The Musical Geometry of Genes

Generating Rhythms from DNA

A l v A R o YA n e z

时间
C
A
右
时间
S
乙
A

DNA encodes all sorts of information that makes us human, 但,
aside from encoding genes, could DNA also encode for a mapping
of musical rhythms in a very abstract way? This project sought to
generate rhythms out of DNA and compose a musical piece out of a
gene’s rhythmic sequence. Computational rules inspired by geometric
analyses of rhythms guided the mapping of DNA’s molecular structure
into rhythmic timelines and melodic scales; these basic structures were
then used to compose a song according to the sickle cell gene DNA
顺序. The rhythms generated by this “genetic analysis” alternate
pleasantly between even and odd time signatures.

GeoMeTRiC RhYThMS And dnA

The discovery of deoxyribonucleic acids (DNA) 和他们的
role in encoding the information that makes us human has
inspired scholars from numerous corners of academia. 在
musicology, DNA’s unique geometric properties have typi-
cally been explored with sonification studies that primar-
ily generate melodies out of gene sequences [1–5]. To my
知识, 然而, no academic studies have attempted
to generate geometric rhythms out of DNA’s geometric prop-
erties, as I could not find other published descriptions of
DNA-derived rhythms in literature. This is surprising given
the almost natural opportunity to relate rhythms and DNA
by looking at their geometry. Rhythms can be ascribed geo-
metric properties like shapes in mathematics if understood
as timelines of k sounded onsets and n total pulses that repeat
over time in a circle diagram, also known as polygon nota-
的 (见图. 1 for an example) [6]. DNA is famous for its
attractive and highly conserved molecular geometry; seeing
such an opportunity, I therefore used geometry as an abstract
means to generate rhythms out of DNA molecules, and I used
these rhythms to compose a whole musical piece out of a
DNA sequence: the sickle cell gene [7].

Alvaro Yanez (student), New York University Abu Dhabi, 邮政信箱 129188,
阿布扎比, U.A.E. 电子邮件: ayanez@nyu.edu. ORCID: 0000-0001-9309-1885.

See www.mitpressjournals.org/toc/lmj/29 for supplemental files associated with
this issue.

如图. 1. The clave son in polygon notation (k = 5, n = 16). Geometric
properties arise from the timeline (a symmetric pentagon; thick contour) 和
time signature (4/4, a hexadecagon; thin contour). (© Godfried Toussaint [19])

Turning DNA Molecules into Rhythms

DNA is a long molecule made out of four basic subunits [8].
These precursors are adenosine monophosphate (AMP),
thymidine monophosphate (TMP), guanosine monophos-
phate (GMP) and cytidine monophosphate (CMP; 如图. 2) [9].
These four basic units bond with each other in specific or-
ders to form long sequences called genes. Molecularly, AMP,
TMP, GMP and CMP have regular structures. These consist
of three chemical groups: one central ribose sugar (central
highlight in each panel of Fig. 2), one phosphate group (左边-
most highlight in each panel of Fig. 2) and one nitrogenous
根据 (rightmost highlight in each panel of Fig. 2). In AMP,
the nitrogenous base is adenine (A); in TMP, thymine (时间); 在
GMP, guanine (G); and in CMP, cytosine (C). The important
property to note here is neither the names nor the chemis-
try of these subunits but rather that two out of these three
chemical groups are cyclic rings—namely, the central ribose
sugar and the nitrogenous base. Given that rhythms can be
represented using polygon notation (i.e. essentially, a circle
with enclosed polygons; 见图. 1), the polygons formed by
the central ribose sugar and the nitrogenous bases were a

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LEONARDO MUSIC JOURNAL, 卷. 29, PP. 45–49, 2019 45

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in the base and a five-membered second ring in the
根据, AMP’s three circle diagrams have n = 5, n = 6
and n = 5 (分别).

