J. Software Engineering & Applications, 2010, 3, 683-695
doi:10.4236/jsea.2010.37078 Published Online July 2010 (http://www.SciRP.org/journal/jsea)
683
Melody Generator: A Device for Algorithmic
Music Construction
Dirk-Jan Povel
Centre for Cognition, Donders Institute for Brain, Cognition and Behaviour, Radboud University Nijmegen, Nijmegen, The Netherlands.
Received April 15th, 2010; revised May 25th, 2010; accepted May 27th, 2010.
ABSTRACT
This article describes the development of an application for generating tonal melodies. The goal of the project is to as-
certain our current understanding of tonal music by means of algorithmic music generation. The method followed con-
sists of four stages: 1) selection of music-theoretical insights, 2) translation of these insights into a set of principles, 3)
conversion of the principles into a computational model having the form of an algorithm for music generation, 4) test-
ing the “music” generated by the algorithm to evaluate the adequacy of the model. As an example, the method is im-
plemented in Melody Generator, an algorithm for generating tonal melodies. The program has a structure suited for
generating, displaying, playing and storing melodies, functions which are all accessible via a dedicated interface. The
actual generation of melodies, is based in part on constraints imposed by the tonal context, i.e. by meter and key, the
settings of which are controlled by means of parameters on the interface. For another part, it is based upon a set of
construction principles including the notion of a hierarchical organization, and the idea that melodies consist of a ske-
leton that may be elaborated in various ways. After these aspects were implemented as specific sub-algorithms, the de-
vice produces simple but well-structured tonal melodies.
Keywords: Principles of Tonal Music Construction, Algorithmic Composition, Synthetic Musicology, Computational
Model, Realbasic, OOP, Melody, Meter, Key
1. Introduction
Research on music has yielded a huge amount of con-
cepts, notions, insights, and theories regarding the struc-
ture, organization and functioning of music. But only
since the beginning of the 20th century has music be-
come a topic of rigorous scientific research in the sense
that aspects of the theory were formally described and
subjected to experimental research [1]. Starting with the
cognitive revolution of the 1960s [2] a significant in-
crease in the scientific study of music was seen with the
emergence of the disciplines of cognitive psychology and
artificial intelligence. This gave rise to numerous ex-
perimental studies investigating aspects of music percep-
tion and music production, for overviews see [3,4], and
to the development of formal and computational models
describing and simulating various aspects of the process
of music perception, e.g., meter and key induction, har-
mony induction, segmentation, coding, and music repre-
sentation [5-13].
Remembering Richard Feynman’s adage “What I can’t
create, I don’t understand”, this article is based on the
belief that the best estimate of our understanding of mu-
sic will be obtained from attempts to actually create mu-
sic. For that purpose we need a computer algorithm that
generates music.
1.1 Algorithmic Music Construction
The rationale behind the method is simple and straight-
forward: if we have a theory about the mechanism un-
derlying some phenomenon, the best way to establish the
validity of that theory is to show that we can reproduce
the phenomenon from scratch. Applied to music: if we
have a valid theory of the structure of music, then we
should be able to construct music from its basic elements
(sounds differing in frequency and duration), at least in
some elementary fashion. The core of the method there-
fore consists in the generation of music on the basis of
insights accumulated in theoretical and experimental
music research.
In essence, the method includes four stages 1) specifi-
cation of the theoretical basis; 2) translation of the theory
into a set of principles; 3) implementation of the princi-
ples as a generative computer algorithm; 4) test of the
output. This article only describes the three former stages:

Melody Generator: A Device for Algorithmic Music Construction 684
the theoretical background and the actual development of
the algorithmic music construction device. The testing of
the device which calls for a separate dedicated study will
be reported in a separate article.
Compared to the experimental method, the algorithmic
construction method has two advantages: first, it studies
all structural aspects of music in a comprehensive way
(because all aspects have to be taken into account if one
wants to generate music) thus exhibiting the “big pic-
ture”: the working and interaction of all variables; second,
it requires utmost precision, enforced by the fact that the
model is implemented as a computer algorithm. Experi-
mental research in music, because of inherent limitations
of the method, typically focuses on a restricted domain
within the field of music, taking into account just one or
two variables. As a result of this, the interpretation of the
experimental results and their significance for the under-
standing of music as a whole, is often open to discussion.
1.2 Related Work
The possibility to create music by means of computer
algorithms, so-called algorithmic composition, has at-
tracted a lot of interest in the last few decades [14-16].
Algorithmic composition employs various methods [17]:
Markov chains [18,19]; Knowledge-based systems [20];
Grammars [14,21-24]; Evolutionary methods divided
into genetic algorithms, [25] and interactive genetic al-
gorithms [26]; and learning systems [27,28].
Because the method presented here generates music it
could be seen as an instance of algorithmic composition.
But, since its purpose is to serve as a means to test music
theory, it does not merely rely on classical AI methods
but capitalizes on music theoretical insights to guide the
implementation of the music generating device. As such
it resembles the approaches taken by [9,29-31].
