Musical Structure of Geometric Elamite
Melissa Elliott <melissa.b.elliott@gmail.com, https://independent.academia.edu/0xabad1dea>
December 19, 2022
previous: circle, cross, triangle, square, so on and
so forth, up to seven strokes. This lends itself
readily to interpretation as digits. However, the
texts do not seem to represent addition,
multiplication, or any other mathematical
operation. Yet the texts are highly non-random
and exhibit repeating structures at a cadence
better understood in mathematic rather than
linguistic terms.
Abstract
The Konar Sandal “Geometric” tablets, written
partially in Linear Elamite and mostly in an
otherwise unknown script of simple geometric
shapes, have resisted linguistic explanation.
Their structure is better explained not as written
language, but as musical tones to be performed
on an eleven-string harp or lyre. The three
tablets are here analyzed as works of song.
Keywords
Elamite, Linear Elamite, Jiroft, Konar Sandal,
Geometric writing system, music theory, ancient
music, harp, lyre, Pythagorean scale, diatonic
scale, chromatic scale
Jir B’: 
Jir C’: 
Jir D’: 
From the years 2001 to 2006, three
tablets were recovered in Jiroft, Konar Sandal,
Iran and given an approximate dating of 2500 to
2000 BCE (Desset 2014). Each of these tablets
contains a very short text in Linear Elamite1 and
a longer text in a similar but much simpler
writing system which has been termed
“Geometric.” This consists primarily of circles,
squares and triangles with a scattering of
slightly more complex symbols. The extremely
limited symbol inventory precludes that the
Geometric text could express arbitrary
sentences in Elamite or any other attested
language in the region. It could only convey
information from a tightly limited domain.
The majority of the Geometric symbol
inventory can be arranged in a sequence where
each symbol contains one more stroke than the
Figure 1: Symbol inventory (tablet names according to
Online Corpus of Linear Elamite Inscriptions)

Figure 2: Main numeric sequence 1 to 7
When the sequence of one to seven
strokes are interpreted as a seven-note diatonic
scale, the result is, by the opinion of the ear,
well-formed music. The remaining few
Geometric symbols can then be explained in a
musical context which causes a complete
composition to emerge.
1 Due to a lucky coincidence Linear Elamite was largely undeciphered when this paper was begun and largely
deciphered by the time it was nished (see Desset 2022), but the LE labels on these tablets still do not have a
clear translation at present.
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     
    
    
     
    

Figure 3: Tablet Jir B’, front (Geometric) and back (Linear Elamite)
  
     
 
 
   
 
Figure 4: Tablet Jir C’, front (Geometric) and back (Linear Elamite)

  

  AA

Figure 5: Tablet Jir D’, hatch marks represent damage, transition to
Linear Elamite marked in gray
2
> 
Some of the characters are marked with
a dot in the middle. There is no apparent
pattern and tablet B’ has no dots at all. If the
text is music, then it seems most probable that a
dot indicates the note is either longer or shorter
than the others. However, it could indicate
something particular to the instrument the
composer had in mind. This analysis assumes
that a character with a dot represents the same
basic pitch as the same symbol without.
The vertical strokes and dots together
suggest the basics of rhythm. If the tablets were
meant chie y as a memory aid, this would be all
that was needed for accurate performance.
Symbol Interpretation
As mentioned above, the bulk of the
symbols  can be sorted by stroke
count to yield the values 1-2-3-4-5-6-7.
The vertical stroke character, , is not a
value but a dividing line (the one-stroke value
character is the circle). This is evidenced by the
way it marks o f repeating groups of symbols. It
is used on all three tablets, but on B’ in
particular it delineates a highly structured
mathematical pattern (see gure 11) when read
boustrophedon2 from the upper right, which
shall be taken as the reading order for all three
tablets. The symbol groups separated by the
vertical stroke shall here be termed “measures”
and may imply rhythm. The measures on B’
range from two to ve symbols in length, while
the other two tablets each have one very long
measure pre xed and su xed by several shorter
measures.
Since  and  are so similar in structure,
and never appear on the same tablet, this
analysis considers them to be the same value “2”
as written by di ferent scribes. Perhaps the 
was innovated to better visually distinguish 
from .
This leaves four symbol shapes: , , ,
and . They closely resemble the shapes , ,
, and  but are drawn too distinctly and
consistently (often on the same tablet) to be
incidental variation. This group shall be labeled
the “alternate digits” 1’, 2’, 4’ and 5’. The decision
about which is the “main” digit and which the
“alternate” is determined by simplicity of shape,
relative frequency, and the use of symbols in
ascending and descending sequences but it is
possible at least one pair has been identi ed the
wrong way around.
Scale
The most complex character has seven
strokes, and seven tone scales are well-known to
music theory. It cannot be excluded that there
are additional symbols in the system not
attested in our three samples but the system can
be adequately explained on the basis of the
attested symbols alone.
There is no indication within the tablets
about whether the scale is ascending (lowest
note rst) or descending (highest note rst). It
makes little di ference to the analysis of the
structure, though it does matter a great deal for
performing the music as intended. Other
ancient Middle Eastern scales have been
identi ed as descending (Dumbrill 2020), so this
seems the more likely reading. The purely
subjective opinion consensus of early reviewers
of this paper is that the music sounds more
“correct” when played descending.
The most obvious starting point for a
seven tone scale is the Pythagorean scale, which,
despite the name, is known to predate
Pythagoras signi cantly (Franklin 2002). Such a
scale would contain ve whole tones and two
half tones totaling seven. This leaves the four
2 “As the ox plows,” alternating reading direction each line to minimize the reader’s eye movement
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3