规则 3: Noncarbon atoms within each cyclic ring
will determine the bass drum k polygon, i.e. 这
timeline of a drum kit’s bass drum. Application:
Because AMP’s ribose ring only has one noncarbon
atom (i.e. the oxygen atom, 氧 [10]), AMP’s ribose
ring’s circle diagram has a bass drum timeline of
[ X . . . . ]. 相似地, AMP’s base’s diagrams have bass
drum timelines of [ . X . X . . . ] 和 [ X . X . . ] [11].

规则 4: Functional groups attached to each cyclic
ring will determine the snare drum k polygon,
i.e. the timeline of a drum kit’s snare drum.
Application: Because AMP’s ribose ring has two
–OH groups attached, AMP’s ribose ring’s circle
diagram has a snare drum timeline of [ . . x x . ].
相似地, AMP’s base’s diagrams have snare drum
timelines of [X . . . . . ] 和 [ . . . . . ].

The four rules generated 10 rhythmic timelines from 10
cyclic rings in all four DNA subunits; these are shown in Fig.
3. To have one timeline per DNA subunit, I combined each
subunit’s timelines into one timeline [12]. This yielded four
rhythms of unusual time signatures (如图. 4A; online supple-
mental video S1): AMP’s and GMP’s timelines are in 15/4 (或者
5/4, 6/4 和 5/4), and TMP’s and CMP’s are in 11/4 (或者 5/4
和 6/4). These time signatures were a consequence of AMP
and GMP both having a ribose and a double-membered base
ring and of TMP and CMP both having a ribose and a single-
membered base ring. The timelines generated are not too
different from one another: AMP, TMP and GMP progress
similarly, but AMP differs from TMP and GMP in a silent
eighth onset, while TMP differs from GMP due to a shorter
n. CMP is actually equal to TMP, which is a consequence
of TMP and CMP having equal distributions of carbon and
noncarbon atoms and functional groups in the base.

The rhythmic timeline of the first four letters of the sickle
cell gene are illustrated in Fig. 4乙. The time signature odd-
ity reminded me of Dave Brubeck’s Take Five [13], written
in the unusual 5/4 (i.e. k = 5); the oddity in Take Five’s time
signature has been described to both challenge the listener’s

=

=

=

=

=

Rhythmic output (乙)*

氮(circle diagrams)

n

Bass drum onsets (kbass)

Snare drum onsets (ksnare)

如图. 2. Chemical structures of the four basic subunits of DNA. 中央, 最左边
and rightmost highlights in each panel indicate the central ribose sugar, 这
phosphate group and the nitrogenous base of each subunit (A in AMP, T in
TMP, G in GMP and C in CMP). (© Alvaro Yanez)

natural source of inspiration for the mapping of DNA mol-
ecules into rhythms.

I created four rules to map these rhythms. These rules
came about by noting that (A) chemical characteristics within
the cyclic rings could be associated to (乙) rhythmic outputs
into a circle diagram. 即, the size of the ring, the atoms
within it and the functional groups attached to it could be as-
sociated with a circle diagram’s n total pulses and k sounded
onsets. For illustration purposes, all pulses in this work were
written as quarter notes; 然而, this was a stylistic deci-
sion that could be changed. The four rules (summarized in
桌子 1) 是:

规则 1: The number of cyclic rings in the DNA sub-
unit will determine the number of circle diagrams to
be drawn. Application: Because AMP and GMP have
three cyclic rings, they yield three circle diagrams
(TMP and CMP yield two).

规则 2: The number of atoms in each cyclic ring will
determine n, the number of total pulses of its respec-
tive circle diagram. Application: Because AMP has a
five-membered ribose ring, a six-membered first ring

TABle 1. Summary of the geometric rules for the rhythmic timelines.