1.3 Organization of the Paper
The present article is organized as follows. In Section 2
the theoretical foundation of the method is described: the
theoretical starting point, the basic assumptions, the in-
sights regarding the configuration of the time dimension
and the ensuing constraints, the configuration of the pitch
dimension and ensuing constraints, and the basic con-
struction rules for generating melodies. In Section 3, the
implementation of the algorithm is discussed: the various
functions of the program, its underlying structure, its user
interface, and the implementation of the tonal context
and the construction principles.
2. Theoretical Foundation
Before describing the theoretical basis of the project, I
should point out that what is being presented here is a
particular set of theoretical notions based on a specific
interpretation of the findings in the literature. Thus, I do
not claim that this is the only possible theoretical basis,
and certainly not that it is complete. The main purpose of
this paper is to study the adequacy of a melody generat-
ing device based on specific theoretical ideas about the
construction of tonal music.
Starting point of the project is the conception of music
as a psychological phenomenon, i.e., as the result of a
unique perceptual process carried out on sequences of
pitches. In the case of tonal music this process has two
distinct aspects: 1) Discovering the context in which the
music was conceived (meter, key, and harmony) and
representing the input within that context. By this repre-
sentation the input, consisting of sounds varying in pitch,
is transformed into tones and chords having specific mu-
sical meanings; 2) Discovering the structural regularities
in the input (e.g., repetition, alternation, reversal) and
using these to form a mental representation [5,7]. These
processes evolve largely unconsciously: What the lis-
tener experiences are the effects of these processes, spe-
cifically the experiences that accompany the expectations
arising while the music develops and the ways in which
these expectations are subsequently resolved. Sometimes
these experiences are described by the terms tension and
relaxation, but these hardly seem to cover the subtle and
varied ways humans may respond to music.
This basic conception of the process of music percep-
tion has guided the choice of assumptions, and the de-
velopment of the models of music construction described
below, as well as the shaping of the interface of the
computer algorithm.
2.1 Basic Assumptions
The model is based on the following assumptions: 1)
Tonal music is conceived within the context of time and
pitch, where time is configured by meter (imposing con-
straints as to when notes may occur), and pitch by key
and harmony (imposing constraints as to what notes may
occur). 2) Within that context tone sequences are gener-
ated using construction rules specifying the (hierarchical)
organization of tones into parts, and of parts into larger
parts etc., relating to concepts such as motives, phrases,
repetition and variation, skeleton, structural and orna-
mental tones, etc.
In line with these assumptions two components may
be discerned in the program: one component that man-
ages the context, and another that handles the construc-
tion rules.
Below, we discuss the configuration of the time di-
mension, the configuration of the pitch dimension, the
interaction between these dimensions, the basic princi-
ples of music construction, and the resulting constraints
and rules.
2.2 The Time Dimension of Tonal Music
The time dimension in tonal music is configured by me-
ter. Meter is a temporal framework in which a rhythm is

Melody Generator: A Device for Algorithmic Music Construction 685
cast. It divides the continuum of time into discrete peri-
ods. Note onsets in a piece of tonal music coincide with
the beginning of one of those periods.
Meter divides time in a hierarchical and recurrent way:
time is divided into time periods called measures that are
repeated in a cyclical fashion. A measure in turn is sub-
divided in a number of smaller periods of equal length,
called beats, which are further hierarchically subdivided
(mostly into 2 or 3 equal parts) into smaller and smaller
time periods. A meter is specified by means of a fraction,
e.g., 4/4, 3/4, 6/8, in which the numerator indicates the
number of beats per measure and the divisor the duration
of the beat in terms of note length (1/4, 1/8 etc.), which is
a relative duration.
The various positions defined by a meter (the begin-
nings of the periods) differ in metrical weight: the higher
the position in the hierarchy (i.e. the longer the delimited
period), the larger the metrical weight. Figure 1 displays
two common meters in a tree-like representation indicat-
ing the metrical weight of the different positions (the
weights are defined on an ordinal scale). As shown, the
first beat in a measure (called the down beat) has the
highest weight. Phenomenally, metrical weight is associ-
ated with perceptual markedness or accentuation: the
higher the weight, the more accented it will be.
Although tonal music is commonly notated within a
meter, it is important to realize that meter is not a physi-
cal characteristic, but a perceptual attribute conceived of
by a listener while processing a piece of tonal music. It is
a mental temporal framework that allows the accurate
representation of the temporal structure of a rhythm (a
sequence of sound events with some temporal structure).
Meter is obtained from a rhythm in a process called met-
rical induction [32,33]. The main factor in the induction
of meter is the distribution of accents in the rhythm: the
more this distribution conforms to the pattern of metrical
weights of some meter, the stronger that meter will be
induced. The degree of accentuation of a note in a
rhythm is determined by its position in the temporal
structure and by its relative intensity, pitch height, dura-
tion, and spectral composition, the temporal structure
Figure 1. Tree-representations of one measure of 3/4 and
6/8 meter with the metrical weights of the different levels.
For each meter a typical rhythm is shown
being the most powerful [34]. The most important deter-
miners of accentuation are 1) Tone length as measured
by the inter-onset-interval (IOI); 2) Grouping: the last
tone of a group of 2 tones and the first and last tone of
groups of three or more tones are perceived as accentu-
ated [33,35].
2.2.1 Metrical Stability
The term metrical stability denotes how strongly a
rhythm evokes a meter. We have seen that the degree of
stability is a function of how well the pattern of accents
in a rhythm matches the pattern of weights of a meter.
