in relation to the primaries by reversing the components of the secondaries. Since the tablet goes to such lengths to underline this feature, it cannot be doubted that the primary intervals were considered as moving in the opposite direction to the secondary intervals for some reason. And that reason may have been due to their use as neumes. Before applying the results of this discovery to the notation, it is necessary to make sure that the previous assumptions about the notation are valid, and that they are the only possible assumptions. It was presumed that the neumes used the intervals conjunctly. May the melodic value have been, after all disjunct; indeed, is it possible that the symbols denoted harmonic, rather than melodic, intervals? The argument must turn on the function of the numerals. At first sight the numbers may reasonably be supposed to denote repetitions. If the intervals were harmonic, repeated from one to five23 times, then the music was hardly worth writing down. It might be argued that the notation represents an accompaniment rather than melodic material, which latter would have been memorized, the singer using the accompaniment as an aide-meimoire. Common sense must counter this proposition by saying that it is inconceivable that a particularly elementary accompaniment, easily improvised, would be committed to writing, but that a more complex melody would be left to chance. Such a situation, to paraphrase Dr. Johnson, would result in that which is not worth writing being written. Commonsense, often largely ignored as a basis for argument, dictates two axioms that must be assumed for any notation. The first has already been propounded, that there must be some point in writing music; the second follows from it: it is apodictical that the notation must be capable of expressing one melodic phrase as clearly as another. This principle obtains even in early Western neumes of the campo aperto type, the degree of ambiguity being more or less constant. It may reasonably be ex- pected, since the Babylonian intervals were exact, that a notation based upon them would be capable of the more or less exact representation of any melodic material. This being so, the possibility that the numbers denoted repetitions of symmetrical melodic fragments can be excluded on the grounds that the notation could not express anything other than a few fixed formulae. On similar grounds the theory that the interval-names were used to represent one note only, the numbers indicating repetitions, can be dismissed; in any case there would be no point in using both 'primary' and 'secondary' intervals. The possibility that the numbers 23 And possibly ten: see below p. 378.

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This content downloaded from 194.81.230.99 on Wed, 24 Aug 2016 14:58:27 UTC All use subject to http://about.jstor.org/terms represented strings, as in the CBS tablet, may also be ruled out. Although notation by string-numbers or 'notes' seems most logical to us, so does writing in letters rather than syllabically. Since cuneiform writing was not alphabetic, neumatic notation should hardly come as a surprise. The strict neume + number sequence, and the appearance of numbers 1-5 (plus io) only, allows the categorical rejection of the possibility of notation by string-numbers. The numerals must therefore represent modifications of the basic pattern of the neumes. Such modification would certainly be necessary in order to convert the interval names into a workable and sufficiently flexible notation. Irrespective of whether the intervals were treated as conjunct or disjunct, the numbers could extend or subtract from their nominal value. If disjunct, the process of defining an interval in one way, then modifying it with a numeral whereby the interval is completely redefined, would be pointless, not to say farcical. This is another ground, therefore, for supposing that the intervals were conjunct. The scheme that emerges from this discussion is as follows. The neumes were derived from the interval names, the distinction between primary and secondary intervals being used as a division between ascending and descending motion. The exact amount of the rise or fall of the notes nominally defined by the interval could be modified by a number. (This fits in with the observable pattern of the tablets iln which i and 2 are the most common numerals, followed by 3, 4 and 5, all in rank order.) In this way any melodic phrase could be written, except that more than one repetition of the same note would be cumbersome to express, involving the use of the same symbol + number (i) ma-ny times. No examples of this phenomenon occur in the new tablets; indeed, a striking feature is that no interval-symbol is ever repeated consecutively. It might be argued (i) that note- or formula-repetition, being rare in this music, is therefore not found in the surviving remains, just as the interval isartum is not found although it may be inferred; (ii) this phenomenon could be taken to show that the numerals expressed repetitions-but this alternative has already been rejected; (iii) note- and/or formula- repetition may have been indicated by the 'residual terms' to which attention has been called earlier. This last possibility seems most likely. Although the notation postulated would therefore fulfil the axio- matic requirements stated earlier, there are other ways in which the symbols and numbers could be used as a means of writing music. For example, the numbers might represent extra repetitions of the last note of the interval if greater than nominal value, or modifi- cations if less. Or refinements such as quiescent notes and other such devices may be imagined. It will readily be appreciated, however, that every complexity of this nature makes the notation more difficult to read and write, without a commensurate increase