规则

规则 1

规则 2

规则 3

规则 4

Chemical input (A)*

氮(rings in the monomer)

氮(atoms in the ring)

Noncarbon atoms in the ring

Functional groups in the ring

*氮(X) = number of X

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ability to keep track of the beat and “keep
the brain more active while listening and
performing” [14]. These “genetic” rhythms
are not only oddly timed, 然而: 他们
also alternate with even time signatures.
This reminds me of the work of Dream
Theater, a progressive rock band famous
for virtuosic alternation between time sig-
natures. In The Count of Tuscany [15], 为了
实例, the time signature starts in 3/4
(0:00–1:02) and begins alternating in 1:03–
2:36 with a repeated sequence of 6/8, 9/8,
6/8 和 12/8 to form the core of the piece. A
second instance of this unusual alternation
can be found 9:33–10:12, where the piece
follows an ABAB structure in which A =
7/8, 15/16, 7/8 和 4/4 and B = 7/8, 15/16, 7/8
和 19/16. 这里, the rhythms generated by
DNA resemble Dream Theater’s style more
than that of Dave Brubeck because we ob-
tained oddly timed rhythms whose time
signatures alternate. These mixed time
signatures could also be written in an ar-
bitrary number of different ways; nonethe-
较少的, regardless of how you choose to write
他们, the underlying rhythmic timelines
will never be regular when compared to
each other. An additional illustration of
how DNA sequences can be mapped into
rhythmic timelines using this method is
shown in Fig. 4C, where the “rhythm” of
the first four letters of the MAOA gene are
depicted.

TuRninG dnA MoleCuleS

inTo MelodiC SCAleS

Having generated four rhythms from
DNA, I then generated melodic scales
that would help me constrain the com-
positional process to a narrower range of
notes from which to pick. I took advantage
of the geometric isomorphism between
rhythms and scales described by Tous-
saint in The Geometry of Musical Rhythm
[16]. 简而言之, this isomorphism converts
rhythms into melodic scales (and vice
versa) by using a rhythm’s circle diagram
polygon. If we overlay a timeline’s polygon
into an n = 12 circle diagram, where each
“onset” represents a note of the chromatic
规模 (with C as the zeroth onset), 那么
k timeline resulting from this overlay in-
dicates which notes should be played. 为了
例子, AMP’s ribose timeline (如图. 3A; A
triangle with corners at onsets 0, 2 和 3)
transposes into the scale C-F-G (如图. 5A; A
triangle with corners at onsets 0, 5 和 7).

如图. 3. Chemical structures and circle diagrams of the resulting rhythmic timelines. Chemical structures
(左边) and resulting rhythmic timelines (正确的) of AMP (A), TMP (乙), GMP (C) and CMP (d). (kbass indicated
in black shading; ksnare indicated in red shading [gray in print edition].) (© Alvaro Yanez)

如图. 4. (A) Full rhythmic timeline of each DNA subunit. Time signature for each full rhythmic timeline
indicated by box length (kbass indicated in black shading; ksnare indicated in red shading [gray in print
版]). (乙) Rhythmic timeline of the first four letters of the sickle cell gene: ACAC [20]. (C) Rhythmic
timeline of the first four letters of the MAOA gene: CATA [21]. (© Alvaro Yanez)

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Yanez, The Musical Geometry of Genes 47

to compose a two-minute long piece with
verses, choruses, a bridge and a solo; 使用
全部 586 letters in the sequence, 在另一
手, would have given a very long piece.
The song’s rhythmic “backbone” was
generated by substituting each letter with
its respective timeline (according to the
“rhythmic library” in Fig. 4). The accom-
panying chord progression was generated
by trying out progressions from each time-
line’s transposed scale (i.e. the “melodic li-
brary” in Fig. 5) and by modifying these
chords at will to obtain a pleasurable pro-
进犯, as the scales generated did not in-
herently sound pleasing. This method gave
me both a rhythm and a chord progres-
sion from which I could start improvising
creatively, like artists playing composing
游戏. Adding a creative component to
the composition was important to me be-
cause I wanted the final composition to be
perceived as a fluid song, 而不是
rigid outcome of a geometric “code.”

To facilitate the creative process, 我
subdivided the 52-lettered sequence into
smaller sequences that I could compose
piece-wise. I decided that these smaller
structures would be multiples of four,
based on The Count of Tuscany’s alternat-
ing four-tuple main theme (1:03–2:36) 和
ABAB structure (9:33–10:12). Subdividing the sequence eased
the compositional process because the piece’s time signature
sequence was as random as the gene sequence itself. Giving
me a localized structural context to work with facilitated the
creative aspect of this exercise.