This relation may be quantified by means of the coeffi-
cient of correlation. If the metrical stability of a rhythm
(for some meter) falls below a critical level, by the oc-
currence of what could be called “anti-metric” accents,
the meter will no longer be induced, leading to a loss of
the temporal framework and, as a consequence, of the
understanding of the temporal structure.
2.2.2 Basic Constraints Regarding the
Generation of Tonal Rhythm
Meter imposes a number of constraints on the use of the
time dimension when generating tonal music: 1) it de-
termines the moments in time, the locations, at which a
note may begin; 2) it requires that the notes are posi-
tioned such that the metrical stability is high enough to
induce the intended meter.
2.3 The Pitch Dimension of Tonal Music
The pitch dimension of tonal music is organized on three
levels: key, harmony, and tones. These constituents
maintain intricate mutual relationships represented in
what is called the tonal system. This system describes
how the different constituents relate and how they func-
tion: e.g., how close one key is to another, which are the
harmonic and pitch elements of a key, how they are re-
lated, how they function musically, etcetera. For a review
of the main empirical facts see [4]. It should be noted
that these relations between the elements of the tonal
system do not exist in the physical world of sounds (al-
though they are directly associated with it), but refer to
knowledge in the listener’s long-term memory acquired
by listening to music.
Key is the highest level of the system and changes at
the slowest rate: in shorter tonal pieces like hymns, folk-
songs, and popular songs there is often only one key
which does not change during the whole piece.
A key is comprised of a set of 7 tones, the diatonic
scale. The tones in a scale differ in stability and the de-
gree in which they attract or are attracted [36]. For in-
stance, the first tone of the scale, the tonic, is the most
stable and attracts the other tones of the scale, directly or
indirectly, to different degrees. The last tone of the scale,
the leading tone, is the least stable and is strongly at-

Melody Generator: A Device for Algorithmic Music Construction 686
tracted by the tonic. Phenomenally, attractions are ex-
perienced by a listener as expectations.
A key also contains a set of harmonies, basically in-
stantiated by triads built on the 7 degrees of the scale.
The triads on the 1st, 4th, and 5th degree are the primary
ones. Like the tones, the harmonies, depending on their
stability, may either attract or be attracted by other har-
monies [37-39]. We start from the assumption that tonal
melodies are built upon an underlying harmonic progres-
sion [40].
These musical functions only become available after a
listener has recognized the key of the piece in a process
analogous to finding the meter, called key induction. For
an overview see [13].
2.3.1 Basic Constraints Associated with Key and
Harmony
Once a selection for a particular key has been made, the
tones of the diatonic scale are the primary candidates for
the construction of a melody. The non-key or chromatic
tones play a secondary role and can only be used under
strict conditions and mainly as local ornaments. The se-
lection of a specific harmonic progression reduces the
selection of tones even more since the tones within some
harmony must, in principle, be in accordance with that
harmony: only the tones that are part of the harmony can
be sounded together with it. These tones are called har-
monic tones or chord tones. There are melodies only
consisting of chord tones (e.g., Mozart, Eine kleine
Nachtmusik), but most melodies also contain non-chord
tones (e.g., suspensions, appoggiatura’s, passing tones,
neighbor tones etc.) (Figure 2).
As non-chord tones form dissonances with the har-
mony their use is restricted: they must be “anchored” by
(resolved to) a succeeding chord tone close in pitch [41,
42]. Most often a non-chord tone is anchored immedi-
ately, i.e., by the next succeeding tone, but it can also be
anchored with some delay, as in the case of F A G, in
which G is a chord tone and F and A are non-chord tones.
Figure 2. Three melodic fragments with different distribu-
tions of chord tones and non-chord tones (indicated +). (a)
only chord tones; (b) non-chord tones on weak metrical
positions; (c) non-chord tones on strong metrical positions
2.4 Relations between Meter and Key
Above it was mentioned that the notes within a key differ
in stability. In general, the more stable a note, the more
structurally important it will be in the melody. From this
it follows that stable notes, in order to enforce their
prominent role, tend to appear at metrically strong posi-
tions.
This, however, is not always the case: sometimes a
non-chord tone is placed on a beat (a strong position) and
resolved by a chord tone on a weaker metrical position
(appoggiatura). See note example c in Figure 2. These
different uses of non-chord tones is style dependent, see
[43].
2.5 Principles of Melody Construction
So far I have described the major characteristics of the
context within which tonal music is constructed: Meter
which defines the positions at which notes may begin and
the perceptual salience of these positions. Key defining
the basic units of a tonal piece: tones and chords, their
relation and their musical function. And lastly the har-
monic progression underlying a melody that defines the
chord tones and non-chord tones. Now the question must
be answered how a melody is generated within this con-
text.
We start with the following basic principles: 1) A me-
lody consists of parts that may consist of subparts, which
in turn may contain subparts, etc., thus forming a hierar-
chical organization; 2) Parts are often created from other
parts by means of variation; 3) A part consists of a ske-
leton of structural tones, which may be elaborated (or-
namented) to different extents.