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This content downloaded from 194.81.230.99 on Wed, 24 Aug 2016 14:58:27 UTC All use subject to http://about.jstor.org/terms in flexibility; so the scheme proposed here is most likely. It has already been noted that those tablets which have an extant tuning designation in the colophon specify nid qabli tuning; h. 6, the most considerable fragment, is among them. A transcription may therefore be attempted on the lines suggested. But first there are one or two difficulties that need mentioning or recapitulating. There is the problem of the 'residual terms' linked, as has been supposed, with the question of note and possible formula repetitions. Until more information is forthcoming, little can be said on these points. Nor can the relationship of words to music be satisfactorily discussed, for there is no apparent correlation between words (or syllables) and neumes (or notes). There may have been some con- ventional manner of allocating one to the other (cf. plainsong or Anglican chant). More likely the 'residual terms' contain amongst them some means of expressing nuances of underlay which are not at present apparent. Another difficulty is the appearance of the number IO, which does not fit in with the theory. But, as can be seen, it is the only numeral above 5 to appear in the tablets, and therefore appears anomalous in any light. It seems probable, therefore, that io was a conventional sign, possibly having some connection with underlay and note-repetition, but not taken in the same sense as the other numerals. With the proviso that these difficulties remain unresolved, we may proceed to a transcription of h. 6. In nzd qabli tuning, the neumes will have the following values, if 'primary' intervals are reckoned as ascending, as opposed to descending secondaries:

tnit qablitum tuning

I II III IV V VI VII VIII IX (X XI)

primary intervals:

(tii GABRI) igartum embubum nit qablitun qablitum

kitmum (pitum)

Secondary intervals:

: nr*J 4 -Jr - tilpanum titur qablitum titur ifartum zirtum serum salsatum

e - ributum tilpanum titur qablitum

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This content downloaded from 194.81.230.99 on Wed, 24 Aug 2016 14:58:27 UTC All use subject to http://about.jstor.org/terms The octave in which each neume is to be read will, of course, depend on context, as does do re mi of the tonic sol-fa. This causes no difficulty in practice. The tablet can then be read as follows:

h. 6

kablite 3 irbute 1 kablite 2 titim isarte 10 o ta mari

titim isarte 2 zierte 1 sahri 2 [gaEatc] 2 irbute 2

tuppuau 1 sassate 2 irbute X sassate X titar kabli 1 titimn iarte 4

zirte I sahri 2 Miate 4 irbute 1 niat kabli 1 iahri [1]

) i _ , ,-

Sassate 4 gahri 2 ladUatc 2 sahri I iassate 2 irbutc 2

kitme':7-- 2 kablite 3 kitmc 1 kablitc_S 4 kitme I kablite t 5?

There are several rather disjointed features in this transcription; in particular the progression irbute i nat kabli i 'sahri, which includes a tritone. It cannot be expected that none will occur, but it might reasonably be assumed that they would be rare, since, as has already been seen, the tritone was regarded as dissonant. However, if the relationship of the primary and secondary intervals is reversed, i.e., if primary intervals are read downwards, and vice versa, the trans- cription is improved out of all recognition:

primary intervals:

nis GABRI idartum embubum nit qablitum qablitum = isgi ?

kitmum (pitum)

Secondary intervals:

LJ - I do tilpanum zitur qablittum titur igartum zirtum serum iailatum

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This content downloaded from 194.81.230.99 on Wed, 24 Aug 2016 14:58:27 UTC All use subject to http://about.jstor.org/terms ributum tilpantm titur qablitum

_= Q~~~~~~~~~~~~~~~~~~~~~~~~~~~~ _ _ _- e -1- __ ___

[gi XI titim ijarte 10 usta mari

D~~~~~~~~~~~~~~~~r -

There are several ways in which this reversal might be justified; they . 7 wouldh.r appear reasonable or lame, depending on the sceptici'sm of the,) reader. / It is sufficient,- I however, to point to the greatly improved transcription. The way the words fitted to the music, what the residual terms meant and the significance of the number i o, not to speak of the vali'dity of the method of transcription, are questions which may be expected to be illuminated by further discoveries. Meanwhile, the remaining fragments of any considerable size are transcribed below: 0 do - : -- , - * ...- + _ lL E _ _- :,- >~~~~~-a ' -- r :

kablite 3 irbute 1 E gahri I s'a'iate 2 ? iaEiiri nit kibli 4

titar kabli 1 tit [im iaarte iaiate 2 ir-bute 3 kitme 1

VO 14

h2 e ahy tri2 zirtes? f ate tori 2 zirte 2 wat tri 2r? Jteil irbut

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This content downloaded from 194.81.230.99 on Wed, 24 Aug 2016 14:58:27 UTC All use subject to http://about.jstor.org/terms sassate 2 Gnat kabli I zi]rte IO sahn 3 ]4 J2? sassate 3

