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‘Leading notes’ in ancient Near Eastern and Greek music and their relation to instrument design

Authors:
RICARDO EICHMANN – LARS-CHRISTIAN KOCH –
FANG JIANJUN (HRSG.)
Studien zur Musikarchäologie X
Klang – Objekt – Kultur – Geschichte
Sound – Object – Culture – History
Vorträge des 9. Symposiums der Internationalen Studiengruppe Musikarchäologie
im Ethnologischen Museum der Staatlichen Museen zu Berlin, 9.–12. September 2014
Papers from the 9th Symposium of the International Study Group on Music Archaeology
at the Ethnological Museum, State Museums Berlin, 09 12 September, 2014
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Eichmann, Ricardo / Koch, Lars-Christian / Fang, Jianjun (Hrsg.):
Studien zur Musikarchäologie X ; Vorträge des 9. Symposiums der Internationalen
Studiengruppe Musikarchäologie im Ethnologischen Museum der Staatlichen Museen
zu Berlin, 9.–12. September 2014.
[Red.: Orient-Abteilung des Deutschen Archäologischen Instituts].
Rahden/Westf.: Leidorf, 2016
(Orient-Archäologie ; Bd. 37)
ISBN 978-3-89646-667-9
‘Leading Notes’ in Ancient Near Eastern and Greek
Music and Their Relation to Instrument Design
Stefan Hagel
Zusammenfassung
Eine Analyse antiker Musikdokumente sowohl
in ugaritischer Keilschriftnotation aus der späten
Bronzezeit als auch in griechischer Melodienotation
aus den Jahrhunderten um die Zeitenwende be-
leuchtet belegte und mögliche ‚Leittonfunktionen‘
in melodischen beziehungsweise dichordharmo-
nischen Schlussformeln. Ihre Verteilung und Funk-
tion wird anhand der Instrumentaltechnik der kul-
turell bestimmenden Saiten- und Blasinstrumente
(Leiern und Doppeloboen) diskutiert, wobei grund-
legende Eigenheiten der antiken Musik von physi-
schen Grundlagen und einfachen musikalischen
Axiomen hergeleitet werden.
In modern Western music, a leading note is usu-
ally understood as the note a semitone below a fi-
nal which is perceived and typically used to ‘lead’
the melody towards this final. Such a leading note
is naturally present as the seventh degree of major
modes, but also employed in minor modes using a
sharpened seventh degree (‘harmonic’ and ‘melod-
ic’ minor scales). This usage of the term is evident-
ly formed by Western hearing conventions, con-
founding the basic idea of a musical function with
that of a particular interval size. In the present paper
I shall employ the term in a more inclusive sense, as
any note adjacent (within the Gebrauchsskala) to a
focal note and typically preceding this focal note in
melody – particularly in melodic closures.
This definition requires some clarifications.
Firstly, the classification of ‘typically’ is exactly what
needs to be established. Secondly, what is a ‘closure’?
When working with a large corpus of melodies, one
might concentrate exclusively on performance-final
notes, which are largely unequivocal. But alas, the
available pool of extant ancient notated music in-
cludes only a very limited number of preserved
finishes, so that we need to evaluate performance-
internal potential closures as well. These, however,
may be either restful (as would normally be expected
for performance ends) or suspensive.1 By definition
the latter combine elements of closure with elements
of non-closure, which makes their inclusion ambigu-
ous. We will discuss the relevant examples below.
Despite the differences in sources and notation
systems, I will once more draw comparisons be-
tween Greek and Near Eastern music. Though it is
important to keep the temporal, geographical and
cultural separation in mind, I think the two bod-
ies of evidence may shed some light on each other
exactly because they follow different approaches.
Anyway, there is little doubt that Near Eastern
music as reflected in the cuneiform sources and
later ancient Greek music are in some way connect-
ed, through intimate contact in historical times no
less than, plausibly, by continuing supra-regional
characteristics of late Bronze Age musical culture,
including heptatonism based on strings tuned in al-
ternate fifths and fourths.2
1 The Near Eastern Evidence
Let us start with the earlier sources. The cuneiform
musical texts build on the idea of what we may call
‘dichords’, combinations of two strings on a model
instrument, which form an interval either of the
fifth/fourth type (including a tritone or a dimin-
ished fifth in one place in the scale) or of the third/
sixth type (each being a major or a minor sixth or
third, depending on the tuning). Ten years ago I ar-
gued that the rudimentary musical notation on the
well-known hymn tablets from Ras Šamra, which
employs these dichords, is best understood as pro-
viding a basic intervallic harmonisation for a (non-
notated) melody.3 In this way it proved possible
to make musical sense of statistical distributions as
well as typical sequences and types of sequences. In
1 Cf. the discussion in Cosgrove 2011, 167 181.
2 Cf. Franklin 2006; Franklin 2011; Franklin 2015; for my
doubts about lyres with as few as four strings cf. Hagel 2008.
3 Hagel 2005a.
Stefan Hagel134
particular, I pointed to the fact that in several plac-
es dichords realised as thirds on the nine-stringed
model instrument precede a fourth or fifth in such a
way that one of the notes of the latter is located be-
tween those of the former. In other words, the third
‘closes in’ towards that note. Such sequences ap-
pear clearly favoured: there are no less than nine in-
stances in the small corpus, while the calculation of
a weighted expectation value shows that one would
expect only 2.09, if the observed pool of dichords
were randomly arranged. The chance of finding so
many more actual instances purely by accident is
less than 1 in 3000, so we may be virtually sure that
the observed sequences had in fact a musical signifi-
cance. Here we may be observing sequences indicat-
ing some kind of closure, since a priori one would
expect that the more resonant intervals of the fifth/
fourth type are more likely to correspond to rest-
ful positions in the performance than the third/sixth
dichords. This appears to be confirmed by the num-
bers that accompany the dichords in the notation.