The hierarchical organization of tonal music has been
described by many authors. Bamberger [44] describes the
hierarchical organization of tunes in terms of trees con-
sisting of motives, phrases, and sections connected by
means of 3 organizing principles: repetition, sequential
relations, and antecedent-consequent relations. Lerdahl &
Jackendoff [7] conceive of the organization of tonal
pieces in terms of hierarchical trees, resulting from a
time-span reduction (based on the rhythmical structure)
and a prolongational reduction expressing harmonic and
melodic patterns of tension and relaxation. Schoenberg
[45] describes the hierarchical organization of classical
music on several levels: large forms (e.g., sonata form),
small forms (e.g., minuet), themes (e.g., the period and
the sentence consisting of phrases and motives).
The idea that the surface structure of a melody can be
reduced by a stepwise removal of less important tones
thereby revealing the underlying framework or skeleton
has a long history in music theory. Schenker [46] laid the
theoretical foundation for the notion which was formal-
ized in [7]. Similar ideas are found in [9,29,31,43,47].
Baroni et al. [30] proposed a set of transformations by

Melody Generator: A Device for Algorithmic Music Construction 687
which a melodic skeleton can be elaborated into a full-
fledged melody (see Subsection 2.5.2). Marsden [31]
proposed a framework for representing melodic patterns
yielding a set of elaborations to produce notes between
two parent notes.
In view of the foregoing, we must first decide how to
form a skeleton and next how to elaborate it. In line with
the two major units of tonal music, the (broken) chord
and the scale, and based upon analyses of large samples
of tonal melodies, two models emerged: the “Chord-
based model” and the “Scale-based model”. The Chord-
based model builds a melodic skeleton from chord tones,
whereas the skeleton in the Scale-based model consist of
a scale fragment. The application described below con-
tains a third model, called Basic, which is useful to com-
pare tone sequences that are created either within or
without a tonal context. The latter model will not further
be discussed here.
2.5.1 The Chord-Based Model
This model is based on the following assumptions: 1) A
melody is superimposed upon an underlying harmonic
progression; 2) A melody consists of structural tones (a
skeleton) and ornamental tones; 3) The skeleton is as-
sembled from chord tones; 4) Skeleton tones are primar-
ily located at metrically strong positions. To actually
generate a skeleton melody within this model, apart from
the parameters related to the rhythm and the harmonic
progression, a few additional parameters are needed to
further shape the skeleton, namely: Range (determining
the highest and lowest note), Contour (the up-down
movement of the melody), Location (on beats or
down-beats), and Interval (the size of the steps between
the successive notes of the skeleton). After generation of
the skeleton it may be elaborated or ornamented to dif-
ferent degrees by means of an algorithm that interpolates
notes between the notes of the skeleton. More informa-
tion will follow in Section 3.
2.5.2 The Scale-Based Model
The Scale-based model is largely based on the same as-
sumptions as the Chord-based model, with one essential
difference: the skeleton is not formed of a series of chord
tones, but consists of a scale fragment. The idea that the
skeleton of tonal melodies consist of scale fragments has
been proposed, among others, by [30,48]. The latter au-
thors studied melodies from a period of almost 10 centu-
ries and concluded that “...every melodic phrase can be
reduced, at its deep level, to a kernel which not only pro-
gresses by conjunct step, but which is also monodirec-
tional”. This rule applies to the “body” of the phrase, not
to a possible anacrusis, or “feminine ending”. The vari-
ability on the surface is seen as the result of the applica-
tion of two types of transformations to the kernel: linear
transformations (repetition, neighbor, (filled) skip), and a
harmonic transformation. The latter transformation,
called “chord transposition”, substitutes a note for an
other note of the underlying harmony. The relative fre-
quency of harmonic transformations increases over time
(Händel, Mozart, Liszt). Figure 3 presents the reverse
Figure 3. The reduction of two melodies to their kernel. The kernel of melody a consists of an ascending scale fragment fol-
lowed by a descending fragment. In the descending fragment the D is not realized in the surface. The highest level of melody
b. consists of the scale fragment F Gb Ab (bars 1, 6, 9 respectively), of which each tone is augmented with a descending scale
fragment. In bar 4 the Ab is replaced by F and in bar 11 there is an downward octave jump

Melody Generator: A Device for Algorithmic Music Construction 688
process in which melodies are reduced to their kernel.
After a skeleton has been generated (either on the
beats or the down-beats), it may be elaborated by one of
the mentioned transformations or a combination of these:
repetition, neighbor note, skip, or chord transposition.
Implementation is detailed in the next section.
3. Implementation: Melody Generator
The next step consisted in the implementation in an algo-
rithmic form of the notions and models for melody gen-
eration detailed above. This has led to the program Mel-
ody Generator that, as its name suggests, generates me-
lodies. We chose for melodies rather than complete piec-
es mainly to keep the problem manageable. Moreover,
melodies form a core aspect of tonal music, and many
aspects of music construction are involved in their gen-
eration.
The program has a structure suited to generate, modify,
play, display, store and save tonal melodies, and an in-
terface suited to control these various aspects of the
process. Consequently, Melody Generator evolved into
an aid to gain an in-depth, hands-on understanding of
tonal melody and its construction, enabling the user to
study closely the consequences of changing the various
parameters while building a melody. Melody Generator
is programmed in REALbasicTM [49], an object-oriented
language that builds applications for Macintosh, Win-
dows, and Linux platforms from a single source code.