ebbu]bi 1 irbute 1

h. 9 R?7

na] t kabli 3 isgi 1 tita[r kabli I sahri I[

R6 h. 19

e.J ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ni]t kibli 3 iSgi 1 titar kabli C J1 zirie 5 sahri a4J4zwe]J irbute 2 duppwz[u

h. 21 R?2 -) k V r - J2? irbute I 1 irbute [ tit] isarte 1 ladsakte ] asate2

irbute [ ] sassate E n]at kabli <4> titar kabli 2 titiUsarte

M & . , .

irb] ute 1 sassate 1 t?Ippltl 1 [ IJaare I ttupp[wzNu

By way of conclusion, it may be remarked that the notation as interpreted here occasionally offers an alternative method of rendering a particular melodic phrase. This feature is found in other notations, including our own. It is interesting to note, therefore, that in these fragments the same melodic motive appears four times, each time differently written. Unfortunately the 4 after nat kabli in h. 21, and the position of isgi are editorial. Though it would be a somewhat circular argument to say that presence of these repeated formulae vindicates at the same time both the interpretation of the notation and these reconstructions, it is also too much to accept that these appearances are coincidental; an element of confirmation may therefore be reasonably assumed.

POSTSCRIPT A delay in publication has given me the opportunity (kindly allowed to me by the Editor) to refer to H. M. Kiimmel's article 'Zur Stimmung der babylonischen Harfe', Orientalia, 39 (I970), published after this article was written. Kummel proposes a new explanation of the naming of the octave-species, rejecting mine in Iraq, xxx (which I now withdraw) as over-contrived. He takes the order of the first 'chapter' of U 7/80 as being the normal order of the octave-species (i.e. the reverse of the order

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This content downloaded from 194.81.230.99 on Wed, 24 Aug 2016 14:58:27 UTC All use subject to http://about.jstor.org/terms presented in the first music example presented above, and of the tablet KAR I58 viii), and points out that in this sequence each new scale is named after the tritone which must be perfected in order to modulate from the old scale into the new. This convincing explanation renders the order of KAR I58 viii something of a mystery, but at the same time provides a parallel for the reversal postulated for the transcriptions in this article. H. G. Guterbock's article, 'Musical Notation in Ugarit', Revue Assyriologique, 64 (1970), of which I saw a draft, has also appeared. I am again indebted to Prof. Guterbock, and also to Dr. Kummel, for kindly sending me offprints. Many of the new readings proposed by these scholars have been able to be incorporated in the previous pages. I have hesitated, however, to adopt the reading um-bu-be instead of tup-pu-nu. If correct, this would dispose of the equivalence tupPunu=tilpanum= GIS.SUB.BA, which latter would now be read isqu (i.e. esgi), which itself must then be discarded as the equivalent of nis GABRI). Confirmation for this shift appears in the identification of ]ABA.RI and ]RI in five places in the fragments. I prefer to keep an open mind until more tablets are unearthed, although the musical result of making these changes is almost negligible for the tablets and theory so far presented. However, the four- fold occurrence of the same melodic formula, mentioned in the last paragraph of this article, would be reduced to two. It is this, coupled with the somewhat fragmentary basis for the proposed readings, which causes me to demur (probably wrongly) for the present. I am still unable to offer any solution as to how the words were fitted to the music, or as to the significance of the possibly related 'residual terms'. It may be that renewed investigations into the problem of Semitic metre will provide some clues in the problem of underlay, but studies so far published have yielded little of substance. However, a re-reading of Romer's 'Sumerische "K6nigshymnen" ' (Leiden, I965) and the review by Hallo in Bibliotheca Orientalis, convinces me that the problem is not insoluble. The use of the refrain, found in both the Sumerian hymns and the notation tablets, provides one point of attack; the other is furnished by the complex strophic structures of some of the Isin-hymn tunes such as the tigi, adab and balbal; these forms must have made use of repeated melodic material; this is the only way their terminology makes sense, at least to me. The adab, for example, had one or more bar-sud and s'a-ba-tuk sections in pairs, a sa-gid-da with antiphon, sa-gar-ra with antiphon and a concluding urubi. Since there is no textual repetition in the bar-sud and sa-ba-tuk sections, there must have been a musical repeat. Study of these hymns, and of the apparently strophic form of the zaluzi, may eventually lead to a solution of the problem of the relationship of words to music.

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