Even though the musical interpretation of those
numbers is not clear, it seems evident that higher
numbers correspond to some sort of higher promi-
nence (which might have been achieved, for in-
stance, by repetition or duration).4 Of course, large
portions of a performance may employ non-restful
harmonisation – in fact, this is perhaps what we
would expect from a modern Western perspective –
while the most restful events might occur only in a
few places. This must caution us against interpreting
mere sums of incidences or notated numbers as evi-
dence for harmonic priority. On the other hand, we
may very well expect that the most restful positions
are prominent as well. Therefore, average notated
numbers (totals of numbers found with a dichord
divided by the number of occurrences) are probably
the best guide to harmonic importance and may be
associated with the idea of restfulness. An analysis
of all the published Ras Šamra fragments corrobo-
rates this hypothesis: the average of the numbers
accompanying fifth/fourth dichords is 2.08, as op-
posed to only 1.61 for the third/sixth dichords.5
Moreover, the highest mean number is attributed to
the fourth/fifth dichord ¯d qabli (2.57),6 which also
holds the highest total of accompanying numbers,
though it is by no means the most frequent one oc-
curring: two third/sixth dichords are attested more
often, and one just as often as ¯d qabli.7
All this suggests a straightforward interpreta-
tion of the mentioned dichord successions where
a third leads to a fifth/fourth: it is plausible that
such combinations were favoured as a, if not the
typical way of arriving at a restful position. This
becomes even more likely considering that in four
of the nine attested cases the target dichord is no
other than n
ı¯
d qabli – as we have seen, arguably the
harmonic centre of the pieces’ mode.
How would such successions have worked
in practice? A certain characteristic of harmonic
movement observed in the fragments suggests, with
an error probability of one in seven, an instrument
of nine notes, exactly like the model instrument of
cuneiform school musical lore.8
Certainly I do not want to suggest that no
other notes but those of the notated dichords
were played or sung – I would rather argue for
a kind of variant heterophony based on the no-
tated harmonic structure – but at least the notated
dichords were of considerable significance, and
it is likely that both of their notes were sounded
together or in close proximity whenever they
were notated (whether on a string instrument or
a double pipe or across various instruments of a
small orchestra). All in all I am confident that a
contemplation of the abstract scheme presented
by the notation may be a useful guide to what the
Bronze Age musicians themselves considered as
structurally important, if only because of all the
elements present in performance, it was precise-
ly the dichords that they singled out for noting
down.
By definition, a dichord notation can only pro-
vide us with two potential leading notes, without
telling us, which of these was in fact the one used
by the singer(s) (who I am convinced did not per-
form multipart song any more than the Greeks
did later, even where more than one vocalist was
involved). With such a strong preference for in-
strumental leading notes, it is at least quite unlike-
ly that the vocal melody did not employ any of
the two but arrived at the final note by a larger in-
tervallic jump of a third or more. In addition, hav-
ing another melodic note would establish a regu-
lar triple harmonisation, as seems incompatible
4 Hagel 2005a, 307 – 311.
5 From this calculation, the few occurrences of the number
sign for ‘10’ have been excluded, since this ‘number’ is al-
most certainly not to be taken literally (cf. Hagel 2005a,
309 310). If they are included, the means rise to 2.28 as op-
posed to 1.72, which similarly supports the present argu-
ment. Note that the figures presented here cannot be de-
rived from the table in Hagel 2005a: there the total number
of occurrences of each dichord in the tablets is counted,
whether the associated numbers are preserved or not, while
the calculation of means naturally evaluates only dichords
whose accompanying number can be read.
6 Followed by qablı¯tu, another fifth/fourth dichord,
with 2.27.
7 It may be significant in this context that the hymns are,
as far as we see, all in the tuning named, after the dichord,
¯d qabli, but I am not convinced that this is much more
than a coincidence: after all, in most of the tunings on the
nine-stringed model instrument, ¯d qabli is one of the ‘oc-
tave-enhanced’ dichords and therefore likely to gain modal
prominence also in other tunings. Note that qablı¯tu (above,
no. 6) also falls within this category.
8 Hagel 2005a, 320 with no. 88.
‘Leading Notes’ in Ancient Near Eastern and Greek Music and Their Relation to Instrument Design 135
with all the ancient evidence. Therefore, it is on
the one hand possible that there was a standard
melodic choice corresponding to one note of the
third/sixth dichord, the other being its standard
harmonic counterpart. On the other hand, the
voice may have been free to use one or the other.
In the former case, melodic conventions would
have been independent and in a certain sense prior
to harmonic conventions; in the latter, a harmonic
conception might have been more fundamental.
As long as no corresponding melodies are known,
we cannot know.
Converted to stave notation, the discussed pro-
gressions include the following four:9
rebu¯ tu n
ı¯
d qabli: 2 – 7–(9) 1 4–(8) [4 instances]
šalšatu embu¯ bu: 1 – 6–(8) 3 7 [3 instances]
še¯ru išartu: 5 – 7 2 6–(9) [1 instance]
titur qabl
ı¯
tu kitmu: 2 – 4–(9) 3 6 [1 instance]
It will be noticed that the much more frequent
first two examples require doubling the nomi-
nal higher string at the lower octave, as is to be
expected on a non-modulating nine-stringed in-
strument. This is confirmed by the ‘retuning text’
UET VII 74, where the ninth string is retuned to-
gether with the second.
It may be significant that the note towards
which the thirds ‘close in’ is not randomly any of
the two notes of the target dichord. In the first
three instances, where the target dichord appears
as a fifth, it is the lower note of that fifth, tran-
scribed as e, f and g respectively. In the last case,
where the target dichord can, within the ranges of
the canonical nine notes, only appear as a fourth,
it is the higher note of this fourth, c’. In the con-
text of the system, which is generally based on
functional invariance between notes an octave
apart, the targeted notes are therefore function-
ally similar (just as in modern Western music c in
a chord c-e-g is harmonically equivalent to c’ in g-
c’-e’). That the note to which the potential leading
notes actually lead is functionally the bottom note
of the fifth and not its top note (and conversely
the top note of a fourth and not its bottom note)
may naturally be understood on the basis of the
fact that fifths formed from notes of similar sound
form a less complex compound pitch spectrum
than do fourths, other factors being equal. (Com-
pare again the fact that a modern Western g-c’-e’
chord is musically interpreted as a variant of c-e-g,
meaning that the note conceived as basic is derived
from a normalisation where it sits at the bottom
of a fifth.)
The discussed set, therefore, appears to form a
coherent, probably traditional class of harmonic
progression. Even though it targets fifths/fourths
dichords, of course not all of the instances would
have marked some kind of closure. For reasons set
out above, a restful character is quite likely for the
first one, while the second, albeit significantly fre-
quent, cannot have represented more than a tran-
sitory rest point, if perceived as a closure at all.10
In the given tuning, it is interesting to see that the
lowest note (d) was more likely to function as a
leading note towards its higher neighbour than to
receive modal focus itself. We need to bear this re-
lation in mind.