The program can be downloaded free of charge at
http://www.socsci.ru.nl/~povel/Melody/.
In this context only a concise description is presented.
A proper understanding of the application can only be
obtained from a hands-on experience. More detailed in-
formation about the implementation, the functioning and
use of the parameters can be obtained by clicking the
Help menu on the interface or the various info buttons on
the interface of the program. A user guide can be found
at http://www.socsci.ru.nl/~povel/Melody/InfoFilesMGII
2008/User Guide.html. The interface of Melody Genera-
tor, shown on Figure 4, comprises a number of panes
serving its three main functions: Generation, Display/
Play, and Storage. These three functions are described in
some detail below.
Following the distinction introduced above, I will
successively describe the implementation of the tonal
context and that of the construction principles.
3.1 Context
3.1.1 The Time Dimension
The time aspect is controlled by means of the following
parameters: Duration (No. of bars), Meter (4/4, 3/4, 2/4,
6/8), Gap (between Parts), Density (relative number of
notes per bar), Syncopation, and Rhythmical constraint.
The latter parameter determines the degree of rhythmical
similarity among bars. A description of the use of these
parameters can be obtained by pressing the info button on
Figure 4. Interface of melody generator version 4.2.1, showing a melody generated using the Chord-based model

Melody Generator: A Device for Algorithmic Music Construction 689
the pane “Time Parameters” of the program. A detailed
description of the algorithm to generate rhythms, varying
in density and metrical stability, is also presented there.
3.1.2 The Pitch Dimension: Key and Harmony
Melody Generator has parameters for selecting a key
(and mode) and for selecting a harmonic progression.
Various template progressions are provided, partly based
upon Schenker’s notion that tonal music is constructed
by applying transformations on a “Background” consist-
ing of a I-V-I harmonic progression (Ursatz), [50-52].
Basic harmonic templates typically begin with I and end
with V-I (full cadence) or V (half cadence). The interme-
diate harmonies are derived from Piston’s “Table of
usual root progressions” [53].
This table, shown here as Table 1, lists the transition
probabilities between harmonies in tonal music. These
probabilities are loosely defined by the terms “usually”,
“sometimes” and “less often”. Since the choice of a chord
is only determined by the immediately preceding chord, it
only provides a first-order approximation of harmonic
progressions in tonal music.
Also needed is a structure representing the various
elements of the selected key and their mutual relations
(mentioned above in Subsection 2.3). This includes in-
formation concerning the specification of the scale de-
grees, their stability and their spelling, the various chords
on these degrees, etc. This information is accumulated in
the object KeySpace. Figure 5 displays one octave of the
KeySpace of C-major.
3.2 Construction
To effectively construct melodies we need a structure
allowing the flexible generation and modification of a
hierarchically organized temporal sequence consisting of
parts and subparts, divided into bars, in turn divided into
beats and “slots” (locations where notes may be put). For
this purpose an object called Melody, was designed com-
prising one or more instances of the objects Piece, Part,
Bar, Beat, Slot, and Note. See Figure 6. Since any part
may contain a subpart, the hierarchy of a piece can be
extended indefinitely.
The generation of a melody progresses according to
the following stages: Construction, Editing, (Re)arrange-
ment, and Transformation.
3.2.1 Part Construction
Construction is performed in the “Melody Construction”
pane: after setting the Meter and Key parameters and
pushing the “New Melody” button, the first Part of a
melody may be generated either stepwise or at once. In
the stepwise mode, the various aspects of a melody: its
Rhythm, Gap, Harmony, Contour, Skeleton, and Orna-
mentation are generated in separate steps. Prior to each
Table 1. The table of usual root progressions for the Major
mode from Piston & DeVoto. Given a chord in the first
column, the table shows the chords that succeed that chord,
usually (1st column), sometimes (2nd column), or less often
(3rd column)
Chord Usually followed
by
Sometimes
by
Less often by
I IV or V VI II or III
II V IV or VI I or III
III VI IV I, II or V
IV V I or II III or IV
V I VI or IV III or II
VI II or V III or IV I
VII III I -
Figure 5. Part of the object KeySpace used in the construction of melodies

Melody Generator: A Device for Algorithmic Music Construction 690
Figure 6. The object melody
step the relevant parameters (indicated by highlighting)
may be set. Each aspect can at each time be generated
anew, for instance with a different parameter setting to
study its effect on the resulting melody. The order in
which the aspects can be constructed is controlled by
enabling and disabling the construction buttons and by
means of little “lights” located left of the buttons (see
Figure 4). By pushing the “Done” button the generation
of a Part is terminated.
3.2.2 Structure-Based Construction
In the chord-based model it is possible to construct a
melody with a pre-defined structure of parts. Examples
of such structures are: A B A, A A1 A2 B, Ant Cons, [A
VBV] [Dev AI BI], in which the capital letters A-G are
used to identify parts, a digit following a letter to indicate
a variation, and the Roman numerals I, II ... VII to iden-
tify the initial or final harmony of a part; Ant and Cons
are used in the Antecedent-Consequent formula. Other
reserved words are Dev for Development, and Coda in-
dicating a part at the end of a structure. The user can add
custom structures using the above coding.