 
  
alternate digits 1’, 2’, 4’ and 5’ in dire need of
explanation. One possibility is that they
represent the next octave, so that 1’ is consonant
with 1, so on and so forth. The drawback to this
reading is that it introduces many highly
awkward intervals to the music. There is also the
puzzling detail that while 3 and 6 are
exceedingly common values in the text, there is
no symbol that can be construed as 3’ or 6’.
Both of these di culties can be resolved
under a Pythagorean interpretation. 1’, 2’, 4’ and
5’ represent the half tones not included in the
main diatonic scale, giving a span of 11
semitones that we might call “chromatic.” 1’
would be between notes 1 and 2, so on and so
forth, perhaps to be read aloud as “one and a
half.” The lack of symbols for 3’ and 6’ then
allows the main scale to be precisely identi ed
as WWHWWH. When descending, this would
begin on note A in modern Western terms; when
ascending, on note G. This happens to precisely
match a stereotypical pair of conjunct diatonic
tetrachords in the ancient Greek system
documented many centuries later (Anderson
1994).
The oldest surviving book on musical
theory, Elements of Harmony by Aristoxenus in
the fourth century BCE, makes a very speci c
claim about the history of scales: “Of these
genera the diatonic must be granted to be the
rst and oldest, inasmuch as mankind lights
upon it before the others; the chromatic comes
next.” (Translation of Macran 1902.) This is
transparently not true of every musical culture,
but the Geometric tablets re ect precisely this
development: a scale of seven “white keys” to
which were added four “black keys” consisting
of variants of the previous symbols.
There are several ways to construct a
Pythagorean-like scale from scratch, but given
the overwhelming preference for the perfect
fourth as illustrated in gure 7, the best
explanation should be a cycle of fourths. This
can be done with strings without any special
measuring tools or advanced mathematics, so
there is no reason to suppose the method was
beyond the means of the Elamites.
The lack of an attested 7’ or 8 symbol for
B♭ which would make the scale truly chromatic
may simply be down to rarity. It more likely was
theoretically undesirable: omitting it gives the
scale a clear middle point in 4 (which would be
the “mese” in Greek terms) and imparts an
elegant equivalence to the spans 1-4 and 4-7
which can also be understood in terms of Greek
diatonic tetrachords. Since 7 was the end of the
original diatonic scale, there would have been
minimal compositional use for a half step
beyond it. The square (4) is the most common
value alongside the circle (1), as makes sense if it
functions like a “mese,” and the perfect fourth
such as between 1 and 4 or between 3 and 6 is
the most common interval by a signi cant
margin.
It should be noted that there is no way
of reconstructing the exact reference pitch, if
indeed there even was such a thing; the tuning
may have been highly individualized. As such
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4
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Figure 6: Scale interpreted as Pythagorean-like diatonic with additional half tones to
form a chromatic scale, descending
(each black key symbol is a variant of the symbol on the white key to its right)
60
60
45
45
30
30
15
15
0
0
1
2
3
4
5
6
7
8
9
10
0
count of individual interval occurrences
across all three songs
0
1
2
3
4
5
6
7
8
3 https://upload.wikimedia.org/wikipedia/commons/2/20/Jiroft_culture_inscriptions.jpg
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5
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9
10
count of individual interval occurrences in
randomly generated song
Figure 7: Intervals calculated in semitones (not in scale degrees) without directionality across the real
songs and a randomly generated song of the same length as the three real songs together
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leaps between 1 and 6 are in tablet C’, which