Unfortunately, the ambiguity in determining
an actual melodic leading note out of the two not
only renders it impossible to assess the relation be-
tween leading notes above and below the final, but
also makes it difficult to estimate the respective
9 I equate the highest note of the system (string 1, qudmum)
with modern e’, which has the enormous advantage of fa-
cilitating comparison with ancient Greek and Roman lyre
tunings, which it makes the most sense to notate in the
same way (cf. Hagel 2009). As Greek and Near Eastern
lyres were historically connected in some way, and as
the Greco-Roman lyre is pitched for accompanying male
voices, there is also some probability that a similar nota-
tion might reflect a similar pitching. The ancient natural
key, Lydian, which supports ‘Dorian’ tunings, thus corre-
sponds to Near-Eastern n
ı¯
d qabli. With this transcription,
the actual Greek pitch would have been about three quar-
ters of a tone above modern concert pitch. Cf. Shehata –
Hagel 2012, Diagram 3.
10 Cf. the low average accompanying number of embu¯ bu
(1.33).
Stefan Hagel136
importance of tones and semitones. However,
we can state that all but one of the observed eight
progressions involve a semitone besides a tone. A
random selection of target notes in the octave, in
contrast, would yield only four such progressions
out of seven, the other three involving only tones
(having a semitone both below and above is in-
compatible with a diatonic scale). Under this point
of view, the sample is quite clearly not random –
the chance to obtain such a large quantity of semi-
tones in a random sample is only about 1 in 20.11
This gives reason to propose the hypothesis that
semitones may have played a role as leading notes
in the few fragments of Bronze Age music we pos-
sess, although we cannot ascertain whether this ex-
tended to their melodic use or was only part of in-
strumental harmonisation. Most importantly, we
must bear in mind that we are dealing here with
fragments that were most probably all composed
in the same mode or at least tuning – no general
conclusions are warranted.
For the sake of comprehensiveness, an after-
thought may be in place. Three of the dichord
names appear to reference another dichord: besides
išartu we find titur išartu, besides qabl
ı¯
tu, titur
qabl
ı¯
tu, and n
ı¯
d qabli may or may not be related
to qabl
ı¯
tu. If those terminological links reflected a
genuine musical reality, typical harmonic progres-
sions are certainly a plausible option, especially
when taking into account the meaning of titur,
which is generally translated as bridge or causeway
(the meaning of n
ı¯
d is less clear). To be sure, no
such progressions between the members of these
pairs are found in the Hurrian hymns; however, as
these are younger by centuries than the establish-
ment of the dichord names (and moreover not even
in Akkadian language), the music for which the
latter were coined may have been quite different.
At any rate, here is a transcription of the pairs in
question:
titur išartu – išartu
titur qabl
ı¯
tu – qabl
ı¯
tu
n
ı¯
d qabli – qabl
ı¯
tu
Obviously each of them involves one or two
possible leading notes, but it is difficult to say much
more. The two instances of titur work very differ-
ently – but that is a notorious problem that any
interpretation needs to face. After all, we cannot
even assume that the direction implied in the tran-
scription is valid. It is certainly the more likely for
the titur cases, if (a big if) these indicate potential
closures; about n
ı¯
d qabli, not even that much can
be said.
2 The Hellenistic Evidence
From the sad scraps of Near Eastern music we
turn to the happier field of Greek musical scores
(including the globalised Greek music of Roman
imperial times), with dozens of readable melodies
and melody fragments scattered over a period of
about 600 years. Most of these are vocal music,
which means they come with a text and often a
recognisable metre, which in turn helps us greatly
in determining potential locations of musical clo-
sure: we would expect it to occur not only at the
end of the performance, but also at the end of in-
dividual sections and, to a lesser degree, of indi-
vidual metrical periods or verses (where in turn
suspensive closures are likely to play a greater
role).
Similarly, it is often not too difficult to estab-
lish modal hierarchies between the notes of a piece,
based on their frequency or repetition rate or their
harmonic relation to other focal or final notes12
including the evaluation of non-suspensive internal
breaks, where the danger of circularity is at least
mitigated by taking the text and the metre into ac-
count as well.
Here is my list of extant closures, quoted
from the edition by E. Pöhlmann and M. L. West
(DAGM), with transcriptions following the new
standard I have proposed,13 comprising only clo-
sures where the final note is reached from one of its
neighbours in the scale.
2.1 A) Falling Cadences
DAGM 23: Seikilos Song
At its very end the brief melody ventures below its
previous range, terminating at a note a fourth and
an octave respectively below the two melodic focal
notes. Note that the final g ~ c+50 was a typical bass
note on certain types of auloi: on such instruments,
it is not possibly approached from below, there be-
ing no adjacent lower note.
titur išartu – išartu
titur qabl
n
11 p=0.0503.
12 For a discussion of tonal hierarchies in the fragments cf.
West 1992a, 177 – 189. 283 – 326; Hagel 2009, 219 – 250.
256 326; Cosgrove 2011, 181 194; Hagel 2012.
13 Pöhlmann – West 2001; Hagel 2009, 452 453.
‘Leading Notes’ in Ancient Near Eastern and Greek Music and Their Relation to Instrument Design 137
DAGM 42: Pap. Michigan 2958.3, 8, 9, 10
Here dramatic dialogue is set to music; several extant verse ends can be determined.14 The two in lines 8
and 10 end, via a step of a whole tone, on I, which is the central string (mése¯) of the cithara and a traditional
harmonic centre,15 and which also seems a reasonable harmonic centre in the Hyperiastian mode, as can be
gleaned from other fragments.16
Others, in line 3 and 9, stand out for terminating an emotional question in the high region of the
voice:17
DAGM 40: Pap. Oslo 1413a.16
Here also a verse end is discernible in stichic metre set to music (though it corresponds only to a weak
grammatical break); the final note is here S, doubtless a traditional final by being the traditional lowest
note (hypáte¯) of the early lyre. In accordance with the Lydian key (which establishes a ‘Dorian’ tuning), the
penultimate note (parypáte¯ R) is a semitone above the final.
DAGM 50: Pap. Berlin 6870.12
A clearly citharodic Paean once more ends on hypáte¯ S. However, as the key is Hyperiastian, this time the
adjacent higher note (khro¯ matike¯
´ O) is located a whole tone above it.
14 I exclude the verse end in 13 (δ
᾿αὖ μ᾿ ἔτι), which falls in the middle of a grammatical phrase and is consequently marked by non-
restful Z, a tone above I.
15 Cf. below n. 31.
16 Cf. Hagel 2009, 302.
17 I include line 3 in accord with the verse division proposed by Pöhlmann and West; however, the preceding rest on the papyrus
suggests a different division.