The default way of constructing is part by part in
which the user separately sets the parameters for each
part. However, it is also possible to construct a structured
melody automatically in which case the different parts
are all constructed consecutively using randomly selected
Time and Pitch parameters and default variations (if ap-
plicable). A detailed description is provided on the inter-
face.
An example of a structure based melody is shown be-
low.
3.2.3 Editing
By right-clicking in the melody a drop-down menu ap-
pears that enables to add a note or to change the pitch of
an existing note (Figure 7).
A melody can also be transposed or elaborated. The
degree of elaboration is determined by the setting of the
density parameter in the “Time parameters” pane. Elabo-
rations may again be removed.
3.2.4 (Re)arrangement
After one or more Parts have been generated, Parts can
be removed, moved and duplicated using the drop-down
menu shown in Figure 7.
3.2.5 Transformation
After a Part has been finished (the Done button having
been pushed) the user may apply one or more transfor-
mations. Such transformations are most useful to create
variations of a Part. The Transformation panel is opened
either by right clicking on the Part and selecting “Trans-
form Part”, or by left-clicking and pushing the appearing
“Transform?” button. Next, the Transform pane will be
shown and the Part being transformed will be highlighted
in red. At present the following transformations can be
applied to a Part: Increase elaboration, Decrease elabo-
ration, Transpose 1 (applies a transposition of 1, 2, or 3
steps within the current harmony), Transpose 2 (applies a
transposition of 1-7 degree steps up or down, thereby
adjusting the harmony), Change Pitch (changes the
pitches of the Part keeping rhythm and harmony intact),
Change Rhythm (changes (only) the rhythm of the Part).
More options will be added in the future. Applied trans-
formations can be undone by clicking Edit: Undo Editing

Melody Generator: A Device for Algorithmic Music Construction 691
Figure 7. The drop-down menu showing various possibilities to manipulate aspects of the melody
(ctrl z, or cmd z).
3.2.6 Example of a Melody Generated within the
Chord-Based Model
Once the parameters for rhythm, harmony and contour
are set, a skeleton consisting of chord tones is generated.
For the contour a choice can be made between the fol-
lowing shapes: Ascending, Descending, U-shaped, In-
verted U-shaped, Sinusoid, and Random (based on [43,
54]). Subsequently, the skeleton may be elaborated us-
ing an algorithm that interpolates notes between the
notes of the skeleton. Figure 8 presents a skeleton mel-
ody (a) and three ornamentations differing in density (b,
c, d).
3.2.7 Example of a Melody Generated within the
Scale-Based Model
After a rhythm has been generated a skeleton consisting
of an ascending or descending scale fragment is created.
Next a harmony fitting with the skeleton is set, after
which the skeleton may be ornamented. As explained in
Subsection 2.5.2, four types of ornamentation have been
implemented: Repetition, Neighbor note, Skip, and
Chord transposition. In addition, the user may select a
“Random” ornamentation in which case an ornamenta-
tion is randomly chosen for each bar. A detailed descrip-
tion of this model can be found on the interface of the
program. Figure 9 presents a melody based on a skeleton
consisting of a descending scale fragment that is subse-
quently ornamented in different ways.
3.2.8 Example of a Multi-Part Melody
Figure 10 shows a multi-part melody based on an A B
A1 B1 A B structure in which A and B are an Antecedent
and Consequent part respectively, and A1 and B1 varia-
tions of A and B.
A few more examples of multi-part melodies can be
found at http://www.socsci.ru.nl/~povel/Melody/.
3.3 Display and Play Features
Each step in the construction of a melody is displayed in
the “Melody” pane and can be made audible by clicking
the Play button in the “Play parameters” pane. The main

Melody Generator: A Device for Algorithmic Music Construction 692
parameters in this pane refer to: what is being played
(Melody only, or combined with Root and/or Beat;
Rhythm only), Tempo, and Instrument (both for Melody
and Root).
3.4 Storing and Saving Melodies
A melody can be stored temporarily in the “Melody
store” on the interface (right click in the Melody). Melo
dies in the Melody store can be played, sent back to the
Melody pane, or pre- or post-fixed to the melody in the
Melody pane (by right clicking in the Melody store). A
melody can also be exported in MIDI format (right click
in the Melody). The melodies stored in the Melody Store
can be saved to Disk in so-called mg2 format by clicking
the “Save to File” or “Save to File As” buttons. Upon
clicking the “Export as MIDI” button, all melodies in the
“Melody store” pane are stored to Disk in MIDI format.
Figure 8. Example of a melody generated within the chord-based model. (a) A skeleton melody; (b)-(d) the skeleton elaborated
with an increasing number of ornamental notes. Color code: red: skeleton note, black: chord-note; blue: non-chord note
Figure 9. Example of a scale-based melody, showing a skeleton consisting of an ascending scale fragment, followed by 5 dif-
ferent elaborations: repetition, neighbor, skip, chord transposition, and random (chord transposition in the first bar and
neighbor in bars 2 and 3). Color code: red: skeleton note, black: chord-note; blue: non-chord note
(a)
(b)
(c)
(d)

Melody Generator: A Device for Algorithmic Music Construction 693
Figure 10. Example of a multipart melody built on the structure Ant, Cons, Ant1, Cons2, Ant, Cons, i.e. an Antecedent-
Consequent formula repeated twice in which the first repetition is slightly varied (ornamented)
3.5 Additional Functions
Apart from the functions that may be invoked from the
main interface, a few additional functions are available
through the Menu, such as displaying the current KeyS-
pace, displaying properties of the notes in the melody,
changing the display parameters, displaying information
about the operation of the program, etc.