makes heavy use of alternating structures, so the
statistical bump seems to be a peculiarity of this
song rather than a trait of the system in general.
If the text is music, then the intervals
should not be randomly distributed, nor lumped
too much towards the large end. A computer
program was written to generate random music
under the eleven-tone system illustrated in
gure 6. The random song is the same length as
the three real songs end-to-end to allow direct
numerical comparison. The charts in gure 7
show clearly that the intervals in the Geometric
tablets are not random, and are weighted
towards the low end with a special emphasis on
4 and 5 semitones, or the major third and the
perfect fourth, under the interpretation
described in section “Scale.” Of note is that there
is exactly one interval of zero, from two
diamonds in a row on tablet D’. In random data
we would expect many repetitions, and in a
phonetic system of so few symbols we would
also expect signi cantly more repetitions. When
looking at photographs of the tablets3, it is
Intervals
One di culty is that a few of the
intervals in the above scale interpretation are a
bit large, exceeding a fth (seven semitones).
The largest possible interval, from 7 to 1 (ten
semitones), occurs twice on tablet C’. However,
in both instances, the 7 and the 1 are on
opposite sides of a dividing line. This may imply
a lull in the ow which prevents the interval
from sounding jarring. There are also several
leaps between 1 and 6, nine semitones. The
nine-semitone interval is signi cantly more
common than other intervals above ve
semitones (see gure 7); the seven-semitone
interval is not nearly as common as one would
expect given the perpetual appeal of the perfect
fth. Alternate scale interpretations were
considered which might cause more fths to
appear, but none were satisfactory and a great
preference for the fourth over the fth is the
only thing that ts. Most of the nine-semitone
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the scale should be understood as relative to
some arbitrary pitch “”.
possible that one of the diamonds is really a
poorly drawn oval, which would make for no
repetitions at all.
a highly musical sequence of descending and
ascending tones alternating with the base tone
of 1, shown in gure 10. Removing the interior
base tones, the sequence goes 1-2-3-4-3-2-1. This
can only have a mathematical, not a linguistic,
explanation. The dot on the 4 suggests emphasis
at the climax of the movement. Tablet D’
contains a similar sequence 4-1-3-1-2-1-2-1.
Tablet B’ has less in the way of
monotonic sequences but far more in the way of
Melodic Structure
When mapped as ordered tones, the text
of the Geometric tablets reveal patterns that
would be highly unlikely to appear in natural
language. In particular, both melodic curves and
alternations between notes are clearly visible.
Figure 8 illustrates a melodic curve near
the beginning of tablet D’. It a rms the
reading of 4’ as between notes 4 and 5
on the scale as it neatly slots between
notes of value 3 and 6 on the curve. It is
being used for decorating the curve with
a minor complication as it returns to its
origin point.
If the curve in tablet D’ could be
termed a triangle wave of ascents and Figure 8: Melodic curve in tablet D’ demonstrating the use of the “black
descents, then the end of tablet C’
key” note  or 4’ for subtle decoration on the progression 6-3-1-3-6-3-1
illustrated in gure 9 contains a
sawtooth wave with repeated steps
downward and leaps back to the origin
point. The pattern displays modulation
between values 1 and 1’ and between 4
and 4’. The fact that all three sets of
notes end on 7 suggests that there is
indeed no 7’ in the system. This pattern
further a rms that placing the alternate
digits as adjacent to their main digits is
Figure 9: Sawtooth-type pattern in tablet C’ showing modulation between
correct.
1 and 1’ and 4 and 4’
Near the beginning of tablet C’ is



