Stefan Hagel138
Similar figures are found at verse ends within the composition (ll. 7 and 10). Here, however, the impres-
sion of a final closure is neutralised because the two verses are linked by an additional short note that, though
still sung to the last syllable of the previous verse, acts melodically as an introduction to the following:
DAGM 53: Pap. Oxy. 3161 recto fr. 4.4
A period end exhibits final and penultimate notes similar to the previous example; the key of this dramatic
fragment cannot be established with confidence (also Hyperiastian, or rather Hypolydian?).
DAGM 38: Pap. Oxy. 2436.ii.4
A dramatic verse ends with what was almost certainly the lowest note on typical Roman-period citharas
(hyperypáte¯ F), in contrast to the foregoing items. However, there is no reason to regard this closure as
anything but restful, since this final note chimes in with the modal framework found in the rest of the
melody, which emphasises the notes a fourth and an octave above it – likely a typical way of employ-
ing the keys between which the piece modulates (Lydian and Hypolydian; the quoted passage is from a
Hypo lydian stretch).
DAGM 59: Pap. Oxy. 1786.2 and 5
A similar ending is twice exemplified in the famous Christian hymn from Oxyrhynchus, which almost
certainly was also performed to the lyre. The mode is again Hypolydian.
2.2 B) Rising Cadences
DAGM 28: Mesomedes, Hymn to Nemesis, 1
Unfortunately, the last line of the hymn is lost (unless one considers the item to consist of two separate pieces).
Even so, it may be instructive to contemplate its first verse, which is both textually self-contained and ends on
the focal note of the hymn (which would also be the final note of the supposed first piece); cf. below DAGM 24
and 25. However, it seems that a rising sequence of three notes would not easily terminate a composition.
‘Leading Notes’ in Ancient Near Eastern and Greek Music and Their Relation to Instrument Design 139
DAGM 40: Pap. Oslo 1413a.18
Above, we encountered a weak verse-break on this papyrus, where the lower final was reached from above.
Here, in an apparently stronger break, the traditional central note (mése¯ I), a fourth higher, is approached
from below.
DAGM 24: Invocation of the Muse
The end of this short piece is preserved; it moves from the later bottom note of the later lyre (hyperypáte¯ F)
to the older bottom note (hypáte¯ S):
The closure is already prefigured in the opening half-verse:
DAGM 25: Mesomedes, Invocation of Calliope and Apollo
Both the conclusion and its anticipation in the address in the first half-verse are paralleled in the second
invocation from the same set of pieces transmitted in medieval manuscripts (they are all in the Lydian key):
In contrast, the ends of the first two verses (which are hexameters) display no restful qualities, but ap-
pear to urge on to the brief final colon (a lekythion). Both end, after the traditional two melodic excursions
that appear to have characterised hexametric performance from pre-Homeric times onward,18 with a series
of three rising notes. The first terminates on hyperypáte¯ F, the note below hypáte¯, which in turn had been
established as start and end note at the outset – consequently its neighbouring note is implicitly marked as
non-final and therefore suspensive:
18 Cf. Hagel 1994; Hagel 2004b.
Stefan Hagel140
The other terminates in the higher region on mése¯ I: here the suspensive character seems to be achieved
by a combination of melodic rise and relatively high pitch:
DAGM 27: Mesomedes, Hymn to Helios, 7, 23 and 25
S is also the final in another hymn in the collection. Once more its modal status is already introduced in the
opening, with the first verse sporting the now well-known finish on FS:
The piece ends by combining the same option with that of approaching the final from above; quite unu-
sually, an identical cadence is already found on the last verse but two. S appears first after a plunge down
to F, but becomes the true final only after a melismatic excursion to the notes above it. The entailing resolu-
tion of the long penultimate position into three notes on a single syllable is exceptional in what remains of
Mesomedes’ compositions. Plausibly, it is introduced precisely for the melismatic effect, which does not so
much extend the melody as lend weight to the final; consequently, I decided to discuss this instance among
the other examples of FS rather than those (fewer) of RS.
DAGM 39: Pap. Oslo 1413a.8 and 14
Twice periods end on the melodic focal note S preceded by F. In the first instance, this is part of a rising
figure (in accord with the accentuation of the proper name Achilles, frequently found at verse end already
in the Iliad), potentially indicating a lower degree of restfulness.
‘Leading Notes’ in Ancient Near Eastern and Greek Music and Their Relation to Instrument Design 141
DAGM 50: Pap. Berlin 6870.1
In the paean whose end was discussed above the tonality is once more introduced in the opening ad-
dress, which both starts and ends with FS.
DAGM 51: Pap. Berlin 6870.13
The same papyrus also contains fragments of two instrumental pieces, presumably for aulos. One features
period end (discernible by a prolonged note before a rest) on FS, which is the equivalent, in instrumental
notation, of what we know from vocal notation as FS.
DAGM 53: Pap. Oxy. 3161 recto, fr.1.3 and 7
In another dramatic fragment, S thrice serves as a final. Only in a single instance is the preceding note also
preserved; it is once more F:
In another place, a rest indicates a break after Z, a frequent but otherwise not especially prominently
used note. Too little is preserved of the context to determine the grammatical nature of the break:
3 Interpretation
Figure 1 sums up the presented evidence; it includes
both certain and possible closures, differentiating
them by the width of the arrows, while excluding
cases which we could identify as almost certainly
suspensive, especially where standing in contrast to
one or more clearly restful examples in the same
piece. Ascending and descending closures are
about equally frequent (47 % of the safer instances
and 54 % of all possible examples are ascending).
However, semitone steps towards the final are very
rare (6 %/14 %). They occur exclusively in falling
endings, which is a corollary of the fact that ancient
music seems never to grant final status to the func-
tional notes do and fa.
As is to be expected, the bulk falls within the
lower part of the usual gamut, according to a gen-
eral linguistic and musical tendency of associating
pitch fall with utterance end.19 But as has already
become clear in our brief survey above, possible
finals are by no means distributed randomly even
in that region, nor are the ways they are reached in
melody. Instead, the majority of cases (59 %/61 %)
involve the same final, S.