The final product of this project, a two-minute-long piece
that I titled E8Q, can be found in the online supplemental
files (Audio S1). Like the gene sequence’s letters, the rhythm
of the piece does not repeat itself, but this lack of repeti-
tion does not seem to sacrifice musicality. Astoundingly, 这
song’s rhythm holds a somewhat regular and periodic struc-
真实. This is entirely due to the choice of DNA as a source of
musical inspiration. Because DNA consists of a sequential
combination of four subunits from which two are bigger than
the other two (i.e. AMP and GMP versus TMP and CMP),
the resulting rhythmic sequence (i.e. the two different 15/4
timelines and the two equal 11/4 时间线) produce a struc-
ture that sounds odd and unusual, but not too unusual when
permuted. 最后, the chemical similarity between
DNA subunits, and its ability to combine into a sequence,
allows DNA to produce unusual rhythms that are musically
attractive despite being irregular.

ConCluSion

A deep analysis of geometry in the context of rhythms and
biochemistry enabled me to map DNA sequences to rhythms
and scales. Using rules inspired in DNA’s cyclical rings, 我

如图. 5. Chemical structures and circle diagrams of the resulting melodic scales. Chemical structures
(左边) and resulting melodic scales (正确的) of AMP (A), TMP (乙), GMP (C) and CMP (d). (Sounded onsets
indicated in black and red shading [gray in print edition]). (© Alvaro Yanez)

Using this methodology, I transposed each of the rhythmic
timelines generated in Fig. 3 into their respective melodic
scales (如图. 5; online supplemental video S2). (When a poly-
gon’s corner landed between onsets rather than on an onset,
the nearest clockwise onset was chosen to be sounded.) Hav-
ing generated both rhythmic timelines and melodic scales
out of DNA, I then proceeded to compose a piece out of a
well-studied gene sequence: the sickle cell gene.

CoMpoSinG A SonG ouT oF A Gene

The composition of a musical piece out of the sickle cell gene
followed a similar methodology to that of eighteenth- 和
nineteenth-century artists playing composing games. 这些
games challenged artists to compose waltzes on the spot using
two dice. The number sequence drawn by the dice decided
a priori the meter, scale and chords that the artist should
使用. Artists would draw on a mental “library” that associated
(also a priori) every dice combination to precomposed chord
progressions in the meter and scale indicated [17].

Inspired by the concept of using dice’s randomness to com-
pose a piece’s “backbone,” I used the first 52 letters of the
sickle cell gene sequence to accomplish the same purpose.
These letters are ACACTCGCTT CTGGAACGTC TGAG-
GTTATC AATAAGCTCC TAGTCCAGAC GC [18], 在哪里
A stands for AMP, C for CMP, T for TMP and G for GMP.
I arrived at the number 52 by experimenting with several
values first. I thought 52 letters would be significant enough

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generated geometric polygons that could be used both as
rhythmic timelines and melodic scales. These timelines and
scales, when ordered according to the gene sequence of the
sickle cell gene, created a “backbone” from which I composed
a two-minute song that alternated randomly but pleasantly
between two unusual time signatures: 11/4 和 15/4. I know
of no such prior compositional exercise in musicology.

所以, the main lesson of this project—that chemical
structures can be related to rhythmic structures to create a
musical “backbone” over which one can improvise and com-
pose—has the potential to serve as an original and abstract
compositional technique for artists seeking to relate biology
and music even more intimately.

Acknowledgment

I deeply thank Godfried Toussaint (New York University Abu Dhabi) 为了
his active support in the development of this project.

参考文献和注释

1 右. Takahashi and J.H. 磨坊主, “Conversion of Amino-Acid Sequence
in Proteins to Classical Music: Search for Auditory Patterns,” Genome
生物学 8, 不. 5 (2007) p. 405.

2 S. Ohno and M. Ohno, “The All Pervasive Principle of Repetitious
Recurrence Governs Not Only Coding Sequence Construction But
Also Human Endeavor in Musical Composition,” Immunogenetics
24, 不. 2, 71–78 (1986).