Figure 10: descent and ascent interleaved between a repeating base note in tablet C’
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








M 1-2
Instrument
The Elamites enjoyed a wide variety of
instruments with special emphasis on the harp
and lyre (Rostami 2020). The system as here
analyzed contains eleven distinct notes. The
oldest lyre in the world, recovered from the
grave of the Sumero-Akkadian Queen Pu-abi,
hosted exactly eleven strings (British Museum
item 121198,a). The dating of this lyre at
2600-2400 BCE aligns nicely with the dating of
the Geometric tablets and may typify the
instrument which the composer had in mind.
The alternating structure of some passages is
typical of plucked string music. It therefore
seems most likely that this music was intended
for a harp or lyre.
Falsi ability
Due to the highly subjective experience
of music and the wide variety
of cultural norms in its
creation, it’s impossible to say
14
with absolute certainty
whether a decontextualized
14
sequence of symbols is
“really” music. What can be
14
said without subjectivity is
that the tablets exhibit cyclic
14
patterns and ascending and
descending sequences of
6 2’
numbers, and that they can
be coherently explained
6 2’
within a framework of music
theory concepts such as the
6 2’
Pythagorean scale, the perfect
fourth, and the diatonic
tetrachord.
6 2’
One means by which the
musical hypothesis could be
43
M 3-5
341
43
M 6-8
3143
1 6 4 2’ 3
M 9-11
341
43
M 12-14
3143
1 6 4 2’ 3
M 15-17
326
2 5’ 2’ 3
M 18-20
1 3 2 1’
43
M 21-23
326
2 5’ 2’ 3
M 24
1 3 2 1’
Figure 11: Tablet B’ with measures in left-to-right reading order, realigned and colorized to reveal
repetitions centered around multiples of 3
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structured repeating phrases. Every single
measure appears either two or four times. The
general pattern is that a measure repeats itself
either three or six measures after its rst
appearance. The measure containing the values
“4 3” is particularly interesting: it appears as the
rst measure, then three measures after that,
then six measures after that, then nine measures
after that. If one loops around at the end of the
song, then the “4 3” at the beginning of the
tablet comes six measures after the last, creating
an in nite cycle of 3-6-9-6-3. When played in
isolation, the song ends sounding unresolved on
note 1’; when looped, it resolves and continues
seamlessly. This re ects a high degree of
intentionality and planning, and suggests the
song had a speci c functional purpose that
called for repeating it an inde nite number of
times until the activity at hand was concluded.
falsi ed is to demonstrate another, more directly
practical mathematical explanation for the
symbol sequences, such as the calculations for
an object’s volume. Another would be to
demonstrate the symbols encode coherent
linguistic information. A third would be to come
to a clear understanding of the Linear Elamite
labels and demonstrate that they declare
another non-musical purpose.
Bibliography
Anderson, Warren. (1994.) Music and Musicians
in Ancient Greece, Appendix B: Scale Systems
and Notations. https://www.academia.edu/
43290611/
Anderson_1994_Music_and_musicians_in_Ancient_
Greece
Desset, Francois. (2014). A new writing system
discovered in 3rd millennium BCE Iran: the Konar
Sandal ‘Geometric’ tablets. https://
Conclusion
It’s music.
www.academia.edu/5428670/
A_NEW_WRITING_SYSTEM_DISCOVERED_IN_3rd_
MILLENNIUM_BCE_IRAN_THE_KONAR_SANDAL_
GEOMETRIC_TABLETS
The Geometric notation system is
straightforward, easy to read, easy to write, and
easy to learn (see Appendix). It is certainly
easier to interpret than the few surviving
notations in cuneiform. It is perhaps a great loss
to the history of music that the system does not
seem to have escaped Konar Sandal before the
Linear Elamite writing system faded from use.
If the texts are to be accepted as music,
then current thought on dating would place
them as older than the Hurrian Hymns of the
14th century BCE (Dumbrill 2020), and therefore
the oldest music yet recovered.
Desset, Francois et al. (2022). The Decipherment
of Linear Elamite Writing. https://
www.degruyter.com/document/doi/10.1515/
za-2022-0003/html?lang=en
Dumbrill, Richard. (2020). Birth of Music Theory,
sections “U.7/80 = UET VII, 74 (Circa 1800 BC),
right column” and “Hurrian Text H.6”. https://
www.academia.edu/44818683/
Birth_of_music_theory
Franklin, John Curtis. (2002.) Diatonic Music in
Greece: A Reassessment of its Antiquity. https://
Resources
Midi and MP3 renderings of the music,
as well as the script that was used to generate
the random song in gure 7, may be found here:
www.academia.edu/7860932/
_Diatonic_Music_in_Greece_A_Reassessment_of_its_
Antiquity_Mnemosyne_56_1_2002_669_702
https://github.com/0xabad1dea/geometric-elamite
Macran, Henry Stewart. (1902.) The Harmonics
of Aristoxenus, Book 1, section 19. https://
Special Thanks
The author of this paper is a computer
scientist and is grateful for the input of
historical musicologist Richard Dumbrill.
This paper uses the “Elamicon” font
provided by https://center-for-decipherment.ch/
archive.org/details/aristoxenouharmo00aris/
Rostami, Mostafa and Mansourabadi, Mostafa.
(2020). String Instruments Depicted in the
Paintings of Ancient Elam. https://
tool/
eijh.modares.ac.ir/article-27-32675-en.html
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Appendix
An early reviewer of this work decided to
make the rst new contribution to the
Elamite musical corpus in about four
thousand years. As with the older tablets, it
is to be read boustrophedon from the
upper right. The scale is according to gure
6, and a dot is used to indicate a long note.
Further contributions to the collection are
most welcome. Source: https://twitter.com/
h0m54r/status/1515641971397873671 (This
Twitter account is no longer active and
may instead be contacted at https://
mastodon.social/@h0m54r )
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