4 Material Causes: Lyre
Above I have already described this note as the tra-
ditional bass note of the seven-stringed lyre, called
hypáte¯ (‘topmost’) according to its physical position
on an instrument held tilted when playing. With
such a limited resource as seven notes (excluding
the fancy trick of eliciting overtones, which is hard-
19 Cf. e. g. Devine – Stephens 1994, 435 452.
Stefan Hagel142
ly feasible in the usual manner of playing), the co-
incidence of melodic final and lowest available note
on the instrument is all but natural. Even when the
voice departed from the ambitus of the accompani-
ment, it was desirable to end on a common note.20
However, our scores date from 200 to 800 years
after the demise of the seven-stringed instrument
in favour of lyres with nine, eleven and perhaps
even more strings (whether the fifteen-stringed lýra
mentioned by Ptolemy is an heir to the old lyres
as regards playing technique and repertoire is ques-
tionable21). So it is no surprise that the scores do
not reflect a state in which S would most typically
have been preceded by its upper neighbour. In-
stead, this is true only for 30 % (29 %, counting the
doubtful instances as well). In the majority of the
discussed closures on S, it is preceded by F, a whole
tone below, and this cadence accounts for no less
than 41 % (43 %) of our observed total. We know
from the so-called koine¯
´ hormasía that this note was
part of Roman-period tunings,22 called diápemptos,
‘a fifth from [the central string]’, or hyperypáte¯, ‘be-
yond hypáte¯ ’, and it most probably was introduced
as early as the fifth century BCE, when our sources
mention instruments of nine and eleven strings.23
Notably, in our best source for early modal scales
the Dorian covers not only the ‘Dorian octave spe-
cies’ down to S, but an entire ninth down to F (cf.
Fig. 1).24 The association of the Dorian scale with a
ninth is all the more noteworthy because, as far as
we see, the whole given set of non-diatonic scales
does not primarily belong in the context of lyres at
all, but rather of auloi. Given the primacy of the
Dorian (and its special association with the lyre) in
Greek thought, it may be significant that one of the
early modulating diagrams was expressly confined
to twenty-eight quartertones (which is a ninth),
that of all the reported early scales only the Do-
rian extends to such an ambitus, and that the sys-
tem can be plausibly reconstructed as incorporating
the other scales within the range of the Dorian.25
All in all, there is reason to believe that in the early
fourth century BCE the idea of a ‘Dorian ninth’ had
already spread from lyre playing into the sphere of
auletic scales.
At any rate, at least in Roman imperial times,
when the greater part of the surviving scores
were written, hyperypáte¯ F had been around long
enough to attract modal prominence in certain
kinds of music, so that it now appears as a final in
its own right (not that the evidence would allow
us to conclude, ex silentio, that this had not been
the case much earlier). However, while hypáte¯ S is
more often reached from below, hyperypáte¯ F is
only found in falling closures, as if the range of the
extended cithara prescribed the melodic options,
precluding notes outside it from becoming part of
conventional melodic cadences.
With fewer strings, a similar mechanism be-
comes less likely, because the voice would more of-
ten depart from the ambitus of the instrument any-
way. Thus the archaic seven-stringed instrument
with its restricted tonality may have been coupled
with the vocal melody to a lesser degree, function-
ing a bit more as a rhythmical and harmonising in-
strument.26 Consequently we may wonder whether
a melodic closure on FS may have been traditional
even before the adoption of an extra F string. Such
an option may have been especially beneficial in
non-strophic song, when the melody followed, to
whatever degree, the contours of the Greek word
accents and sentence intonation.27 In particular, it
would have allowed the archaic poets to combine a
faithful melodic rendition of an end-accented word
with a restful cadence on the bass note of their in-
strument. Since end-accented words at verse-end,
including strong breaks such as between sentences
or scenes, abound in Homeric poetry (key names
such as Akhilleús, Odysseús, Akhaioí or Zeús most
frequently appear in final position), this would
have been a most powerful musical tool both for
epic singers and for citharodes who adopted epic
repertoire, furnishing it with more elaborate melo-
dies.28
When strumming their lyres (which is the play-
ing technique generally shown in the iconogra-
phy), the Greeks must have sounded more than
one note simultaneously; otherwise this technique
does not make much sense.29 There being no hint at
20 Cf. ps.-Arist. Probl. 19.39. To be sure, in addition to the
common note we must expect that at least another lyre
string was struck; more below.
21 Cf. Hagel 2009, 77 80.
22 Hagel 2009, 122 – 132.
23 West 1992a, 62 64; cf. Hagel 2009, 80 92.
24 Aristid. Quint. 1.9, p.18 20 Winnington-Ingram; cf. Barker
1982, 183 4; Barker 1989, 419 n.112; Barker 2007, 45 48;
Hagel 2009, 390 393. The notes, however, may have been
added by the Roman-period writer who transmits the
scales, which his sources probably specified merely as a list
of intervals.
25 Cf. Hagel 2000, 177 182; Hagel 2015, 371 385
26 Cf. along these lines Aristoxenus contrasting contemporary
(fourth-century BCE) focus on melody with an earlier pre-
dilection for rhythm: Ps.-Plut. Mus. 1138b.
27 Such a correlation can be proven for the traditional tech-
nique of Homeric song down to at least the seventh century
BCE (Hagel 1994; cf. West 1981; Danek 1989) and is well
known from later scores from the second century BCE on
(e. g. Devine – Stephens 1994; Cosgrove – Meyer 2006), so it
would be surprising if the practice had not been used in the
intermediate period as well.
28 Cf. West 1981 and West 1986 on ps.-Plut. Mus. 1132b–f: καὶ
γὰρ τὸν Τέρπανδρον ἔφη κιθαρῳδικῶν ποιητὴν ὄντα νόμων
κατὰ νόμον ἕκαστον τοῖς ἔπεσι τοῖς ἑαυτοῦ καὶ τοῖς Ὁμήρου
μέλη περιτιθέντα ᾄδειν ἐν τοῖς ἀγῶσιν “[Heraclides] also
said that Terpander, being a composer of citharodic nómoi,
in each single nómos adorned his own hexameters and those
by Homer with melodies, singing them in the contests”.