3 J. Dunn and M.A. 克拉克, “Life Music: The Sonification of Proteins,”

列奥纳多 32, 不. 1, 23–32 (1999).

4 S. Alexjander and D. Deamer, “The Infrared Frequencies of DNA
Bases: Science and Art,” IEEE Engineering in Medicine and Biology
Magazine 18, 不. 2, 74–79 (1999).

5 X.J. Shi, Y.Y. Cai and C.W. Chan, “Electronic Music for Bio-Mole-
cules Using Short Music Phrases,” Leonardo 40, 不. 2, 137–141 (2007).

6 Godfried Toussaint, The Geometry of Musical Rhythm: What Makes
a “Good” Rhythm Good? (纽约: CRC Press, 2013) PP. 13–14.

7 The sickle cell gene is a gene that encodes for a protein that is impor-
tant for the proper function of red blood cells. The gene’s technical
name is HBG2, and mutations in HBG2 cause sickle cell anemia.
Sickle cell anemia is a condition in which red blood cells no longer
look smoothly biconcave but like a sharp sickle and hence cannot
transport oxygen around the body as effectively.

8 J.D. Watson and F.H.C. Crick, “Molecular Structure of Nucleic Ac-

ids,“ 自然 171 (1953) PP. 737–738.

9 S.J. Elledge, Z. Zhou and J.B. 艾伦, “Ribonucleotide Reductase:
Regulation, Regulation, Regulation,” Trends in Biochemical Sciences
17, 不. 3, 110–123 (1992).

11 Both carbon and hydrogen atoms were intentionally left out of the
mapping methodology. In organic chemistry, hydrocarbons build
the simplest skeletal structures of all organic compounds. 因此, 我
determined that their fundamental and ubiquitous presence in all
organic compounds would not add the variety that a rhythmic map-
ping procedure based on atomic differences would require.

12 I avoided arbitrariness by putting the ribose timeline first, followed
by the nitrogenous base timeline, 因为, during the chemical syn-
thesis of DNA, the ribose ring comes first, and the bases attach to it.
For bases that generated two timelines, the six-membered timeline
went first because the scientific community defines the starting point
of the base as the six-membered ring.

13 Dave Brubeck, Take Five, sound recording (1959).

14 Evelyn Lamb, “Uncommon Time: What Makes Dave Brubeck’s
Unorthodox Jazz Stylings So Appealing?” Scientific American
(11 十二月 2012): www.scientificamerican.com/article/uncommon
-time-dave-brubeck (访问过 10 十二月 2017).

15 Dream Theater, The Count of Tuscany, sound recording (2009).

16 Toussaint [6] PP. 51–55.

17 Gerhard Nierhaus, Algorithmic Composition: Paradigms of Auto-
mated Music Generation (Mörlenbach: SpringerWienNewYork,
2009) p. 36.

18 Nucleotide, “Homo sapiens monoamine oxidase A (MAOA) gene,
complete cds,” National Center for Biotechnology Information: 万维网
.ncbi.nlm.nih.gov/nuccore/AH002871.2 (访问过 2 十二月 2017).

19 Toussaint [6] p. 25.

20 Nucleotide, “Homo sapiens hemoglobin subunit gamma 2 (HBG2),
mRNA,” National Center for Biotechnology Information: www.ncbi
.nlm.nih.gov/nuccore/NM_000184.2 (访问过 2 十二月 2017).

21 看 [19].

稿件收到 26 七月 2018.

10 In the chemical structures given in Figs 2 和 3, carbon atoms are
represented by corners and noncarbon atoms are represented by
their atomic symbols (as indicated in the Periodic Table of Ele-
评论). H: hydrogen; 氧: oxygen; 氮: nitrogen; 和P: phosphorus.

AlvARo YAnez was a student at New York University Abu
Dhabi, where he studied biology with a specialization in brain
and cognitive science, and premedical and health studies.

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Yanez, The Musical Geometry of Genes 49

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