4. Conclusions
This article describes a device for the algorithmic con-
struction of tonal melodies, named Melody Generator.
Starting from a few basic assumptions, a set of notions
were formulated concerning the context of tonal music
and the construction principles used in its generation.
These notions served as the starting points for the devel-
opment of a computer program that generates tonal me-
lodies the characteristics of which are controlled by
means of adjustable parameters. The architecture and
implementation of the program, including its multipur-
pose interface, are discussed in some details.
Presently, we are working on a formal and systematic
validation of the melodies produced by the device in or-
der to obtain a reliable estimation of the positive and
negative qualities of its various aspects. This evaluation
will provide the necessary feedback to further develop
and refine the algorithm and its underlying theoretical
notions. Results of this evaluation will be reported in a
forthcoming publication.
5. Acknowledgements
My former students Hans Okkerman, Peter Essens, René
van Egmond, Erik Jansen, Jackie Scharroo, Reinoud
Roding, Jan Willem de Graaf, Albert van Drongelen,
Thomas Koelewijn, and Daphne Albeda, all played an
indispensable role in the development of the ideas un-
derlying the project described in this paper.
I am most grateful to David Temperley for his support
over the years, to Hubert Voogd for his help in tracing
and crushing numerous tenacious bugs, and Herman
Kolk and Ar Thomassen for suggestions to improve the
text.
REFERENCES
[1] W. V. D. Bingham, “Studies in Melody,” Psychological
Review, Monograph Supplements, Vol. 12, Whole No. 50,
1910.
[2] H. Gardner, “The Mind’s New Science: A History of the
Cognitive Revolution,” Basic Books, 1984.
[3] D. Deutsch, (Ed.) “The Psychology of Music,” Academic
Press, 1999.

Melody Generator: A Device for Algorithmic Music Construction 694
[4] C. L. Krumhansl, “Cognitive Foundations of Musical
Pitch,” Oxford University Press, 1990.
[5] D. Deutsch and J. Feroe, “The Internal Representation of
Pitch Sequences,” Psychological Review, Vol. 88, No. 6,
1981, pp. 503-522.
[6] K. Hirata and T. Aoyagi, “Computational Music Repre-
sentation Based on the Generative Theory of Tonal Music
and the Deductive Object-Oriented Database,” Computer
Music Journal, Vol. 27, No. 3, 2003, pp. 73-89.
[7] F. Lerdahl and R. Jackendoff, “A Generative Theory of
Tonal Music,” MIT Press, Cambridge, 1983.
[8] H. C. Longuet-Higgins and M. J. Steedman, “On Interpret-
ing Bach,” In: B. Meltzer and D. Michie, Eds., Machine
Intelligence, University Press, 1971.
[9] A. Marsden, “Generative Structural Representation of
Tonal Music,” Journal of New Music Research, Vol. 34,
No. 4, 2005, pp. 409-428.
[10] D. J. Povel, “Internal Representation of Simple Temporal
Patterns,” Journal of Experimental Psychology: Human
Perception and Performance, Vol. 7, No. 1, 1981, pp. 3-
18.
[11] D. J. Povel, “A Model for the Perception of Tonal
Music,” In: C. Anagnostopoulou, M. Ferrand and A.
Smaill, Eds., Music and Artificial Intelligence, Springer
Verlag, 2002, pp. 144-154.
[12] D. Temperley, “An Algorithm for Harmonic Analysis,”
Music Perception, Vol. 15, No. 1, 1997, pp. 31-68.
[13] D. Temperley, “Music and Probability,” MIT Press,
Cambridge, 2007.
[14] D. Cope, “Experiments in Music Intelligence,” MIT Press,
1996.
[15] E. Miranda, “Composing Music with Computers,” Focal
Press, 2001.
[16] R. Rowe, “Machine Musicianship,” MIT Press, 2004.
[17] G. Papadopoulos and G. Wiggins, “AI Methods for Algo-
rithmic Composition: A Survey, a Critical View and
Future Prospects,” Proceedings of the AISB’99 Sympo-
sium on Musical Creativity, Edinburgh, Scotland, 6-9
April 1999.
[18] C. Ames, “The Markov Process as a Compositional
Model: A Survey and Tutorial,” Leonardo, Vol. 22, No. 2,
1989, pp. 175-187.
[19] E. Cambouropoulos, “Markov Chains as an Aid to
Computer Assisted Composition,” Musical Praxis, Vol. 1,
No. 1, 1994, pp. 41-52.
[20] K. Ebcioglu, “An Expert System for Harmonizing Four
Part Chorales,” Computer Music Journal, Vol. 12, No. 3,
1988, pp. 43-51.
[21] M. Baroni, R. Dalmonte and C. Jacoboni, “Theory and
Analysis of European Melody,” In: A. Marsden and A.
Pople, Eds., Computer Representations and Models in
Music, Academic Press, London, 1992.
[22] D. Cope, “Computer Models of Musical Creativity,” A-R
Editions, 2005.