29 On lyre strumming cf. Lawson 2005.
‘Leading Notes’ in Ancient Near Eastern and Greek Music and Their Relation to Instrument Design 143
ancient chords of more than two functional notes
in the octave, we would a priori assume that the
paradigm of ‘dichordal’ harmonisation extended to
the Classical world as well, as we need to acknowl-
edge for the inherently dichordal music of the aulos
anyway. Speculating further, we might therefore
wonder about the most plausible instrumental re-
alisation of such a rising cadence. If the singer ar-
ticulated what later became known as hyperypáte¯
and notated as F, the note one octave higher would
have suggested itself as the most natural accompa-
niment. This note (Ö) was almost certainly present
in most if not all early tunings.30 In the cadence, the
most plausible other note of the supposed dichord
would have been the bass note’s higher neighbour
(R or O), in the most typical instrumental way of
arriving at the bass note. Expressed in Near East-
ern string numbers, this combines to a dichord
succession of 2 – 7–(9) (1)–?–8. This matches the
dichordal cadence we found favoured in the Hurri-
an hymns: 2 – 7–9 1 4–8. Would, once the ninth
string had been added, a typical Greek dichordal
cadence on the lyre have been identical with an
Ugaritic-Hurrian one a thousand years earlier? If
so, was it already part of a common inheritance dat-
ing from the Bronze Age? We cannot exclude the
possibility, but as the facts underlying our specula-
tion can all be explained merely by the layout and
playing technique of the lyre, the factual parallels
need not be anything more than the results of con-
vergent evolution (granting a culture-crossing idea
of intervallic harmony, as appears entailed by the
common usage of double pipes). Moreover, in a
Greek context, the most likely candidate for the
second note in the final dichord, marked above as
‘?’, is not the Hurrian hymns’ string 4, but rather
mése¯ I, corresponding to string 5.31 Anyway, his-
toric speculations apart, there can be no doubt that
the nature of the typical cadences found in the an-
cient Greek musical documents was substantially
influenced by the material substrate of lyre prac-
tice.
5 Material Causes: Aulos
However, it would be foolish to neglect the influ-
ence of the double-pipes, so omnipresent in Clas-
sical culture, on ancient hearing conventions. Here
one might of course point to tonal characteristics
that it shared with the lyre – so our most frequent
final S is also the bass note of the Louvre aulos,32
or on a pair of pipes from Pompeii, the treble note
coincides with that of the cithara. But this would
not explain much, as the pipes might have been
modelled on the strings.
On the other hand, I believe that one traditional
double-pipe design – more or less the only well-de-
fined type we can describe so far – may bear on our
topic exactly in details that do not reflect character-
istics of the lyre. This type of aulos is preserved in
two specimens from Hellenistic Egypt, known as
the ‘Louvre’ and the ‘Berlin’ aulos.33 Their intricate
connection with Greek theory is evinced by their
bass notes being that of the model double octave,
while that scale’s central note (‘functional mése¯’) is
the highest that is available on all pipes. The highest
finger hole, on the other hand, is located an elev-
enth above the bass note, a relation that is almost
certainly determined by the fact that the cylindrical
pipes overblow to the twelfth: by overblowing, the
scale is extended seamlessly (the Berlin aulos is spe-
cially suited for such a technique, and also sports
speaker holes).
Now, from the basic choice of a bass note alone,
several important modal constants can be derived
– I will at present leave aside the question wheth-
er these historically result from the choice of the
bass note, or whether, conversely, the bass note
of theory was adopted with a view to traditional
aulos design. As the bass note is a functional la, the
non-overblown treble is a re (cf. Fig. 2). The high-
est note on the lower pipe is the octave of the bass
note, once more la, but in a region that can be fin-
gered in the primary playing position, at the top of
both pipes, where it is possible to use all five fingers
(the thumb hole is always second from the top).
This may be motivated on the one hand by the need
to have this note of the highest musical importance
available on both pipes (it is the typical focal note of
the musical documents dating from before the turn
of the Christian era), and on the other perhaps also
by the desire for a not too small difference between
the ranges of the two hands, in order to maximise
the overall playable range as well as the number of
playable concords.34 From the two top notes thus
defined and the number of five fingers per hand,
the ranges within a diatonic scale can be derived:35
30 When speculating about the tuning of the seven-stringed
lyre, later Greek sources either propose a sequence of two
tetrachords, making the note in question the treble note, or
a gapped octave, with what later was the third note from the
top missing. This also leaves the note in question in place –
forming a fourth with the central string, it seems to have
been of particular importance.
31 Cf. e. g. Winnington Ingram 1936, 4 9; West 1992a, 219;
Hagel 2009, 117 – 122.
32 Cf. Hagel 2004a; Hagel 2014.
33 For the latter cf. Hagel 2010, and in general, Hagel 2009,
332 343. An argument for dating back an essentially simi-
lar instrument to the fourth century BCE is developed in
Hagel 2005b.
34 Note however that the playing ranges on preserved early
auloi generally differ by only one finger hole, just as on the
mentioned pair from Pompeii.
35 Within the typical pitch ranges of auloi, only heptatonic
scales with comparatively evenly spaced notes come into
question – which are essentially variants of diatonic.
Stefan Hagel144
five steps below high re we obtain fa, five steps
below la, do. The lowest note of these stretches is
played with all fingerholes above it closed, so its
position is not literally fixed (and can be adjusted
by means of plugs or a single turning sleeve on the
Berlin aulos), but the notes in question are present
on both surviving examples. Neither fa nor do stand
in a consonant relation with any of the prominent
notes so far established (nor do they play a promi-
nent role in the surviving melodies), which excludes
them as potential members of the primary modal
framework. Instead, two other candidates stand out
in the playable region. Firstly, the lower re stands at
the distance of an octave from the top note, a fifth
from the higher la, and (consequently) a fourth
from the bass note. The playable triplet re – la – re’,
a fourth above a fifth, is naturally complemented by
sol, a fourth above the lower and a fifth below the
higher end of the same span. The resulting struc-
ture, an octave divided into two fourths separated
by a tone, was described as the embodiment of har-
monía from the fifth century BC on.36 The concept
may well have united lyre-based and aulos-based
musical thought: while the earliest source for the
concept appears to talk about the lyre as the model
for harmonía, a movement in a well-known piece
for aulos was also called harmonía,37 a name that
is difficult to understand (most pieces would have
been ‘harmonious’ in a broad sense) unless it spe-
cifically emphasised the intervallic framework by
which the term had come to be defined.
We may reckon that the most typical music
played on instruments such as the Louvre and Ber-
lin auloi evolved within this harmonía. Different
‘modes’ would have been available by variously
stopping holes below or above the fingers, but
none other would equally avail itself of the con-
sonances built into the instrument while using all
the fingers, including the thumbs.38 With harmonic
focal notes of re on the one hand and sol or la on
the other, re would typically function as the final.
Of course, on an aulos of this make a low final al-
ways comes with a higher accompanying note, as is
entailed in the dichordal paradigm which we found
in the Near Eastern system and have, somewhat
hypothetically, applied to the Greek lyre as well.
Anyway, the low final re is played with only the
small finger lifted, as is sol on the higher pipe. The
lowest notes on both pipes, in contrast, must per-
form a non-restive function, creating suspension
which calls for resolution towards the primary
modal axis. In other words, the lowest notes must
be expected to function (also) as a kind of leading
notes towards their higher neighbours (or, in the
case of the higher pipe, perhaps also towards la,
their higher neighbour but one). We may therefore
imagine typical auletic cadences to have involved
the lifting of one or both small fingers.
Whether we understand the basic choice in the
design of this type of aulos as having re as the treble
note or as having la as the bass note, it has become
evident that from this basic choice an unbroken
chain of musical and physical trivia quite neces-
sarily leads to a configuration where focal notes,
and especially a low final, may typically be reached
from below via a step of a whole tone. In this way,
traditional instrument design appears to be related
to the fact that, as far as we currently see, ancient
Hellenistic music knew leading notes below the fi-
nal only as whole tones, in obvious contrast to later
Western music.
Finally, we may try to tackle the question of
harmonic chicken and egg. Was the selection of
leading notes dictated by an instrument design that
was motivated by entirely different ideas, or were,
contrarily, the instruments designed to play music
including a preconceived idea of whole-tone lead-
ing notes? The problem is not as intractable as it
may seem, if we consider possible alternative au-
los designs that would come with rising-semitone
leading notes.
Some requirements for such pipe pairs have by
now become obvious. Firstly, they need to span at
least an octave in order to incorporate a harmonía-
like structure not falling short of the musical capac-
ity of the extant auloi. Secondly, in order to com-
bine this with a lower leading note, their total range
must exceed the octave by one step – a semitone
step, in our imaginary case. Accordingly, the hands
may overlap by no more than two fingers – with at
least three additional fingerholes at the higher end
on one pipe (for the following cf. Fig. 3). Since this
is the maximum found on extant auloi, and many
have a larger overlap,39 we will not consider designs
with an even larger difference in hand position. The
treble note will therefore be an octave (nine minus
one steps) above the low final. In order to have a
36 Philolaus, fr. 6a = Nicom., Ench. 9, p.252.17 22, referring
to lyre strings; Aristotle in ps.-Plut., 1139b–c (apparently
quoting a source of Pythagorean hue). Explicit ancient
awareness that harmonía was not simply homonymous
with dià pasôn, ‘octave (as an interval size)’, is shown in
Porph., In Ptol. Harm. 1.5, p.96.21 23 Düring, with the
important emendation by Raffa (2014): τῇ δὲ διὰ πασῶν –
τῷ συστήματι, ὡς καὶ Θεόφραστος ἔφη – ἔθεντο ἁρμονίαν “to
the concord of the octave – in the sense of a musical scale,
as Theophrastus has also remarked – they gave the name
harmonía”. The entire resonance of the term may have been
something like “a set of notes, four of which, including the
bounding ones, form a consonant skeleton of a well-divided
octave, with the rest distributed in one of many meaningful
ways within the larger gaps”.
37 Cf. West 1992b, 33.
38 A possible exception is the configuration with two finger
holes below the higher hand closed, so that its bass note
becomes re. Modally, this is but a variant of that discussed.
39 This includes the hypothetical Dorian spondeîon pipes
I have proposed (Hagel 2009, 408 412).
‘Leading Notes’ in Ancient Near Eastern and Greek Music and Their Relation to Instrument Design 145
leading note a semitone below the final, the final
may be either do (resembling our major scale) or fa.
The second option can be excluded as harmonically
inferior to the observed design. Instead of a nice
harmonía framework, its octave is divided as fa – si
– do – fa’, with a tritone and a diminished fifth in
the places of the required lower fourth and upper
fifth respectively.40
The major-scale option looks more promis-
ing at first glance, with a well-formed harmonía
being constituted by the functional degrees do –
fa – sol – do. However, the layout of its higher
pipe is physically problematic for two reasons.
I will start with the lesser: when there is only a
semitone between the index hole at the top and
the thumb hole, this results in a very small hole
distance, especially in the highest region. Since
each pipe is supported by one hand only, it is
normally secured by the triangle formed by the
index, thumb and some lower finger. The smaller
the distance between the first two, the less stable
the grip and the more wearying is it to uphold it
for a longer period. Acting on a lever that is only
half as long, the index finger needs to exert twice
the force as on the extant pipes with whole tones
at the top. The hand position becomes even worse
when the thumb hole is opened. This is because
the thumb, being the instrument’s only support,
cannot be lifted from the hole, but must be rolled
away from it. Since its joints only allow doing
so in the upward direction, the tip of the thumb
would basically end up right opposite the index
finger, with the result that stability now depends
on the fragile reed in the mouth of the player.
All this is not necessarily detrimental, since the
reed must also counterbalance the pressure of the
lower fingers whenever the index finger is lifted.
Nevertheless, even after twenty-years experience
with playing various kinds of aulos, my hands
definitely do not like experimenting with such a
modified position.
More importantly, a semitone below the treble
hole is also detrimental to the overall span, because
it is precisely the distance between thumb and index
finger that adds a good deal to the total stretch of
the hand. On the higher pipes of an aulos based on
do, this potential is neglected, while at the same time
putting additional demands on the other fingers, be-
cause all the remaining distances below the thumb
are implemented by whole tones. The result is an
even more strenuous fingering. The same problem
applies, by the way, also to the alternative option
based on fa, which we have excluded above on other
grounds – only that there it affects both pipes. It is
clear that no such twisted finger hole layout would
possibly arise in an organological history that starts
from putting holes in comfortable positions which
are subsequently refined for better sound. On the
other hand, it is almost as difficult to conceive a de-
liberate move towards such an unpractical design
for musical reasons – especially as it is not clear at
all what those reasons might be, when a comfortable
fingering provides a perfectly consonant instrument.
In short, it seems that a musical culture in
which double pipes play a central role is not easily
compatible with our familiar leading notes of the
rising-semitone type, and we may have succeeded
in explaining fundamental choices of ancient music
culture on the basis of instrumental physics, com-
bined with a few well-grounded musical axioms.
40 Similarly, Hellenistic music avoids lyre tunings that do
not entail a complete four-note harmonía, as emerges from
Ptolemy’s list of contemporary cithara harmogaí, which
cover only four out of the possible seven octave species
(Dorian to Hypophrygian, ranging from the Lydian to the
Iastian key), with a hint at the modulating inclusion of the
next in the circle of fifth (Iastiaiólia). The other two would
destroy the framework by retuning one of the two central
strings. For the interpretation of Ptolemy’s tunings within
the notation system, cf. Hagel 2009, 56 68.