[23] M. Steedman, “A Generative Grammar for Jazz Chord
Sequences,” Music Perception, Vol. 2, No. 1, 1984, pp.
52-77.
[24] J. Sundberg and B. Lindblom, “Generative Theories in
Language and Music Descriptions,” Cognition, Vol. 4,
No. 1, 1976, pp. 99-122.
[25] G. Wiggins, G. Papadopoulos, S. Phon-Amnuaisuk and A.
Tuson, “Evolutionary Methods for Musical Composi-
tion,” Partial Proceedings of the 2nd International Con-
ference CASYS’98 on Computing Anticipatory Systems,
Liège, Belgium, 10-14 August 1998.
[26] J. A. Biles, “Genjam: A Genetic Algorithm for Generat-
ing Jazz Solos,” 1994. http://www.it.rit.edu/~jab/
[27] P. Todd, “A Connectionist Approach to Algorithmic
Composition,” Computer Music Journal, Vol. 13, No. 4,
1989, pp. 27-43.
[28] P. Toiviainen, “Modeling the Target-Note Technique of
Bebop-Style Jazz Improvisation: An Artificial Neural
Network Approach,” Music Perception, Vol. 12, No. 4,
1995, pp. 399-413.
[29] M. Baroni, S. Maguire and W. Drabkin, “The Concept of
a Musical Grammar,” Musical Analysis, Vol. 2, No. 2,
1983, pp. 175-208.
[30] M. Baroni, R., Dalmonte and C. Jacoboni, “A Computer-
Aided Inquiry on Music Communication: The Rules of
Music,” Edwin Mellen Press, 2003.
[31] A. Marsden, “Representing Melodic Patterns as Networks
of Elaborations,” Computers and the Humanities, Vol. 35,
No. 1, 2001, pp. 37-54.
[32] H. C. Longuet-Higgins and C. S. Lee, “The Perception of
Musical Rhythms,” Perception, Vol. 11, No. 2, 1982, pp.
115-128.
[33] D. J. Povel and P. J. Essens, “Perception of Temporal
Patterns,” Music Perception, Vol. 2, No. 4, 1985, pp.
411-440.
[34] F. Gouyon, G. Widmer, X. Serra and A. Flexer, “Acoustic
Cues to Beat Induction: A Machine Learning Approach,”
Music Perception, Vol. 24, No. 2, 2006, pp. 177-188.
[35] D. J. Povel and H. Okkerman, “Accents in Equitone
Sequences,” Perception and Psychophysics, Vol. 30, No.
6, 1981, pp. 565-572.
[36] D. J. Povel, “Exploring the Elementary Harmonic Forces
in the Tonal System,” Psychological Research, Vol. 58,
No. 4, 1996, pp. 274-283.
[37] F. Lerdahl, “Tonal Pitch Space,” Music Perception, Vol.
5, No. 3, 1989, pp. 315-350.
[38] F. Lerdahl, “Tonal Pitch Space,” Oxford University Press,
Oxford, 2001.
[39] E. H. Margulis, “A Model of Melodic Expectation,”
Music Perception, Vol. 22, No. 4, 2005, pp. 663-714.
[40] D. J. Povel and E. Jansen, “Harmonic Factors in the
Perception of Tonal Melodies,” Music Perception, Vol.
20, No. 1, 2002, pp. 51-85.
[41] J. J. Bharucha, “Anchoring Effects in Music: The
Resolution of Dissonance,” Cognitive Psychology, Vol.
16, No. 4, 1984, pp. 485-518.

Melody Generator: A Device for Algorithmic Music Construction 695
[42] D. J. Povel and E. Jansen, “Perceptual Mechanisms in
Music Processing,” Music Perception, Vol. 19, No. 2,
2001, pp. 169-198.
[43] E. Toch, “The Shaping Forces in Music: An Inquiry into
the Nature of Harmony, Melody, Counterpoint, Form,”
Dover Publications, NY, 1977.
[44] J. Bamberger, “Developing Musical Intuitions,” Oxford
University Press, Oxford, 2000.
[45] Schoenberg, “Fundamentals of Musical Composition,”
Faber and Faber, 1967.
[46] H. Schenker, “Harmony,” Chicago University Press,
Chicago, 1954.
[47] V. Zuckerkandl, “Sound and Symbol,” Princeton Univer-
sity Press, Princeton, 1956.
[48] H. Schenker, “Free Composition (Der freie Satz),” E.
Oster, Translated and Edited, Longman, New York, 1979.
[49] M. Neuburg, “REALbasic. The Definitive Guide,”
O’Reilly, 1999.
[50] M. G. Brown, “A Rational Reconstruction of Schenkerian
Theory,” Thesis Cornell University, 1989.
[51] M. G. Brown, “Explaining Tonality,” Rochester Univer-
sity Press, Rochester, 2005.
[52] Jonas, “Das Wesen des musikalischen Kunstwerks : eine
Einführung in die Lehre Heinrich Schenkers,” Saturn,
1934.
[53] W. Piston and M. Devoto, “Harmony,” Victor Gollancz,
1989.
[54] D. Huron, “The Melodic Arch in Western Folksongs,”
Computing in Musicology, Vol. 10, 1989, pp. 3-23.