Stefan Hagel146
Ancient Sources
Aristidis QuintiliAni
De Musica libri tres. Ed. by R. P. Winning-
ton-Ingram (Leipzig 1963).
nicomAchus
Encheiridion, in: C. v. Jan (ed.), Musici
scriptores (Leipzig 1895).
PorPhyrius
In Ptol. Harm.: Porphyrios Kommen-
tar zur Harmonielehre des Ptolemaios.
Ed. by I. Düring, Göteborg Högskolas
Årsskrift 36/1 (Göteborg 1930).
Porphyry’s Commentary on Ptolemy’s
Harmonics: A Greek Text and Annotated
Translation (Cambridge 2015).
Ps.-AristoteliAn Problems
in: C. v. Jan (ed.), Musici scriptores (Leipzig
1895).
Ps.-PlutArch
Mus.: Plutarchus, Moralia VI.3. Ed. by
K. Ziegler (Leipzig 1964).
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Mode in Ancient Greek Music (Cambridge).
Stefan Hagel148
Fig. 1 Summary of closures found in ancient Greek musical scores (made by Stefan Hagel).
‘Leading Notes’ in Ancient Near Eastern and Greek Music and Their Relation to Instrument Design 149
Fig. 2 Modal concepts entailed by traditional aulos design (made by Stefan Hagel).
Stefan Hagel150
Fig. 3 Hypothetical double-pipe designs for rising semitone leading notes (made by Stefan Hagel).
... On ancient leading notes and especially F F and R R (in the frequent Lydian key) as typical leading notes to final S S, cf. Hagel 2016. 10 Hagel 2018a160. ...
Article
Full-text available
When contextualising the ancient Greek solmisation system, known from Aristides Quintilianus and one of Bellermann’s Anonymi, within its musical and linguistic environment, it emerges that it hardly predates the Roman Imperial period, an important part of whose musical schooling it appears to have formed. The system seems based on a combination of the various vowels’ intrinsic F2 pitch and intensity and reflects the harmonic hierarchies of contemporary music, shedding a much more favourable light on the music-psychological relevance of Aristides’ gendered musical notes than is conventionally assumed.
... 4 Judging from the tonality, or are much more likely candidates for the "final note" than would be (cf. Hagel 2009a, 301-2;Hagel 2016). Consequently, the standard edition takes the traces after the melisma as continuing the song, if perhaps only for one or few more syllables. ...
Chapter
The system of melodic notation, which was invented in Classical Greece and used through Late Antiquity, is set out and explained in its likely historical development, its relation to vocal and instrumental music‐making, and its reception by Aristoxenian theory as well as in Roman‐period schooling. The “chamber pitch” of the ancient system is addressed as well as the question of modern transcription. Special attention is also given to the symbols used for clarifying rhythmical ambiguities. Finally, one of the more recently published papyrus fragments helps illustrate the problems related to interpreting an ancient score and particularly its rhythm.
Article
Apart from the better studied musical 'handbooks' of the Roman period, mostly fo-cused on matters of harmonics and sometimes rhythmics, there was a type of text known as 'Musics'. The article discusses their characteristics, their function in ancient schooling and their relation to extant texts and excerpts, most notably the collection known as Bellermann's Anonymi. The 'instrumental exercises' found at the end of these are evaluated as instrumental pieces posing various challenges to beginners on the aulos; a new rhythmical reconstruction is proposed for one of them.
Article
It has long been known from the extant ancient Greek musical documents that some composers correlated melodic contour with word accents. Up to now, the evidence of this compositional technique has been judged impressionistically. In this article a statistical method of interpretation through computer simulation is set forth and applied to the musical texts, focusing on the convention of correlating a word's accent with the highest pitch level in the melody for that word: the Pitch Height Rule. The results provide a sounder basis for judging evidence for the operation of this convention in specific pieces and a sharper delineation of its use in the history of ancient Greek music. The ‘rule’ was used by at least some composers from the late second century BC through the second century AD, but there is no certainty that it was used before or after this period. In some cases where previous scholars have discovered the rule's operation, statistical analysis casts doubt. Of special interest is the showing that one piece long judged as offering no evidence of the use of the rule probably displays an inversion or parody of the rule for rhetorical-musical effect.
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An Ancient Christian Hymn with Musical Notation
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cosgrove, ch. 2011 An Ancient Christian Hymn with Musical Notation. Papyrus Oxyrhynchus 1786 (Tübingen).
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dAnek, g. 1989 ‚Singing Homer'. Überlegungen zu Sprechintonation und Epengesang, Wiener Humanistische Blätter 31, 1 – 15.
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devine, A. m. – stePhens, l. d. 1994 The Prosody of Greek Speech (New York/ Oxford).
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FrAnklin, J. c. 2006 Lyre Gods of the Bronze Age Musical Koine, The Journal of Ancient Near Eastern Religions 6, 39 – 70.
Is nīd qabli Dorian? Tuning and Modality in Greek and Hurrian Music
2005a Is nīd qabli Dorian? Tuning and Modality in Greek and Hurrian Music, Baghdader Mitteilungen 36, 287 -348.
An Ancient Christian Hymn with Musical Notation. Papyrus Oxyrhynchus 1786: Text and Commentary, Studien und Texte zu Antike und Christentum 65
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  • Cosgrove
2012 Review of: Ch. Cosgrove, An Ancient Christian Hymn with Musical Notation. Papyrus Oxyrhynchus 1786: Text and Commentary, Studien und Texte zu Antike und Christentum 65, Tübingen 2011, Jahrbuch für Antike und Christentum 55, 157 -161.
Ancient European Lyres: Excavated Finds and Experimental Performance Today Ancient Greek Music in Performance
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lAwson, g. 2005 Ancient European Lyres: Excavated Finds and Experimental Performance Today, in: S. Hagel – Ch. Harrauer (eds.), Ancient Greek Music in Performance (Vienna), 93 – 119.
Documents of Ancient Greek Music: The Extant Melodies and Fragments (Oxford). rAFFA, m. 2014 On the Text of Theophrastus fr. 717 Fortenbaugh
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PöhlmAnn, e. – west, m. l. 2001 Documents of Ancient Greek Music: The Extant Melodies and Fragments (Oxford). rAFFA, m. 2014 On the Text of Theophrastus fr. 717 Fortenbaugh, Classical Quarterly 64, 409 – 410.